AERE WORKSHOP ON RECREATION DEMAND MODELING
The Association of Environmental and Resource Economists
The Final Report for
Cooperative Agreement No. CR-812056
June 20, 1985
Principal Investigators
Kerry Smith
Vanderbilt University
Edward R. Morey
University of Colorado
Robert D. Rowe
Energy & Resource Consultants
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DISCLAIMER
Although prepared with EPA funding, this
report has neither been reviewed nor
approved by the U.S. Environmental
Protection Agency for publication as an EPA
report. The contents do not necessarily
reflect the views or policies of the U.S.
Environmental Protection Agency, nor does
mention of trade names or commercial
products constitute endorsement or
recommendation for use.
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TABLE OF CONTENTS
INTRODUCTION
PAPERS
The Logit Model and Exact Expected Consumer's Surplus
Measures: Valuing Marine Recreational Fishing
Edward R. Morey and Robert D. Rowe
The Varying Parameter Model: In Perspective
William H. Desvousges
Valuing Quality Changes in Recreational Resources
Elizabeth A. Wilman
Modelling the Demand for Outdoor Recreation
Robert Mendelsohn
A Model to Estimate the Economic Impacts on Recreational
Fishing in the Adirondacks from Current Levels of
Acidi fication
Daniel M. Violette
Modeling Recreational Demand in a Multiple Site Framework
Nancy E. Bockstael, W. Michael Hanemann, Catherine L. Kling
The Total Value of Wildlife Resources: Conceptual and
Empirical Issues
Kevin J. Boyle and Richard C. Bishop
Exploring Existence Value
Bruce Madariaga and K. E. McConnell
A Time-Sequenced Approach to the Analysis of Option Value
Theodore Graham-Tomasi
APPENDIX A
APPENDIX B
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Introduction
AERE WORKSHOP ON RECREATION DEMAND MODELING
Edward Morey
Robert Rowe
V. Kerry Smith
This introduction describes the objectives and organization
of the first AERE Workshop conducted under EPA Cooperative
Agreement CR-812056-01-0 in Boulder, Colorado May 17-18, 1985 and
further describes the level of participation and reaction by
participants to the workshop. The topic of the workshop was
issues associated with modeling the demand and valuation of
recreational resources. Three themes that are associated with
the current research on the economics of valuing outdoor
recreational resources provided the basis for organizing a day and
a half of sessions at the workshop.
The first of these themes was in the modeling of the role of
site attributes and determining the demand for recreational
sites. There has been increased interest in the development of
models for describing recreational behavior that take account of
attributes that distinguish recreational sites. For example, in
the case of water-based recreation, water quality would be one
attribute that would influence the character and types of
activities that could be undertaken in water-based recreation
sites. By contrast, for hunting recreation, the density and
types of game resources influencing the likelihood of successful
hunting experiences would be an alternative kind of
characteristic. In addition to these characteristics which fall
under the direct control of those managing the recreational
]
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resources, there are also measures of congestion and the physical
features of the facility which may in some cases be either
directly or indirectly controlled. Three competing frameworks
for modeling these site attributes have arisen in the current
literature. They include the so-called varying parameter model,
the hedonic travel cost model, and the development of generalized
indirect utility function models. Since each of these frameworks
has different data requirements and makes different implicit
assumptions about the structure of individual preferences and the
role of site attributes in them, it was judged to be quite
important that we develop an understanding of the inter-relationsh
between the models and their potential uses in the valuation of
these amenity resources.
Closely related in this modeling question is the issue,
considered in the second session, of how to model the demands for
recreational sites within a given region. Once again, the sites
are likely to be differentiated by characteristics, but what is at
issue is the strategy adopted in trying to represent an
individual's selection of these sites when patterns of use may be
such that only a subset of the sites are actually selected for
recreational use. The description of the role of site
substitution possibilities and the valuation of changes in site
amenities in this context becomes quite important. For example,
it is entirely possible that a change in the characteristics of
one site may well lead to a change in the sites selected by
individuals for their recreational choices. Thus, sites that
were not used under one configuration of site attributes may be
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used under another and the welfare valuation problem becomes
increasingly complicated if the framework used to describe the
demand for sites and the role of substitution among sites does
not accommodate this possibility.
Each of the three models described above offers the
potential, with differing restrictive assumptions, for
accommodating site substitution behavior. However, they do not
reflect it in the general way that was described above. One
model, for example, estimates the demand for site characteristics
alone and not the sites. This implies that only one site is
ultimately selected and all sites can be converted into
equivalent units of recreational services. Thus, the selection
of a site, once the conversion function is known, is apparent.
Another of the models restrictively assumes that each individual
visits all of the sites. The restrictive assumptions in these
models raise the general question of how to model consumer demand
theory allowing for corner solutions (i.e., the selection of zero
consumption levels for some commodities). This, of course,
introduces the substantive problems associated with welfare
analysis in discrete choice situations. Thus, the interaction of
all of these problems provided the basis for the second session.
The issues here had a great deal in common with those in the
first session and were discussed in a way that reflected that
interaction.
The objective of the third session was to appraise our
current understanding of the modeling of non-user values.
Particular attention was focused on the implications of the
conceptual definition of existence value and the ability to
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measure existence values. In addition, the implications of the
theoretical definition of option value for its empirical
estimates were also a part of the third session.
Over fifty participants attended the first workshop. The
format for the workshop eliminated formal discussants of papers
and instead relied upon interaction of authors, involvement of the
session chairpersons, and commentary from the floor to draw out
the inter-relationships between the papers. Copies of all of the
papers were available to authors before the workshop and to all
other participants at the outset of the workshop in a loosely
bound format which facilitated presentation and commentary.
Having access to the papers turned out to be essential to
promoting interaction between authors and participants. All
participating in the workshop who commented to the organizers
suggested the discussion was lively and the interaction
exceptionally interesting.
The attached papers represent the drafts of the papers
submitted for the workshop. We will now be contactint Professor
Ronald G. Cummings, one of the editors of Water Resources
Research to determine if there is interest in devoting part
of an issue to shortened versions of the papers.
A
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The Logit Model and Exact Expected Consumer's Surplus Measures:
Valuing Marine Recreational Fishing*
Edward R. Morey
Department of Economics
University of Colorado
Boulder, Colorado 80309
Robert D. Rowe
Energy Resource Consultants
P.O. Drawer 0
Boulder, Colorado 80306
May 1985
Abstract
A random utility model of recreational demand is developed which assumes that
utility has a random component from the individual's perspective at the
beginning of the season. The specific application is to marine recreational
fishing along the Oregon coast. The model is used to derive an exact expected
consumer's surplus measure. If the individual is risk neutral, this expected
consumer's surplus measure can be interpreted as an option price; an option
price is how much a fisherman would pay at the beginning of the season for the
option of visiting a particular site even though he might not ever actually
visit that site. This expected consumer's surplus measure is also related to
the more conventional deterministic consumer's surplus measure.
*We wish to thank Phil Graves, Dan Huppert, and Doug Shaw for their comments.
The research underlying this paper was partially supported by the National
Oceanic and Atmospheric Administration (NOAA Contract: NA83ABC00205) .
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In this paper a multinomial logit model of recreational fishing demand is
specified and estimated. The specific application is to marine recreational
fishing in Oregon. The model is used to calculate the expected compensating
and equivalent variations associated with changes in catch rates and those
associated with the elimination of different fishing sites and modes (man-made
structures, beach and bank, charter boat and private boat) along the Oregon
coast. If the fisherman is risk neutral, these exact expected consumer's
surplus measures can be interpreted as "option prices". 1 For example, the
expected compensating variation for the eliminating of a site/mode is the
amount a risk neutral fisherman would pay at the beginning of the season for
the option of fishing at that particular site/mode. A fisherman's expected
consumer's surplus for the elimination of a site/mode is an increasing func-
tion of the probability that he would have visited that site/mode and this
expected consumer's surplus is positive even if he never would have actually
visited the site. The expected compensating variation is also related to the
more conventional deterministic compensating variation which is the amount an
individual would be willing to pay (or have to be paid) to bring about (or
accept) a change in the cost or characteristics of a site/mode if he knew he
was going to choose that site/mode with certainty.
The random utility logit model is one of the few utility-theoretic models
hhat can be estimated with the recreational data that is usually available.
Most recreational demand data is collected by conducting on-site interviews at
one or more sites. The Marine Recreational Fishery Statistics (MRFS) Survey
used in this study is a prime example of one that conducted on-site interviews
at a number of sites. In such a survey one observes each individual's desti-
nation on only one of their trips during the season. No attempt is made to
determine where they went on their other trips. Given this type of data, one
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can only estimate the substitution possibilities among the alternative site/
modes in a consistent utility-theoretic framework if one assumes that the
utility function is additive across fishing trips.^ The random utility logit
model is one of few models that is consistent with this assumption but that
does not unrealistically require that the fisherman visits the same site/mode
on each trip.
The need for a utility-theoretic model is critical if the estimated
demand functions are to be used to derive consumer's surplus measures. If
one's intent is to just predict demand then it is not as critical that the
estimated demand functions are consistent with an underlying utility function,
but since the measurement of consumer's surplus is just a disguised attempt to
measure utility itself, utility-theoretic consistency is necessary when
welfare measures are estimated. Given this and given the type of recreational
data usually available, policy makers require a method of deriving exact
expected consumer surplus measures from the logit model; methods to do this
have recently been developed by McFadden (1981), Small and Rosen (1981) and
Haneman (1985). This paper provides an empirical example.
Unlike most random utility logit models, the model presented in this
paper assumes that utility has a random component from the individual's
It
perspective at the beginning of the season. This alternative interpretation
of the random utility logit model is what allows us to interpret the exact
expected consumer's surplus measures as option prices.
Section I outlines a multinominal logit model of site/mode choice, while
Section 11 describes the data and the empirical results. The derivation of
exact expected compensating (and equivalent) variations from the logit model
is explained in Section III. As an example, these are calculated for the
elimination of salmon and other fishing opportunities due to pollution in the
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Columbia river. The expected welfare effects of a salmon enhancement program
are also reported. Section III concludes with a discussion of the relation-
ship between the expected and deterministic compensating variation. Section
IV is a brief concluding summary.
I. A Multinomial Logit Model of Site/Mode Choice
For each individual in the sample we observe only one fishing trip where
we know which site/mode the individual chose. The individual chose this trip
from among the J x M alternatives where J is the number of alternative sites
(coastal counties in Oregon) and M is the number of alternative modes.
Let the probability that individual i chooses site j mode m on a given
J M
trip be n- . where £ £ ir_. 1ml= 1- Therefore, if there are N independent
j=l m=l
individuals in the sample and we only observe one trip for each individual,
the likelihood function for the sites chosen by the N individuals is
N J M
(i) l = n n n . yJmti
i=l ] = 1 m=l Jmi
til
where y . = 1 if individual i chooses site i mode m on the : trip
1 jmti J v
and zero otherwise.
The standard logit model derives the it- - from a random utility model
^ jmi 1
(RUM) such that the probabilities are a function of the costs of visiting each
of the site/modes and the catch rates at each of the site/modes.^ Assume that
the utility individual i receives if he chooses to fish at site/modes jm is
^jrati Pjmi' ajml' ajm2' * **' ajm5^ + Ejmti
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where
is individual i's budget for the period in which each trip takes place
p. . is the cost of a trip to site i mode m for individual i
jmi ^ J
ajmk "'"S avera9e catch rate for species k at site j mode m, k = 1, 2,
.... Species 1 = Salmon, 2 = Perch, 3 = Smelt and Grunion, 4 =
Flatfish, and 5 = Rockfish/Bottomfish
and
The random component is assumed known to the individual on the day
each trip is taken, but £. varies across individuals, site/modes and
^ jmti
from trip to trip. At the beginning of the season, the individual does
not know the values e- will take on each trip. The variable.^, is
jmti ^ jmti
therefore random from the individual's perspective at the beginning of
the season but deterministic on the morning each trip is taken. The
variable is completely random from our perspective. The vector
eit ~ ^ ejmti^ "'"S therefore a set of random variables with some joint
c.d.f. Fe(eit)~
Equation (2) is a conditional indirect utility function that assumes utility
is additive both across site/modes and trips. Conditional utility, has
a random component from our perspective and from the individual's perspective
at the beginning of the season. On each trip, the individual always chooses
that site/mode that provides the greatest utility, but the utility maximizing
site/mode varies from trip to trip in a way the individual cannot predict.
The standard logit model specifically assumes that6
(2a) Ujmti = S0Bi " 0OPjmi + 0lajml + 02ajm2 + %ajm3 + 04ajm4 + %ajm5+ ejmti
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The conditional indirect utility function (2a) implies that the choice of
alternatives is independent of B^; i.e., there is no income effect. This
specification was chosen because there is no data on B^. The parameter is
the constant marginal utility of money. The probability that individual i
will choose site j mode m is therefore
<3> \]mi = ProbtUjmti > U*sti VI,.]
The standard logit model assumes that the vector of random variables s^t has
an Extreme Value Distribution; i.e., that the joint c.d.f. is
J M _e.
(4) Fs(e.t) = exp[- J J e Jmtl]
j-1 m=l
It can be shown that
_ •,/ V v I_e0(p£si " Pjmi) + 0l(a£sl " ajml) + S2(a£s2~ ajm2}
(3) ^jmi " lf I I 6
J £-1 S=1
+ ... + 85(3^5 - ajm5)]
The likelihood function in terms of the data and the 3 parameters is obtained
by substituting (5) into (1). The maximum likelihood estimates of the
parameters are those values of the 0 parameters that maximize this likelihood
function. These are most easily obtained by maximizing the log of the
likelihood function (6) rather than the likelihood function itself.
N J M
(6) InL = J J I yjmti ln "jmi
i=l j=l m=l
N J M J M [-8oCP,,± " P1ml) + Bl(aisl " nl' +
""III 7W, 1" I I e w J
i=l j~l m=l £=«1 s=l
02(a£s2 " ajm2) + ••• + %(a£S5 " ajm5)J
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II. Data and the Empirical Results
The data come from the 1981 MRFS intercept survey along the Pacific coast
(U.S. Department of Commerce, NOAA (1983)). Fishermen were intercepted and
interviewed at numerous sites along the Oregon coast. Information was
collected about the intercept trip, particularly catch data, which was the
main purpose of the survey. Data was collected on the total number of trips
each individual took during the season however, except for the intercept trip,
there was no data collected on the distribution of those trips across sites.
Other than catch rates, the only individual-specific information is county of
residence and expenses on the intercept trip. This lack of individual-
specific data, while unfortunate, simplifies estimation because in this case
the log of the likelihood function (6) can be written in the simplified form
C J M
(6a) InL =* Y Y Y Y. In ir •
c=l jil m=l Jmc Jmc
I I 1 Y- \ln I 1 ^P*sc PJmc^ + ^a£sl ajml^
c=l j=l m=l ^mc f £=*1 s=l
+ B2(a£s2 ajm+ **• + e5(a£s5 ~ ajm5^
where
C is the number of counties of origin (there are 36 counties in Oregon)
tjmc "'"S Pro'3ability that an individual from origin county c will
choose site j mode m
and
^jmc "'"S num^er individuals who took trips from origin county c to
site j mode m
Since C is much smaller than N, the maximum of (6a) can be computed more
rapidly than the maximum of (6).
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The Oregon coast was divided into seven macro sites (coastal counties).
The sites, south to north, are Curry, Coos, Douglass, Lane, Lincoln, Tilamook,
and Clatsop counties. The 5,855 Oregon residents in the sample came from all
36 counties in the state.
Assume that the cost of a trip to site j mode m for individuals from
county c (p. ) equals travel costs plus the value of time in transit plus
JulC.
site/mode cost; i.e.
(7) p. = 2(Distance from c to j ) .112 + (2(Distance c to j)/4 0)3.35
v ' / * jmc
+ average on-site/mode costs at site j mode m
+ (required nights of lodging)(average per-night lodging costs)
where
.112 was the per-mile cost of operating an automobile in 1981 (U.S.
Bureau of the Census (1981))
Distances were measured from the population center of county c to the
nearest coastal point in county j
$3.35 is the 1981 minimum wage (U.S. Bureau of the Census (1981))7
40 mph was assumed to be the average speed of travel
Required nights of lodging were assumed to be zero if the distance from c
to j was less than 150 miles, one if between 150 and 300 miles and two if
between 300 and 450 miles
The average per-night lodging costs were $19.32 (Rowe, et al (1985))
The average mode costs were $3.87 for man-made structures, $2.87 for
beach and bank, $52.80 for charter boat and $22.83 for private boat
(Rowe, et al (1985))
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A few representative costs are reported in Table 1. The costs in the sample
vary from $4.83 to $329.24. The high range follows from several considera-
tions: it is much cheaper to fish near home; off-shore fishing is much more
expensive than on-shore fishing; fishing from man-made structures is one
dollar more expensive than beach and bank fishing because there is often a fee
to fish from a pier and the marginal cost of charter boat fishing is $29.97
higher than the marginal cost of fishing from a private boat.
The catch rates for the five most important species are reported in Table
2.® There is a substantial variation in catch rates across sites, modes and
species. Note that most salmon are caught from boats and that salmon catch
rates are higher for charter boats than for private boats. Charter boat
operators have more information about the location of this important game
fish. Perch, on the other hand, are caught mostly from shore modes.
The data were used to find those values of g that maximizes (6a). A
Newton-type search algorithm was used.9 The maximum likelihood parameter
estimates are reported in Table 3. On the basis of likelihood ratio tests,
the Costs Only Model explains the allocation across site/modes significantly
better than the Random Allocation Model and the Costs and Catch Rate Model
explains significantly better than the Costs Only Model. Both costs and catch
rates are important determinants of where an individual will fish. Notice
that the coefficient on perch (82) is negative; the negative sign may be
indicating that the presence of perch makes it less likely that more desirable
species are present. The negative coefficient does not mean that fisherman
dislike perch per se.
The estimated probabilities for the different site/mode alternatives (5)
are reported in Table 4 for individuals from five representative counties of
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origin. Notice how these estimated probabilities depend on distance, mode
costs and catch rates. Private boats are more "attractive" than charter
boats, probably due to the cost differential, and beach and bank is more
attractive than man-made structures. Distance is obviously important and
on-shore is more attractive than off-shore.
III. Exact Expected Consumer Surplus Measures
A. Theory
Let P° = [p^ ] be the initial matrix of costs for an individual from
c LrjmcJ
county c,
P' = [p- ] be the new matrix of costs for an individual from county c,
c jmc
be the initial matrix of site/mode catch rates
and
A' = [ajpfr] be the new matrix of site/mode catch rates.
McFadden (1981), Small and Rosen (1981) and Hanemann (1985) have each shown
that for the logit model outlined in this paper the expected per trip
compensating variation (and equivalent variation) associated with a change
from A0) to (P^, A') is
(8) CV - EV = —
c R
0
ln ^ I X e( 8°P^inC + Sia^ml + + + S5ajm5
j=l m=l
-ln 3 \ J e(~80pjmc + 0lajml + 82ajm2 + ••• + 05ajm5)
j=l m=l
for an individual from county c. The CVc and EVc are equal because the chosen
conditional indirect utility function (2a) assumes there is no income effect.
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Following Hanemann (1985), the derivation of equation (8) proceeds as
follows. Remember that
Ujmti = 30Bi " e0Pjmi + hajml + 32ajm2 + •** + S5ajm5 + ejniti (2a)
t h
is individual i's conditional indirect utility function on the trip for
site ] mode m. Therefore the unconditional indirect utility function for
individual i is
(9) vit = vCP^ A, Bi, eit)
= max[U1;Li, U12i Uimi» •**» Ujli» Ujmi' **•' UJli' * * * »UJMi^
= max[U(Bi, pUi, am, an2, a115) + ellti. •••» »ajmi»
ajm2' *" * 'ajm5^ + U^Bi ' pJMi,aJMl' aJM2» * * * ,aJM5* + eJMti^
The variable is the utility obtained by individual i if he maximizes his
utility when confronted with the choice set (P^> A, B^, e^t)* Note that
is deterministic from the individual's point of view on the day the trip is
taken, but a random variable from our perspective and a random variable from
the individual's perspective at the beginning of the season. Since is a
random variable, we need to use its expected value to determine the expected
welfare impact of a change from A0, B^) to A', B^). The expected
value of v^t (V^) is
(10) Vi - V(P., A, Bi) = E[v(P., A, B±, e±t)]
Note that doesn't depend on t. The variable is the expected maximum
utility associated with the choice set (P^, A, B^)'.
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Equation (10) can be used to define the expected compensating variation
(CV^) and expected equivalent variations (EV^) in the random utility
framework. Define the CV^ and EV^ such that
(11) V(PJ, A', B1 + CV±) = V(Pj, A°, B±)
and
(12) V(P[, A', B±) = V(P°, A°, B.-EV1)
Defined in this way, the CV^ is the compensation (or payment) associated with
the change that would make the expected maximum utility after the change the
same as it was before the change. if (P^> A') is preferred to (P£* A0) then
the absolute value of CV^ is the amount a risk neutral individual i would pay
at the beginning of the season for the option of facing choice set A' )
rather than choice set (Pi'
A0) on one of his trips.Since utility is
additive across trips, individual i will pay a total of at the beginning
of the season for the option of facing choice set (P^> A' ) for the entire
season, where is the number of trips individual i will take during the
season. if (P^> A0) is preferred to (P^> A') then CV^ is how much a risk
neutral individual i would have to be paid at the beginning of the season to
voluntarily accept the choice set A') on one of his trips. The EV^ (12)
is the compensation (or payment) associated with the initial state that would
make individual i's expected maximum utility without the change equivalent to
his expected maximum utility with the change.
Given the conditional indirect utility function (2a) and utilizing (11)
and (12), Hanemann (1985) has shown that
(13) CVt - CTl - IV" - vp
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Intuitively, [V° - V^] is the difference between the expected maximum utility
in the two states. Since (3q is the constant marginal utility of money, (1/Bq)
is the inverse of the marginal utility of money. Therefore, multiplying
[V° - V^] by (l/g0) converts the expected utility change into a money metric
of the expected change. The CV^ equals the EV^ because there is no income
effect.
If it is assumed that e^t in the conditional indirect utility function
(2a) has an Extreme Value Distribution, the logit assumption, then it can be
shown that
J M (~8nP°- i + 8ia°- i + 8oa4 o + ••• + 8ca°. ,-)
(14) V- - + In I I e 0 ^ 1 Jml ^ jB2 5 J°5
j*l m-1
and that
J M (—8rtp'. , + 3ia'. , + Boa'- o + ••• + c)
(15) V! = 6nB. + J I e 0 J,nI 1 ^ 2 Jm2 5 Jm5
1 j=l m=l
The equation for the CVc and EV£ (8) is obtained by substituting (14) and (15)
into (13) and noting that all individuals from the same county are effectively
identical.11
B. An Example: The Estimated Compensating Variations, CVc's, Associated
with Increased Pollution in the Columbia River
Equation (8) can be used to calculate the CV^/s associated with the
elimination of on-shore, off-shore, and all fishing opportunities in Clatsop
county (the Oregon county at the mouth of the Columbia river). An increase in
agricultural and industrial pollution in the Columbia river could drastically
affect this fishery. The CVc's for the Clatsop fisheries, along with for
comparison the CVc 's for the elimination of the fisheries in Douglass and
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curry, are reported in Table 5 for seven representative counties of origin.
In general, note the importance of distance; that the CVs for the on-shore
fishery are significantly larger than for the off-shore fishery and
that each CVc for the elimination of both modes is larger than the sum of the
CVc's for the elimination of each mode separately.
A fisherman from Clatsop county will pay $14.60 at the beginning of the
season for the option of being able to fish from an on-shore mode in Clatsop
county on one of his trips, a fisherman from Portland (Multnomah county) will
pay $4.55 for the same option and a fisherman from Curry county will pay
effectively nothing for this option. Compare these with the probability that
an individual would have chosen an on-shore mode in Clatsop county (see Table
4); the probability for Clatsop residents is .63, .27 for Portland residents
and effectively zero for residents of Curry county.
Fisherman will pay significant amounts for the option of fishing at modes
that they might not ever actually visit. For example, a fisherman from
Multnomah would have paid $4.55 for the option of shore fishing in Clatsop,
county on a single trip even though the probability that the individual would
have actually chosen this site/mode is only .27. This CVc is significant
from a policy perspective because Multnomah residents took an estimated
211,300 fishing trips in 1981 (Rowe et al (1985)).
Rather than assuming that pollution in the Columbia river affects all
marine species one might hypothesize that it only affects salmon. The CVc's
for the elimination of the salmon fishery in Clatsop county are reported in
Table 6 for individuals from seven representative counties of origin.
Comparing these estimates with those in Table 5 and remembering that most
salmon fishing is from off-shore modes, one sees that salmon explain
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approximately sixty percent of the consumer's surplus associated with the
Clatsop off-shore fishery. Since, unlike other species in Clatsop county,
most salmon are captured by charter boats (see Table 2), one suspects that
much of the potential consumer's surplus from the salmon fishery has been
captured by the charter boat operators. Table 7 reports the CVc's for a
salmon enhancement program in the Columbia river that increases the off-shore
salmon catch rates in Clatsop county from 1.27 to 2.27 for charter boats and
from .70 to 1.70 for private boats. These CV^'s are negative indicating the
amount the individuals would pay to bring about the change. These estimates
are all larger than the corresponding CV^s for the elimination of salmon in
Clatsop county (Table 6) because a lot of the increased catch is captured by
private boats and the marginal cost of fishing from a private boat is
considerably less than the marginal cost of fishing from a charter boat.
C. Relating the Expected Compensating Variation, CV^, to the Deterministic
Compensating Variation
Most of the empirical consumer's surplus literature that deals with
continuous choices calculates compensating and equivalent variations
implicitly assuming that the utility function does not have a random
component; that is, the calculated consumer's surplus measures implicitly
assume that the individual knows with certainty what bundle they will consume
both before and after the exogeneous change in prices and characteristics. We
will refer to these measures as deterministic consumer's surplus measures and
consider deterministic compensating variations. The discrete choice analog to
the continuous choice deterministic compensating variation is the compensation
(or payment) associated with a change that would make the individual's utility
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Page 15
after the change equal to his utility before the change given that the
individual knows with certainty which of the discrete alternatives will be
chosen both before and after the change. The intent of this section is to
define deterministic compensating variations in the discrete choice model,
calculate them for a salmon enhancement program, and then relate these
deterministic discrete choice compensating variations to the expected
compensating variations (CV^'s) that were derived from our RUM.
Let us begin with a simple case where the individual is choosing site j
mode m with certainty and then the catch rates at the site increase all costs
and all other catch rates remaining constant. The individual will obviously
continue to choose site j mode m with certainty. An example would be an
individual who chose the charter boat mode in Clatsop county with certainty
and then, ceteris paribus, the charter boat catch rate for salmon in Clatsop
county increases. It is of interest to ask how much this individual would
have paid per trip to increase this single catch rate. Define the determin-
istic compensating variation associated with an improvement in the character-
istics of the site/mode, jm, that the individual would have chosen with
certainty both before and after the change, DCV^(jm/jm), as
» UCBj. + DCVj.Cjm/jm),
ajml * ajm2 * ajm5^ +
where
U(B. , p° . , a' , a' , a' ) > U(B. , p° al a°. ,, a° ,)
v i' jmi jml jm2' ' jm5' v jml jm2 jm5
1 9
Note that the random components cancel. If the conditional indirect utility
function (2) has the linear form (2a), (16) can be solved for the
deterministic compensating variation
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Page 16
(17) DCV^/Jm) - - a'ml) + - a'^) + - a^)
+ B4(ajm4 " a>4' + B5(ajo5 " ajm5>l
In the case of a salmon enhancement program that only affects site j mode m,
ajmk = ajmk ^ = •••'*>• Therefore, given our parameter estimates and
assuming the salmon catch rate increases by one
(17a) DCV.Cjm/jm) = DCV(jm/jm) = l/30[ ^(a^ - a^)]
= 1/.0681 [.9770(1)] = $14.34
One more salmon per trip is worth $14.34 per trip if the individual would have
chosen this alternative with certainty before the change. Note that this
magnitude does not depend on the individual's county of origin or the specific
site mode considered.
Relating this deterministic compensating variation, DCV(jm/jm), to the
expected compensating variation associated with the same improvement in the
characteristics of site j mode m, CV^(jm), Hanemann (1983) has shown that
(18) CVi(jm) » TTjmi DCV(jm/jm)
The expected compensating variation, CV^(jm), derived from the RUM is smaller
than the deterministic compensating variation, DCV(jm/jm), because of the
uncertainty associated with the choice of site/modes. This approximation has
a lot of intuitive appeal and if we didn't already know DCV(jm/jm) it could be
used to approximate it given estimates of the CV^(jm) and the estimated
probabilities,
Equations (16) and (17) identified the deterministic compensating
variation associated with an improvement in the site/mode that the fisherman
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Page 17
was initially choosing with certainty. Relating the CV^ to its deterministic
equivalent is much more complex if the quality of the site/mode that was
initially chosen with certainty declines because then we cannot be sure which
site/mode the individual will choose after the change. Consider, for example,
a case where pollution eliminates just the beach and bank mode in Clatsop
county. It is of interest to ask how much an individual will pay per trip to
stop the elimination of the beach and bank mode in Clatsop county if that
individual would have chosen that site/mode with certainty. In this case, we,
know for certain that the individual is precluded from visiting the eliminated
site/mode, but we don't know for certain which alternative will be chosen if
the trip still occurs. However, we can identify the deterministic
compensating variation associated with an individual who initially chose site
j mode m with certainty and who chooses site £ mode s with certainty after
site j mode m is eliminated as
(19) U(Bi, P^, ajmi> ajm2' ajm5^ + ejmti
» U(B1+ DCVit(jm/£s), p^si, a^, a'^, a'^) +
If the conditional indirect utility function (2) has the linear form (2a),
(19) can be solved for the deterministic compensating variation
(20) DCVltO/ts) - (p^ - p^) + 1/ B0[ B^(ajnl - a'^) + 62(a°jln2 - a^2)
+ S3(ajm3 " ais3) + S4(ajm4 " ais4) + %(ajm5 " ajs5) + £jmti " e£stl!
The deterministic compensating variation, DCV^^Cjm/£s), is how much individual
i will pay on trip t to stop the elimination of site j mode m if he would have
chosen site j mode m with certainty before it was eliminated and site £ mode s
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Page 18
with certainty after it was eliminated. For example, using (20) and the
parameter estimates, one can calculate that the deterministic compensating
variation for the elimination of beach and bank fishing in Clatsop county is
$28.23 + (e72ti ~ s62ti^"^^ ^or fisherman i from Clatsop county who
switches with certainty to the beach and bank mode in Tilamook. Of the
$28.32, $23.49 is attributable to the increased travel cost and $4.74 to the
fact that the quality of beach and bank fishing is lower in Tilamook county.
If the same individual was forced to switch to the private boat mode in
Douglass county the CV^t(jm/is) would be $101.43 + (£72^1 ~ e34ti^*^81. Of
the $101.43, $99.02 is attributable to increased travel cost, $19.96 is
attributable to the switch to the more expensive mode and minus $16.55 is
attributable to the fact that the quality of the fishing improves. Note that
each CV^t(jm/£s) can only be determined up to its random component, ((Ejrati
W-0681)-
Relating the CV^ for the elimination of site j mode m, CV^(jm), to the
(jm/fcs)'s
result that13
DCVlt(jm/*s)'s it can be shown that one obtains the intuitively appealing
J M .
(21) CV (jm) - I I tC DCV (jm/is)
1 ft-1 s-1 *
except when
and m=s
where
tt^s^ is the probability that individual i will choose site Z mode s on a
given trip if site j mode m is no longer available.
The expected compensating variation, CV^(jm), weights each deterministic
compensating variation, DCV^t( jm/Jls), by the probability that it measures the
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Page 19
welfare impact of the actual switch. The expected compensating variations for
the elimination of beach and bank fishing in Clatsop county, CV^(jm), can be
calculated using (8). It is $6.48 for fishermen from Clatsop county, $2.40
for fishermen from Multnomah county and effectively zero for fishermen from
Douglass county. The probabilities, , can be calculated using (5) with J
£S1
and M reduced to reflect the elimination of site j mode m. However, in this
case, knowledge of the CV^(jm) and the is n°t sufficient to approximate
the DCV^ jm/£,s) .
If utility has a random component, the expected compensating variation,
rather than the deterministic compensating variation, is the preferred welfare
measure. The deterministic measure is only appropriate if we know with
certainty what the individual will do. This raises some serious questions
about deterministic consumer's surplus measures that are derived from
constrained deterministic utility maximization models but where the estimated
system of demand functions has a random component. The random component means
that the individual's behavior is not known with certainty so expected, rather
than deterministic, consumer's surplus measures are the appropriate welfare
measure. The implicit assumption that utility is deterministic is untenable
once the random component has been added to the demand functions. 1 •+
IV. Conclusion
A RUM of recreational demand is developed which makes the conventional
assumption that utility is random from the investigator's perspective and
unlike other random utility models also assumes that utility has a random
component from the individual's perspective at the beginning of the season.
The model is used to derive the exact expected consumer's surplus measures
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Page 20
associated with changes in the costs and characteristics of the different
site/modes. The assumption that utility is random from the individual's per-
spective at the beginning of the season implies that the expected consumer's
surplus measures can be interpreted as option prices if the fisherman is risk
neutral. If a site/mode might increase in quality, the associated expected
compensating variation is how much a risk neutral fisherman would pay per trip
at the beginning of the season for the option of experiencing this increase in
quality even though he might not ever choose to actually visit that site/
mode. If a site/mode might decrease in quality, the associated expected
compensating variation is how much a risk neutral fisherman would pay per trip
for the option of not having to experience this quality decline even though he
might not ever actually choose to visit that site/mode. These option prices
vary across sites for a given individual as a function of the site/mode's
characteristics (catch rates) and costs, and across individuals for a given
site as a function of the individuals' characteristics (location of residence,
etc.). The expected compensating variation is then related to the more
conventional deterministic compensating variation which is the amount the
individual would pay to bring about a change in the characteristics or cost of
a site/mode if he knew that he was going to choose that site/mode with
certainty. The expected compensating variation derived from the random
utility model is smaller than the deterministic compensating variation because
of the uncertainty associated with the choice of site/modes.
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Page 21
FOOTNOTES
1. In terms of the option value literature, option value equals option price
minus expected consumer's surplus. Therefore, if the individual is risk
neutral option price equals the expected consumer's surplus. See Smith (1983)
for a summary of the option value literature.
2. If additivity across trips is not assumed, the choice of a site/mode on a
given trip would not be independent of the choice of site/mode on other trips
and demand could only be estimated in a consistent utility theoretic manner if
there was a complete record of where each individual went during the entire
season.
3. Morey (1981) used a logit model to estimate the demand for Colorado ski
areas. Caulkins, Bishop and Bouwes (1984) used one to estimate the demand for
a number of lakes in Wisconsin. However, neither paper derives exact expected
consumer surplus measures.
-. The more conventional assumption is that utility is always deterministic
from the individual's perspective, but random from the investigator's
perspective due to unobserved variables.
The standard logit model is defined here as a multinomial logit model that
assumes the conditional indirect utility function has the linear form specified
in (2a) and where the random component in (2a), ^as an Extreme Value
Distribution (4). This standard logit model should be contrasted with some of
its recent generalizations. Logit models that assume has an Extreme
Value Distribution are referred to as independent logit models (McFadden
(1974)) whereas logit models that assume that has a Generalized Extreme
Value Distribution are referred to as generalized logit models (McFadden (1978,
1981)). The standard logit model considered in this paper is therefore an
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Page 22
(Continued) independent logit model. Logit models can also be catagorized
as to whether they admit income effects; that is, whether or not the discrete
choice probabilities are a function of the consumers budget. Until recently,
most logit models did not admit income effects. The standard logit model
considered in this paper assumes no income effects. For more details see
footnote 6 and Hanemann (1985) who considers expected consumer's surplus
measures in the context of generalized logit models with income effects,
c. Most of the empirical logit literature assumes that the conditional
indirect utility function (2) has this simple linear form. One could
alternatively adopt the more general form
Ujmti = 80Bi ~ 80pjmi + hjm(ajml* ajm2' "•» ajm5) + ejmti
If one doesn't restrictively assume that h. (a.. jm jml' ajm2' ajm5) =
^ ®kaimk' estimation is more difficult and many of the derived equations
k=l J
(e.g. (5), (6) and (8)) adopt more complex functional forms but the theoretical
results remain effectively the same. The critical factor is that this more
general specification maintains the standard logit assumption that the choice
of alternatives is independent of B^.
All consumer surplus measures are a positive function of the assumed value
of time. The value of time is typically assumed to be between 20 and 50 of
the manufacturing wage rate; $3.35 is approximately 40 of the manufacturing
wage. For a survey of the empirical literature on the value of time see
Cesario (1976).
The catch rate for species k at site j is the average catch rate for
species k at site j for all individuals in the sample who visited site j. For
more details see Rowe et al (1985).
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Page 23
5. The specific program used is the unconstrained Non-Linear Optimizaton
Solver (Dennis and Schnabel (1983)). Ameniya (1981) has shown that the log of
the likelihood function for the standard logit model is globally concave which
implies that it has only a single global maximum. One therefore does not have
to worry about the algorithm converging to a local maximum which is not the
global maximum.
10. The CV^ could also be interpreted as our expectation of the amount
individual i would pay on the morning of the trip to bring about the change.
On the morning of the trip, is deterministic from the individual's
perspective so individual i knows exactly how much he would pay to face the
choice set (pi> A'); for example, the individual will pay nothing if the
change only improves a site that is not chosen. However, since v i is a random
variable from our perspective we don't know the exact amount individual i will
pay on the morning of the trip and we can only determine how much the
representative individual will pay (CV^). This latter interpretation of the
CV^ is the more conventional interpretation but in the model presented here
both interpretations are correct (see footnote 4).
11. A number of things about the CVc's (8) should be noted. Hanemann (1985)
shows that the CVc's derived from the standard logit model (8) are invariant to
monotonic transformations of the conditional indirect utility function (2a).
This result depends critically on the standard logit assumption of no income
effects. Therefore, the derived CVc's (8) do not imply cardinal preferences
and care must be taken so as to not inappropriately attach meaning to the
cardinal properties of these expected compensating variations. For more
details see Morey (1984). The absence of income effects also allows us to
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Page 24
11. (Continued) relate the CV (and EV ) to an area under an expected
c c
Marshallian demand curve. This is the random utility analog to the determin-
istic result that the Marshallian and Hicksian demand functions coincide when
there are no income effects. For example, if the cost of site j mode m
decreases the CVc (and EVc) for that change is the area under site j mode m's
expected Marshallian demand curve between the two cost levels. For more
details see Hanemann (1985).
II. Feenberg and Mills (1980) derive a measure that is equivalent to the
deterministic compensating variation measure defined in (16) and use it to
estimate the benefits of an improvement in a site's water quality.
13. The exact formula is
J M
CV.(jm) 11 f DCV (jm/zs) f (e^Jde
1 i=l s=l At(jm/£s) Xt £
except when j=l
and m=s
where /-
At(jm/£s) = j£|u;uti < u°sti < u°mti and u^. < u^ti for nu * 2s * jm
The set At(jm/£s) is that part of the joint density function of e that implies
site j mode m will be chosen with certainty on trip t before it is eliminated
and that site I mode s will be chosen with certainty after it is eliminated.
The approximation (21) is obtained by ignoring the random components in the
DCVit(jm/Is)1s.
I-.. As noted earlier, Feenberg and Mills (1980) estimate a discrete choice
random utility model but then calculate benefits using deterministic compensat-
ing variations. In the continuous choice literature, a non-random utility
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Page 25
14. (Continued) function is usually assumed and one then adds a random
component on to the derived demand functions in an ad hoc manner. Consumer's
surplus measures are then calculated maintaining the implicit assumption that
the estimated utility function is still deterministic. Morey (1985) provides
one of many examples.
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Page 26
REFERENCES
Ameniya, Takeshi, "Qualitative Response Models: A Survey," Journal of Economic
Literature 19 (December 1981), 1483-1536.
Caulkins, Peter P., Richard C. Bishop, and Nicolaas W. Bouwes Sr., "The Travel
Cost Model for Lake Recreation: A Comparison of Two Methods for
Incorporating Site Quality and Substitution Effects," working paper, U.S.
Environmental Protection Agency (1984).
Cesario, Frank J., "The Value of Time in Recreation Benefit Studies," Land
Economics 52 (1976), 33-41.
Dennis, John E., and Robert B. Schnabel, Numerical Methods for Unconstrained
Optimization and Nonlinear Equations (New Jersey, Prentice Hall 1983).
Feenberg, D. and E.S. Mills, Measuring the Benefits of Water Quality
Improvement (New York: Academic Press, 1980).
Hanemann, W. Michael, "Marginal Welfare Measures for Discrete Choice Models,"
Economic Letters 13 (1983), 129-136.
, "Welfare Analysis with Discrete Choice Models," working paper,
Department of Resource and Agricultural Economics, University of
California, Berkeley, March 1985.
McFadden, Daniel, "Conditional Logit Analysis of Qualitative Choice Behavior,"
in Zarembka P. (ed.) , Frontiers of Econometrics (New York: Academic
Press, 1974) .
, "Modelling the Choice of Residential Locations," in Karlquist, A.,
L. Lundquist, F. Snickars, and J.L. Weibull (eds.), Spatial Interaction
Theory and Planning Models (Amsterdam: North Holland, 1978).
.¦ "Econometric Models of Probabilistic Choice," in Manski, Charles
F., and Daniel McFadden (eds.), Structural Analysis of Discrete Data with
Econometric Applications (Cambridge: MIT Press, 1981).
Morey, Edward P.., "The Demand for Site-Specific Recreational Activities: A
Characteristics Approach, " Journal of Environmental Economics and
Management 8 (December 1981), 245-271.
, "Confuser Surplus," The American Economic Review 74 (March 1984),
163-173.
, "Characteristics, Consumer Surplus, and New Activities: A Proposed
Ski Area" The Journal of Public Economics, (forthcoming 1985).
Rowe, Robert D., Edward P.. Morey, Arthur D. Ross, and W. Douglass Shaw, Valuing
Marine Recreational Fishing on the Pacific Coast. Report prepared for the
National Marine Fisheries Service, National Oceanic and Atmospheric
Administration, La Jolla, California, March 1985.
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Page 27
Small, Kenneth A., and Harvey S. Rosen, "Applied Welfare Economics with
Discrete Choice Models," Econometrica 49 (Jan: 1981), 105-130.
Smith, V. Kerry, "Option Value: A Conceptual Overview," The Southern Economic
Journal (1983), 654-668.
U.S. Bureau of the Census, Statistical Abstracts of the United States: 1981:
102 Edition. Washington, D.C. (December 1981).
U.S. Department of Commerce, NOAA, Marine Recreation Fishery Statistics Survey,
Pacific Coast, 1981-82. Current Fisheries Statistics No. 8323,
NOAA/NMFS. Washington, D.C. (November 1983).
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Page 28
TABLE 1
Cost Per Trip to Each Site/Mode in Oregon from Five Representative Counties
in Coastal and Central Oregon*
From/To Curry Coos Douglass Lane Lincoln Tilamook Clatsop
Curry 1.96 28.97 41.89 50.11 89.80 116.82 161.97
Douglass 79.23 32.50 28.19 50.51 87.84 115.64 124.25
Clatsop 161.59 112.90 99.98 91.76 52.07 25.45 1.96
Multnomah 167.46 118.77 95.67 84.71 50.90 29.75 37.19
(Portland)
Deschutes 136.78 105.46 94.89 86.67 93.32 116.42 125.03
(Central)
*The costs reported in this table include travel costs and the opportunity cost
of the individual's time in transit but do not include the on-site/mode costs.
The average on-site/mode costs are $2.87 for beach and bank, $3.87 for man-made,
$52.80 for charter boat and $22.83 for private boat.
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Page 29
TABLE 2
Catch Rates for Oregon
(average number of fish per day-trip)
Mode* Curry
Coos
Douglass
Lane
Lincoln
Tilamook
Clatsop
Salmon
MM
.03
.51
0
0
.01
0
.03
BB
.16
.06
.08
0
.01
.04
0
CB
.49
1.21
1.28
1.28
.60
.40
1.27
PB
.41
.85
1.02
1.02
.51
.37
.70
Perch
MM
3.22
3.15
2.57
2.92
.77
1.15
1.27
BB
1.00
4.97
2.83
1.00
2.88
1.24
2.87
CB
0
0
0
0
0
0
0
PB
0
.56
0
0
.60
.01
0
Smelt
MM
.84
.76
.04
0
.01
0
0
and
BB
0
.52
1.39
0
.91
0
0
Grunion
CB
0
0
0
0
0
0
0
PB
0
.02
0
0
0
0
0
Flatfish
MM
0
.01
.08
.01
.05
0
.16
BB
0
.06
.06
0
.11
0
.85
CB
0
0
0
0
0
.02
0
PB
0
0
0
0
.41
.01
0
Rockfish/
MM
.02
1.40
1.29
4.72
1.00
.69
.46
Bottomfish
BB
.33
.94
1.98
.80
1.71
.28
1.43
CB
0
6.85
0
0
5.15
.45
0
PB
3.15
1.45
1.00
0
1.35
.31
0
*MM = Man-made structure, BB = Beach and Bank, CB = Charter Boat, PB = Private Boat
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Page 30
TABLE 3
Maximum Likelihood Parameter Estimates
Smelt and Rockfish/ Likelihood
Price Salmon Perch Grunion Flatfish Bottomfish Function
Random
Allocation
across
Site/Modes
-19,506
Costs Only
-.0550
-14,645
Costs and
Catch Rates
-.0681
.9770
-.2605
.3621
.6079
.2346
-14,084
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Page 31
TABLE 4
The Estimated Probability that an Individual from County c Will Visit Site j Mode m
on a Given Trip for Five Representative Counties in Coastal and Central Oregon
(rounded to nearest percent)
From/To
Mode* Curry
Coos
Douglass
Lane
Lincoln
Tilamook
Clatsop
Curry
MM
.18
.06
.01
.02
0
0
0
BB
.31
.02
.03
.01
0
0
0
CB
.02
.03
0
0
0
0
0
PB
.25
.04
.02
.01
0
0
0
Douglass
MM
0
.15
.11
.05
0
0
0
BB
.01
.06
.23
.03
0
0
0
CB
0
.07
.02
0
0
0
0
PB
0
.09
.14
.03
0
0
0
Clatsop
MM
0
0
0
0
.01
.05
.27
BB
0
0
0
0
.01
.05
.36
CB
0
0
0
0
0
0
.04
PB
0
0
0
0
.01
.03
.16
Multnomah
MM
0
0
0
.01
.05
.18
.12
(Portland)
BB
0
0
0
.01
.06
.18
.15
CB
0
0
0
0
.01
.01
.02
PB
0
0
0
0
.03
.09
.07
Deschutes
MM
0
.04
.05
.17
.08
.01
.01
(Central)
BB
0
.02
.10
.12
.08
.01
.01
CB
0
.02
.01
.02
.02
0
0
PB
0
.02
.06
.09
.05
.01
.01
*MM = Man-made structures, BB = Beach and Bank, CB = Charter Boat, PB = Private Boat
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Page 32
TABLE 5
The Estimated Per-trip CVc's Associated with the Elimination of On-shore Fishing (S),
Off-shore Fishing (B) and All Fishing (A) at Three Macro Sites (Clatsop, Douglass and
Curry) for Individuals from Seven Representative Counties of Origin (rounded to the
nearest cent)
Multnomah Deschutes
At/From Mode Clatsop Tilamook Lincoln Douglass Curry (Portland) (Central)
Clatsop
S
14.60
1.83
.19
.01
0
4.55
.26
B
3.29
.56
.06
0
0
1.30
.08
A
26.08
2.47
.25
.01
0
6.35
.35
Douglass
S
.01
.25
1.07
6.19
.65
.08
2.37
B
.01
.12
.50
2.61
.31
.04
1.08
A
.02
.37
1.61
10.38
.97
.12
3.64
Curry
S
0
0
.01
.12
9.66
0
.09
B
0
0
.01
.06
4.58
0
.05
A
0
0
.02
.18
20.36
0
.15
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Page 33
TABLE 6
The Estimated Per-trip CVc's Associated with the Elimination of Salmon Fishing in
Clatsop County for Individuals from Seven Representative Counties of Origin
(rounded to the nearest cent)
Multnomah Deschutes
Clatsop Tilamook Lincoln Douglass Curry (Portland) (Central)
1.80 .32 0 0 ."3 .33
TABLE 7
The Estimated Per-trip CVc's Associated with a Salmon Enhancement Program in Clatsop
County (increasing each of the off-shore salmon catch rates by one) for Individuals
from Seven Representative Counties of Origin (rounded to the nearest cent)*
Multnomah Deschutes
Clatsop Tilamook Lincoln Douglass Curry (Portland) (Central)
-4.22 -.88 -.10 0 0 -1.93 -.14
*The CVc's are negative indicating the amount the individuals would pay to bring
about the change.
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THE VARYING PARAMETER MODEL: IN PERSPECTIVE
by: William H. Desvousges, Ph.D.
Research Triangle Institute
Center for Economics Research
Research Triangle Park, North Carolina 27709
ABSTRACT
This paper describes the use of the varying parameter model for valuing
an improvement in a characteristic (water quality) of a recreation site.
This model is a multisite model that relates variations in the travel cost
demand parameters to differences in site characteristics. The paper dis-
cusses the implicit assumptions and data requirements of the model and
compares them to other recent models. It also demonstrates the importance
of model estimation with truncated dependent variables. The paper presents
benefits estimates for water quality changes at 22 recreation sites and
compares these with other recent estimates.
I . INTRODUCTION
In their relatively brief history, environmental and resource econ-
omists have devoted considerable attention to determining the value of
nonmarketed goods. Spurred by the need for valuation information to assist
in recreation management planning, these economists have developed several
models for deriving this information. Chief among these models is the
travel cost model, which draws from the rich legacy of Clawson [1959] and
Clawson and Knetsch [1966]. With its origins in trying to value the serv-
ices of a recreation site, this approach uses travel distance and related
costs as the implicit "price" that recreationists are willing to pay for
using the services of recreation sites.
Many of the empirical applications of the travel cost model have
measured either the value of an entire recreation site (see Dwyer, Kelly,
and Bowes [1977], Loomis and Sorg [1982], and Bockstael, Hanemann, and
Strand [1 984]) or the value of using some part of a large resource like a
national forest for recreation. More recently, recreation research in
support of planning needs has shifted to more subtle types of valuation
questions--the value of incremental changes, such as additional hiking
trails or campgrounds, in the quality of existing resources. These ques-
tions emphasize the need for valuing a change in the quality of the services
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provided by the site. The policy evaluation requirements of the U.S. Envi-
ronmental Protection Agency (EPA) has further emphasized the importance of
this new direction in recreation research. For example, in accordance with
Executive Order 12291, EPA must measure the benefits of water quality
changes for all major regulations. In effect, therefore, given a major
regulation affecting a water body such as a river, EPA must estimate the
value of a quality change in one of its characteristics—water quality.
Not surprisingly, several recent studies have focused on measuring
quality changes (e.g. , see Brown and Mendelsohn [1984], Morey [1981, 1984,
forthcoming], Vaughan and Russell [1982a], and Smith, Desvousges, and
McGivney [1983a,b]). Following the insights of the hedonic literature,
these studies view quality changes as changes in the levels of the attri-
butes or characteristics of recreation sites. Each has taken a different
tack in the course of modeling how changes in these attributes affect
recreationists' choices.
This paper has two objectives. Our first is to profile the varying
parameter model used by Vaughan and Russell [1982a] and ourselves to value
water quality changes. The essence of this model is that differences in
characteristics among recreation sites will be reflected in the travel cost
demand equations for these sites. In our profile of this model, we will
describe briefly its key features, implicit assumptions, and data require-
ments. We also will highlight some of the issues in using the model to
value water quality changes at a recreation site.
Our second objective is to provide some perspective on the varying
parameter model by placing it in the context of the other recent studies
that value quality changes. To provide this perspective, we will compare
the varying parameter model to the models used in these studies. In addi-
tion, we will contrast our application of the varying parameter model with
that of Vaughan and Russell [1982a],
Section II of this paper provides some background on the valuation
issues covered in these recent papers. Section III highlights key features
and assumptions of the varying parameter model. Section IV discusses the
data requirements for the varying parameter model, along with those of the
other approaches. Section V illustrates how we used the model to value
water quality changes at 22 recreation sites. Section VI provides some
implications for future research. Section VII lists references cited in
this paper.
I I. BACKGROUND
Several themes are common to the recent papers by Morey [1984, forth-
coming], Vaughan and Russell [1982a], and Brown and Mendelsohn [1984], One
is the use of indirect methods in attempts to value quality changes. That
is, by employing either behavioral or technical assumptions about household
behavior, they all relate the demand for a nonmarketed good, or character-
istic, to the observed demand for a marketed good. In keeping the focus of
this paper within the confines of the variants of the indirect approach
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used in these papers, we are ignoring the contingent valuation studies that
use a survey-based approach to directly elicit households' values for these
quality changes. 1
Another important theme appearing in varying degrees in each of these
papers is the role of a recreation site's characteristics in reflecting
quality changes. For example, Figure 1 shows that our varying parameter
model views the demand for a recreation site's services as a function of
its characteristics. A water quality improvement from WQ1 to WQ2 in Fig-
ure 1 causes an increase in the demand for visits to the site at every
implicit price or travel cost. Our model considers the influence of qual-
ity changes from a quantity or visits perspective. Visits to sites with
D(WQo)
Q
Figure 1. Travel cost demand function with
water quality improvement.
aIt also is important to note that a survey-based data collection effort
underlies each of the studies mentioned above. The main difference be-
tween these surveys is that individuals were asked to recall recreation
experiences during a season and not directly asked to value the quality
changes. However, there is nothing to prevent a survey from asking both
types of questions. For example, the National Hunting, Fishing, and Wild-
life survey asks both types of questions. We also asked both questions in
Desvousges, Smith, and McGivney [1983] and found them to be excellent
complements.
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different levels of water quality will differ in their quality. Although
we cannot measure the quality differences among visits of different sites,
we assume that the parameters of a travel cost demand equation are func-
tions of the site characteristics. This assumption enables us to value the
change in quality of any characteristic by linking it to a change in the
demand for the site's services.
The Brown and Mendelsohn [1984] also emphasizes the importance of site
characteristics. However, they view the problem of valuing quality changes
as a price index problem. In their model, consumers minimize the cost of
producing each combination of recreation site characteristics. They esti-
mate a price index by regressing travel cost for a given origin zone to
each site on the vector of characteristics provided by each site. Repeat-
ing this process for each origin zone defines a modified "recreation hedonic
price function" for each zone. By taking the partial derivative of each
function with respect to a characteristic (e.g., water quality), they
obtain the marginal implicit price of the characteristic. Performing the
same task for other characteristics and using the features of each origin
zone's population, they estimate the demand for all the recreation site's
characteristics.
Morey's [1984, forthcoming] approach places even greater emphasis on
the role of characteristics in valuing quality changes. Focusing on the
demand for an activity instead of on that for a site, Morey incorporates
the physical characteristics of activities and personal characteristics of
an individual into an expenditure function. He uses this function to
define welfare measures for changes in either the cost or physical charac-
teristics of the activities.2
Finally, all these studies use data from visits to multiple sites to
implement their models. For example, Vaughan and Russell [1982a] use
information from a sample of fee fisheries for their varying parameter
model, while we use data from 22 Corps of Engineers general purpose, flat-
water recreation sites and Morey [1984 forthcoming] estimates his model for
fifteen Colorado ski sites. Brown and Mendelsohn [1984] have the largest
universe of sites, with information on steelhead fishing at over 140 dif-
ferent rivers in Washington. The multiple site orientation reflects a
shift in direction away from the single-site orientation of the majority of
the early travel cost studies. This shift is due primarily to the emphasis
on valuing quality changes in a site's characteristics which requires
variation across sites for implementing any of the models.
2Morey [forthcoming] argues that when characteristics of an activity are
included in a demand function, the activity's name is unnecessary to
explain the demand for that activity. That is, only the characteristics
are important. On a substantive level, this view ignores the possible
importance of "context" effects that influence consumer behavior. For
example, Schoemaker [1980] showed respondents evaluating the same gambles
differently in the context of a lottery rather than insurance.
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III. THE MODEL
To highlight our interpretation of the varying parameter model, we
adopt the household production framework. For simplicity, we assume that
the household consumes two final service flows or basic commodities—a
recreational activity, Zr, and a nonrecreation composite service, Zn.3 By
combining time, market purchased goods, and the services of a recreation
site, the household is assumed to produce a recreation service flow (e.g.,
swimming or fishing). For a recreation season, the price of fishing at the
recreation site is the implicit time, travel, and other incremental costs
incurred in visiting the site. Visits to a site during a season are the
corresponding measure of the quantity of the site's services demanded by
the household.4
The household's objective function can be viewed as maximizing the
utility derived from these activities, subject to a "full" income constraint
(i.e., a constraint combining the budget and time restrictions facing the
household) and the production functions for the final services flows.5 The
two most important components of this objective function for our application
are the budget constraint and the household production function for recrea-
tion services. The first of these is given in Equation (1):
Y = wtw + R + L = Pn+1 Xn+1 + X P.X. + (Td, + ctx + w0tvl)Vl
1=1 (1)
+ (Td2 + ct2 + w0tv2)V2 ,
where
Y - full income (i.e., including wage income, wt , nonwage
income, R, and foregone income, L)
w = market wage rate
3The terms household and individual will be used synonymously. (For the
specific underlying assumptions see Becker [1974].)
4Bockstael, Hanemann, and Strand [1984] point out that this is a key sim-
plification of the household's decision process. They suggest that house-
holds engage in a two-tiered decision process. First, it decides to fish
or swim and then chooses the site at which this activity will occur.
Unfortunately, the data precluded our ability to analyze this decision
process because it contained a household's seasonal visits to a particular
site. This feature of the data poses other difficulties; these are dis-
cussed in the next section.
5For discussion of the household production framework in general terms, see
Pollak and Wachter [1975], Deyak and Smith [1978] and Bockstael and
McConnell [1981] consider the implications of the framework for recreation
models.
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t = work time
w
X. = ith market goods used in production of the nonrecreational
service flow (i = 1, 2,...,n)
P. = price of ith good (i = 1,2,...,n + 1)
Xn+^ = market good used in production of recreation service flow
T = vehicle related travel cost per mile
d. = round-trip distance to jth site (j = 1,2)
<3
c = individual's opportunity cost of travel time to a site
t. = round-trip travel time to jth site (j = 1,2)
<3
w0 = opportunity cost for time onsite
tvj. = time onsite per trip to jth site (j = 1,2)
Vj = number of trips to jth site in specified time horizon.
This formation of the consumer choice problem embodies several implicit
assumptions. For ease of exposition, we assume that the individual con-
siders the use of only two different sites. The time onsite is assumed to
be constant across all trips to each site, implying that the implicit
prices to the individual for a change in either the time onsite per trip or
the number of trips will be interrelated.6
Finally, our statement of the budget constraint allows for a general
treatment of the opportunity cost of time. However, in practice we have
used the wage rate as a proxy for the value of the household time. As
Bockstael, Hanemann, and Strand [1984] point out, the wage rate is the rel-
evant measure of opportunity cost only to the extent that households can
adjust their marginal hours worked at its wage rate. In addition, the
household may face constraints on when and how their available time occurs.
That is, they may be required to work only 40 hours a week or 50 weeks a
year. In effect, some households may be unable to adjust the number of
hours worked or may be able to do so only by moonlighting at a lower wage
rate. While the more complete view of time costs by Bockstael, Hanemann,
and Strand [1984] is consistent with our model, it is precluded by the
available data.
6This specification also implies that the choice of trips to the site and
time onsite are jointly determined. Thus, if onsite time costs are in-
cluded in the implicit price of a trip, a simultaneous equations estimator
must be considered. Further details are developed in the third section of
this paper.
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The alternative treatments of time costs across the recent studies
does provide some useful perspective, however. For example, with data
available only on their recreation sites and not users, Vaughan and Russell
[1982a] used the two extreme values for time costs—zero and the full wage
rate—and evaluated the sensitivity of their results to these extremes.
Brown and Mendelsohn [1984] used income as a proxy for the wage rate,
examined the robustness of demand regressions using different percentages
of the wage rate, and presented results for time valued at 30 percent of
the proxy wage rate. Morey [1984, forthcoming] uses the minimum wage for
his sample of college student skiers.
The picture that emerges from all the studies is the inadequate treat-
ment of the opportunity cost of time in recreational demand models. While
Bockstael, Hanemann, and Strand [1984] have clarified some important aspects
of this thorny problem, the confusion continues. The biggest single problem
stems from analysts forgetting that opportunity cost is the relevant measure
of all costs. Simply because travel time in scenic areas is enjoyable does
not mean we ignore the full opportunity cost of that travel time. This
remains an important area for future research.
To consider the appropriate treatment of site characteristics in a
recreational demand model requires us to specify their role in household
production activities. Equation (2) provides a general statement of the
production function for a recreation activity (fishing), with a. designat-
ing the vector of attributes for site j: ^
Z = f (X ._ , V.,t -,a.) (2)
r rv n+1' j' vj' y K >
For this two-site example (i.e., j = 1,2), this formulation assumes that
either site can contribute to the production of Z , with. the relative
productivity of each site determined by its characteristics. Assuming
¦fr(-) is strictly monotonically increasing in all arguments, we can derive
a conversion function for site services (holding t . eaual for j = 1 and 2)
as the ratio of the visit requirement functions forJthe two sites at the
same level, of output and other inputs (i.e., solving (2) for V. in terms of
its arguments for j = 1,2). This function enables us to convert measures
of visits to sites with different characteristics into a single measure of
the use of all sites.
In general terms, our production function implies that the conversion
function depends on the level of output, Z^, a variable not easily measured.
However, following Lau's [1982] analysis, we can assume that this input
conversion function is independent of the level of the activity produced,
implying that the production function must have an augmentation form (i.e.,
= fr(Xn+,),H(a.)V.,t .), where H(a_.) = augmentation function). In other
words,rour conver^iod faction reflects the contribution of each attribute
to the relative productivity of each site. For example, improved water
quality would enhance the productivity of a site in providing fishing or
swimming. Nevertheless, our conversion function does implicitly assume
that only site characteristics will determine the substitutability between
sites. In this view, the conversion function is used to adjust for differ-
ences in characteristics between two sites, the two sites would be perfect
substitutes.
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The assumptions of nonjointness and homotheticity in household produc-
tion activities involving recreation sites, together with the augmentation
format for the contribution of site characteristics, permit a direct inter-
pretation of the travel cost demand model. More specifically, the house-
hold's cost function for the recreational service flow can be written as
Equation (3) below:
TC = g(Zr)*G(Pn+1,w0,hj/H(aj)) , (3)
where
h. = Td. + ct..
J J J
The demand for a site's services will be given as:
aTC/ahj = l/H(aj)-g(Zr)-G3(Pn+1,w0fhj/H(aj)) , (4)
where
G3(•) = the partial derivative of G(-) with respect to its
third argument.
Thus, the travel cost demand model can be interpreted as the derived
demand for a site's services associated with the production of recreational
services. This derived demand function will be related to Zr, PQ.^» the
implicit price., hand H(a.). Moreover, when the model is specified with
trips as a function of travel costs, income, and other socioeconomic vari-
ables describing the features of the individual, it implicitly assumes Xn+^
is given and that the optimal Z can be expressed as a function of income
and the travel costs (and not tne "prices" of other final service flows
such as £ in our case). Finally, since site attributes will determine the
productivity of a unit of a site's services, the parameters of each travel
cost demand function should all be a function of site characteristics, as
given in Equation (5) below.7
1 nV • — bn(an ., a„ a, .) + b-, (a~ a0...... a, .)h.
jm ov lj' 2j' ' kj 1V lj' 2j' ' kjy jm
+ b2(a, - ,a_ ,a. .) Y + 1 8 (a,. ,a_ .....)Z + e .
2V lj' 2j' ' kjy m Ksv lj' 2j' sm jm
(5)
where
Ym = family income for mth individual as a proxy for full income
Z = sth socioeconomic characteristic for the mth individual,
sm
'Brown and Mendelsohn [1980] have approached the same type of problem and
utilized a hedonic travel cost framework to describe behavior. The theory
underlying their model parallels our analysis. However, their framework
leads to models capable of deriving the demand for an attribute of a site
rather than the demand for a site with specific attributes.
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With the main features of our conceptual foundation developed, the key
assumptions merit some additional discussion. One of the most crucial
assumptions is the ability of our conversion function to reflect the influ-
ence of substitute sites. That is, we assume that the differences in site
attributes are capable of reflecting all aspects of substitution opportun-
ities. Although a site's characteristics are likely to have an important
influence on substitutability among sites, our model ignores the effect of
different prices for obtaining the site attributes. For example, a fisher-
man would consider the time and travel costs for a site as well as its
water quality. This limited role for substitution opportunities reflects
the inadequacy of our data set rather than an inherent deficiency of the
varying parameter model. We were unable to identify the alternative sites
our sample of recreationists visited during the season.
The assumptions of nonjointness and homotheticity in the households'
recreation production are also important. Extending our earlier fishing
example, homotheticity implies that a fisherman's marginal rate of technical
substitution between labor (or time) and capital remains constant as the
rate of fishing activity increases (along a ray from the origin). Clearly,
this is a simplification because it is likely that a fisherman would sub-
stitute more capital--a bigger boat or motor or more sophisticated elec-
tronics—for his time or labor input—when he increases his rate of fishing.
By assuming hometheticity we are not allowing these kinds of adjustments in
production, which could cause us to overstate the cost of producing the
fishing activity.
Nonjointness is also a simplification that is unlikely to be reflected
in the "real world" of recreation activities. For example, it is a rela-
tively simple matter for a fisherman to spend time camping, picnicking,
swimming, or just boating during a fishing trip to a recreation site. By
attributing all the costs to the production of fishing, we are misspecifying
our travel cost model by overstating the cost of fishing.8
How do these assumptions compare with those required to implement the
models from other recent studies? Table 1 highlights the key assumptions
that are employed in other recent recreation models. For example, the
Vaughan-Russell [1982a] version of the varying parameter model assumes that
the type of fish species available at a recreation site is the site char-
acteristic that reflects a change in water quality. This view leads them
to estimate separate travel cost demand equations for each species. The
crucial question is how well available fish species reflects water quality
changes. This is probably suitable for fishing--Vaughan and Russell's main
objective—but it does not address how water quality changes affect other
activities.
8In Desvousges and Smith [1984] we have examined the role that activities
play in our conceptual component of the varying parameter travel cost
model. We suggest that the relevant question is, "How do you add up the
various individual demands for a site's services when different types of
activities are undertaken?" Unfortunately, the available data were not up
to the empirical tasks that we demanded of it for this aggregation question.
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TABLE 1. IMPLICIT ASSUMPTIONS
Author
Assumption
Vaughan-Russell [1982a]
Species type is most important site
attribute for valuing water quality
changes.
Brown-Mendelsohn [1984]
Hedonic price function serves some
purpose as in conventional hedonic.
Hedonic price function in linear.
Morey [forthcoming]
Activity is weakly separable. Nonjoint-
ness in production. Homothetic demand
functions. All characteristics are
specified.
In addition, Vaughan and Russell do not explicitly address the inter-
relationships between demands for different species. Are these important
considerations for a household? For example, does it decide between visit-
ing a catfish site and a trout site? One could imagine that other site
characteristics (e.g. , scenic beauty) would influence the choice of a site
and that these characteristics might affect catfish sites differently than
trout sites. In summary, the Vaughan-Russell model seems plausible for the
specific purpose for which it was intended, but it would require consider-
able modification to make it a more general purpose model.
Brown and Mendelsohn [1984] make three important assumptions in imple-
menting their hedonic travel cost model. First, they assume that their
hedonic price function plays a role similar to that of other such functions
(e. g. , housing markets). Using their example, the steel head fisherman is a
price taker who responds to the hedonic price function that defines how the
price of a fishing trip will change as the mix of site characteristics
change. In the conventional hedonic model, this function is an equilibrium
relationship that results from the actions of alLdemanders and suppliers
of the commodity, steelhead fishing trips. Although it is relatively easy
to see how individuals are allocated to different points along this func-
tion depending on their value for a characteristic in a housing market, it
is not clear how this allocation is performed in steelhead fishing. In
other words, how does this price function perform as the equilibrating
mechanism for the steel head fishing market?
The second implicit assumption of the Brown and Mendelsohn model is
that the hedonic price function is linear. The linear form implies that
individuals can repackage site characteristics in any combination they
choose. This assumption seems inappropriate for recreation sites that may
have some characteristics that are difficult to alter. While it may be
easy to alter fish density with a stocking or some other fish management
program, it is more difficult to change the degree of crowdedness or scenic
beauty at a recreation site.
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Finally, the Brown and Mendelsohn model does not address the discrete
nature of many recreation decisions. That is, they estimate hedonic price
equations for a season rather than for a specific trip. Thus, we do not
obtain any insight about the discrete choice that steelhead fishermen make
between the relevant choice set of sites.
The Morey approach also requires several implicit assumptions before
it can be employed to model recreation demand. For example, Morey [forth-
coming] assumes that activities are not jointly produced—the same assump-
tion we employed in our varying parameter model. This assumption has the
same effect of overstating costs of an activity as in our application.
Morey imposes an additional simplifying assumption that the households'
ability to produce recreation activities exhibits constant returns to
scale. Using Morey's skiing example, a doubling of inputs such as skiing
time and equipment results in a doubling of skiing activity. Thus, Morey's
view of activity production is similar to the simplistic character assumed
in our varying parameter model. This reflects more an overall lack of
understanding about recreation activities than an inherent flaw in either
models.
To estimate his model, Morey assumes that his main activity of
interest--skiing--is weakly separable from all other activities. This
implies that consumer demand, and subsequent expenditures on skiing, are
unaffected by other activities, such as relaxing in a mountain environment
or driving for pleasure. If this separability assumption does not hold,
the expenditure share model Morey estimates may be incorrectly specified.
A final implicit assumption in the Morey model is that all the rele-
vant characteristics of an activity are specified in the individual's
demand function. While this is a plausible assumption, it appears to be a
difficult one to implement. For example, Morey includes four characteris-
tics in his restrictive constant elasticity of substitution (CES) demand
function9 but is only able to include two characteristics in less restric-
tive generalized CES (GENCES) demand function because of the estimation
requirements for the complex model. If Morey's model requires that all
characteristics be included, there seems to be some inconsistency between
two different forms of his model.10
9The CES is restrictive in the sense that it assumes that the demand func-
tion is homothetic. This assumption implies that the demands for recre-
ation activities all have unitary income elasticities. In effect, skiing
becomes an essential good.
10The situation may be even more complicated because it appears that the
two characteristics—total skiing area and skill-specific skiing area-
included in the GENCES Model are interdependent. In fact, it seems that
the quantity of skill-specific skiing area is a subset of the total area.
Morey does not discuss the potential significance of reducing character-
istics from four to two in his two model versions or the interrelation-
ships between characteristics.
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In summary, each of the recent multiple site models for valuing
changes in a site attribute requires implausible assumptions about either
the production of, or demand for, recreation activities. In almost all
instances, the lack of realism in the assumptions can be traced to two
causes—the inadequacy of our understanding of household's recreation
behavior and the egregious quality of the available data. Our lack of
understanding of household behavior is due in part to the distance econo-
mists generally keep from the subjects whose behavior they attempt to
model. This distance also is reflected in our inattention to the types of
data requirements of our revealed preference models, the focus of the next
section of this paper.
IV. DATA
The Federal Estate component of the 1977 Nationwide Outdoor Recreation
Survey conducted by the Department of the Interior provided the source for
visitor information to estimate our travel cost models. The Federal Estate
includes all federally owned lands with public outdoor recreation areas. A
total of 13,729 interviews with recreationists were conducted at 155 sites
during the time of the survey. We limited our analysis to 43 U.S. Army
Corps of Engineers sites with consistent visitor data because they provided
a fairly comparable range of water-based outdoor recreational activities.
A separate data source, the Corps' Recreation Resource Management System,
provided information on the site attributes, including a variety of measures
of the facilities available and natural features of each site.11 The
National Water Data Exchange (NAWDEX) supervised by the U.S. Geological
Survey was the source for the water quality data. To establish a linkage
between the water quality monitoring stations and the sites, the latitude
and longitude of stations and recreation sites were used. Monthly readings
were collected for the months from June through September for 1977 and the
years before and after the survey to supplement the 1977 information in
cases of missing data. Nonetheless, only 33 of the 43 sites had sufficient
information for the other site characteristics and the water quality param-
eters. 12
The character of our data has an important implication for our estima-
tion of the varying parameter model. Specifically, our data are from a
1;1The specific measures of site characteristics considered were total
shoremiles; total site area; pool surface area; number of developed
multipurpose recreational areas at the site; number of developed access
areas on the site; number of picnic locations; number of developed camp
locations, boat launching lanes, and private and community docks at the
site; and the number of floating facilities at the site.
12Seven measures of water quality were collected, including dissolved
oxygen, fecal coliform density, pH, biochemical oxygen demand, phosphates,
turbidity, and total suspended solids. In addition, two indexes of water
quality were also considered—the National Sanitation Foundation (NSF)
index and the Resources for the Future (RFF) index developed by Vaughan
[1981] and underlying the RFF water ladder.
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survey of users conducted at each of the recreation sites. This type of
survey is commonly used in recreation studies because it identifies users
at a reasonable cost. However, it provides no information on individuals
who chose not to use the site. This causes the measure of quantity demanded,
the trips to a site for a season, to be truncated at one. In addition, the
coding procedures used in the survey caused this variable to be censored
for the highest levels of use. (The last trip interval was recorded as six
or more trips.) Screening our sites to eliminate the ones most severely
affected by these problems reduced our sample to 22 sites. Table 2 summar-
izes the characteristics of these sites and their users.13
To assess the representativeness of the data used in estimating our
varying parameter model, we have evaluated them from both a demand and
supply perspective.14 While these kinds of comparisons can be treacherous,
the objective was not to be precise. Rather, it was to make a general
comparison in fairly crude terms that would serve to identify broad simi-
larities or differences.
On the demand side, we compared the characteristics of the users of 43
Corps of Engineers sites with those of the general public and with those of
the users of other Federal Estate lands. Compared to the general public,
users of the Corps of Engineers sites are more likely to be younger, to be
Caucasian, and to be employed as craftsmen or foremen. They also are more
likely to live in rural areas, to have attained slightly higher levels of
education, and to earn higher incomes. In comparison with users of other
Federal Estate lands, users of the Corps of Engineers sites are less edu-
cated and are less likely to be employed professionals or technical workers.
They also earn lower incomes, are more likely to live in rural areas, and
are more likely to have visited a site closer to their residences. On the
whole, the users of Corps sites are fairly typical of a broad spectrum of
the population.
On the supply side, we compared activities supported by the Corps of
Engineers sites with those supported by other water-based sites on State
and Federal Estate lands. Generally, all the sites support a broad range
of activities, with boating, fishing, swimming, picnicking, and camping the
most popular. Differences seem to be most prevalent in less popular activ-
ities like horseback riding. The Corps of Engineers sites are representa-
tive of sites that support flatwater boating and fishing, as well as exten-
sive camping. In summary, our Corps sites seem representative of a large
share of water-based recreation sites.
13In subsequent analysis we have taken two additional steps: we acquired
missing characteristics data to help us estimate the model for all our
sites, and we developed a maximum likelihood estimator to account for the
truncated and censored dependent variable. Unfortunately, we found that
our model performed best for the 22 sites. For more details, see
Desvousges and Smith [1984],
14For more details see Desvousges and Smith [1984],
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TABLE 2. THE CHARACTERISTICS OF THE SITES AND THE SURVEY RESPONDENTS SELECTED FROM THE FEDERAL ESTATE SURVEY
Characteristics of survey respondents Number
Site characteristics Predicted
„ _ . „ .. r. I waqe rate Household Income Visits (T
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For perspective on the data requirements of our varying parameter
model, we can compare them with the data used in the other recent studies.
Table 3 summarizes the key features of the data used in each study includ-
ing the type of survey, sample size, variable measurement, and the type of
characteristics information. Several interesting points can be gleaned
from this table. For example, the data from these studies are all drawn
from populations of users. In effect, they do not yield information about
households who have not chosen to engage in some type of outdoor recreation
activity. As we noted earlier, this has important implications for the
types of statistical estimation models. Bockstael, Hanemann, and Strand
[1984] also point out that data sets based only on users do not allow for
zero consumption of a recreation site's services (i.e., corner solutions
are excluded).
In addition, the data contain no information on the discrete choices
households make among sites when deciding on the one they are going to
visit. Bockstael, Hanemann, and Strand [1984] suggest that this also is
an important dimension of the recreation decision that is too frequently
ignored in recreation demand models. Even the recreation participation
surveys that include both users and nonusers (e.g., see Vaughan and Russell
[1982b]) do not address the choice among sites. Generally, the focus of
participation surveys is limited to the recreate/not to recreate choice and
not to a profile of all choices during a season.
There also are some significant differences among the data from the
studies summarized in Table 3. For example, Vaughan and Russell obtained
visit and site data from the owner/operators of the recreational fee fish-
eries, while the other three studies had surveys of the users of these
sites. The Vaughan and Russell survey approach assumes that owner/operators
have accurate understanding of both their customers and their site charac-
teristics. It is somewhat analogous to the key informant survey method
that is popular in anthropological and organizational management research.
In addition, the Morey [forthcoming] data set has the most limited cov-
erage of a population. It is limited to a subset of the skiing population-
college student skiers. The Brown-Mendelsohn [1984] data have the largest
coverage of one group of recreationists, containing interviews from 5,000
fishermen. Our data set has the most extensive coverage of recreationists
engaged in a wide range of water-based recreation activities.
Finally, there are some subtle differences among the data on site
characteristics among the various studies. The data used with the two
varying parameter models have the most detailed, descriptive information of
site characteristics. By contrast, the Morey and Brown-Mendelsohn data
sets included only relatively few site characteristics-^ and 3 character-
istics, respectively. Brown and Mendelsohn used perception-based measures,
the mean values from respondents' ratings of each of the three characteris-
tics for the 140 plus rivers in their study. Unfortunately, we have almost
no information on the relative performance of different measures of the
same characteristics to make a more definitive judgment of the most appro-
priate measure.
-------
TABLE 3 PROFILE OF DATA USED IN RECENT RECREATION DEMAND MODELS
Models
Varying parameter
Data features
Desvousges-Smith [1984]
Vaughan-Russell [1982]
Hedonic travel cost
Brown and Mendelsohn [1984]
Characteristics demand
Morey [forthcoming]
Sample size and
composition
Dependent variable
Travel cost and
related expenditures
Sociodemographic
variables
Substitute site
visits
Site characteristics
Activities
Personal interview survey of
1,781 visitors at 22 Corps
of Engineers recreation sites
across the United States.
Visits per capita per season.
Separate estimates of travel
tine, onsite time, used $0.08
variable cost for mileage,
predicted wage for time cost.
Standard variable list plus
several attitudinal variables.
Manager assessment of impor-
tance of substitutes.
Corps estimates of access,
area, pool size, fish species;
facilities; site manager's
assessment of congestion levels.
List of all activities on
"surveyed" visit but no alloca-
tion of time spent on different
activities.
Mail interview survey of owner-
operators of 149 recreational
fee fisheries across the United
States.
Mail interview of 5,500 licensed
fishermen in Washington.
Owner-operator reported estimates Miles and hours for visitors in
of total visitors allocated by
origin zone.
One-way zone travel cost
($.076 per mile) plus fee or
same plus travel time valued
at BEA hourly wage rate for
zone.
Average income and population
for zone from new area file.
Owner-operator assessment of
degree of competition.
Access, area size, surrounding
countryside, congestion, fish
species provided by owner/
operator.
Type and number of fish
caught.
63 origin zones for over 140
rivers.
Travel costs at $0.10 or $0.20/
mile and time at 30 percent,
60 percent and 100 percent wage
rate; different models for
different length trips.
Income, fishing experience.
Number of trips to each site
and average length of trip.
Mean value of respondents'
assessments of congestion,
scenic beauty, and fish density.
Steelhead fishing
Survey of 163 single college
student skiers
Expenditure shares sample
individuals for 15 sites.
Travel time cost at $1.15
minimum wage; lift ticket prices
for each site; unspecified
value for distance costs.
Skiing ability; family
characteristics
Number of trips to each site
and length of visit.
Estimates of acres of ski runs,
acres of specifically designed
ski runs, vertical transport
feet, and average snow fall.
Downhill skiing
-------
What are the lasting impressions that we take from reviewing these
data? Clearly, none of the data sets is ideal. All involve compromises.
Most were collected for purposes other than the one for which they were
used in these studies. Thus, many questions that would be relevant to
recreation demand models were omitted from the surveys in favor of ones
that fulfill other objectives. As noted earlier, the treatment of the
opportunity cost of time is inadequate in all the surveys.
One impression still nags at us. This impression stems from the
analysts who view contingent valuation and revealed preference models
reviewed in this paper as competitors. In our view, they are better comple-
ments than substitutes. For example, the types of information needed to
deal with the data problems for the models discussed in this paper could be
included in a contingent valuation survey effort. If the attention fre-
quently devoted to questionnaire development in contingent valuation were
spent on designing data for indirect methods, the ability of our models to
perform would improve substantially.15 Yet these issues will remain unre-
solved unless there is funding for basic research on recreation demand
models and subsequent primary data collection.
V. ESTIMATION AND RESULTS
In this section we briefly review our estimation procedures for the
generalized travel cost model. In addition, we provide some summary results
on the benefits of improving site characteristic—water quality—based on
our model. Both the procedures and results are based on additional research
over the last 2 years and differ significantly from those presented in
Desvousges, Smith, and McGivney [1983],
The major focus of our revised model is to address the estimation
problems created by the censored and truncated nature of our dependent
variable. As noted earlier, this character of our variable visits is
attributable to the onsite data collection that included only users, along
with the coding procedure used by the interviewers for the maximum number
of visits. To address these problems, we have reestimated each demand
function with a maximum likelihood (ML) estimator that takes account of the
truncation in visits at low levels of use and the censoring in the upper
levels of use. Under the assumption of a normal error structure, with
truncation at zero16 and censoring at k, the likelihood function is given
in Equation (6):
15The complimentarity between contingent valuation and the revealed prefer-
ence models is a two way street. For example, practitioners of contingent
valuation would benefit substantially from the kind of model development
that goes hand in hand with revealed preference approaches. Smith [1985]
and Hanemann [1984] imply that contingent valuation will never fully
mature unless it can develop models of how respondents answer the valua-
tion questions.
16The truncation at zero arises because the dependent variable for the
demand function was the logarithm of visits.
-------
L(p, a2, InV) = II
ieSi
I «K1nV.-pX.)/a)
l-C-pX./a))
where
InV.
natural log of the number of visits to the site by the ith
individual
0 = paramter vector (1 x k)
X. = vector of independent variables describing ith individual
1 (k x 1)
ct2 = variance in the error associated with each site's demand
function
Sx = set of observations with 0 _< InV. < k
S;> = set of observations with lnV._> k
<}>(•) = density function for the standard normal variate
-------
TABLE 4. MAXIMUM LIKELIHOOD AND OLS ESTIMATES OF GENERAL MODEL BY SITE
LN VISITS or0 «• a, (T+M) COSTS + a2 INCOME
Site name
Site
No,
Estimator
Intercept
T+M cost
Income
Function
value R*
df
Arkabutla, Lake, MS
301
ML
2.33
(8.21)
-0.0473
(-6.20)
1.9 x 10"6
(0.11)
-24.00
-
OLS
1.58
(9.99)
-0.0093
(-3.09)
6.2 x 10~S
(0.67)
0.15
58
Lock and Dam No. 2 (Arkansas
River Navigation System), AR
302
ML
2.31
(2.31)
-0.0125
(-0.28)
1.6 x 10~5
(64.95)
-17,67
OLS
2.31
(9.76)
-0.0125
(-2.30)
-1.8 x 10"5
(-1.08)
0.14
38
Belton Lake, TX
304
ML
2.94
(4.62)
-0.0727
(-2.70)
1.2 x 10*5
(0.42)
-23.61
-
OLS
1.69
(9.38)
-0.0052
(-2.47)
2.6 x lO-6
(0.29)
0.12
50
Benbrook Lake, TX
305
ML
2.45
(1.54)
-0.0472
(-1.09)
8.3 x 10"5
(0.60)
-16.01
-
OLS
1.83
(10.70)
-0.0054
-4.11)
6.0 x 10"6
(0.80)
0.30
43
Blakely Mt. Dan,
Lake Ouachita, AR
30?
ML
2.44
(24.03)
-0.0374
(-13.63)
-9.6 x lO-6
(-0.88)
-18.17
-
OLS
1.70
(10.08)
-0.0079
(-5.14)
-7.6 x lO-6
(-0.98)
0.24
88
Canton Lake, OK
308
ML
3.96
(8.94)
-0.2788
(-12.50)
1.4 x id-4
(11.23)
-12.51
-
OLS
1.77
(8.61)
-0.0206
(-5.28)
7.1 x 10~6
(0.86)
0.28
71
Cordell Hull Dam and
Reservoir, TN
310
ML
2.91
(87.61)
-0.0657
(-22.02)
3.8 x 10"6
(0.90)
-25.26
-
OLS
1.86
(14.13)
-0.0139
(-6.00)
-1.2 x 10~8
(-0.01)
0.34
101
DeGray Lake, AR
311
ML
2.36
(3.55)
-0.0267
(-1.57)
-1.5 x 10"S
(-0.56)
-17.81
-
OLS
1.79
(7.71)
-0.0070
(-3.00)
-6.9 x 10"5
(-0.73)
0.17
46
Grapevine Lake, TX
314
ML
2.71
(6.41)
-0.0311
(-3.43)
1.8 x 10~5
(1.42)
-26.92
-
OLS
1.80
(16.12)
-0.0073
(-8.80)
8.5 x 10"6
(1.70)
0.47
89
Greers Ferry Lake, AR
315
ML
2.10
(15.91)
-0.0287
(-9.84)
2.8 x 10"5
(3.20)
-51.84
-
OLS
1.48
(14.08)
-0.0065
(-9,02)
8.4 x lo"6
(1.42)
0.28
214
Grenada Lake, MS
316
ML
4.92
(8.97)
-0.0924
(-4.58)
-3.5 x 10"5
(-0.58)
-29.47
-
OLS
2.04
(12.61)
-0.0085
(-4.36)
-1.0 x 10"5
(-0.68)
0.22
73
(continued)
-------
TABLE 4 (continued)
Site name
Site
No.
Estimator
Intercept
T+M cost
Income
Function
value R2
df
Hords Creek Lake,
TX 317
ML
2.77
(5.07)
-0.0502
(-2.38)
-6.5 x 10"5
(-2.22)
-13.49
-
OLS
1.73
(8.22)
-0.0050
(-2.11)
-2.1 x 10~5
(-1.76)
0.19
51
Melvern Like, KS
322
ML
-2.42
(-2.19)
-0.1797
(-20.00)
7.4 x 10~5
(2.56)
-14.17
-
OLS-1
1.30
(4.47)
-0.0079
(-1-66)
4.1 x 10"6
(0.32)
0.06
42
Millwood Lake, AR
323
ML
' 1.43
(2.97)
-0.0331
(-6.15)
7.4 x 10~5
(2.97)
-20.14
-
OLS
1.43
(7.94)
-0.0081
(-3.99)
1.8 x lO-5
(2.14)
0.25
50
Mississippi River
Pool 6, MN 325
ML
1.49
(2.67)
-0.0565
(-1.75)
5.8 x 10"5
(1-41)
-22.21
-
OLS
1.41
(7.45)
-0.0074
(-4.39)
1.3 x 10"5
(1.53)
0.22
68
New Savannah Bluff
& Dam, GA
: Lock 329
ML
3.28
(2.24)
-0.0538
(-0.68)
-5.6 x 10"5
(-0.59)
-19.51
-
OLS
1.8S
(8.39)
-0.0067
(-1.44)
-9.8 x 10~6
(-0.70)
0.06
36
Ozark Lake, AR
331
ML
1.98
(3.70)
-0.0230
(-14.25)
1.2 x 10"5
(0.36)
-8.27
-
OLS
1.66
(8.52)
-0.0046
(-4.44)
-8.8 x lo"6
(0.66)
0.31
49
Philpott Lake, VA
333
ML
2.21
(4.77)
-0.0335
(-22.71)
2.2 x 10~5
(0.80)
-8.80
-
OLS
1.90
(9.28)
-0.0087
(-4.40)
-1.7 x 10"6
(-0.13)
0.36
35
Proctor Lake, TX
337
ML
4.09
(6.59)
-0.0643
(-2.14)
5.0 x 10~6
(0.27)
-6.63
-
OLS
2.06
(13.61)
-0.0134
(-7.50)
1.2 x lo"6
(0.19)
0.54
49
Sam Rayburn Dam &
Reservoir, TX
339
ML
1.60
(1.64)
-0.0744 '
(-2.52)
1.0 x 10~5
(0.23)
-14.41
OLS
1.46
(7.06)
-0.0094
(-2.83)
1.0 x 10~6
(0.13)
0.11
64
Sardis Lake, MS
340
ML
2.48
(7.01)
-0.0095
(-2.05)
1.5 x 10"5
(0.64)
-100.97
-
OLS
1.81
(20.73)
-0.0030
(-3.17)
4.3 x 10-6
(0.78)
0.05
202
Whitney Lake, TX
344
ML
-0.378
(-0.17)
-0.0166
(-1.04)
3.0 x 10"5
(0.83)
-98.95
-
OLS
1.41
(13.07)
-0.0025
(-1.80)
3.2 x 10"6
(0.72)
0.02
201
-------
substantial differences in the results. Water quality, as measured using
dissolved oxygen, has a positive and statistically significant effect on
the intercept but not the other two estimated demand parameters. Moreover,
the record with respect to the other site characteristics is not as good as
was reported for the first generation version of the model. Few character-
istics would be judged to be significant determinants of these site demand
parameters. Thus, these results taken alone do not provide a compelling
case for accepting the revised model based on the ML estimates of site
demand parameters.
However, we should note that our size is relatively small and the
degree of discrimination required of these models is quite demanding. This
is compounded by the quality of available data on both water quality and
other site characteristics. Nonetheless, we must conclude that our attempts
to improve the site demand estimates has led to more questions about the
plausibility of the second stage equations for the generalized travel cost
model.
To evaluate the implications of this revision to the generalized
travel cost model, we completed two sets of comparisons. First, Table 5
presents estimates of the incremental changes in Marshallian consumer
surplus for two levels of improvement in water quality for each version of
the model across a range of different sites. These benefits are calculated
for a "representative" user of each site who has the average travel cost as
his price, the maximum travel cost as the choke price, and the average
household income of users of each site. In the three columns following the
site number code of Table 6, the specific values for each of these variables
are reported. The remaining four columns report the estimated benefits per
season (in 1977 dollars) for two water quality improvements--boatable to
fishable and boatable to swimmable—conditions. Both changes are measured
using dissolved oxygen and the standards defined by Vaughan [1981].17
Several results from this table are quite striking. For example, the
estimates based on our first generation model are substantially larger than
those of the ML based model. Improvements from boatable to fishable range
from $39.97 for the Arkansas River to $155.73 for Millwood Lake. By con-
trast, the ML estimates are as low as $0.39 with the largest estimate for
Millwood Lake of $33.62. As a percent of the first generation results, the
ML estimates range from 0.4 percent to 72 percent. However, most sites
fall within a somewhat narrower range of 3 percent to 33 percent. Thus,
these results imply a substantial difference in the valuations derived from
each of the two models.
Our second comparison attempts to gauge the plausibility of each set
of estimates based on what has been found in earlier studies of the recrea-
17The values for dissolved oxygen are given as follows: (a) improvement
from boatable to fishable is assumed to be associated with a change from
45 to 64 percent saturation; (b) improvement from boatable to swimmable
is assumed to be associated with a change from 45 to 83 percent saturation.
-------
TABLE 5. GENERALIZED LEAST-SQUARES ESTIMATES USING MAXIMUM
LIKELIHOOD SITE DEMAND ESTIMATES
Independent
Travel cost
Income
vanabTes3
1 ntercept
parameter
parameter
1 ntercept
-0.044
-0.022
0.17 x 10"4
(-0.024)
(-0.431)
(0.657)
Shore
0.001
-0.11 x 10~4
-0.60 x 10~7
(0.782)
(-0.382)
(-1.449)
Access
-0.039
0.27 x 10"2
0.14 x 10"5
(-1.071)
(1.301)
(0.074)
Water pool
1.461
-0.089
-0.86 x 10~4
(1.030)
(-1 .522)
(2.731)
DO
-3
-6
0.020
-0.10 x 10
-0.24 x 10
(2.076)
(-0.286)
(-0.766)
VDO
-6.47 x 10~5
1.48 x 10~7
5.28 x 10~10
(-2.077)
(0.127)
(0.573)
R2
0.475
0.196
0.455
F
2.89
2.50
2.68
definitions for
the site characteristics are:
Shore:
Total shore miles
at side during peak
visitation period.
Access:
Number of multipurpose recreational and
developed access
areas at the site.
Water pool:
Size of hte pool
surface relative to total site area.
DO: Dissolved oxygen (percent saturation).
VDO: Variance in dissolved oxygen.
-------
TABLE 6 A COMPARISON OF BENEFITS ESTIMATES FOR WATER QUALITY IMPROVEMENTS FOR THE
FIRST. AND SECOND GENERATION MODELS'
Average
income
Average
travel
cost
Maximum
travel
cost
Boatable to
fishable
Boatable
to swimmable
Site
No
First
Second
First
Second
Arkabutla Lake, MS
301
13,184
20.04
209.35
104.57
29.37
274.20
66.13
Lock & Dam No. 2
Arkansas River, AR
302
10,409
3.04
70.01
33.37
29.01
83.45
67.42
Belton Lake, TX
304
17,279
33.18
302.86
115.84
9.62
331.45
21.34
Benbrook Lake, TX
305
19,135
30.23
344.44
124.64
6.53
366.68
14.52
Blakey Mt. Dam,
Lake Ouachita, AR
307
17,144
45.39
286.03
43.54
3.38
131.73
7.41
Canton Lake, OK
308
17,392
32.30
106.16
42.83
4.90
101.59
10.94
Cordell Hull Reservoir, TX
310
15,491
29.65
184.35
68.75
14.21
173.75
31.52
DeGray Lake, AR
311
19,235
42.04
210.48
82.72
10.37
218.39
22.59
Grapevine Lake, TX
314
19,309
38.45
307.28
114.12
3.86
323.63
8.51
Grenada Lake, MS
316
9,199
24.57
207.05
99.16
19.17
262.04
43.53
Hords Creek Lake, TX
317
16,263
33.46
304.01
112.35
3.11
321.87
6.89
Melvern Lake, KS
322
18,087
31.48
130.50
56.21
5.46
136.35
12.14
Millwood Lake, AR
323
18,630
37.62
309.24
155.73
33.62
461.81
74.15
Mississippi River Pool
No. 6. MN
325
19,589
52.23
843.86
100.17
0.39
300.51
0.84
New Savannah Bluff
Lock & Dam, GA
323
12,609
18.65
157.36
84.32
13.07
209.64
29.53
Ozark Lake, AR
331
12,654
58.71
457.44
94.66
6.34
291.05
14.07
Philpott Lake, VA
333
14,268
26.09
268.76
117.99
16.79
328.58
37.54
Proctor Lake, TX
337
17,510
46.08
172.41
68.93
0.82
178.22
1.80
Sam Raybum Dam
& Reservoir, TX
339
19,515
40.23
155.30
49.30
9.35
122.62
20.46
Sardis Lake, MS
340
13,141
36.08
429.20
128.98
9.19
338.58
20.46
Whitney Lake, TX
344
18,688
35.40
303.62
109.70
6.73
315.02
15.03
"These are the Marshallian
finite choke price.
consumer
surplus estimates for
each site using
the maximum
travel cost
in each case as a
-------
tion values of water quality improvements. Table 7 presents the first
water quality change—boatable to fishable—and compares our estimates with
the second generation framework reported estimates (including our own
earlier work [Smith, Desvousges, and McGivney, 1983a]). Table 7 reports
the estimates derived from the travel cost models on both a per-trip and a
per-day basis in 1982 dollars.18
Two aspects of these results are especially important. First, our
initial model's benefit estimates for the Corps sites are substantially
outside the range from past studies for these types of recreation areas.
However, when the model was applied to the Monongahela River sites, its
estimates clearly fall within the range anticipated by past experience.
This discrepancy in performance accentuates the importance of site char-
acteristics. That is, the characteristics of the Monongahela sites are
substantially smaller and have fewer access points, but have a larger
fraction of each site's area associated with water (i.e., the river) than
the other Corps sites. Thus, using the first generation of the model to
predict the demand for the Monongahela River site was a projection substan-
tially outside the range of values for the site characteristic variables.
By contrast, the second generation model provides benefit estimates
for the Corps sites that are more consistent with the valuations for water
quality improvements obtained with earlier studies. Thus, we have an
unusual example of a situation in which the parameter estimates do not
provide a strong case for a model but the end use of its estimates does.19
VI. IMPLICATIONS
Several implications for future research emerge from our discussion of
the varying parameter model and its relationship to other recent recreation
demand models.
The varying parameter model is a plausible practical model
for valuing the changes in site characteristics. Its main
weaknesses stem from inadequate data on substitute sites and
18These are based on the average number of trips for each site and the
average number of days reported for the trip in which the respondents to
the survey were interviewed. Actual trips were selected rather than pre-
dicted trips because the latter will be a biased estimate from a semi-log
function. Moreover, there are additional problems in selecting the pre-
dicted number of trips for normalization. There are predictions available
at each level of water quality that might be used as the base in evaluating
each water quality change. Since the actual water quality conditions at
these sites often were closer to or exceeded fishable conditions, actual
use was judged to provide a better normalizing factor than the available
estimates.
19See Klein et al. [1978] for a general discussion of these issues as they
relate to selecting an objective function for selecting statistical esti-
mators of the parameters of economic relationships.
-------
TABLE 7. A COMPARISON OF ALTERNATIVE ESTIMATES OF THE BENEFITS OF WATER
QUALITY IMPROVEMENTS FROM BOATABLE TO FISHABLE
CONDITIONS IN 1982 DOLLARS3
Study Original estimate 1982 dollars
Vaughan-Russell
[1982]
$4.00 to $8.00 per person per day was
the range over the models used (1980
dollars)
$4.68
to
$9.37
Loomis-Sorg [1982]
$1.00 to $3.00 per person per day over
regions considered; based on increment
to value of recreation day for cold-
water game fishing (1982 dollars)
$1.00
to
$3.00
Smith, Desvousges,
and McGivney
[1983a]
$0.98 to $2.03 per trip using first
generation generalized travel-cost
model with Monongahela sites, boatable
to fishable water quality (1981 dollars)
$1.04
to
$2.15
First Generation
Generalized Travel
Cost Model
$5.87 to $54.20b per trip ($2.24 to
$122.00 per visitor dayc) for Corps
sites, change from boatable to
fishable water quality (1977 dollars)
$9.35
($3.57
to
to
$86.34
$194.35)
Second Generation
Generalized Travel
Cost Model
$0.08 to $5.43 per trip ($0.04 to
$18.78 per visitor day) for Corps
sites, change from boatable to
fishable water quality (1977 dollars)
$0.13
($0.06
to
to
$8.65
$29.92)
Q
The Consumer Price Index was used in converting to 1982 dollars. The scaling
factor for the conversion from 1977 to 1982 was 1.593.
^These estimates relate only to the Marshallian consumer surplus (M2).
cThe reason for the increase in the range for benefits per day is that some trips
were reported as less than a day. The appropriate fractions were used in devel-
oping these estimates.
-------
jointly produced
recent studies all
assumptions about
recreation activities. Yet the
seem to require some type of
household behavior.
other
unrealistic
Data quality is important. All of the recent studies are
hampered by inadequate data. Attempts to improve the quality
of data collection for indirect or revealed preference
models would pay handsome dividends.
Focus groups with a relatively small number of recreators in
group discussions could yield valuable insights about the
household's decision process for recreation. Topics could
include discrete nature of decisions, perceptions of site
attributes, and the nature of household production of recre-
ation activities.
Statistical problems like truncation and censoring can have
substantial effects on the benefit estimates derived from
travel cost models. Studies that fail to deal with these
problems may have significant estimation problems.
Contingent valuation and the travel cost approach are good
complements. Data required for one approach can prove
useful for the other.
The recent models valuing quality changes are significant improvements
over their predecessors. Yet further improvements await better understand-
ing of household's recreation decisions and dramatically better data.
VII. REFERENCES
Becker, G. S., 1974, "A Theory of Social Interactions," Journal of Political
Economy, 1974, pp. 1063-93.
Becker, Gary S., 1981, A Treatise on the Family. Chicago: University of
Chicago Press, 1981.
Bockstael, Nancy E., W. Michael Hanemann, and Ivar E. Strand, Jr., 1984,
Measuring the Benefits of Water Quality Improvements Using Recreation
Demand Models, Volume II, Benefit Analysis Using Indirect or Imputed
Market Methods, CR-8-11043-01-0, preliminary report prepared for
Office of Policy and Resource Management, U.S. Environmental Protec-
tion Agency, University of Maryland, College Park, Maryland, 1984.
Bockstael, Nancy E., and Kenneth E. McConnell, 1981, "Theory and Estimation
of the Household Production Function for Wildlife Recreation," Journal
of Environmental Economics and Management, Vol. 8, September 1981,
pp. 199-214.
Brown, Gardner, Jr., and Robert Mendelsohn, 1980, "The Hedonic Travel Cost
Method," unpublished paper, Department of Economics, University of
Washington, December 1980.
-------
Brown, Gardner, Jr., and Robert Mendelsohn, 1984, "The Hedonic Travel Cost
Method," Review of Economics and Statistics, 1984.
Clawson, M., 1959, "Methods of Measuring the Demand for and Value of Outdoor
Recreation," Reprint No. 10, Resources for the Future, Inc., Washington,
D.C., 1959.
Clawson, M., and J. L. Knetsch, 1966, Economics of Outdoor Recreation,
Washington, D.C.: Resources for the Future, Inc., 1966.
Davidon, S., R. Fletcher, and M. Powell, 1963, "A Rapidly Convergent Descent
Method for Minimization,' The Computer Journal, Vol. 6, 1963, pp. 163-68.
Desvousges, William H., and V. Kerry Smith, 1984, "The Travel Cost Approach
for Valuing Improved Water Quality: Additional Considerations," draft
report prepared for Office of Policy Analysis, U.S. Environmental
Protection Agency, Washington, D.C., Research Triangle Institute,
Research Triangle Park, North Carolina, September 1984.
Desvousges, William H., V. Kerry Smith, and Matthew P. McGivney, 1983, A
Comparison of Alternative Approaches for Estimating Recreation and
Related Benefits of Water Quality Improvements, report prepared for
U.S. Environmental Protection Agency, Research Triangle Institute,
Research Triangle Park, North Carolina, March 1983.
Deyak, Timothy A., and V. Kerry Smith, 1978, "Congestion and Participation
in Outdoor Recreation: A Household Production Approach," Journal of
Environmental Economics and Management, Vol. 5, March 1978, pp. 63-80.
Dwyer, John F. , John R. Kelly, and Michael D. Bowes, 1977, Improved Procedures
for Valuation of the Contribution of Recreation to National Economic
Development, Research Report No. 128, Water Resources Center, University
of Illinois, at Urbana-Champaign, 1977.
Hanemann, W. Michael, 1984, "Welfare Evaluations in Contingent Valuation
Experiments with Discrete Responses," American Journal of Agricultural
Economics, Vol. 66, August 1984, pp. 332-41.
Klein, R. W., L. G. Rafsky, D. F. Sibley, and R. D. Willig, 1978, "Decisions
with Estimation Uncertainty," Econometrica, Vol. 46, November 1978,
pp. 1363-88.
Lau, Lawrence, J., 1982, "The Measurement of Raw Materials Inputs," in
V. Kerry Smith and John V. Krutilla, eds., Explorations in Natural
Resource Economics, Baltimore: Johns Hopkins, 1982, pp. 167-200.
Loomis, John, and Cindy Sorg, 1982, "A Critical Summary of Empirical Esti-
mates of the Values of Wildlife, Wilderness and General Recreation
Related to National Forest Regions," U.S. Forest Service, Denver,
Colorado, 1982.
-------
Morey, Edward R., 1981, "The Demand for Site-Specific Recreational Activities:
A Characteristics Approach," Journal of Environmental Economics and
Management, Vol. 8, December 1981, pp. 345-71.
Morey, Edward R., 1984, "Characteristics, Consumer Surplus and New Activities:
A Proposed Ski Area," unpublished paper, University of Colorado,
Boulder, Colorado, 1984.
Morey, Edward R., forthcoming, "Characteristics, Consumer Surplus, and New
Activities: A Proposed Ski Area," Journal Public Economics, forthcoming.
Pollak, Robert A., and Michael L. Wachter, 1975, "The Relevance of the
Household Production Function and Its Implications for the Allocation
of Time," Journal of Political Economy, Vol. 83, April 1975, pp. 255-77.
Schoemaker, Paul J.H., 1980, Experiments on Decisions Under Risk: The
Expected Utility Hypothesis, Boston: Kluwer-Nijhoff, 1980.
Smith, V. Kerry, 1985, "Some Issues in Discrete Response Contingent Valua-
tion Studies," Northeastern Journal of Agricultural and Resource
Economics, 1985.
Smith, V. Kerry, William H. Desvousges, and Matthew P. McGivney, 1983a,
"The Opportunity Cost of Travel Time in Recreation Demand Models,"
Land Economics, Vol. 59, No. 3, August 1983, pp. 259-78.
Smith, V. Kerry, William H. Desvousges, and Matthew P. McGivney, 1983b, "An
Econometric Analysis of Water Quality Improvement Benefits," Southern
Economic Journal, October 1983.
Vaughan, W. J., and C. S. Russell, 1982a, "Valuing a Fishing Day: An
Application of a Systematic Varying Parameter Model," Land Economics,
Vol. 58, November 1982, pp. 450-63.
Vaughan, W. J., and C. S. Russell, 1982b, Freshwater Recreational Fishing:
The National Benefits of Water Pollution Control, Washington, D.C.:
Resources for the Future, Inc., November 1982.
-------
VALUING QUALITY CHANGES IN RECREATIONAL RESOURCES
by: Elizabeth A. Wilman
The University of Calgary
Calgary, Alberta T2N 1N4
ABSTRACT
From a general consumer utility maximization model, which
describes a consumer's quality and quantity choices, a number of
specific models are derived, including multiple site travel cost models,
and the hedonic model. However, the transition from the general model
to estimation of the parameters involves dealing with a number of
issues. These include parameter identification, the use of weak
complementarity and path-independence assumptions, and the question of
whether the estimated demand curves are adequate approximations to
compensated demand curves. These issues are explored for each of the
specific models. One of the models, the hedonic model, is estimated,
and applied to the valuation of quality changes in deer hunting sites in
the Black Hills National Forest of South Dakota.
The research on which this paper is based was undertaken as part
of the Forest Economics and Policy Program at Resources for the Future
and was supported by funds from Resources for the Future, the U.S.
Department of Agriculture, and the National Science Foundation.
-------
INTRODUCTION
Biologists and ecologists have for some time been aware that
forest management practices can affect wildlife populations through
their influence on the availability of desirable wildlife habitat. *
Scientists who study human motivations in a recreational setting have
known that the satisfactions hunters derive from hunting experiences are
influenced both by the environment in which the hunting takes place and
2
by whether or not they are successful. However, unlike such forest
products as timber, wildlife habitat and pleasing recreational environ-
ments do not have readily observable market prices. For public agencies
charged with the management of forest resources, this has made provision
of outputs such as timber, for which the benefits are easily determin-
able, easier to justify than nonmarket resources services such as wild-
life habitat or pleasing recreational environments, for which benefits
are not easily measured.
Assessment of the demand for and value of these nonmarket resource
services can help to strengthen the underpinnings for multiple use
management practices. However, because what forest management practices
do is change the levels of resource services available at locations in
the forest, it is necessary that primary emphasis be placed on valuing
changes in the levels of resource services provided. The next section
of this paper will set out a general model for the measurement of the
economic efficiency benefits from management practices that increase the
level of certain resource services (deer habitat and a desirable hunting
environment) . From the general model a number of specific models can be
derived, including a number of variants of the travel cost model, and
the hedonic travel cost model. These specific models are discussed in
-------
section III, where consideration is given to the assumptions involved in
identifying the relevant demand curves, and using them to value resource
service changes. Finally, in section IV one of these models, the hedonic
travel cost model, is estimated and wildlife habitat improvement benefits
to hunters in the Black Hills National Forest in South Dakota are calcu-
lated.
I!. THE GENERAL MODEL
(i) Bac kground
In general two types of approaches are possibilities for measur-
ing the economic efficiency benefits from the provision of wildlife
habitat and a pleasing hunting environment for hunters. One, the con-
tingent valuation approach , uses direct questioning techniques to obtain
values for hunting days, visits or seasons, or simply for the existence
of certain types of wildlife. This approach is exemplified by the work
of Mitchell and Carson (1981), Brookshire, Thayer, Schulze and d'Arge
(1982), Desvouges, Smith and McGivney (1982), Bishop, Heberlein and
Keely (1983), and Brookshire, Eubanks and Randall (1983). The other
approach, and the one which is used here, uses information on the actual
behavior of hunters to infer the benefits they derive.
More specifically, the behavior that is observed in the second
approach is the hunter's choice of a hunting site. A forest environment
can be viewed as providing a set of hunting sites. Hunting benefits
have often been assessed directly in terms of hunters' demands for
visits to these sites using a consumer's surplus measure of benefit.
However, the demands for visits to these sites can be viewed as being
- 2 -
-------
derived from the attributes or characteristics of the sites and demands
may be assessed for these characteristics. The consumer's surplus
approach can then be used to assess benefits associated with obtaining a
certain level of the characteristic or of a change in the availability
of the characteristic.
In the case of recreational deer hunters, at least one of the
relevant characteristics would be expected to be the probability of
bagging game. The literature on the motivations of hunters (Potter,
Hendee and Clark [1973]; More [1973]; and Stankey and Lucas [1973])
shows that bagging game is a necessary, although not necessarily the
most important, element of a recreational hunting experience. Hence
vegetative characteristics that provide desirable habitat for game are
likely to have some appeal for hunters. However, it is also true that
vegetative and landform characteristics that provide a pleasing land-
scape for hunters will be important.
Given that forest vegetative characteristics can affect the hunter's
recreational experience both directly and indirectly, through the provi-
sion of wildlife habitat, management practices which affect these vege-
tative characteristics are likely to affect the quality of the hunting
experience and therefore the benefits provided to hunters. What is done
in this paper is to use observations on hunter choices of sites in the
Black Hills National Forest, along with information on the costs asso-
ciated with these choices, to assess the benefits associated with manage-
ment practices that increase the availability of desirable hunting sites.
(ii) The Formal Model
The model used in this study is a consumer utility maximization
model. The consumer chooses site quality, the number of recreation
- 3 -
-------
visits, and the amounts of other goods and services to consume, based on
his utility function, his budget constraints, and the prices or marginal,
costs of quality units, visits and other goods and services. Here the
numeraire good X represents all other goods and services, and the
utility function is assumed to be weakly separable such that neither the
marginal utility of visits nor the marginal utility of quality is
affected by the level of X. Nor is the marginal utility of X affected
by the level of visits or quality. The cost function for visits is
assumed to be such that the cost of each visit has a fixed component
that is independent of the quality choice, and a variable component that
depends upon the quality choice.
Let the recreationist's utility function be
U (x) + U (n, q) 1
where: x is a numeraire good;
n is the number of visits;
q is the site quality characteristic.
The cost function is assumed to be of a form such that the marginal cost
price of a visit can be changed without affecting the choice of q. The
cost function is
; = x + (h+K(q))n ;
where: h is the part of the cost of a visit which is independent
of q;
K(q) is the part of the cost of a visit which depends
upon q;
the price of the numeraire good is unity.
The first-order conditions for n and q are
U
^=11 + K(q) 2
x
U
Tt = n ' K
Ux q
- 4 -
-------
In general, (3) and (4) imply a simultaneous equation system with
four unknowns, n and q, and their prices. The change in the resource
service is modeled as a shift in K , and what must be measured is the
q
benefit (consumer's surplus change) from this shift. However, in its
general form the household production function model is not particularly
useful for estimation purposes, or for calculating consumer's surplus
changes. In deriving, from this general model, a more specific model,
which can be estimated, and will allow consumer's surplus calculations
to be made, there are a number of issues which must be addressed. These
can be grouped into four categories.
1) Can the parameters of the cost and demand functions be
identifled?
2) Can weak complementarity be assumed?
3) Is the line integral measurement of consumer's surplus path
independent?
4) Can it be assumed that the measurable Marshallian demand
curve is a reasonable approximation for the compensated
demand curve?
These categories are not entirely independent of one another.
The assumption of weak-complementarity can limit the number of demand
and supply curves that need to be identified. If the Marshallian and
compensated demand curves are equivalent, path-independence in the
measurement of consumer's surplus is guaranteed. In the next section
some specific models that can be derived from the general model are
considered, with a view to how each specific model deals with these four
issues.
- 5 -
-------
III. SPECIFIC MODELS
(i) The Single Site Travel Cost Model
If there is only one site, then q is perfectly inelastically
supplied, and can be taken as exogenous. This means that the demand-
supply system is reduced to the two equation system containing the
demand and supply curves for n. Since q is not a choice variable, the
marginal cost of n is simply h, which is also exogenous. This leaves
the demand curve for n, the only relationship requiring estimation,
identified.
If q is an exogenous predictor variable in the demand curve for n,
then an increase in q at the site will shift the demand curve, and there
will be a consumer's surplus change. Does this change measure the bene-
fit the consumer obtains from the increase in q? This depends upon the
answers to the second, third and fourth questions posed in section II.
First consider the weak complementarity assumption. This assump-
tion says that if n = 0, U = 0 (Maler [1974]). If there are no visits
taken to the site, an increase in q yields zero marginal utility. This
assumption is usually regarded as a reasonable one, and its use ensures
that there is no additional benefit from the change in q that is not
measured by the change in the area under the compensated demand curve
for n.
The final two issues both are related to the fact that, in gen-
eral, the estimated demand curve will be a Marshallian demand curve, and
not a compensated demand curve. The former incorporates income effects,
the latter does not.
The path-independence assumption is important because, in gen-
eral, a shift in the supply curve for q will mean that the consumption
- 6 -
-------
of both q and n will change. Path-independence is required in order for
the benefit measure to be unique. If g^(n,q,x) is the inverse demand
function for n, and g2(n,q,x) is the inverse demand function for q (with
x as the income level) path-independence on the demand side requires
that g, = g0 . That is, the income effects embodied in the changes in
lq Zn
q and n must be the same. On the cost side the path-independence
assumption requires that = ^nq* In this case = 0, since
: = hn.
Finally, there is the question of whether the estimated
Marshallian demand curves are reasonable approximations to the com-
pensated demand curves which correctly measure the welfare gains or
losses from exogenous changes. In the general model the assumptions of
a constant U and U U = 0 are sufficient to ensure that the
x qx = nx
Marshallian and compensated demand curves are equivalent. In any
specific case these are unlikely to hold exactly. However, as Willig
(1981) has shown, :: q and n account for only a small portion of the
consumer's total budget, then the income effects associated with the
changes in n and q will be small, and the Marshallian demand curves will
be reasonable approximations to the compensated ones. As a practical
matter it is possible to estimate income elasticities of demand for n
and q. If they are small, the Marshallian demand curve will suffice.
If they are large, then an approach, such as that suggested by Hausman
(1981) may be required to calculate the compensated demand curves from
the Marshallian demand curves. In general the approach used in travel
cost models is to assume explicitly or implicitly that the Marshallian
demand curve is an adequate approximation.
- 7 -
-------
(11) The Multi-Site Travel Cost Model
Cross-sectional data with multiple sites are usually used to
obtain the variation in q necessary to estimate the effect of a shift i
q_ In the simplest case it is assumed that each consumer still faces a
perfectly inelastic supply curve for q. However, since different sites
are of different quality, exogenous variation in the level of q is
introduced. Although there are multiple sites, from the point of view
of any given consumer there are no substitute sites. A comparison of
the consumer's surpluses generated by sites with different levels of q,
measures the benefit from an increase in q. This is essentially the
model used by Desvouges, Smith and McGivney (1982), and by Vaughan and
Russell (1982). It can be written as:
Vi ¦ £(v V
where: n.. = visits to site i by a consumer at location j;
q/* = quality level of site i;
h. . = cost of visitinq site i from location i.
If the no substitutes model is not considered to be appropriate
then the prices and qualities of substitute sites need to be included
as predictors, and (5) becomes:
nij = f(V hij' V q£' h£j V hzj) (6)
where: k through z are substitute sites for i.
Now an increase in q must be simulated by a comparison between
sites with different q^, but the same prices and quantities for the
substitute sites, k through z. There is a question of how to specify
the substitute sites. Site k, for example, could be a specific site, o
it could be merely a site of a specific quality level. If the former
specification is used, then it will be difficult to hold all of the
costs of visiting the substitute sites constant, while increasing
-------
It may be easier to replace the substitute price and quality terms with
an index of overall substitute availability and quality. This is what
is done in the multiple site travel cost models, such as those of
Cesario and Knetsch (1976).
The second alternative is to group together sites of a given
quality level , and identify them as site type k. The substitute cost
variable for site type k, for an individual from location j, is the
minimum cost required to visit a site of type k. Burt and Brewer
(1971), and Cicchetti, Fisher and Smith (1976) used this type of model.
Suppose there are m site types. Then for an individual at location j a
system of m demand equations exists.
nij = fl^hlj* h2j' h3j' •••' hmj^
n2j =f2(hlj' h2j' h3j' hmj)
•
tl f (h, . y hn . ) h« .) • « • } h . )
m 3 ia I3 23' 1113
Now an increase in q at a given site changes its site type. This
means that the price of a higher quality site type is lowered, and the
price of a lower quality site type is increased. The original con-
sumer's surplus amount can be measured by starting with the original^b
through h , and increasing them until through nm all equal zero. The
new consumer's surplus (after the site type change) is measured in the
same way, except that the altered price set is used as the starting
price set. The benefit measure is the difference between the old and
new consumer's surplus amounts.
There is another way to use the model in (7). Since through
n . are all functions of h, . through h the sum of nn. through
*3 *3
11 . must also be a function of h, . through h .. Now define
raj I3 ^ 1113
- 9 -
-------
h. = min(h, ., tu., tu. , . . . , h .), and K (q ) through (
J J J J J J J
~ • • • »
h. ~
OR
n = g(h , K (qi), K (q2), K (q ) , K (qj). c
J J J J J J
NOW a consumer's surplus calculation for a given set of K_. (q^)
through K_. can be carried out by increasing h until n. = 0. A
change in some of the K^(q^) through K^. can be made and the con-
sumer's surplus recalculated. The difference between the new and old
consumer's surpluses measures the benefits from the change in site type.
The multiple site models all rely on identification of demand
curves for visits to sites. These demand curves are identified because
site prices are exogenous. Since weak complementarity (U = 0 and
= 0 when n = 0) is either explicitly or implicitly assumed, identi-
fication of visit demand curves is sufficient to allow measurement of
benefits from changes in q, or in some of the K^.(q^) through K_.
In the no substitute case, or when the prices and qualities of
substitutes remain unchanged, the path-independence conditions, and the
conditions to ensure approximation of the compensated demand curves, are
as discussed in section III (i). In the multiple site model used by
Burt and Brewer (1971), the q change is replaced by multiple price
changes. Path independence requires that the income effects associated
with each of the price changes be the same. Close approximation to the
compensated demand curves requires that the income effects associated
with these price changes are small. When (7) is replaced by (8) or (9)
- 10 -
-------
K. is perfectly elastic, then a fixed K. is equivalent to a fixed set
jq jq
of K^(q^) through K_. (q^) in (8) or (9), and (10) can be identified. In
the more general case the K_.
q(q)
function will have an endogenous com-
ponent, which depends upon the level of q chosen, and an exogenous com-
ponent (Ej) depends upon the consumer's location relative to the various
sites. In this case E. can be used as an instrument in estimating the
3
demand curve for n.
It is also worth noting that if the utility function has a form
such as (11), and the cost function is as in (2), that the choice of q
will be independent of the choice of n.
U (x) + n U (q) + U (n) 11
This has the advantage that the system of four simultaneous
equations' in n and q and their marginal cost prices can be treated as
a block recursive system, q and are determined by the first block
(containing the demand and marginal cost curves for q) , and can be
treated as exogenous in the second block (containing the demand and
marginal cost curves for n) . This result is also quite sensible, in
that it allows the choice of q for a given visit to be taken inde-
pendently of the number of visits.
So far we have determined that a demand curve for n can be iden-
tified. With the usual weak-complementarity assumption, the benefit
from an exogenous increase in q (or decrease in Kjg) can be measured by
the change in the area under the demand curve for n, and above the mar-
ginal cost curve for n. However, there may be cases in which h does
not exhibit sufficient variation to allow the demand curve for n to be
estimated, or n does not exhibit variation. In these cases it may be
worthwhile to consider estimating the demand curve for q.
- 12 -
-------
Consider the first case where h. is invariant, but n does exhibit
J
variation. Let h..(q) = K(q,E_.), where E_. is the exogenous shift
component - dependent on variation in origin location. Assume two
alternative forms of the utility function.
First assume the form in (11), where the consumer's choice of q
is the same for every unit of n. Then if U =0 and C =0 when q = 0
1 n n M
the demand and supply curves for q can be used to calculate the con-
sumer's surplus from one visit. Since each visit yields the same
consumer's surplus, n sill either stay at its original level, or be
reduced to zero, depending upon the level of E.. This means the total
consumer's surplus change is the change for one visit multiplied by the
original level of n. However, unless = 0, the = 0 assumption will
not hold. This means that if the E^. change is great enough to reduce n
to zero, nh_. must be netted out in measuring the consumer's surplus
loss.
Alternatively assume the utility function has the form of (12).
U (x) + Uj_ (qL) + U2(q2) + U3 (q3> + . . . + ^(q^) ::
where: the subscripts refer to visits 1 through n.
In this case n will change as E^. changes. If the marginal
utility functions for q for each visit are constant as E^ shifts, and
U = C =0 when q = 0, the consumer's surplus change for each visit
n. n
can be measured. The changes are then aggregated over the visits to
obtain the total consumer's surplus change. However, again will not
equal zero. Here this means that in general h(An) must be netted out in
measuring the total consumer's surplus change. If the E^ change reduces
q to zero, Ail becomes n.
If n is invariant, although h. and E^ change, then either the
supply of n must be fixed, due to some constraint like a fixed season
- 13 -
-------
length, or the utility function must have a form like (13).
U(x) + n U (q) 13
This is the same form as (11) but with = 0. With this utility
function n will remain at its original level until h. + K(q,E_.) is
increased to the point where a visit yields no consumer's surplus. At
that point n becomes zero. With (13) as the utility function, n can be
regarded as indeterminate. That is, the variables and K(q,E_.) do not
affect its level, only whether it will be zero or positive.
Whether n is fixed on the supply side, or indeterminate because
of the nature of the utility function, n can be treated as exogenous in
the demand and supply curves for q. If it does not exhibit significant
variation it may be omitted as an explanatory variable.
If n is exogenous, weak complementarity conditions are only of
concern for the cost side, and only if E_. before (or after) the shift is
such as to reduce q to zero. In such a case hn must be netted out in
measuring the consumer's surplus change.
If the hedonic model results in changes in both n and q (or
changes in through qn) then path-independence must also hold.
However, if n does not change the conditions are irrelevant, because
there is only one path. Finally the Marshallian demand curves should be
reasonable approximations to the compensated demand curves. If n is
fixed, this requires only that the income effect of the change in E be
small.
There is another variant of the hedonic model, which is essen-
tially the simple repackaging model of Fisher and Shell (1971) and
Muelbauer (1974). It is particularly relevant if the characteristic q
- 14 -
-------
is a variable similar to "the probability of bagging game," which must
be defined over a fixed time period. In such cases, the utility func-
tion in (13), might better be written as:
u(x) + u(Q)
where: Q = nq.
With (14) as the utility function and (2) as the cost function,
the first order conditions can be summarized as:
n „K ." + K<1>
q q q
With this model n can still be exogenous, if it is fixed by some
constraint on the supply side. However, the utility function in (13)
will not result in the choice of n being indeterminate. But, even if n
is determined by (15), it is still possible, because the production
function Q = n is known, to calculate the demand for q, and the benefit
from a change in E_., as if n were fixed (Wilman 1984). However, since n
is fixed only arbitrarily, the path-independence and compensated demand
curve approximation conditions will need to involved both n and q.
:v Multiple Characteristics
So far site quality has been described in terms of one charac-
teristic. However, it is possible that site quality really has more
than one dimension. Here it is assumed that that site quality has two
independent dimensions q and s, and that the consumer makes his choice
of site taking into account both of these dimensions. However, only
one of these, q, is assumed to be manageable.
The second characteristic, s, complicates matters only if s, or
its marginal cost price, cannot be treated as to be predetermined in the
demand and supply curves for n or q. If s is exogenous, then it can be
- 15 -
-------
assumed to remain constant as the price of n and q (or its marginal
cost) are varied. With no change in s, path-independence conditions are
not altered, and there are no additional income effects to consider in
evaluating the extent to which the Marshallian demand curve approximates
the compensated demand curve.
If s is not exogenous, but its marginal cost price is, then the
latter can be assumed to remain constant as the price of n, and q (or
its marginal cost) varies. Using the approach of shifting the demand
curve for n, the weak complementarity assumptions need to be extended
to include 1^=0 and Cg = 0 when n = 0. The path-independence assump-
tions must be extended to include g~ = g0 , g~ = g, , C = C and
3q °2s 3n °ls sq as
C = C , where gjCqjS.njx), g2(q,s,n,x) and g3(q,s,n,x) are the
inverse demand curves for n, q and s respectively. If the Marshallian
demand curves are to approximate the compensated demand curves, then it
must additionally be true that the income effects implicit in the
changes in s are small. If the demand for q is to be estimated, with n
fixed, then the additional conditions required are the same, except in
the case of path-independence, where any conditions involving n can be
ignored.
If neither s nor its marginal cost are totally exogenous, then
there must be some exogenous shift variable, on either the demand or
supply side, which affects s but not q. This can be used as an
instrument in the demand curve for n, or, if n is fixed, in the demand
curve for q. The weak complementarity and path-independence conditions
are as discussed above, and the income effect implicit in any change in
s should be small if the Marshallian demand curve is to approximate the
compensated demand curve.
- 16 -
-------
(v) The Model Used in the Case Study
The hedonic travel cost model was used in the case study. This
was in part because, the data collected exhibited little variation in
h_., and in part because the quantity variable.- n, was observed to have
very little variation. Two quality variables, q and s, were used,
although only q was manageable.
In estimating the hedonic model it was necessary to treat the
quantity variable as days, rather than visits. Although the latter is
more common in travel cost models, the latter was used here for two
reasons. First, when the probability of bagging game (or a proxy for
it) is used as a quality characteristic, that probability must be cal-
culated for a given time period. Second, it was apparent in observing
the pattern of tradeoff between visit length and the number of visits
that Black Hills deer hunters regarded the two as perfect substitutes.
A hunter would take only one long visit or many one-day visits depending
upon the relative cost of a day used to increase visit length versus a
day used as an additional visit. Hunters close to the Black Hills took
a number of one-day visits. Hunters further away took only one long
visit. This suggests that the hunters themselves treated the day,
rather than the visit, as the quantity unit of consumption. The
assumption of a fixed n is reasonable if n is measured in days, but not
if n is measured in visits. Using nv as visits and n^ as days per
visit, with y as the marginal cost of an extra day of visit length, two
3
versions of the hedonic model were estimated.
- 17 -
-------
Version One: The quantity variable n is assumed fixed.
Utility function: u(x) + U^n.q) + U2(n,q,s)
Cost function: x + nvfh + K(q) + J(s,q) + -yn^]
First order conditions for q and s:
U, /U + U0 /U = n [K + J ]
Iq x 2q x v q q
U„ /U = n J
2s x v s
Version Two: Q = nq.
Utility function: U(x) + U^(Q) + L^CQjs) i;
Cost function: x + nv[h + K(q) + J(s,q) + 711^] II
First order conditions for Q and s:
h + K(q) + J(s,q) +
1/Uk[U1Q + V = , "
= "T = (Kq + V (Vn)
v. /u = n j
2s x v s
In case of hunters taking many one-day visits = n. For
hunters taking one long visit n = 1.
Two alternative assumptions with respect to s were used to
identify the demand and marginal cost curves for q. First, it was
assumed that the U- and J functions were such that s would be chosen
independently of q or n, and could be treated as predetermined in the
demand and marginal cost curves for q. Alternatively an instrument was
found that could be used for s in the marginal cost and demand curves
for q.
- 18 -
-------
(vi) Some Additional Considerations
There are three potential problems that could arise, but did not
prove to be too serious in this study. The first is selectively bias.
This would occur if non-hunters would have tended to choose different
levels of q, s or n than hunters, given the same prices. For a dis-
cussion of this problem see Heckman (1976).
Second there is the question of whether benefits are more appro-
priately measured using per capita (expected) quantity units or condi-
tional quantity units. Brown and co-authors (1983) have shown that the
two alternatives give different benefit estimates, and that in general
the per capita measure should be used because the probability of visita-
tion, as well as the conditional quantity level changes across travel
cost zones. However, when estimating benefits from a change in site
quality, rather than the full benefits from the site, it is not clear
that this is a problem. The benefit from the quality change is composed
of two parts: (i) the additional willingness to pay for the same
expected use level, and (ii) the willingness to pay for an increase in
expected use level. The first part can be measured by estimating the
additional willingness to pay for the existing conditional quantity, and
multiplying it by the probability of visitation. That is, conditional
quantity units can be used and the adjustment for the probability of
visitation made after the conditional benefits have been calculated.
The second part does involve an increase in the expected use level.
However, especially if the expected demand curve for quantity units is
relatively inelastic, it may be quite small relative to the first part.
In the hedonic model, with n fixed, a change in the probability of
visitation means new visitors, and what needs to be measured is the
- 19 -
-------
average consumer's surplus (across new visitors) for n quantity units
at the improved quality level, multiplied by the increase in the
probability of participation.
Finally there is a potential problem in the observation of n, if
the probability of bagging game affects the number of days hunted. If
there is a bag limit, this may well be the case. The number of days
hunted would be:
V (q,n) = 1 + (1—q) + (1-q)2 + . . .(l-q)n 1
where: n = the maximum number of days a hunter would take as
q+0;
v = the expected number of days;
- = the probability of bagging game on a given day.
What is observed for any given hunter is one point on the dis-
tribution of V. Across a number of hunters with the same q, a mean
value of V can be observed.
The question is whether it is possible to tell, by observing the
V choice of hunters with the same E. but different h. level, if n can be
3 3
taken as fixed. The relationship in (24) implies V < 0. If V I 0,
q - q
then the observed V is a good approximation to n. However, if V < 0,
the level of V would be inversely related to the level of q, even
if n was constant. If n is fixed and the utility function is
U(x) + V(q,n) U(q), then for the one-day visits case the first order
condition for q is:
1/Ux[UV Vq + + K-j
-------
V(q,n) reveal much about the pattern of variation on n. In the case of
Black Hills hunters is relatively small, and it seems likely that if
V is invariant to changes in h_., n will be similarly invariant.
I".". THE CASE STUDY
The case under consideration involved forest management practices
in the Black Hills National Forest of South Dakota. After preliminary
investigation, as to the nature of the sites that seemed to be desirable
due to a greater probability of success , or a greater number of hunters
(correcting for accessibility), two quality attributes or character-
istics were derived. One, HEIGHT, is an elevation variable. This was
used as the s variable. Hunters seemed to like to get away from the
main highways and back into the more rugged parts of the Black Hills.
The q variable was MGDEAD. This variable is a proxy for forage provided
in small openings. It was constructed using a forage variable, calcu-
lated from basal areas of ponderosa pine, and a proxy variable for
openings.^ Since elevation is not a variable which can be subject to
management actions, demand curves were estimated only for MGDEAD. This
variable represents habitat desirability, and is therefore a good proxy
for bag probability. It may also represent some aspects of the hunting
environment that hunters find desirable for reasons other than a desire
to bag game.
For the first version of the hedonic model the demand curve to be
estimated for q is of the form
; = f(E,S, D) :s
where S = the level of s (HEIGHT) (which is determined
independently of q or n), or alternatively an
instrument for s;
D = a vector of demand shifters;
E = the exogenous marginal cost price for MGDEAD, or
its instrument.
- 21 -
-------
The variation in E results from the fact that there are a set of
five origin towns with different locations around the edge of, and
within, the Forest. This is shown by Figure 1 on the following page.
The towns are Rapid City, Sturgis, Custer, Hot Springs and Lead-Deadwood.
As the assumption of a fixed n is crucial, it is worthwhile to
investigate whether the data support it. The following relationship was
estimated for one day visits (n = n):
n = 5.52 - 0.05 h + 2.22 STURGIS + 6.63 CUSTER "
standard (0.77) (0.15) (1.24) (1.21)
errors
0.73 HOT SPRINGS +2.67 LEAD-DEADWOOD
(1.45) (1.10)
R2 = 0.17
F = 7.6
N = 191
Support is given to the fixed n assumption, by the fact that the
coefficient of h is not significantly different from zero. However,
both the coefficient for Custer, and that for Lead-Deadwood are sig-
nificantly different from zero. In the case of Custer, this is caused
by a few influential outlying observations with very large values for n.
If these observations are eliminated Custer does not have a coefficient
significantly different from zero.^ In the case of Lead-Deadwood, there
is no such set of outlying observations. The question is whether this
deviation from the fixed n assumption will have a significant influence
on the results. This question will be reviewed below when the marginal
cost of MGDEAD estimates are made.
The marginal cost curves for MGDEAD for the five towns are not
directly observable. However, assuming that hunters from the same
origin town have different preferences with respect to q and s, then
- 22 -
-------
3lrck Hiu-s
nat/omal
forest
RRPID
ci ry
U3
y
0
tO
&
500 T« bF\K6Tfi
FIGURE 1. THE BLACK HILLS NATIONAL FOREST IN SOUTH DAKOTA
- 23 -
-------
their different demands will trace out the total cost curve for MGDEAD
from that origin. These total cost curves were estimated for each down,
both using all observations and excluding the outlying observations
mentioned above.^
Using both sets of observations, for each town the total costs
of hunting for the season were regressed on the levels of MGDEAD and
HEIGHT, and on a distance variable designed to represent h (DISTANCE).
The latter was intended to distinguish between the many one-day visits
case and the one long visit case. These predictor variables were used
in linear and non-linear (cross-product) forms. Table 1(a) gives one
the better fitting total cost equations for each of the five towns,
using the complete data set. The equations in Table 1(b) were estimated
using the constrained data set (excluding observations with n > 15).
The marginal cost of MGDEAD for each town was calculated by
taking the partial derivative with respect to MGDEAD. Marginal cost
estimates derived from the equations in Tables 1(a) and 1(b) are pre-
sented in Tables 2(a) and 2(b). Since these marginal cost estimates for
MGDEAD do not vary with the level of MGDEAD, they can be used as prices
in the demand function for MGDEAD, as long as HEIGHT is exogenous. Since
the marginal cost price for MGDEAD for the consumer from Lead-Deadwood
is zero, the fact that Lead-Deadwood deviates from the fixed n assump-
tion does not cause the marginal cost estimate to deviate from what it
would be were the assumption met. Both linear and semilog versions of
the demand functions are estimated. Weighted versions (to correct for
heteroscedasticity) are also estimated. These are shown in Tables 3(a)
and 3(b).
- 24 -
-------
TABLE 1(a). ESTIMATES OF THE TOTAL COST RELATIONSHIP
RAPID CITY
STURGIS
CUSTER
HOT SPRINGS LEAD-DEADWOOD
Dependent Variable Total Cost
INTERCEPT
HEIGHT
MGDEAD
DISTANCE
DHEIGHT
DMGDEAD
OPEN
DOPEN
STAY
POPEN
25.26
(8.01)**
0.12
(0.02)**
0.041
(0.018)**
0.16
(0.03)**
0.84 x 10~*
(0.55 x 10"°)
Total Cost
59.24
(29.94)
-0.033
(0.065)
0.031
(0.18)
0.00060
(0.00050)
0.74 x 10":?)
(0.24 x 10"J)**
-2.15 x 10"^
(9.03 x 10"')**
Total Cost Total Cost
-47.60
(79.66)
-0.13
(0.25)
0.25
(0.08)**
135.57
(86.74)
-0.44
(0.31)
0.0019
(0.00021)**
-93.18
(132.04)
Total Cost
34.13
(25.98)
0.11
(0.05)**
-0.0053
(0.030)
83.70
81.1
PMGDEAD
SQUARE
R2
2
Adjusted R
F
L
N
0.54 x loj 0,00045
(0.18 x 10"V* (0.00015)**
0.53 0.44 0.75
0.52 0.37 0.73
60.11 5.98 32.11
-1,320.1 -202.4 -174.1
276 44 36
0.12
(0.40)
0.76
0.72
20.13
-130.3
31
0.019
(0.14)
0.23
0.09
1.63
-127.6
27
Where:
- the average elevation of hunting sites chosen minus 4,500 ft. (1,371.6 a).
- the forage generated by the average basal area per acre of ponderosa
pine at the hunting sites visited, multiplied by the average number of
dead trees per acre. The latter is a proxy for the probability of
forage being in small openings (less than 10 acres [4.0 ha]).
- HEIGHT x MGDEAD.
• distance from the origin town to the closest point in the Black Hills
National Forest.
- DISTANCE x HEIGHT.
- DISTANCE x MGDEAD.
- DISTANCE x OPEN.
- whether any trips were overnight trips.
HEIGHT
MGDEAD
OPEN
DISTANCE
DHEIGHT
DMGDEAD <
DOPEN
STAY
PHEIGHT - STAY x HEIGHT.
POPEN - STAY x OPEN.
PMGDEAD - STAY x MGDEAD.
SQUARE - HEIGHT x HEIGHT.
Bracketed numbers are standard errors.
**IndicateB significance at 0.05 level (two-tailed test).
- 25 -
-------
TABLE 1(b). ESTIMATES OF THE TOTAL COST RELATIONSHIP - CONSTRAINED DATA SET
Dependent Variable
INTERCEPT
HEIGHT
MGDEAD
DISTANCE
DHEIGHT
DMGDEAD
OPEN
DOPEN
STAY
POPEN
PMGDEAD
SQUARE
R2
2
Adjusted R
F
L
N
RAPID CITY
Total Cost
25.26
(8.01)**
0.12
(0.02)**
0.041
(0.018)**
0.16
(0.03)**
0.84 x 10~t
(0.55 x 10"°)
0.54 x 10
-4
(0.18 x 10
0.53
0.52
60.11
-1,320.1
276
-4
STURGIS
Total Cost
42.44
(23.41)
0.005
(0.05)
0.08
(0.14)
0.00048
(0.00039)
0.00050
(0.00019)**
-1.31 x 10"6
(7.16 x 10"')
CUSTER HOT SPRINGS LEAD-DEADWOOD
Total Cost Total Cost Total Cost
)**
0.56
0.51
9.57
-186.8
43
-13.17
(56.15)
-0.12
(0.26)
0.17
(0.08)**
0.00032
(0.00026)
0.43
0.36
6.16
-127.9
28
225.35
(117.39)
-0.77
(0.44)
0.0019
(0.00052)**
-238.16
(153.32)
-0.0014
(0.00083)
0.80
(0.54)
0.39
0.25
2.91
-119.9
29
34.13
(25.98)
0.11
(0.05)**
-0.0053
(0.030)
83.70
81.1
0.019
(0.14)
0.23
0.09
1.63
-127.6
27
Where: HEIGHT * the average elevation of hunting sites chosen minus 4,500 ft. (1,371.6 m).
MGDEAD » the forage generated by the average basal area per acre of ponderosa
pine at the hunting sites visited, multiplied by the average number of
dead trees per acre. The latter is a proxy for the probability of
forage being in small openings (less than 10 acres [4.0 ha]).
OPEN = HEIGHT x MGDEAD.
DISTANCE * distance from the origin town to the closest point in the Black Hills
National Forest.
DHEIGHT - DISTANCE x HEIGHT.
DMGDEAD - DISTANCE x MGDEAD.
DOPEN - DISTANCE x OPEN.
STAY « whether any trips were overnight trips.
PHEIGHT - STAY x HEIGHT.
POPEN « STAY x OPEN.
PMGDEAD - STAY x MGDEAD.
SQUARE - HEIGHT x HEIGHT.
Bracketed numbers are standard errors.
**Indicates significance at 0.05 level (two-tailed test).
- 26 -
-------
TABLE 2(a). MARGINAL COST ESTIMATES FOR MGDEAD
Rapid City 0.041
Sturgis (0.74 x 11-3 - [0.22
Custer 0.25
Hot Springs 0.0019 x HEIGHT
Lead-Deadwood I
-5
x DISTANCE])HEIGHT
TABLE 2(b). MARGINAL COST ESTIMATES FOR MGDEAD - CONSTRAINED DATA SET
Rapid City
Sturgis
Custer
Hot Springs
Lead-Deadwood
0.041
,-3
(0.50 10 - [0.13
0.17
0.0019 x HEIGHT
10~5 x DISTANCE])HEIGHT
- 27 -
-------
TABLE 3(a). DEMAND CURVES FOR MGDEAD USING PRICEH
Dependent
Variable
Linear Linear
Unweighted Weighted
MGDEAD
MGDEAD
Semilog
Unweighted
LOG • (MGDEAD)
Semilog
Weighted
LOG (MGDEAD)
Linear With
Instrument
MGDEAD
INTERCEPT
HEIGHT
PRICEH
AETERLESS
INCOME
YRSHUNT
R2
F
303.38
(27.88)**
0,34
(0.04)**
-324.72
(122.25)**
10.24
(17.59)
-0.09
(0.10)
2.21
(0.76)**
0.17
20.46
520
295.38
(24.90)**
0.33
(0.03)**
-215.84
(109.70)**
16.49
(15.76)
-0.045
(0.09)
1.49
(0.69)**
520
5.69
(0.05)**
0,64 x 10 ?
(0.73 x 10"V*
-0.565
(0.236)**
0.08
(0.03)
—A
-0.33 x 10 .
(0.20 x 10_J)
0.005
(0.001)**
0.16
19.19
520
5.67
(0.05)**
0.62 x 10~l
(0.71 x 10 )**
-0.420
(0.22)**
0.015
(0.03)
0.89 x 10~l
(0.18 x 10 )
0.003
(0.001)**
387.67
(34.56)**
520
-353.02
(264.65)
-39.47
(20.72)
-0.06
(0.12)
2.79
(0.94)**
0.04
4.39
435
Where: MGDEAD
the forage generated by the average basal area per acre of ponderosa
pine at the hunting sites visited, multiplied by the average number
of dead trees per acre. The latter is a proxy for the probability
of forage being in small openings (less than 10 acres [4.0 ha]),
the average elevation of hunting sites chosen minus 4,500 feet
(1,371.6 m).
0.041 for Rapid City, [0.00074 - (0.0000022 x DISTANCE)] >: HEIGHT
for Sturgis, 0.25 for Custer, 0.0019 x HEIGHT for Hot Springs, and
zero for Lead-Deadwood,
1 if the hunter applied for anterless license, 0 if he did not.
the hunter's income level in hundreds of dollars,
the number of years the hunter has hunted.
Bracketed numbers are standard errors.
**Indicates significance at the 0.05 level (two-tailed test).
HEIGHT
PRICEH
ANTERLESS
INCOME
YRSHUNT
- 28 -
-------
TABLE 3(b). DEMAND CURVES FOR MGDEAD USING PRICEJ - CONSTRAINED*DATA SET
Linear
Unweighted
Linear
Weighted
Semilog
Unweighted
Semilog
Weighted
Linear With
Instrument
Dependent
Variable
MGDEAD
MGDEAD
LOG (MGDEAD)
LOG (MGDEAD)
MGDEAD
INTERCEPT
316.43
(29.23)**
296.93
(26.17)**
5.69
(0.06)**
5.67
(0.05)**
418.98
(37.40)**
HEIGHT
0.35
(0.0039)**
0.34
(0.04)**
0.00064
(0.00009)**
0.00064
(0,00007)**
PRICEJ '
-522.63
(211.82)**
-277.61
(192.40)
-0.92
(0.41)**
-0.59
(0.39)
-1248.86
(447.41)**
ANTERLESS
10.38
(17.74)
17.30
(15.82)
0.09
(0.03)
0.17
(0.033)
-39.41
(20.68)
INCOME
-0.94
(0.10)
-0.05
(0.09)
-0.00003
(0.00020)
0.7 x 10"5„
(0.19 x 10~J)
-0.04
(0.12)
YRSHUNT
2.22
(0.77)**
1.46
(0.70)**
0.004
(0.0014)**
0.0033
(0.0014)**
2.85
(0.94)
R2
0.17
0.16
0.05
F
20.66
19.09
•
5.87
N
510
510
510
422
Where: MGDEAD = the forage generated by the average basal area per acre of ponderos
pine at the hunting sites visited, multiplied by the average number
of dead trees per acre. The latter is a proxy for the probability
of forage being in small openings (less than 10 acres [4.0 ha]). .
HEIGHT = the average elevation of hunting sites chosen minus 4,500 feet
(1,371.6 m).
PRICEH = 0.041 for Rapid City, [0.00050 - (0.0000013 x DISTANCE)] x HEIGHT
for Sturgis, 0.17 for Custer, 0.0019 x HEIGHT for Hot Springs, and
zero for Lead-Deadwood.
ANTERLESS = 1 if the hunter applied for anterless license, 0 if he did not,
INCOME = the hunter's income level in hundreds of dollars,
YRSHUKT = the number of years the hunter has hunted.
Bracketed numbers are standard errors.
^Indicates significance at the 0.05 level (two-tailed test).
- 29 -
-------
When HEIGHT is not treated as exogenous, the instrument ANTERLESS
(if the hunter applied for an anterless hunting permit) was used in its
place. ANTERLESS was the one socioeconomic variable which exhibited
a much higher correlation with HEIGHT (r = -0.24) than with MGDEAD
(r = -0.06). In using this instrument, observations were included
only for towns whose marginal cost price for MGDEAD did not depend
upon HEIGHT. Only the linear unweighted version of the demand curve
was estimated using ANTERLESS as the instrument for HEIGHT. The results
are shown in the rightmost column of Tables 3(a) and 3(b).
Now enough information has been generated to obtain measures of
the consumer's surplus change that would occur due to some management
action. It has been noted that the marginal cost price for MGDEAD for
the Lead-Deadwood consumer is zero. This is because of the easy
accessibility to an area exhibiting high levels of MGDEAD. One question
that might be asked involves determination of the additional consumer's
surplus that would be obtained by a hunter from another town were the
characteristic made equally easily available to him at the same level.
Now we will calculate the consumer's surplus benefit that a hunter from
Custer would obtain were he to have the same marginal cost for MGDEAD as
a hunter from Lead-Deadwood, with the marginal cost of HEIGHT remaining
constant, is analyzed here.
This is not an abstract example. The Norbeck timber sale is
scheduled to take place on forest compartment 302. This compartment is
roughly the same distance from Custer, as compartment 703, currently
exhibiting higher MGDEAD values, is from Lead-Deadwood. A main purpose
of the sale in compartment 302 is to increase deer habitat. This will
be done by reducing average basal area per acre to around 70 and
- 30 -
-------
TABLE 4. VEGETATION CHARACTERISTICS BY SUBCOMPARTMENT
Town
Subcompartment
Average Basal
Area Per Acre
(per ha.)
Existing/Post-Norbeck
Pounds Per Acre
of Forage*
(kg. per ha.)
Existing/Post-Norbeck
Custer
30204
30206
30207
30208
30209
30210
161
116
146
146
147
124
57
64
101
39
80
86
56
143
76
76
75
121
494
427
196
721
305
269
Lead-Deadwood
70301
70302
70303
70304
70305
70307
46
85
82
76
G o
n. a.
n. a.
n. a.
n. a.
n. a.
n. a.
620
275
292
332
208
409
n.a.
n.a.
n.a.
n.a.
n.a.
n.a.
¦^Calculated from forage equation in Pase and Hurd (1957).
n.a. = not applicable.
- 31 -
-------
distributing the cutting in a pattern of small openings. Table 4 shows
the average basal area per acre and forage per acre for compartment 703.
This is compared with the current situation in 302 and projected the
post-sale situation.
First consider the current situation in subcompartments in the
vicinity of Custer, and in the vicinity of Lead-Deadwood. Table 4 shows
the values of the key variables for the compartments.
The result of the Norbeck sale in terms of our model is that the
marginal cost of MGDEAD to a hunter from Custer would drop to that of a
hunter from Lead-Deadwood, zero. Tables 5(a) and 5(b) give consumer's
surplus changes for a hunter who was hunting prior to the marginal cost
change. Consumer's surplus changes are calculated for the five alter-
native demand equations of Tables 3(a) and 3(b). Based on Table 5(a),
the consumer's surplus gain for a Custer hunter is in the $99 to $124
g
range. In 1980 there were 844 hunters from Custer. This would have
meant aggregate benefits for Custer hunters in the neighborhood of
$94,000, or $15 per member of the population of Custer County.
In fact the number of hunters may change, although it is not pos-
sible with current data to estimate the extent of the change. If the
decrease in the marginal cost of MGDEAD results in new hunters, these
new hunters may well obtain greater consumer's surplus changes than
existing hunters. For these new hunters the best consumer's surplus
estimate we can obtain is the full consumer's surplus after the marginal
cost change net of fixed costs. In the case of Custer this amount is
the sum of the $99 to $124 change and the original total consumer's
surplus amount, minus fixed costs. The maximum this could be is $243 to
- 32 -
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$393 per new hunter. The present participation rate for Custer County
is 0.14, higher than any other county. If this were to increase to 0.15
there would be about 56 new hunters who would in the aggregate obtain an
annual increase in consumer's surplus of $13,600 to $22,000. Added to
the $94,000 for existing hunters this gives a total of between $107,600
to $116,000. Using Table 5(b) amounts, the comparable range would be
between $69,800 and $77,000.
Table 4 also provides estimates for a similar management change
that would produce a vegetative pattern, similar to that in the vicinity
of Lead-Deadwood, in the vicinity of each of the other towns. One can
note that smaller benefits accrue to hunters from other towns. Part of
the reason for this is the relatively large cost reductions experienced
by Custer hunters. Hunters from Hot Springs and Custer currently have
the greatest marginal costs for MGDEAD. Substantial reductions in cost
can be expected to yield substantial benefits. Another part of the
reason is that hunters from Custer tend to choose higher elevations than
hunters from other towns except Lead-Deadwood. As the elevation vari-
able (HEIGHT) is a demand shift variable, this results in higher con-
sumer's surplus estimates.
The $99 to $124 benefit range for a.Custer hunter is for one
hunting season. If a management policy were instituted to maintain the
situation that produced these benefits , rather than to maintain the
existing situation, then it would be possible to evaluate it by allowing
benefits to occur annually and calculating the present value of benefits
from the policy. For example, if the new vegetative pattern resulting
from harvesting in 302 were to be maintained for 20 years and annual
- 33 -
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TABLE 5(a). CONSUMER'S SURPLUS CHANGES - VERSION 1
Town
Linear Linear Semilog Semilog Linear With
Unweighted Weighted Unweighted Weighted Instrument
Rapid City
Sturgis
Custer
Hot Springs
Lead-Deadwood
113
124
120
io:
76
99
51
TABLE 5(b). CONSUMER'S SURPLUS CHANGES - VERSION 1 - CONSTRAINED DATA SET
Rapid City
Sturgis
Custer
Hot , Springs ,
Lead-Deadwood
50
63
49
63
51
82
TABLE 5(c). CONSUMER'S SURPLUS CHARGES - VERSION 2 - CONSTRAINED DATA SET
Rapid City
Sturgis
Custer
Hot Springs
Lead-Deadwood
20
86
60
20
94
64
78
62
- 34 -
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benefits of $112 per hunter were to accrue at a 6 percent discount rate,
then the present value of discounted benefits would be $1,300 per
hunter. If the number of hunters did not change this would be
$1,097,000 in the aggregate. Allowing the participation rate to
increase by one percentage point would bring this amount to around
$1,300,000. Using Table 5(b) values this is reduced to around $800,000.
For purposes of sensitivity analysis it is useful to consider
what the consumer's surplus change would have been had the second
version of the hedonic model (Q = nq) been used. If the constrained
observation set is used, there will be no differences in the marginal
cost price estimates. However, it is now possible to take account of
the fact that n = 8 for Lead-Deadwood, as compared to n = 5 for the
other towns. If n is to be treated as constant along the demand curve
for q, the observed q for Lead-Deadwood must be replaced by 8/5 q for
the consumer's surplus change calculation. This results in the con-
sumer's surplus change calculations in Table 5(c). Using the mean of
these consumer's surplus amounts the benefit estimate would be $950,000.
Overall, the sensitivity testing produced a range of individual
consumer's surplus change amounts of $62 to $124, and a range of total
benefit estimates of $800,000 to $1,300,000. The Version 2 results
based on the constrained data set, are roughly in the middle of the
range and are judged to be the most reasonable estimates.
CONCLUSIONS
The hedonic model applied in the Black Hills case study is one of
the specific models than can be derived from the general household pro-
duction function model. The methodology used here has some similarities
to those used by McConnell (1979) and Mendelsohn (1983).
-------
In section I four issues that arise in going from the general
model to the specific model were mentioned; identifiability, weak com-
plementarity, path-independence and compensated demand curve approxima-
tion. In section II these issues were discussed with respect to a
number of specific models, including the hedonic one. However, the
identifying restrictions and other assumptions used here are not the
only possible ones.
It is clear that at least some subset of the demand and cost
functions must be identifiable, and that this does involve certain
restrictions. However, the range of possibilities for identification
have not been well investigated. The form of the cost function is one.
area where further investigation would be useful. Here exogenous
variation was introduced into the cost function through specifying
different origins with the same level of h. but different costs of
J
obtaining s and q. Assuming that s and q are not perfectly jointly
supplied, and that the set of exogenous demand shifters affecting q is
not identical to the set affecting s, then the marginal cost curves for
q and s can be identified. If the change in the marginal cost of q is to
be simulated by exogenous variation across origin towns, then it is also
necessary that there be variation across towns in the marginal cost of q
that is independent of variation in the marginal cost of s. Are such
assumptions realistic, and if so, in which cases?
Without sufficient variation in recreationists' preferences, the
estimation of the total cost function and the marginal cost curves is
not possible. Certainly if all consumers were identical it would not be
possible to estimate any of the cost curves. In general, this approach
is limited by the number of sites actually visited by consumers from a
- 36 -
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given origin. An alternative would be, not to use observations on
recreationists' actual visits, but to estimate the cost curves based on
the sites available at a given origin. This would involve a complete
enumeration of sites and the levels of the characteristics available at
each. However, with such an approach., it would be possible to use a
linear programming model to find the least cost ways of obtaining dif-
ferent levels of the characteristics. This would give the information
required for the marginal cost curve. In some cases characteristics may
be perfectly jointly supplied, but this will become apparent in the pro-
cess determining the least cost solutions.
Identification of the demand curve for the characteristic of con-
cern can also be problematical. Although it is clear that there must be
exogenous variation in the marginal cost of q, if the benefits from a
shift in that marginal cost are to be estimated, further restrictions
may be required to estimate the demand curve for q. If the demand
prices for other characteristics, or the characteristics themselves, are
exogenous they will help identify the demand equation for q. If neither
the other characteristics nor their prices are exogenous, then instru-
ments for the endogenous variables are required. These may be either
demand or supply related. In this study ANTERLESS (whether or not a
hunter had applied for a permit to hunt anterless deer) was used as an
instrument for HEIGHT in the demand equation for MGDEAD. In his
recreational fishing study McConnell (1981) used "years of experience"
as a shift variable in the demand equation for quantity of fishing days,
and "number of rod and reel combinations owned" as a shift variable in
the demand equation for the level of quality demanded. The potential
for identification through the selective exclusion of demand shifters
- 37 -
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has not been fully explored. Since there are a number of studies on
attitudes, preferences and motivations of groups of recreationists like
hunters and fishermen, it may well be possible to get some ideas for
selective exclusion from these studies, and to test them in econometric
models.
Restrictions on the form of the utility function can also be used
in identification. If it is to be assumed that every quantity unit con-
sumed by a given consumer has the same levels of the characteristics,
then, if the characteristic choices are taken separately for each
quantity unit, these choices must be independent of the total quantity
level consumed. This implies that the choice of the characteristic
levels must be independent of the choice of n, and that these charac-
teristic levels can be taken as predetermined in the demand curve for n.
In some cases it can also be assumed that n is chosen independently of
the characteristics, and n can be treated as predetermined, or fixed, in
the demand and marginal cost curves for the characteristics.
In general, it will not be observed that each quantity unit con-
sumed by a given consumer has the same characteristics levels. It may
be assumed that this is the result of random variation stemming from
imperfect information. If this is true the mean characteristic levels
can be treated as the intended characteristic level choices.
Another possible reason for different site choices is that the
utility function is different for different quantity units. For
example, on some days a hunter may place a high priority on bagging
game. On other days he may be more interested in the scenery. The
problem is that it is virtually impossible to distinguish different
between quantity units with a bag emphasis and quantity units with a
scenery emphasis. Suppose the utility function is (28):
- 38 -
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U(x) + U(q1) + n2 U(s2> 15
where: = bag type quantity units;
n2 = scenery type quantity units.
Now suppose the cost function is (29) :
x + n^ [h + K(q^) + q^Cs^] + n2[h + K(q2> + q2
-------
The first order conditions are:
V /U = L
q X q
V-/U = 0
S X
Although the model in (35) can be used to value shifts in K^, ::
is worth noting that in this case the cost function would be more appro-
priately estimated using observations on sites visited. Using available
sites and a linear programming approach to estimate the cost function
will only work, if the specific site choices made are not obscured by
averaging.
Another question of relevance in identifying the relevant cost
and demand functions, is how the quality characteristics are related to
the quantity unit in the utility function. Related to this is the
question of what the appropriate quantity unit is, Particularly with
characteristics such as the probability of bagging game, it is clear
that the characteristic must be defined for a fixed time period, such as
an hour, or day of specified length. In this context, using quantity
units of different time lengths makes no sense. Visits can be used as
the quantity unit, only if they are of the same length, or if the level
of the characteristic consumed per quantity unit is adjusted to reflect
visit length.
In this paper we have indicated two forms of the utility function
which might incorporate this "repackaging" approach. In one case the
utility derived from the characteristic q, was multiplied by the number
of quantity units, n. In the other, the level of the characteristic
consumed is Q = nq, and total utility is a function of nq. These two
models can lead to different results. In general, the relationship
between quantity units and quality characteristics has not been well
investigated.
- 40 -
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Related to the question of the appropriate quantity unit is the
question of time costs. Two of the findings in this study were that
visit length tends to increase with travel distance and that weekdays
and weekend days are not viewed by recreationists as having the same
opportunity costs of time. First of all it was observed that as dis-
tance from the Black Hills National Forest increased hunters tended to
switch from taking many one-day visits to taking one long visit. Only a
small set of hunters at intermediate distances tended to take a number
of visits of different lengths. It would appear that another one-day
visit is a perfect substitute for another day added to an existing
visit, and the choice of which way to take an additional day is based
upon the relative cost of the two alternatives. It is also implied that,
for any hunter to take many one-day visits, it must be true either that
there are virtually zero travel costs to the site, or that the oppor-
tunity cost of time increases with visit length. It is at least in part
the latter. Since hunters are more likely to stay overnight if the next
day is a weekend or holiday than if it is a weekday, it appears that a
higher opportunity cost is attached to weekday time than to weekend
time.
By looking at the choice of how to take another day (stay over-
night or go home and come back another time), it was possible to deter-
mine the relative opportunity cost of time associated with a weekday
versus a weekend day or a holiday. The difference was in the neighbor-
hood of $26 per day. Since longer visits are more likely to involve
weekdays than are shorter visits, on the average the opportunity cost
of time for a one-day visit will be less than for a day within a longer
visit, and on average the opportunity cost of a day will tend to
- 41 -
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increase with distance from the site visited. Since time costs can be
important elements of the costs associated with recreation visits, it
would be useful to further explore the generality of this perfect sub-
stitutes case.
Weak-complementarity also involves restrictions on the cost and
utility functions and, can be very useful in limiting the extent of
the additional restrictions required for identification. Tradition-
ally, weak-complementarity has been taken to mean that the marginal
willingness to pay for q is zero when n is zero. However, there are
many other ways in which weak-complementarity can be used and it can
apply to the cost as well as to the demand side of the picture. This
study used the weak-complementarity assumption to imply that when q = 0,
the marginal willingness to pay for n is zero. The justification is
evidence provided by psychologists' studies, showing that "bagging game"
is a necessary part of the hunting experience. On the cost side, this
weak-complementarity assumption is harder to justify. There can well be
a fixed cost such that even sites with zero probability of bagging game
are only available at a positive cost to hunters.
The conditions which allow path-independence and compensated
demand curve approximation are also important considerations. In the
models estimated here, path-independence is most often not an important
consideration. If n and s are exogenous then there is only one path.
If s is exogenous, and the Q = nq repackaging model is used, then the
path independence condition is automatically met because it must be true
that 8jn = §2q = 8q where g^(n,q,x) is the inverse demand function for
q, §2(n»cl>x)» the inverse demand function for n, and gq(Q,X) is the
inverse demand function for Q. If s is not exogenous the conditions
- 42 -
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must also includ^,^ = g^q where g^(Q,S,X) is the inverse demand curve
for s.
When n and s are exogenous the only income effect, which can
affect the degree to which the Marshallian demand curve approximates the
compensated demand curve, is that on q. In the Black Hills case that
income effect turned out to be zero. However, this need not always be
the case. The size of the income effect should always be investigated.
If they are not small an approach similar to that of Hausman (1981)
should be used to derive the compensated demand curve.
Finally, another questions which deserves further attention, is
that of whether or not individual observations are sufficient to esti-
mate the benefits from a decrease in the marginal cost of q to some
recreationists. There are two questions involved. The first is whether
truncation bias exists. That is, do nonparticipants tend to consume
different levels of n, q or s than do participants? If they do then
demand curves based only on participants will reflect both the effect of
price on quantity, and the effect of the truncation.
The second question is whether consumer's surplus changes can be
measured using only data on participants. It has been shown earlier in
the paper that benefits to current users can be measured with such data.
In many cases these will constitute most of the benefits. However,
there is still the possibility that the increased availability of the
quality characteristic, q, will increase the expected use level creating
additional benefits. To measure this we do need to know the extent to
which the probability of participation is increased by the increased
availability of q. In the Black Hills study probability of participa-
tion estimates were available only by county, and this made it impossible
- 43 -
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to know how the probability of participation would change. It was
simply assumed that the probability would change by one percent. It
would, however, be useful to test the effect of a change in a quality
characteristic level, or a change in the marginal cost of a charac-
teristic, on the probability of participation for a given origin. This
necessitates that actual numbers of visitors to a site from an origin be
known as well as the population level of the origin zone.
What is clear from this study is that the general household
production function model can be used to derive a number of more
specific models that can be very useful in estimating the value of
increased availability of resource services to recreationists. This
study has estimated one such model, with some consideration given to how
varying the assumptions to obtain a slightly different model affects the
results obtained. However, it is quite clear that there are a number of
areas in which further research is necessary. Most of these have to do
with the specific assumptions that are most reasonable in applying the
general methodology. Further research should both test the general-
izability of the assumptions used in this study, explore other assump-
tions that might be more reasonable in other cases, and to make com-
parisons between models derived using different sets of assumptions.
The work described in this paper was not funded by the U.S.
Environmental Protection Agency and therefore the contents do not neces-
sarily reflect the views of the Agency, and no official endorsement
should be inferred.
- 44 -
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NOTES
"Based on extensive literature searches. Both Boyce (1977) and
Thomas (1979) have developed relationships which express the suitability
of an area for wildlife habitat in terms of its land and vegetative
characteristics. For example, Boyce, in studying deer habitat in hard-
wood forests in the southern Appalachians, found that forage availa-
bility and the size of openings permitting utilization of forage were
key factors. Thomas' work focusing on the Blue Mountains of Oregon and
Washington provides similar findings.
"In the "Human Dimensions in Wildlife" session at the Thirty-
Eighth North American Wildlife and Natural Resources Conference, all
three papers on the topic (Potter, Hendee and Clark [1973]; More [1973] ;
and Stankey and Lucas [1973]) stressed this point. The paper by More
uses a quotation from the Spanish philosopher Ortega y Gasset (1972) to
illustrate the role of success in hunting. "One does not hunt in order
to kill; on the contrary, one kills in order to have hunted."
"Both of these models assume that all quantity units consumed by
one consumer exhibit the same q and s choices. That is, all days are
consumed at the same site. This is not what is in fact observed. One
consumer may go to a number of different sites. This could be for a
number of reasons. The consumer's utility function and/or cost function
could be such that he specializes his days. Some days may be specialized
in s, and some in q. Alternatively it might be the case that variation
in the q and s choices is caused by a demand for variety that introduces
a small random element into a consumer's site choice. The latter
assumption is used here, and the attribute or characteristic levels
consumed are assumed to be the average levels over all days consumed.
- 45 -
-------
'The calculation was based on work by Pase and Hurd (1957).
log (forage in lbs. per acre) = 3.2260 - 0.00936 (basal area
of ponderosa pine in square feet per acre).
Several adjustments were made based on work done in the Black Hills
National Forest. See "Forest-Browse Coefficient Documentation," mimeo
provided by Leon Fager, Wildlife Biologist, Black Hills National Forest.
"The proxy variable for openings was the average number of dead
trees per acre in the compartment. It was chosen because areas high in
this variable appeared to be attractive to hunters and to have high
success rates. After some discussions with Black Hills Forest personnel
and people from the South Dakota Department of Game, Fish and Parks, it
was hypothesized that the reason for this was that the high numbers of
dead trees were due to mountain pine beetle infestation. The combined
result of the infestation and the management of it created small open-
ings, as trees were removed from around the infested tree or trees.
'Diagnostic statistics proposed by Belsley, Kuh and Welsch (1980)
were used to select influential observations. Three statistics were
used RSTUDENT, DFFITS and DFBETAS. The critical values used to select
influential observations. Observations with the largest number of days
(more than 15) were found to be most influential. Although the fact
that they are found to be influential does not itself justify excluding
them, the fact that these few observations (10) caused the fixed n
assumption to be violated for Custer at least justifies excluding them
for purposes of sensitivity analysis.
Total costs included all travel costs at 8 cents per mile (AAA
variable cost estimate for 1980) plus time costs. The calculation of
time costs made use of the fact that in the Black Hills data it was
- 46 -
-------
observed that hunters living close to the site, take a number of day
visits, while hunters living further away take one long visit. For each
day a hunter is observed visiting the Black Hills (not including the
last day), there is a probability (P) of going home and returning on
another day and a probability (1 - P) of staying overnight. Assuming
the two alternative ways of consuming another day provide the same
utility, the choice will be based on relative costs. When the relative
costs are equals, both probabilities will be 0.5. The relative costs
include both time and money costs. The money costs are largely travel.
Although one might suppose lodging costs to be a factor, lodging costs
were in fact very small. What appeared to be considerably more impor-
tant was whether or not the next day was a weekday. This implied a dif-
ference in the time costs associated with weekdays versus weekends or
holidays. For any given hunter the probabilities will be 0.5 when
TC + tj = t2 (1)
where: TC is the money cost of travel;
tj is the time cost of the next day when the hunter goes
home and comes back;
t2 is the time cost of the next day when the hunter stays
over.
Assuming time is only available in blocks of one day, that no
trip to the site and back takes more than one day, and that time not
spent hunting has a marginal utility of zero, it is possible to vary TC
while holding and t^ constant, to see where the equality holds. This
was done using a logit model. The dependent variable is log(P/1 - P),
which equals zero when P = (1-P) =0.5. The model estimated was:
log(P/1 - P) = a + bD = cH 2
where: a, b and c are parameters to be estimated;
D is the one-way distance from home to site;
H = 1 if the next day is a weekend day or a holiday;
H = 0 if the next day is a weekday.
- 47 -
-------
The result was:
log(P/1 - P) = 1.55 - 0.0097D - 1.55H 3
Setting the left-hand side to zero, when H = 1, D = 0. That is,
if the next day is a weekend day or a holiday, the hunter would only
return home if the distance was zero This implies from (1) that TC = 0
and = t2« If H = 0 , D = 160 or 320 miles round trip. At 8 cents per
mile, TC = $26. Now (1) gives + 26 = tTogether these imply that
weekdays cost $26 more than weekend or holidays. There is no estimate
for the time cost of a weekend, but if we conservatively estimate it at
zero, the time cost for any given day is
PR * 0 + (1 - PR) * 26
where: P^ is the probability of the next day being a holiday
or weekend day;
. - Pp is the probability of the next day being a
weekday.
The total time cost over a season is
[PH * 0 + (1 - PR) * 26]n
where: n is the total number of days hunted.
"There was no actual estimate of the number of hunters from
Custer. However, 270 hunters returned report cards from Custer County.
The average return rate of 32 percent, which seems to be fairly constant
across the counties for which both the number of hunters and report
cards are available, would have meant 844 hunters from the county.
- 48 -
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Vaughan, W.J. and C.S. Russell. 1982. "Valuing a Fishing Day: An
Application of a Systematic Varying Parameter Model," Land
Economics, Vol. 58, No. 4, pp. 450-463.
Willig, R.D. 1976. "Consumer's Surplus Without Apology," American
Economic Review, Vol. 66, pp. 587-597.
Wilman, E., with the assistance of P. Sherman. 1984. "Valuation of
Public Forest and Rangeland Resources" (Resources for the Future
Discussion Paper D-109).
- 52 -
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Model 1 ing the Demand for Outdoor Recreation
Robert Mendelsohn
School of Forestry and Environmental Studies
and
Department of Economics
Yale University
205 Prospect Street
New Haven, Connecticut 06511
* This paper was prepared for a U.S. Environmental Protection
Agency sponsored workshop on valuing recreation held in Boulder,
Colorado in May, 1985. The research, however, was not funded by
the EPA and does not necessarily reflect the views of the Agency.
1
-------
ABSTRACT
This paper critically reviews several of the new
methodologies developed in the last ten years to model the demand
for recreation. The purpose of the review is to assess which
techniques are most appropriate for valuing (1) new sites and (2)
changes to existing sites.
There are three competing approaches to modelling
heterogeneous recreation sites: partitioning, hedonics, and index
models. Partitioning involves grouping sites into small
homogeneous sets and treating each set as a unique good and is
best represented by multiple site travel cost models. Hedonics
involves disaggregating goods into their component
characteristics and modelling the prices and demands for the
characteristics and is best represented in the recreation context
by the hedonic travel cost method. The index models involve
measuring the demand for a standard good and explaining
variations in that demand across goods explicitly in terms of
observable characteristics. Both generalized travel cost and
discrete choice models are members of this last approach.
None of the approaches clearly dominate in all
circumstances. For example, when valuing whole sites, the
partitioning and index models appear best. Partitioning being
preferred when there are a few discrete types of sites, discrete
choice models being preferred when the relevant set of sites
satisfy the independence of irrelevant alternative axiom, and
generalized travel cost being preferred when there is a single
site choice or no observable substitution across sites.
When valuing characteristics, each approach has special
circumstances when it is most appropriate. Generalized travel
cost is best when there is a single site to choose from.
When there are only a handful of site types to choose from and
the relevant characteristic is the distinguishing feature between
two types of sites, multiple site travel cost is best. When
there are multiple sites and independence of irrelevant
alternatives is satisfied, the logit discrete choice models may
be best. Otherwise, tire best available method to measure the
value of characteristics is the hedonic travel cost method. This
is especially evident when there are many sites and the relevant
issue is a small change in characteristics at a single site.
Although there has been a great deal of high quality research
concerning recreation demand modelling in the last ten years,
there remains a need for additional work. All of the available
techniques need refinement and additional development. Further,
there is a need for more comparisons to establish the conditions
under which each method is most appropriate.
2
-------
MODELLING THE DEMAND FOR RECREATION
ROBERT MENDELSOHN
YALE UNIVERSITY
205 PROSPECT STREET
NEW HAVEN, CONNECTICUT 0 6511
INTRODUCTION
Beginning with the pathbreaking work of Marion Clawson
[1959], economists have been trying to develop techniques to
place a dollar value on outdoor recreation for over a quarter
century. In the last ten years, this methodological development
has turned into a virtual revolution as a multitude of state-of
the-art approaches have sprung into existence. The primary
achievement of this new breed of methodologies is their focus on
modelling the heterogeneity of recreation opportunities. By
explicitly recognizing the qualitative component of recreation
sites, these new methodologies are suddenly capable of answering
new and key policy questions. First, what is the net value of
adding a new site with particular characteristics to an existing
system of sites? Second, what is the value of changes in
existing sites either through degradation or enhanced management?
Although the economic tools of supply and demand are
invaluable to the study of resource allocation (microeconomics),
these tools are based on the assumption of a homogeneous set of
goods and services. All units of a good are assumed to be
perfect substitutes both in production and value. Traditional
economic analysis consequently must be modified to address
heterogeneous goods and the issue of quality.
There are three basic approaches to handle the heterogeneity
or quality component of goods in the economics literature at
present. (1) The oldest approach (partitioning) is to segment the
heterogeneous goods into fine enough categories that all the
goods within each category can be considered the same (almost
perfect substitutes). Each category is then treated as a
separate good and traditional demand system models are applied to
examine substitution amongst the categories. (2) The hedonic
methodology treats goods as bundles of homogeneous
characteristics. An implicit market in the characteristic world
is assumed where individual characteristics have prices and
underlying supply and demand curves. (3) The index approach,
like the partitioning model, deals explicitly with choosing one
good amongst many. However, like the hedonic model, the choice
amongst goods is an explicit function of the physical
characteristics Of the goods. Instead of a market for
characteristics, though, this third approach falls back upon an
exogenous index of attributes by which heterogeneous goods are
cardinally ranked. Each of these three basic approaches have
been applied with varying success to model recreation.
In this paper, the leading revealed preference techniques to
value outdoor recreation are reviewed and assessed in terms of
-------
their ability to answer the two policy questions above. Some
drawbacks such as incomplete data are common to every technique.
The focus of this review, however, is upon the relative strengths
and weaknesses of each approach. The special circumstances in
which one technique is preferred or is invalid are identified
whenever possible. The list of methodologies reviewed include:
multiple site travel cost, generalized travel cost, discrete
choice, hedonic travel cost, and gravity models. The paper is
organized around the three basic approaches: partitioning,
hedonics, and index models and concludes with a summary statement
and recommendations for further research.
PARTITIONING
The oldest and perhaps most straightforward approach to
handling a set of heterogeneous goods is to group similar members
of the set into homogeneous categories. Since ail the remaining
members within each category are alike, each category can be
treated as a traditional homogeneous good and the familiar demand
and supply tools of microeconomics can be applied. One advantage
Of this approach is that both the theoretical and econometric
tools are familiar and well developed so that application is
straightforward. Another attractive component of this approach
is that the substitution across categories is explicitly modelled
so that the effect of introducing one type of site on other
existing sites can be easily seen.
The first paper to apply the partitioning approach to
recreation analysis is Burt and Brewer's [1972] analysis of the
recreation value of lakes in Missouri. in this analysis, lakes
were subdivided by natural versus manmade and by size. They
found the demand for manmade lakes was more elastic than the
demand for natural lakes suggesting the two types of lakes are
not at all perfect substitutes. Another important application of
the partitioning approach is the study by Cichetti, Fisher, and
Smith [1976] of ski areas in California. These authors found
considerable substitution amongst ski areas suggesting that the
introduction of yet another site would significantly affect the
demand for the existing set of sites.
These applications illustrate the strength of the partitioning
approach, its theoretical and econometric soundness and its
ability to reveal substitution amongst types of sites. However,
the applications also illustrate the limitations of the
partitioning approach. First the partitioning approach becomes
cumbersome quickly as the number of categories multiply. For
each category, there is another price and another demand
equation. For example, with only three goods, the demand model
can be written:
1 Q1 = F ( PI, P2, P3, W) + el
Q2 = F ( PI, P2, P3, W) + e2
-------
Q3 = F( PI, P2, P3, W) + e3
where Pi is the price of the closest member of type i, Qi is the
visitation sate to site type i, W is a vector of individual
demand shift variables, and ei is the error term in each
equation. As the number of categories increases, each equation
includes more prices and there are more equations until the
number of parameters becomes overwhelming. Note that in both
applications of this method, there are only six categories or
types of sites..
A second issue concerns how to divide the distribution of
sites into discrete types in the first place. When there is a
single parameter of quality, the problem is simply trading Off
between the number of categories to model and the homogeneity
within each category. Obviously, the more categories, the more
similar units can be within each category. Perhaps less obvious
is where to make the divisions. In general, site divisions
should be made to isolate the tails or extreme values of a
distribution. For example, suppose the quality Z of sites is
distributed lognormally and heterogeneity is captured by the
variance of Z within each category. As shown in Mendelsohn
[1984a], the first division should not be around the mean but
rather much further down the tail of the distribution grouping
most of the sites in one category and the extreme members of the
distribution in the remaining category. Further divisions of the
distribution also focus on the highly disparate tail.
The problem of division becomes even more complicated if there
are several dimensions in which to distinguish sites. Without a
predetermined index by which to weight each characteristic, there
are many ways to group the sites all of which could potentially
be valid. By trying different groupings, and reestimating the
resulting equations, one can explore which categories are in fact
distinct and which are really arbitrary divisions which have no
meaning to the consumer. Only if each site is clearly unique,
can an investigator easily avoid this multiple clustering
problem.
The remaining limitations of the partitioning approach
concern applications of the model to policy questions. The
valuation of a new site can only be done if the new site belongs
in one of the existing categories. There is no formal mechanism
to make inferences about new sites which might fall between two
or more existing types of sites. The inability of the approach
to handle a large number of finely tuned categories exacerbates
this problem as new sites must fall into one of only a few
modelled types. If the analysis is designed to value specific
type of new site, the attributes of this new site should be taken
into account when designing the modelled site types. In this
case, if the data permits it, priority should be given to
including a site type which closely mirrors the new site.
The partitioning approach is perhaps
even more
limited in
its
-------
ability to model changes to a site. Changes can be evaluated
only if both the otherwise identical original site and modified
site happen to be distinct modelled categories. For example,
one could have modelled forested trails with a campground and
forested trails without a campground as two distinct categories
Of recreation sites. The construction of a campground on a
forested trail currently without one is equivalent to the
creation of a new site of the campground type coupled with the
destruction of a site of the no campground type. Existing
welfare rules for a simultaneous change in two prices (see
Freeman [1979]) can be used to value the modification in this
special case. If there are multiple characteristic differences
between categories, however, partitioning can only value a change
in all the characteristics. Because partitioning doesn't
explicitly model the effect of individual characteristics on site
value, it cannot distinguish the individual contribution of each
attribute. Thus only in the special circumstance that
modifications change a site from one distinct category to another
is the partitioning approach appropriate for valuing site
characteristics.
THE HEDONIC MODEL
The hedonic model treats goods as bundles of characteristics
or attributes. The explicit market for heterogeous goods is
assumed to be motivated by an implicit market for the underlying
characteristics. Instead of prices of goods, one has prices of
attributes. Instead of a demand and supply curve for goods,
there is a demand and supply curve for attributes. Thus the
tools of traditional economics are applied to an underlying
dimension of consumer choice. However, unlike traditional
markets where units of characteristics are traded individually,
the purchase of characteristics occurs in discrete packages which
cannot be unbundled. The market solution for characteristics
consequently does not have to be a constant marginal price (see
Rosen [1974]). In fact, the marginal price for an attribute can
depend not only on the amount of that attribute purchased but
upon the amount of other attributes purchased as well.
As clearly developed in Rosen [1974], the hedonic model
consists of an assumed market equilibrium and a set of underlying
supply and demand equations. Unlike traditional markets, several
supply and demand equations operate simultaneously, one for each
level of characteristic provided. Consumers and suppliers are
assumed to optimize given the market equilibrium set of prices
(price gradients) . This optimization process can be
characterized in terms of traditional Marshallian demand and
supply curves. The complete hedonic model then includes a
market price gradient P(Z), a set of demand functions for
attributes G(P,W), and a set of supply functions for attributes
H(P,Y):
(2) P = P ( Z )
6
-------
3 : = G( P,W )
: = h ( p, y )
where Y is a vector of supply shift variables such as input
prices and technologies. Since the price gradient in the above
model is nonlinear, the marginal price depends upon the level of
the attribute purchased. Marginal prices are endogenous (only
the price gradient is exogenous) requiring econometric
adjustments for proper estimation of the structural equations
(see Mendelsohn [1984b]).
Because the nonlinearity of the price gradient can be used to
identify the underlying structural equations, there have been
several attempts to identify hedonic structural equations from
single market data ( a single price gradient). Although this
single market approach is technically feasible (see Mendelsohn
[1985]), it is based on tenuous assumptions which are not
testable with single market data. Thus, it is entirely plausible
that single market analyses of hedonic structural equations are
pure nonsense (unidentified).
The identification problem has especially plagued application
of the hedonic method to property values. Because estimation of
implicit prices requires extensive data from housing markets and
because it is difficult to obtain comparable data across housing
markets, multiple market (multiple gradient) housing studies have
rarely been performed (see Palmquist [1982] for a notable
exception). Except for a few questionable studies of demand
functions for attributes, hedonic property studies have been
limited to analyses of price gradients ( see Freeman [1979] for
a review of environmental applications of hedonic property
studies). Because only the price gradient is estimated, these
applications can only value small changes in the available
characteristics. Further, because the studies are tied to
private property values, they are applicable to public land
management in only a few circumstances ( for example, for the
hunting value of wildlife, see Livengood [1983]).
An alternative application of hedonic analysis more pertinent
to the valuation of outdoor recreation on public lands is hedonic
travel cost (see Brown and Mendelsohn [1984] ) . Instead of
analyzing the purchase of sites as with hedonic property studies,
hedonic travel cost focuses on the purchase of access to sites.
Access provides for a single trip the bundle of characteristics
at that site. By exploring how far individuals are willing to
travel amongst sites to get different bundles, one can estimate
the implicit prices or cost of obtaining individual site
characteristics. Thus, the first step in the hedonic travel cost
method is to estimate the implicit prices of characteristics for
each origin by regressing site attributes on travel cost:
: P = P ( Z ) .
Individuals
from different origins
face different price
gradients
-------
because the configuration of available sites and travel distances
change with geographical location. Provided there are sufficient
differences in opportunities (geographical variation) and that
people have not systematically chosen origins because of the
corresponding prices (this problem has plagued the market
segmentation approach to hedonic property studies-see King [1974]
or Strazheim [1974]), the underlying demand curves for site
attributes can be estimated across origins:
3 I = G( P,W ) .
The number of trips a consumer would want to take given the price
gradient he faces could be modelled either in terms of the
exogenous price gradient, the endogenous marginal prices and
average characteristics, or the endogenous average site travel
cost and the average characteristics:
5 Q = B(P(Z),W)=B(P,Z, W)=B(P, Z, W)
l
where econometric adjustments have to be made whenever endogenous
variables (Pi, Z, or P) are used. The system of equations
including the price gradient, the demand for number of trips, and
the demand for attributes captures the tastes of the consumers.
The hedonic travel cost method has been applied to value
steelhead populations in Washington (Brown and Mendelsohn
[1984]), trail characteristics in the Olympic National Park
(Mendelsohn and Roberts [1983], deer density in Pennsylvania
(Mendelsohn [1984c]), and the effect of forestry on recreation in
the Cascade Mountains (Englin and Mendelsohn [1985] ) .
One of the attractive qualities of this approach is its ease
with modelling continuous and numerous characteristics. The
hedonic approach is also attractive when the policy issue is a
small change in the quality of a single site. As long as the
change has no perceptible impact on the price gradient, the
existing hedonic price is a clean measure of the value of the
change. The hedonic model is also facile with policy changes
which alter the system wide level of characteristics
proportionately across all levels of a characteristic. That is,
policy changes which alter the height but not the shape of the
hedonic price gradient are easily measured with the demand curve
for the characteristic.
The hedonic travel cost model becomes more burdensome when
policy changes alter the shape of the price gradient. For
example, suppose the relevant policy issue is to change several
medium quality sites to high quality sites. Such a
transformation could alter the shape of the price gradient
dramatically. For example, suppose the price gradient is
originally linear. The proposed policy change might easily alter
the price gradient to some nonlinear shape. In order to evaluate
the welfare effect of a nonlinear transformation of the budget
curve, one would have to determine the shape of the new price
gradient, compute the individual's optimal choice of sites and
-------
other goods given the new gradient, and then evaluate now much
the consumer values his original position relative to his new
position. Although these calculations are theoretically
feasible, we have little experience in understanding how site
specific changes will alter the price gradient. Thus, this
process of nonlinear adjustment is clearly complex if not also
problematic to practice.
INDEX MODEL
The index model is, in a sense, a hybrid between the
partitioning and hedonic models. Like the partitioning models,
the analysis explicitly models the choice amongst heterogeneous
goods. However, like the hedonic model, that choice is
considered to be an explicit function of the characteristics of
the site. Consumers are assumed to generate cardinal rankings of
available recreation sites on the basis of the objective
characteristics of those sites.
The earliest application of the index approach to recreation
analysis is the gravity models of geographers. In one of the
simplest version of this model, trips are allocated across sites
upon the basis of the square distance to each site and an
attractiveness component of each site Ai (see Huff [1962] ) :
2 n 2
c Q = Q*(1/P)*A / T. [(l/p ) * A ]
i i i j=l j j
Note that the aggregate number of trips taken to the site is
exogenous in the model above. Prices and attractiveness serve
only to allocate the aggregate trips across sites. Further, the
functional form is somewhat restrictive forcing the own and cross
price elasticities to be 2. On the positive side, the original
gravity model does explicitly recognize substitution amongst
sites.
A later more sophisticated version of the gravity model
includes both an allocation component as well as an aggregate
trip component. That is, site quality and site proximity not
only can affect which sites the consumer chooses but also how
many total trips the consumer takes. For example, Ewing[1980]
posits the following more general model:
n n
Q = [W*f( E A *g(P ))] * [A g(P } /e A g(P )]
i k=l k k i i k=l k k
The first term in brackets determines the aggregate number of
trips and the second term allocates the trips across sites.
Further, the use of the function g(P) rather than simply the
square distance generalizes the overall model to incorporate
different price elasticities. The gravity model is essentially a
demand equation model at this point. However, one restrictive
-------
component of this model remains. The cross price elasticities
remain the sane across sites.
A second difficulty also arose in this literature. How can
the quality index A be measured? At least in the early gravity
studies, the attractiveness index became a subjective valuation
of the researcher or simply a redundant measure of Qi/Q. Thus,
the first uses of quality indices to rank sites was not
satisfactory. The indices were not explicitly based upon the
objective characteristic of the site or they did not reflect the
revealed tastes of users.
Further, because the gravity model simply predicts
participation, it alone is insufficient to estimate site values.
Some practitioners of this approach consequently append a value
per trip or day to the end of these models in order to determine
value (see Sutherland [1982], for example). This ad hoc
adjustment fails to recognize that the same choice process which
generates value per trip also determines trip choice.
Consequently, assumptions about functional form used for the
valuation part must be carried through to the trip generation
analysis or the two sections will be inconsistent. Thus, one
cannot use a gravity model to allocate trips across sites and
then turn around and use an entirely different model (such as an
arbitrary travel cost model) to value the individual trips or
days at the site.
Cesario and Knetsch [1976] are the first to recognize the
inconsistency between using separate models for trip allocation
and trip valuation. Cesario and Knetsch consequently adopt a
model similar to the general gravity model above and demonstrate
that it can be used directly to estimate value. By integrating
underneath the implied demand for trips to a site with respect to
travel cost, one can estimate the consumer surplus associated
with any given site. Further, even multiple changes in sites can
be valued using these models provided the demand equations
satisfy integrability conditions.
Unfortunately, as with gravity models in general,
attractiveness is an arbitrary valuation in the Cesario Knetsch
model. In order to make the index approach work, a method to
estimate the appropriate index is needed. Two approaches have
since been developed. The first is generalized travel cost which
builds upon the simple travel cost model. The second is discrete
choice modelling which builds upon the general gravity model
described above.
The generalized travel cost model attempts to explain the
observed differences in the simple travel cost visitation
functions for individual sites by the characteristics of those
sites. For example, if the simple travel cost model of site A is
observed to be vertically above site B, presumably site A has
more quality than site B. Although the original developer
(Freeman [1979]) of this generalization was aware that multiple
site choices complicate this model, most applications of the
10
-------
model assume that only the characteristics of the visited site
matter. The characteristics of the site are consequently assumed
to alter the height and possibly the shape of the simple travel
cost visitation function:
= Q = F{ P , Z )
i i i
Note that by explicitly omitting the attributes of other sites,
the methodology assumes that a site has a fixed value regardless
of available substitutes. This assumption is clearly justified
if one assumes there is only one site available (see Feenburg and
Hills [1980]). In practice, however, the approach has been
applied to examples where there are clearly multiple
opportunities facing each recreation participant (see Vaughn and
Russell [1983] or Desvousges, Smith, and McGivney [1983]).
Implicitly, these applications either assume that (1) the cross
price elasticity between the measured site and all other sites is
zero or (2) the proximity of all other sites is the same for
participants from every ring visiting the measured site. Since
neither of these conditions are likely to hold, the generalized
travel cost model is subject to at least error. There is also a
very real possibility that the model will tend to bias certain
coefficients. In particular, whenever a group of sites tends to
be similar (for example, because of a common natural feature such
as tall mountains) the attribute held in common is likely to be
undervalued (because the close substitution amongst sites here is
being ignored) . In contrast, whenever a site is unusual in
reference to nearby sites, the generalized travel cost model will
tend to overvalue the unusual feature ( the absence of
substitutes is being ignored).
The second approach to measuring quality indices is the
discrete choice model. The discrete choice model has its origins
in the gravity model although it offers a much improved
opportunity to measure the quality index. A second advantage of
the discrete choice method is its explicit development from
utility theory. This strong utility base has permitted both
Morey [1984] and Hanemann [1984] to develop sound welfare
comparisons from this methodology.
The underlying utility model used to justify discrete choice
models assumes each participant possesses an index of attributes
b(Z) which he can apply to rank sites. In its simplest form, the
model assumes that the individual visits and thus values only the
best available site. Consequently, if all consumers were alike
there would be no substitution amongst sites, everyone would
simply go to the best site all the time. Rather than
incorporating substitution into the deterministic component of
the model as with both the partitioning and hedonic models, the
discrete choice models depend upon a random utility component to
replicate observed substitution. Thus although one site might
have a slightly higher ranking than another, the individual may
nonetheless visit the inferior site some of the time depending
upon his random behaviour. More formally, the model posits a
11
-------
probability that each site will be chosen:
9 H = Pr{ U[b(Z )fY—P ;e ] > 0[b(Z ),Y-P ;e ] }
i i i i k k k
The choice depends upon the two deterministic components of the
utility function, b(Z) and all other goods, as well as the random
error terms e. Thus the distribution of visits across sites
depends upon the cardinal ranking from the index and the
variances and possible covariances amongst the error terms. The
greater the difference in quality between any two sites, the more
visits to the better site. The greater the variance, the fewer
visits to the higher quality site.
Estimation of the discrete choice models builds upon the
basic econometric multinomial logit work of Luce [1959] and
McFadden [1973, 198 1] . If the error terms are assumed to be
independently and identically distributed extreme value
variables, then (9) reduces to:
BZ n BZ
(10) H = e i /z e k ,
i k=l
which is just the gravity model in its more general form. This
model can be estimated easily with maximum likelihood techniques.
Morey [1981,1984], Hahnemann [1984,1985], and Peterson,Dwyer, and
Darragh [1984] are the first to apply the technique to
recreation analysis.
There are three remaining problems with the discrete choice
model in increasing importance. (1) The total number of trips or
budget on trips is exogenous. (2) The choice of functional, form
for the utility function is problematic. (3) The substitution
amongst sites is restrictive.
Like the eatly forms of the gravity model, the early
applications of discrete choice treat the total number of trips
as exogenous. To correct for this shortcoming, a trip generation
component needs to be added to the model. This could be done
explicitly as part of the logit formulation, as suggested by
Peterson,Dwyer, and Darragh [1984]:
n BZ al a2 BZ n BZ
(ID Q=[ze k] * [ P * e i/ze k]
i k=l i k=l
The term in the first bracket is the trip generation component
and the term in the second bracket is the trip allocation
component. The above equation can then be estimated with
standard multinomial logit packages. The alternative is to add a
second trip generation demand function for a two equation model.
For example, one could posit a combination of (10) and the
following:
(12) Q = F( P, BZ, W )
12
-------
where P and BZ could reflect the average observed site or
possibly the distribution of observed sites. Since these
variables are endogenous to the two equation model as is Q in
(10), an instrumental variables approach could be used to
estimate both equations.
With all empirical estimation techniques, the question of
appropriate functional form is pressing. With the partitioning
and hedonic models, several forms must be tried to test which
fits the data most closely. However, with the discrete choice
models, functional form issues are even more urgent. Because it
is the utility function which requires the functional form,
casual choices of form result in hidden assumptions about
behavior. Hanemann [1984], for example, demonstrates just how
restrictive simple assumptions like linearity tend to be when
imposed on the utility function. Like functional form choice for
demand functions, several functional forms for the utility
function must be tried. Unfortunately, flexible functional forms
such as the translog demand function do not have equivalently
flexible utility counterparts as yet. Consequently, the
importance of testing the implicit assumptions of functional form
are even more critical with the discrete choice model than with
other empirical techniques.
The third and perhaps most serious drawback of discrete
choice models is the restrictive assumptions about substitution
required to facilitate estimation. One of the properties of the
Luce [1959] model is the assumption of the axiom of independence
of irrelevant alternatives. Differentiating (10) with respect to
In z (j k) , yields:
(13) Sin Jl(i|z tB) / 3ln z (jk) = B z(jk)n (j |z ,B)
B k B
The cross elasticities for each characteristic z(jk) are the same
across all sites and do not depend on the characteristics of the
site(i). For example, if one adds a toilet to some already
developed site j, that toilet would have the same impact on the
choice of all other sites whether or not site i was a developed
campground like j or a remote undeveloped wilderness. Another
quality of this property is that the ranking between any two
sites is not affected by any of the other alternatives. The
restrictiveness of this assumption has been popularly illustrated
with a modal choice example between a car and a red bus. The
introduction of a blue bus, one would expect should affect the
red bus more than the car because it is a perfect substitute for
one but not the other. The model, however, assumes that it
affects use of both existing modes equally.
In order to move away from the axiom of irrelevance of
independent alternatives, Hausman and Wise [1978] have proposed a
multinomial probit alternative. Except for a slight distinction
in the tails of the distributions, the cumulative normal and
logit distributions are quite similar. Hausman and Wise
demonstrate that the probit model with zero off-diagonal
13
-------
covariance terms is equivalent to the logit model. They
consequently add nonzero off-diagonal elements to the error
covariance matrix in order to capture substitution across sites.
Unfortunately, this approach requires one to integrate across all
available choices (sites) in order to estimate. The complexity
of this calculation reduces the number of alternatives possible.
Hausman and Wise, themselves, only use three alternatives and
they suggest that current algorithms can handle no more than five
sites. Of course, five sites is totally inadequate for
developing an index of quality. With only five different
combinations of characteristics, there is no reliable way any
technique could sort out the individual contribution of two or
more characteristics to quality.
A second approach to relax the substitution assumptions of
teh logit model has been suggested by McFadden [1981] . He
suggests using the logit model to estimate a decision tree. With
a decison tree, the multiple site choice problem can be divided
down to a series of more limited choices. For example, to be
completely free of the independence axiom, one could focus on
binomial decisions entirely. For example, the consumer would
first choose which of two classes of sites to visit, then which
of two major subclasses within the chosen class, and ... finally
which of the remaining two sites to visit. Of course, estimation
of this sequential model could follow exactly the reverse process
starting with multiple pairs of sites and ending with a single
pair decision.
The basic problem with the decision tree framework is that it
is arbitrary. Instead of a single restrictive but simultaneous
comparison across all sites, the decision tree framework provides
a highly structured series of pairwise comparisons. Although
this serial analysis is more flexible in that substitution across
sites can vary, the specific order of comparisons dictates the
final substitution observed. In McFadden [1981], the
coefficients depended upon the decision tree chosen. Since
theory does not dictate which tree is to be preferred, the
results of any single tree are arbitrary. It is clearly
important to explore under what conditions a single tree could be
chosen. It would also be helpful to know when all the trees will
provide consistent responses. Unfortunately, it is likely that
the limiting condition is precisely the order independence which
the technique is designed to avoid.
CONCLUSION
This paper is intended to be a critical appraisal of the
state-of-the-art of recreation modelling. Focusing upon the
relative merits of each revealed preference approach, the
limitations of restrictive assumptions underlying each method
have been emphasized. It is important, however, not to lose
sight of the tremendous progress in this area and of the high
quality of current research. Today, the applied researcher has
many options to estimate the value of sites and their
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characteristics. Each of these methodologies are soundly based
in economic theory and econometric practice. Resource valuation
is one of the most exciting and powerful components of natural
resource economics.
Of course, new ideas and new applications generate as many new
quaestions as they answer. Each methodology would clearly
benefit form specific additional research. The aprtitioning
approach, for example, could use some formal work on optimal
grouping or clustering strategies. The appropriate choice of
decision trees in discrete choice models deserves attention. The
bias and lack of precision from the absence of site substitution
in the generalized travel cost model needs to be studied. The
effect of site changes on the hedonic travel cost price gradient
needs to be known.
We, as a profession, are on the edge of measuring the value
of a host of natural resources which have historically escaped
measurement. With adequate support, these new methodological
capabilities can be turned into a vast array of promising new
management and policy techniques.
15
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Bibliography
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Method" Review of Economics and Statistics 66 (Aug.1984) , 427-433.
Burt,Oscar and Durwood Brewer, "Estimation of Net Social Benefits
from Outdoor Recreation, "Econometrica 39 (Sept.1971), 813-828 .
Cesario,F. and Jack Knetsch, "A Recreation Site Demand and
Benefit Estimation Model" Regional Studies 10 (1976),97-104.
Cichetti,Charles, Anthony Fisher, and V.Kerry Smith, "An
Econometric Evaluation of a Generalized Consumer Surplus Measure:
The Mineral King Controversy" F.mrinmpt- r i ra 44 (Nov.1976),1259-
1276.
Clawson,Marion, "Methods of Measuring the Demand for and the
Benefits of Outdoor Recreation" Reprint No. 10, Resources for
the Future, Wash. D.C. 1959.
Desvousges, William, V.Kerry Smith, and George McGivney, "A
Comparison of Alternative Approaches for Estimating Recreation
Related Benefits for Water Quality Improvements"
U.S.EPA,Washington D.C, EPA-230-05-83-001, (1983).
Domencich, T. and D. McFadden. Urban Travel Demand (New York:
American Elsevier Publishing Company. 1975.
Englin,Jeff and Robert Mendelsohn, Measuring The Value of
Managing Forests For Outdoor Recreation". Prepared for the U.S.
Forest Service,Washington D.C. 1985.
Ewing,Gordon, "Progress and Problems in the Development of
Recreational Trip Generation and Trip Distribution Models"
Leisure Sciences 3 (1980) 1-24.
Freeman,Myrick III,The Benefits of Environmental Improvements
(Baltimore:Johns Hopkins Press,1979).
Hanemann,Michael, "Discrete-Continuous Models of Consumer
Demand" Econometrica 52 (May 1984),541-61.
Hanemann,Michael, "Multiple Site Demand Models" in Nancy
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Bockstael,Michael Hanemann, and Ivar Strand (eds.) Measuring
the Renefit s Water Quality Improvement Usi ng Rt?r?rt?a t i on
Demand Dept. of Agr. and Res. Economics,University of
Maryland,1985.
Hausman,Jerry and David Wise, "A Conditional Probit Model for
Qualitative Choice: Discrete Decisions Recognizing
Interdependence and Heterogeneous Preferences" Econometrica
46 (1978),403-26.
Huff,D. "A Probabilistic Analysis of Consumer Spatial
Behaviour" in W.S.Decker (ed.) Emerging Concepts ir
MarketingProceedings of Winter Conference of Amer. Mar~
Assoc. Chicago,1962.
King, Thomas, "The Demand For Housing: A Lancastrian
Approach".Southern Economic Journal 43 (176) , 1077-87.
Livengood,Kerry,"Value of Big Game From Markets for Hunting
Leases: the Hedonic Approach" Land Economi cs 59 (1983), 287-91.
Luce,R. Individual Choice Behavior: A Theoretical Analysis (New
York: Wiley,1959)
McFadden,Daniel,"Econometric Models of Probabilistic Choice"
in Charles Manski and Daniel McFadden (eds.) St riir.tn ra 1
Analysis of Discrete Data wi th Econometric Applications
(Cambridge:MIT Press,1981).
Mendelsohn,Robert,"Emission Transfer Markets: How Large
Should Each Market Be?" in Buying a Better F.nvi ronment.
E.Joeres and M. David (eds.) Land Economics Mongraph No. 6
(1984a),25-38.
Mendelsohn,Robert,"Estimating the Structural Equations of
Implicit Markets and Household Production Functions", Review of
Economics and Statistics 66 (Nov.1984b), 673-677.
Mendelsohn,Robert,"An Application of the Hedonic Travel Cost
Framework for Recreation Modeling to the Valuation of Deer" in
Advances in Applied Microeconomics(ed.V.K.Smi th) , Vol.3(1984c),89-
101.
Mendelsohn,Robert,"Identifying Structural Equations with
Single Market Data" Review of Economics and Statistics
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(forthcoming) 1985.
Mendelsohn,Robert and Peter Roberts,"Estimating the Demand
for the Characteristics of Hiking Trails: An Application of
the Hedonic Travel Cost Method",Dept. of Econ. University of
Washington,Seattle,1983.
Morey,Edward, "The Demand for Site-Specific Recreational
Activities: A Characteristics Approach" .Tnnrna 1 Q f
Environmental Economics and Management 8 (1981) 345-371.
Morey,Edward, "The Choice of Ski Areas: Estimation of a
Generalized CES Preference Ordering With Characteristics" The
Review of Economics and Statistics (forthcoming) (1984) .
Palmquist,Raymond,"The Demand for Housing Characteristics:
Reconciling Theory and Estimation". Working Paper No.25,North
Carolina State University,Dept. of Econ. and Bus.1982.
Rosen,Sherwin,"Hedonic Prices and Implicit Markets: Product
Differentiation in Pure Competition" Journal of Political Economy
82 (January 1974),34-55.
Strazheim,Mahlon, "Estimation of the Demand for Urban Housing
Services From Household Interview Data" Review o f Economics and
Statistics 55 (February 1973),1-8.
Sutherland,Ronald, "A Regional Approach to Estimating Recreation
Benefits of Improved Water Quality" J. o f Envi ronmental Economics
and Management 9 (1982), 229-47.
Vaughn,William and Clifford Russell,The National Benefits of
Water Pr^l 1 i.it i nn Control : Fresh Water Recreational Fishing.
(Baltimore:Johns Hopkins Press,1983).
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A MODFLTO FSTIMATFTIIF ECONOMIC IMPACTS ON RFCRFATK)NAL FISIIINC.
IN TIIF ADIRONDACKS FROM CURRFNT LFVFLS OF ACIDIFICATION
-- DRAFT --
Prepared for:
AFRF Workshop on
Recreation Demand Modeling
May 17-18. 1985
by:
Daniel M. Violette
Fnergy and Resource Consultants. Inc.
P.O. Drawer ()
Boulder. Colorado 8()i5()(>
(:?(>:?) /i/m-fsfsifs
afrft
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1.0 INTRODUCTION
The analysis contained in this paper is part of a project whose goal is to estimate the
economic damages to recreational fishing from current levels of acidification. The
Adirondack Mountain region was selected as the focus for this study since it is the region
where current levels of acidification are believed to be having the greatest deleterious
effect on fish populations. Acid deposition is commonly viewed as a regional problem
since large portions of Pennsylvania. New York. New England and Eastern Canada have
high levels of deposition. However, from the perspective of damages to fish populations,
the fresh water effects of current levels of acid deposition are expected to occur in nar-
rower geographic areas. Two factors must interact before fish populations will experi-
ence adverse effects -- one. the watersheds must be exposed to high levels of acid depo-
sition; and two, the watersheds must be sensitive, i.e., have a low buffering capacity.
Even though broad regions are exposed to high levels of acid deposition, the sensitive
lakes and streams tend to be grouped into smaller areas. Our current efforts are focused
on examining the benefits of reductions in acidification in New York. The regions con-
taining sensitive lakes in New York are essentially limited to the Adirondack and
Catskills mountain regions, and the Hudson Highlands.
A traditional approach for estimating the economic value of recreational sites has been
to use the travel and on-site costs incurred by visitors as a proxy measure of the price
paid to use that site. Early travel costs studies focused on changes in the supply of sites,
i.e., the addition of a new site or the loss of an existing site. The estimation problem
faced by this project is different. Acidification will not change the number of sites
available for fishing, but will change the characteristics of those sites. The reason for
this is that it is not tractable to view each lake as a separate site. There are thousands
of lakes in the Adirondack Ecological Zone, which makes a lake by lake analysis impossi-
ble. Instead, each site must be viewed as a geographic area containing a number of
lakes. Each site can then be characterized by the number of lakes it contains that have
certain characteristics. Possible site characteristics include the number of acres of cold
water, two story, or warm water lakes. In this framework, acidification could, for exam-
ple. result in a change in the number of acres of cold water lakes that are able to support
fish populations. The estimation problem is to determine how a change in these site
characteristics will affect the value of that site as a recreational fishery.
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Two data sets were identified that contain data useful for an analysis of Adirondack
lakes -- the New York Anglers Survey and the Adirondack Ponded Waters Survey. The
New York Anglers Survey contains data on fishing activity throughout the state; how-
ever. the Adirondack Ponded Waters Survey only contains data on lakes and streams in
the Adirondack Ecological Zone. As a result, the geographic scope of the study was
necessarily limited to this area. This may not pose a significant problem for a national
assessment of damages, since documented damages to recreational fisheries at current
levels of deposition have largely been limited to the Adirondack Mountain regions. Lakes
and streams in New England. Minnesota. Wisconsin and selected areas in other regions of
the U.S. are sensitive to acid deposition and may be affected in the future. Neverthe-
less, at the current level of acidification most deleterious effects on recreational fish-
eries are felt to be occurring in the Adirondack Mountains.
The recent environmental benefits estimation literature contains several approaches for
incorporating site characterisitics within a travel-cost framework. Prominent applica-
tions incorporating site characteristics into a travel cost model are Vaughan and Russell
(1982); Desvousges. Smith and McGivney (1983); Morey (1981); Greig (1983); Brown and
Mendelsohn (1984); and Bockstael. Hanemann and Strand (1984). This literature includes
several diverse approaches each with certain strengths and weaknesses. The use of site
characteristics in travel cost models is a recent development. As a result, new applica-
tions and techniques arc1 currently being researched.
The problem of incorporating site characteristics within a travel cost model can be illus-
trated using a conventional Burt and Brewer (1971) type travel cost model. This "conven-
tional" travel cost model estimates a separate demand equation for each fishing site.
These demand functions for "n" fishing sites are shown below.
Site 1 equation: Vlq = B10 + Bn Pn + BJ2 Pj2 + . . . + Bjq Plq + Sqj + U
• • •
(eq. 1)
• • •
Site n equation! VRq = Bn0 + Bnl P„, ~ \2 Pn2 + ... + Bnq Pnq + Cnj Sqj ~ U
where:
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V:n_ the visitation rate to site i from origin q. usually measured in visitors per
10.000 people
Pjq = the price of visiting i from origin q in terms of travel and time costs.
Bjq= the regression coefficients on the price variables
Sqj = socioeconomic variables for origin q
Cnj = regression coefficients on socioeconomic variables
U = random term
For example, the data that would be used to estimate the site 1 equation is simply the
visitation rate, and the travel costs from each of the q origins to each site. The underly-
ing assumption is that the visitation rates to site 1 will be lower for origins more distant
from site 1; that is, as the costs of traveling to site 1 increase the visitation rate will
decline.
In this conventional travel cost model, it is not possible to examine how the character-
istics of the site affects the visitor's demand function. The equation for each site is
estimated separately. As a result, there can be no variability in the site characteristics
of just one site. Several different approaches for incorporating site characteristics
within a travel cost framework have appeared in the recent literature. These new
methods can be classified into several basic approaches:^
1) The varying coefficient travel cost model as characterized by Vaughn
and Russell (1982). and Desvouges. Smith and McClivney (198.']);
2) The explicit utility function approach as characterized by Morey
(1981) and f,rieg (198,']);
:$) The hedonic travel cost model as developed by Brown and Mendelsohn
(198/1).
A variant of the varying coefficient travel cost model was selected for this application.
The varying coefficient travel cost model approach selected for use in this project is
similar to that used by Vaughn and Russell (1982). and Desvouges. Smith and McGivney
(1983). This approach utilizes a two step framework. The first step consists of estimat-
ing a separate visitation-travel cost equation for each site. The second step uses the
* W.M. Hanemann in Chapter 9 of Bockstael et al. (1984) presents a random utility model
based travel cost formulation which also incorporates site characteristics.
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regression coefficients from the step one equations as dependent variables and regresses
these coefficients on the site characteristics. To use a simple example, the conventional
Burt and Brewer visitation demand function for site "i" is:
Viq = Bio + Bil Pi2 + — + Biq Piq N- 2)
where Vj is the visitation rate from origin q to site i and P^q is the travel cost from
origin q to site i. Since a separate equation is estimated for each site, there are "i" dif-
ferent estimates of each coefficient. These regression coefficients represent the rela-
tionship between travel costs and visits. The variability in the magnitue of the regres-
sion coefficients in the different site equations are likely to be due to the relative
desirability of the site in terms of the site's characteristics. This can be tested in the
second step regressions where the regression coefficients are regressed against the char-
acteristics of each site:
Bi0 = A00 + A01 Zli + — + A0k Zki
Bil = A10 + A11 Zli + — + Alk Zki
((HI. .0
• •
• •
Biq = Aq0 + Aql Z li + — + Aqk Zki
where is the level of the k^ characteristic at site i and the A-^ are new regression
coefficients on the site characteristic variables. This two step procedure can be com-
bined into an equivalent one step method by substituting equation 3 into equation 2 to
yield:
Viq = (A00 + A01 Zli + — + A0k Zk0 + (A10 + A11 Zli + — + Alk ZkP Pil + • * *
+ (Aq0 + Aql Zn + ... + Aqk Zki) Piq. (eq. 4)
Equation 4 includes both site characteristics and travel costs as interaction terms. This
equation can be estimated using pooled data across sites.
Generalized least squares (GLS) procedures should be used to estimate equation 3 or
equation 4. This two stage procedure will introduce heteroskedasticity into the error
term of the second stage regressions. The second stage regression using only one site
characteristic as the dependent variable is:
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Bi0 =
v00
+ A
01 Lv
(eq. 5)
The dependent variable Bjq is an estimated regression coefficient from the first stage
regression; therefore, the error term for the regression shown as equation (5) is in-
fluenced by the error in the estimated coefficient. This introduces heteroskedasticity in
the regression equation error term. Simply stated, if the estimated variance of Bjq from
the stage 1 regression in large (i.e., B^q is estimated imprecisely) this will influence the
error term in the regression shown in equation (5). This can be corrected by using GLS
procedures where the estimated standard errors for the regression coefficient from each
site are used as the correcting weights.
The two applications of varying coefficient travel cost model cited previously -- Vaughan
and Russell (1982). and Desvousges. et al. (1983) - found site characteristics to be sig-
nificant in the second stage regression equations. The available data and nature of the
estimation problem makes this application of this technique to the Adirondacks some-
what different from these previous applications of the varying coefficient approach. For
example, Vaughan and Russell (1982) used a sample of fee fishing sites in the North-
eastern United States. These sites were typically widely dispersed geographically making
it unlikely that visitors to one site would have also visited another of the sites included in
the data set and, even if they did, there was no way to learn this from the data. The
Desvousges et al. (1983) visitation data was from 46 U.S. Army Corps of Engineering
recreation sites. Again, these sites were scattered throughout the United States. These
applications can be contrasted to the Adirondacks region being examined in this project
where all of the sites are located in a small region and are, in fact, adjoining. This
results in a visitation data set where many fisherman have1 visited more1 than one site.
The specifics of the data available for this project made it desirable to use a variant of
this two stage approach. Instead of using ordinary least squares techniques to estimate
the coefficients of the first stage site demand equations, a Tobit procedure is used. The
Tobit estimation procedure is able to take full advantage of the available data on
individual fishermen. First used in Tobin (1958). the Tobit procedure estimates both the
probability of an individual visiting a given site as well as the number of days the
individual will spend at that site, given that a visit is made. Taken together, these two
estimates can be used to calculate the expected value of days spent at each site for each
individual.
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The procedure used to incorporate site characteristics within this travel cost model is
very similar to the varying coefficient travel cost model as depicted by equations 2 and
3. The only difference is that the first stage regression coefficients of equation 2 are
estimated using a Tobit procedure. In the second stage, these regression coefficients are
used as the dependent variable and regressed against the site characteristics using a
generalized least squares procedure to correct for heteroskedasticity.
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2.0 DATA
There were two main data sources for this project. These were the 197(5-1977 N(>w York
Angler Survey and the Adirondack Lake and Pond Survey (Ponded Waters Survey). Both
data sets were compiled by the New York State Department of Environmental Conserva-
tion (NY DEC).
2.1 THE NEW YORK ANGLER SURVEY, 1976-1977
The New York Angler Survey for 1976-1977 is the most recent data source from which
information on fishing activity and travel costs can be compiled for the Adirondacks.
The Angler Survey consisted of a questionnaire mailed to a three percent sample of fish-
ermen licensed in New York State between October 1. 1975 and September 30. 1976. The
questionnaire elicited responses about fishing activity in New York State between April
1. 1976 and March 31. 1977. Of the 25.564 questionnaires mailed. 11.721 responses were
received.
The questionnaire consisted of three major sections: one - fishing activities, expendi-
tures. and preferences; two - attitudes and opinions; and three - participant background.
The first section of the Anglers Survey examined fishing activities, expenditures and
preferences. This section collected data on where, for how long, for what species, and by
what methods the respondent fished. Data on expenditures per fishing location for that
year and for total equipment expenditures were also requested. Questions relating to
preferred species, reasons for fishing and what makes a fishing trip successful were
included in this section. The attitudes and opinions section of the Anglers Survey was
mainly concerned with New York's fisheries management programs, procedures and regu-
lal ions.
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The participant background section elicited information on fishing background, whether
or not the respondent belonged to a fish and game club, other recreational activities, and
household income. A summary of the Angler Survey appears in Kretser and Klatt (1981).
Since the 1976-77 Angler Survey gathered information on fishing throughout New York
State, it was necessary to select only observations on fishing trips to the Adirondacks
region. Fishing locations in the Angler Survey are identified by name of water and
county. Relevant observations for this project were chosen by selecting only those fish-
ing locations in counties in which the Adirondacks lie. The counties included are:
Clinton. Essex. Franklin. Fulton. Hamilton. Herkimer. Lewis. Saint Lawrence. Saratoga
and Warren. This resulted in data on 3015 individual anglers who visited 6053 fishing
locations. Thus the average angler who fished in the Adirondacks fished at two different
locations within the Adirondacks.
The 6053 visits by individuals were to 760 different fishing sites. 504 of which were lakes
and ponds, the remainder being rivers and streams. Since adequate site characteristic
data was available only for lakes and ponds, the effective sample size was further
reduced to data on visits to the 504 lake and pond locations.
Data on expenditures in transit to the site and at the site were requested by the Angler's
Survey although not all individuals reported these expenditures. Travel expenditure data
was available for 62.3 percent of the 6053 sites, and on-site expenditure data for 57.3
percent of these sites. Expenditures on equipment were also requested, but improperly
coded and entered onto the tape, therby making this data unuseable.
The Angler's Survey contained no data on distances traveled to each site or time spent
traveling to the site. Distance1 data was estimated manually using the1 Zip Codes included
in the Angler Survey. Given the large number of observations, this was a time consuming
task. Travel time was approximated by assuming an average driving speed and dividing
distance1 by this speed.
Socioeconomic and other respondent background data contained information on household
income, date of birth, years of education, and years of fishing. Other questions in this
section concerned whether the individual had a preferred species to fish for. whether or
not the respondent was a member of a fish and game or other sportsmen's club, and their
participation in other recreational activities. A number of attitudinal questions were
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also included which examined the individual's reasons for fishing, factors important to a
successful fishing trip, and limiting factors for respondents who do not fish as often as
they would like.
2.2 ADIRONDACK LAKE AND POND SURVEY
Site characteristic data was obtained from the Adirondack Lake and Pond Survey*
(ponded Waters Survey). This data base includes information on 3506 ponded waters in
the Adirondacks area. The Ponded Waters Survey is not entirely comprehensive; not
every ponded water in the Adirondack area has a complete record. For example, there
are only 2409 pH records in the most recent chemistry survey data for those waters
which have been surveyed. Also, not all lakes and ponds are surveyed each year. The
most recent survey for a particular water may have been last year, or it may have been
20 or more years ago. Only 1217 of the 2409 pH records date from 1960 to the present.
The New York State Department of Environmental Conservation (NY DEC) is continuing
to update this data base.
The data in the Adirondack Lake and Pond Survey refers to ponded waters only. Stream
fishing is also important in the Adirondacks. There are approximately 5,000 miles of
coldwater fishing streams in the Adirondacks, with about 3500 miles of these open to
public fishing (Pfeiffer, 1979). Over 700 miles of warmwater fishing streams also exist,
with approximately 480 miles open to public fishing (Pfeiffer, 1979). Unfortunately,
stream characteristic data are not as readily available as ponded water data in the
Adirondacks. Miles of streams open to public fishing appears to be available on a county
basis, but may be difficult to obtain on a more disaggregated basis.
Of the general site characteristics, surface area and elevation were the best available,
existing for at least 80 percent of the waters. Shoreline length would be a useful alter-
native to surface area and is listed as a variable in the documentation, but it did not
exist for any waters. Another potentially useful characteristic listed in the documenta-
tion but for which no data exist is the distance to nearest public road or trail. This
accessibility measure could have been quite useful. The public or private ownership
* This survey is continually updated. The survey used in this analysis was the version
available1 in February. 198-1.
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classifications can be useful if it is desired to limit the number of ponds, or surface area
in a site to only those open to public use.
The current management class of a water can be useful for determining the different
types of fishing opportunities available within a site, and their relative importance.
Management classifications in the survey included warm water, two story, cold water and
brook trout fishery classifications. Although only 38 percent of the waters were cate-
gorized by management class, these waters comprise 87.7 percent of the total measured
surface area. Thus this variable may be used with a reasonable level of confidence.
Two issues surround the relevance of the pH and alkalinity data which are available. One
is the fact that much of the data, perhaps a large portion, may be extremely old and thus
no longer accurate. Secondly. pH data existed for only 35 percent of measured surface
area and alkalinity for only 52 percent. As a result, estimates of the effect of acidifica-
tion on fishable acreage of ponds made by others were used in this analysis. Other
research in the National Acid Precipitation Assessment Program has calculated the
change in fishable acres due to acidification
Since 7% minute quads were chosen as the components of the sites, the data extracted
from the original Ponded Waters tape for each individual water needed to be aggregated
by quads. In the current formulation, site characteristics are defined in terms of surface
area. For a given quad containing a number of lakes and ponds, one characteristic is the
total surface area of these ponds. Surface area is also broken down by various discrete
categories of other relevant characteristics. For elevation, there is surface area below
1500 feet, between 1500 feet and 2000 feet, and above 2000 feet. Surface area is also
broken down by the various fishery management classes and ownership categories.
2.3 INTEGRATION OF THE ANGLERS SURVEY AND THE PONDED WATERS SURVEY
The Angler Survey and Ponded Water Survey used different methods for identifying par-
ticular bodies of water and a mapping from one code to the other was necessary. Indi-
In this report, NAPAP funded work by Dr. Joan Baker at North Carolina State
University was used to obtain estimates of how acidification will affect the acreage of
water available for fishing.
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vidual waters in the Ponded Waters Survey are identified by a watershed and pond num-
ber combination. For the Angler Survey, a water name and county was supplied by
respondents. A code was created by the NY DEC for identifying waters in the Angler
Survey which consisted of locating the water in the report. Characteristics of New York
Lakes, Part 1 -- Gazatteer of Lakes, Ponds and Reservoirs (Greeson and Robison,
1970). This was done by coding each water by a number where the first two digits indi-
cated the page and the second two digits the line of the Gazatteer listing the water name
and location. The result was a time consuming process where each lake or pond in the
Anglers Survey had to be be looked up by hand in the Gazatteer and matched to a lake
with hopefully the same name and location in the Ponded Waters Survey. NY DEC per-
sonnel cautioned against a one-to-one mapping of waters due to concerns with the Angler
Survey. A particular concern was that anglers may not always know exactly where they
fished. They may believe they are at one lake or pond when they are actually at a dif-
ferent lake nearby. Or they may use a name for the lake which is different from the
official name for that lake. Also, there can be several lakes within a county with the
same name. In these cases NY DEC personnel had to use their judgement, based on
knowledge of popular fishing areas and species availability in these waters, in coding
fishing locations. Since1 both the Gazatteer and the Ponded Waters Survey include1 identi-
fication of the 7Yi minute USGS quadrangle in which a water's outlet lies, the fishing
locations from one survey to the other were mapped on the basis of 7& minute quads. As
a result, even if the fisherman gave the name of a nearby lake in error, his visit will still
be mapped to the correct site as long as both lakes are in the same 7J& minute quadran-
gle. A more detailed discussion of site selection will be given below.
2.4 SITE SELECTION
Defining sites to be used in the travel cost model raised several issues. One of these
issues has already been discussed, namely the problem of not being able to cross-
reference waters between the Angler and Ponded Waters Surveys on a one-to-one basis.
The use of 7J£ minute quads should serve to mitigate this issue. However, the use of 7&
minute quads poses other problems. Most importantly, the 7Yz minute quad associated
with any lake or pond refers to the quad in which that water's outlet lies. For large
bodies of water, this quad could be several miles from where an angler actually fished.
In other cases, a group of lakes may cross several quad boundaries yet still exist in rela-
tively close proximity with easy access from one to the other, making this group of lakes
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a reasonable candidate for a site (destination). There are few major roads within the
Adirondack^, thus accessibility was another site determinant.
The issues mentioned above were considered when aggregating the individual 7J£ minute
quadrangles into larger sites. The sites were constructed by grouping together as geo-
graphically homogeneous IVi quads as was possible. If the outlet of a lake was in one 7&
minute quad while the body of the lake was in a neighboring quad, both quads were
included in the same site. Sites were also constructed to include groups of similar lakes
such as the Saranac Lakes. Another consideration was the highway system where quads
having a common access were included in the same site. From an empirical viewpoint,
there have to be enough sites for sufficient degrees of freedom in the second step regres-
sion. A site specification resulting in 24 sites was ultimately decided upon.
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Energy and Resource Consultants, Inc.
3.0 THE MODEL
This chapter is divided into three sections. Section 3.1 presents a simple participation
model. A participation model relates recreational activity to the supply and quality of
recreation opportunities available at different sites. Compared to travel cost models,
participation models have less stringent data requirements and assumptions. Participa-
tion models do not use data on travel costs and. therefore, the assumptions required for
travel costs to serve as the basis for calculating consumer surplus based values for the
recreation activity do not have to be imposed. However, participation models do not
have the ability to infer values for the resource from the empirical analysis, but the
model can show how participation is expected to change as recreation opportunities
increase due to improved water quality. If the value of additional recreation days can be
inferred from other sources, then an estimate of the value of the improved water quality
can be obtained by multiplying the increase in recreation days times the value per day.
An empirical model designed to estimate the value of the resource for recreational fish-
ing is presented in Sections 3.2 and 3.3. Section 3.2 takes advantage of the data availa-
ble on expenditures to obtain an estimate of the average per mile travel cost incurred to
produce one fishing day. The ability to estimate this dollars per mile per fishing day
travel cost is important for the analysis since the visitation data from the Anglers Survey
is expressed in terms of fishing days spent at a site and the survey did not contain
information on whether these days were all taken during one trip, two trips or many
trips. Section 3.3 presents the estimation of the relationship between travel costs and
fishing days at each site. Section 3.4 incorporates the characteristics of the site into the
travel cost framework.
3.1 PARTICIPATION MODEL ESTIMATION
The first step analysis of the visitation data consisted of the estimation of a simple par-
ticipation model. As was discussed above, participation models have less stringent data
requirements and assumptions than do travel cost models but they entail the loss of the
3-1
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Energy and Resource Consultants, Inc.
ability to infer values from the estimated model.1 This model relates the number of
fishing days at each of the 24 sites against selected characteristics of the site. The site
characteristics that were used include measures of fishable acres of lakes and ponds, and
the total catch rate defined as the average number of fish caught per fishing day at each
site. Once this model is estimated, it is possible to calculate an estimate of the change
in fishing days due to a change in the site characteristics. In this participation model,
travel costs and distances traveled were not considered, but they are incorporated into
the next phase of the analysis procedure.
The results of the participation model runs are shown in Table 3-1. The coefficients on
the fishable acreage variables are significant in all runs and the magnitudes of the coef-
ficients were consistent across the different specifications. The coefficients on the
acreage variables ranged in magnitude from .061 to .0978. with the majority of the coef-
ficients clustered between .0845 to .0978. The one exception was the coefficient on the
acres of cold water in equation 2 which had a negative sign, but was not significant.
These data show a relationship between the total number of fishing days spent at a site
and fishing opportunities as measured in fishable acreage.
The total catch rate variable did not perform as well as the acreage variables. The catch
rate variable was significant in two of the specifications, but the magnitude of the coef-
ficients varied considerably -- from 49.8 to 199.4. The lack of stability of the coeffi-
cients on the catch rate variable would tend to make predictions based on this variable
less reliable.
The reasonableness of the magnitudes of the coefficients on the acreage variables can be
examined by performing some calculations using equation 1 from Table 3-1. The mean
values across all 24 sites for the variables total days, acres of warm water, and acres of
two story ponds are 1145.8 days, 4516 acres warm water, and 3645 acres of two-story
ponds. Using these values as depicting an "average site." the effect on total fishing days
of a 10 percent reduction in fishable acreage can be calculated:
days = .0958 x (4,r) 1.(5) + .OSIfK.mf))
= 7/l.()6 days
1 This is discussed in more1 detail in Freeman (1979). Chapter 8.
3-2
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Table IM
Participation Models With Total Fishing Days at a Site as the Dependent Variable
((-values are in parentheses)
Regression Park
Number Acres
Acres
\\ a rm
\\ atci
Acres
I wo
Story
Acres
Acres at
less than
1.500 leet in
Klevat ion
I ota
Latch
.084 f)
G5.80)
rz.iM
(./l 18)
.08.) 1
05.90)
-.MO
49. 84
(fUM)
<.849
.0972
(4. f>9)
(-i.:w)
199.4
(1.97)
.0978
(.r).(>(>)
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Energy and Resource Consultants, Inc.
The net result of a 10 percent reduction in fishable acreage at the "average" site is a
reduction of 74 fishing days, or a 6.5 percent reduction in fishing days at the site.
One problem that possibly limits the usefulness of these participation models is the lack
of significance of the cold water acreage variable. Acid deposition is expected to largely
affect cold water lakes and ponds and to have a much smaller effect on warm water and
two-story lakes and ponds. To further examine this particular issue, a second set of par-
ticipation models were estimated. Rather than using total fishing days as the dependent
variable in this model, a new variable defined as brook trout fishing days was used. This
variable was constructed by taking all the days at each site where the individual reported
to have caught at least one brook trout. Other species of fish may have been fished for
and caught as well, but if brook trout were caught, then these days were classified as
brook trout days.
The result of the participation models using brook trout days at each site as the depend-
ent variable are shown in Table 3-2. In contrast to the participation models using total
fishing days, the cold water acres variable in this model had the appropriate sign and a t-
value of 1.38. Although the t-value is low, it is significant at the 80 percent confidence
level with a two-tailed test and significant at the 90 percent level with a one-tailed
test. The catch rate variable was significant and was stable in magnitude across the
specifications examined. These models indicate that a reduction in the brook trout catch
rate from four fish per day to three fish per day would reduce the number of fishing days
at that site by approximately 37 days. Also, the coefficient on the cold water acres
variable was similar in magnitude to the coefficients on the warm water and two-story
acreage variables in the total fishing day participation models.
3.2 ESTIMATION OF PER MILE TRAVEL COSTS
The data contained in the New York Anglers' Survey presents certain problems for its use
in a travel cost valuation model, but it also has certain advantages relative to the type of
data commonly used in travel cost models. One problem with the Anglers' Survey data is
that it contains information on the number of days spent at a site rather than the number
of trips made to a site. This is the reverse of the problem typically faced by travel cost
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Table 15-2
Participation Models Using Brook Fishing Days as the Dependent Variable
((-values in parentheses)
u>
Ui
Regression No.
Cold
Water
Acres
Two
Story
Acres
Brook
Trout
Acres
Acres a(
Creator (ban
2000 l'( in
Klevat ion
Brook
Trout
Catch
Rate
R"
()verall
F
1.
.088
(1-58)
.008(5
(2.(57)
:i7.81
(2.22)
AAb
f).08
2.
. 022/l
(1-52)
152.,%
(1.(57)
.2:59
:5. 1 -r)
15.
.(KM
(.22/1)
.OOf)
(.22f))
U7.98
(2.88)
.:}(){)
:5.1:5
m
3
(ft
(Q
•<
a>
3
Q.
TO
n
in
O
c
n
(ft
r>
o
3
M
c_
—r
(k
3
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Energy and Resource Consultants, Inc.
models where there is data on the number of visits, but generally there is no information
on the duration of the stay. A positive aspect of the Anglers' Survey is that it contains
travel expenditures as reported by the individual. This expenditure data can be used to
obtain estimates of the per mile travel costs. These estimates may be preferred to esti-
mates from external sources such as the often used American Automobile Association's
(AAA) estimates of average travel costs since they may better represent the individual's
perceived travel costs (i.e., the costs on which individuals base their fishing location
decisions). Another advantage of this particular data set is that it contains information
on individuals who visited each site as well as those who chose not to visit the site. The
decision by an individual to not visit a site provides useful information that can be in-
corporated into the estimation of the visitation equation.
Since the New York Anglers' Survey only contains data on the number of days spent at a
site, having a fisherman indicate that he spent eight days at a site does not provide any
information on whether this was one eight-day trip, two four-day trips or four two-day
t rips. Depending on the number of trips taken to provide the eight fishing days at the
site, the travel costs associated with the production of those eight fishing days could be
very different. For example, assume the site is 100 miles away and travel costs are ten
cents per mile, then one round trip would cost $20.00. If the eight days at the site repre-
sented one trip, then the total travel costs to produce those eight fishing days would be
$20.00. or $2.50 per day. If the eight fishing days were the result of four two-day trips,
then the total travel cost would be $80.00. or $10.00 per fishing day.
This problem results in potentially large measurement errors in the estimated travel
costs. It could be solved if there were data on the number of trips and length of trips.
With such data, separate models could be estimated for trips of different lengths. The
problem faced by this analysis is not dissimilar from other travel cost applications that
have used data sets containing information on the trips to a site, but no information on
the number of days at a site. One commonly used procedure to get around this problem
is to use only trips of short distances that most likely represent only one-day outings and
then assume that all days spent at the site are one-day trips. This is a possible option but
is not desirable for this application since the purpose of the model is to obtain an esti-
mate of the total value of the resource. Using a subset of data that represents only one-
day trips could result in biased estimates.
3-6
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Energy and Resource Consultants, Inc.
Given the New York Anglers' Survey data set. the best option for the dependent variable
in the travel cost model was the number of days at the site. For this dependent variable
to be most meaningful in a travel cost model framework, an estimate of the travel cost
incurred per day is desirable. As was shown above, the travel cost required to produce
one fishing day will vary depending on the length of the trip. In turn, the length of trip
could be expected to depend on the distance to the site, the individual's income and other
factors such as the individual's fishing experience. The underlying problem is whether
the travel cost per day can be estimated given data on the distance to the fishing site,
and the number of days spent at the site. Fortunately, the New York Anglers' Survey
contained selected data on expenditures. The Anglers' Survey asked the following
quest ions:
o What amount was spent on travel to and from each fishing location in
each category:
food, drink and refreshments
- lodging
- gas and oil
fares on buses, airlines, etc.
Total expenditures on travel
o What amount was spent at each fishing location on:
food, drink and refreshments
- lodging
- gas and oil
- guide fees
access and boat launching fees
Total expenditures at the site
The goal of the statistical analysis presented in this section is to utilize this expenditure
data to obtain an estimated travel cost per mile per fishing day. If the travel costs
associated with one fishing day can be estimated, then the data on days at a site can be
successfully used as the dependent variable in a travel cost model. It was expected that
the travel costs per mile per day at a site would vary depending on the length of trip.
For example, if a fisherman were to travel 150 miles to reach a site, it is likely that he
would spend a greater number of days at the site than if he only had to travel 50 miles to
reach the site. The higher fixed costs that have to be incurred to reach the more distant
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Energy and Resource Consultants, Inc.
fishing sites would result in these costs being incurred only if the number of days spent at
the site were sufficient to offset the travel costs. For example, assume that out-of-
pocket travel costs are ten cents per mile. If a 50 mile travel distance is associated with
one-day trips, then the 100 miles traveled round trip would result in a total cost of $10 to
yield one fishing day. The travel cost per mile per fishing day would be $10 i-(100 mile *
1 day) = $.10. If 100 mile travel distances (200 miles round trip) are typically associated
with three-day trips, then the travel cost per mile per fishing day would be $20 i-(200
miles * 3 days) = $.033. This implies that the travel costs associated with producing one
fishing day are 3.3 cents per mile for a three-day trip.
3.2.1 Per Mile Travel Cost Estimation Results
The equations used to estimate the per mile travel costs all had the same basic specifica-
tion. Travel expenditures per day were expressed as a function of distance to the site,
the individual's income1, and the number of years the individual had been fishing:
Travel Expenditures per Day = Bj(Distance) + I^Income) + B^years fishing
experience)
The coefficient Bj on distance has the dimension of dollars per mile per day. If signifi-
cant, Bj can be used as an estimate of the travel costs per mile per fishing day. The
data were disaggregated into subsets of visits to sites that were 0 to 75 miles. 0 to 150. 0
to 225. and greater than 225 miles away from the fisherman's residence. Equations using
data on visits to sites 75 to 150 miles, and 150 to 225 miles were also estimated. Table
3-3 presents the estimation results using total travel expenditures per day as the depend-
ent variable. These results are encouraging. The coefficient on the distance variable is
highly significant in all equations except for visits to sites where the distance traveled is
greater than 225 miles. However, this is not surprising in that trips of this length are
more likely to be influenced by factors other than travel costs, in particular, income. As
can be seen from Table 3-3. the income variable was significant only for the longer trips.
The regression equations in Table 3-3 also show the expected relationship between travel
cost per mile per day and the distance traveled to the site. The average cost per mile
per day is higher for the shorter trips, reflecting that trips of short distances likely are
associated with fewer days spent at the site:
3-8
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Table A-A
Regression Results Using Total Site Travel Expenditures per day
As the Dependent Variable
((-values in parentheses)
»
¦>
Distance
Years
()verall
Regression No.
(t-value)
1 ncome
Kxperience
Constant
R"
F
1. Sites 0 to 75 miles from
,()()lv01
,2:54lv01
1.28
Residence
(8.11)
(1.1595)
(-1.77)
(2.(57)
.077
24.22
2. Sites 0 to 150 miles from
,55lv01
. 15:51v01
.418K-0:5
1.50
Residence
(9.78)
(.(>999)
(,29(5K-01)
(2.44)
.0(57
:52.(>:5
15. Sites 0 to 225 miles from
.4:598 IvOl
,24lv01
,2:54lv01
1 .:}:549
.0(5:55
:5().(52
Residence
(10.128)
(.91:57)
(1.42)
(1.95(5)
4. Sites greater than 225 miles
.544K-02
.1:58
-.082
(5.95
from Residence
(¦An)
(2.158)
(-2.07)
(1.(55)
.028
:5.04
5. Sites 75 to 150 miles from
,2:581v01
.482K-01
. 15(5 IvO 1
2.59
Residence
(9.50)
(1.98)
(1.02)
(4.17)
.049
:5:5.4(55
(). Sites 150 to 225 miles from
.97K-01
.(5:57(5
.1:52
-12.48
Residence
(2.05)
(-57)
(1.8(5)
(-1 :59)
.0:5:5
2.87
3
rt>
3
CL
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a>
CO
O
C
n
a>
n
o
3
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Energy and Resource Consultants, Inc.
Distance Traveled to Site
0 - 75
Estimated Travel Costs (t-value)
6.6C per mile per day
(8.11)
0 - 150
5.5C per mile per day
(9.78)
0 - 225
bAC per mile per day
(K).i.'O
groat or than 225
.05£ per mile per day
(0.38)
There is one anomaly in the estimated travel costs shown in Table 3-3. The regression
equation #5 on trips of 150 to 225 miles shows an estimated per mile travel cost that is
larger than those from the equations for visits of 0 to 75 and 75 to 150 miles. There may
be a number of reasons for this result. One possible cause could be a clustering of trips
with travel distances near the lower end of the 75 to 150 mile range; however, additional
analysis of the data would be useful in interpreting this result. Still, the travel costs for
the 0 to 75, the 0 to 150, and the 0 to 225 trip distance subgroups show the expected
relationship and these regressions would not be as sensitive to the clustering of trip dis-
tances within each range. The results of these regressions show a declining relationship
between trip distance and travel cost per mile per day.
A second set of regression equations were estimated using only oil and gas travel ex-
penditures per fishing day rather than total travel expenditures. These costs may better
represent the variable costs of traveling, since food and lodging would have to be pro-
vided on a trip of any distance. Tho same1 indopondont variablos woro usod in tho (estima-
tion. The results are shown in Table 3-4. Again the results are encouraging. The
coefficients on the distance variables are significant in all equations, except for the
visits to sites of greater distances:
Distance Traveled to Site
0 - 75
Estimated Oil & Gas Travel Costs (t-value)
5.8£ per mile per day
(7.8/1)
0 - 150
3.9C per mile per day
(9.71)
0 - 225
2.5C per mile per day
(8.58)
groator than 225
-,003£ per mile per day
(.:«>)
3-10
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Table IM
Regression Results Using Expenditures on Oil and Gas
((-values in parentheses)
Distance Years Overa
Regression No. (t-value) Income Kxperience Constant RJ F
v»
i
Sites 0 to 75 miles from
.579K-0 1
.258K-01
-,'1(571':-01
.8:51
.078
2:5.09
Residence
(7.8/1)
(1.72)
(-1.(579)
(1.9155)
Sites 0 to 150 miles from
.:KM77Iv01
.2527 K-0 1
-. 10(591v01
1,1(5
.0717
:5:5.() 1 (5
Residence
(0.71)
(1.515)
(-1.0(5)
(15.29)
Sites 0 to 225 miles from
.248K-01
. 28fM K-01
.7488K-02
2.1(5(55
.05
2(5.779
Residence
(8.58)
(i.(>:5)
(-.(589)
(4.75)
Sites greater than 225 miles
-.:52(5K-o:5
.101
-,'10:55K-01
/1.855
.0:5
:5.21
from Residence
(-.:«)K-oi)
(2.85)
(-1.59)
(1.827)
Sites 75 to 150 miles from
. 1015K-01
.489K-01
-.00(51
2.(52(5
.028
19.2(57
Residence
((5.42)
01.21)
-.(527)
((5.71)
Sites 150 to 225 miles from
-.1572 IvOl
.¦12:5Iv()l
.952K-02
1 1.97
.0092
.798
Residence
(-i.:«)0)
(•72(5)
(.2:5:55)
(2.15:55)
3
(V
(Q
-<
a*
3
CL
73
(V
w
O
C
o
(V
n
o
3
u>
C_
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3
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Energy and Resource Consultants, Inc.
A third set of regression equations were estimated using total costs (travel and on-site)
divided by days at the site. These equations were estimated for comparison purposes and
as a consistency check. These estimates include expenditures at the site and are not
appropriate for use as travel costs. Still, these estimates are informative. The coeffi-
cient on the distance variable is still dimensioned in dollars per mile per day. Also, it is
possible that site expenditures may be related to distance. If a greater distance is
traveled, then more activities may be required to make the time spent at the site worth
the incremental travel costs. Although this hypothesis is weak theoretically and is
entirely dependent upon the marginal utility and cost of activities available at the site
visited, it is easily tested with this data. The results of these regressions are shown in
Table 3-5. Again, the coefficient on the distance variable was significant except for the
longer trips and declined in magnitude1 as trips of longer duration were included:
Distance Traveled to Site Estimated Total Costs (t-values)
0 - 75 17.0C per mile per day
((;.ir>)
0 - 150 16.1^ per mile per day
(8.(M)
0 - 225 10.9£ per mile per day
(9.20)
greater than 225 per mile-day
(1.7)
Another result from the regressions presented in Table 3-5 worth noting is that income
was a more important variable for explaining total costs per day than for explaining
travel costs only. It seems intuitively plausible to have high recreation expenditures at
the site correlated with high individual incomes.
3.2.2 Estimated Travel Costs: Conclusions
The results of the travel cost estimation are encouraging and indicate that reasonable
estimates of travel costs to provide a fishing day can be obtained. As expected, these
costs tended to vary with the length of trip. In most travel cost models, the per mile
travel cost comes from a source such as the American Automobile Association's pub-
lished estimates of average travel cost per mile. This travel cost per mile estimate
3-12
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Table :5-5
VjJ
I
Vjj
Regression Results Using Total Travel and Site Expenditure per day* as the Dependent Variable
((-values in parentheses)
Distance
Years
()verall
Regression No.
(t-value)
1 ncome
Kxperience
Constant
R"
F
DF
1. Sites 0 to 75 miles from
.17
.01:5(5
-.0(5(5
:5.57
.0(57(5
1:5.91
57(5
Residence
((5.1/5)
(.2:52)
(-2.08)
(2.1(5)
2. Sites 0 to 150 miles from
.02.") 1
.227
.089
11.01
.021(5
:578
517
Residence
(1.J58)
(2.4 7)
(1.11)
(2.47)
15. Sites 0 to 225 miles from
.o-ifjn
.291
.01
4.90
.0:524
15.25
292
Residence
(1.70)
(2.(5/1)
(.14:59)
(.(ill)
4. Sites greater than 225 miles
.()")¦!
.17:59
-.827K-OJ5
10.")(5
.0:505
20.:}:}
19:58
from Residence
((5.78)
(:5./10)
(-.0257)
(8.95)
5. Sites 75 to 150 miles from
.161
.1107
-.22K-01
1.9:5
.0(5")
22.45
95.")
Residence
(8.0:5)
(1.151)
(-.4452)
(.8(57)
(). Sites 1 HO to 225 miles from
.1089
.1 158
.0187
:5.f)(5
.072:5
:}()..5(5
117(5
Residence
(9.20)
(l..r)(5(5)
(./11(5)
(1.85(5)
m
3
(0
(Q
-<
0)
3
Q_
TO
(0
v>
O
c
—I
n
(0
n
o
3
(/>
C_
—4*
(V
3
(/>
D
n
*I)ependent Variable is the individuals total expenditures on travel to the site (includes gas and oil. food and lodging in
transit), plus the cost of lodging, food and activities at the site divided by the number of days spent at the site.
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Energy and Resource Consultants, Inc.
poses problems due to the large variability in per mile costs that results from the varia-
bility in age and type of vehicles (compact cars as compared to Winnebagos).^ The esti-
mates obtained from the regression equations reported in this section are based on
reported expenditure data and, although subject to error, are probably no worse than
those used in other travel cost studies. These estimates may even be preferred in that
they may better represent the individual's perceived travel costs since they are based on
expenditure data supplied by the respondent; and, it is the perceived travel costs that
individuals use when making their site1 selections.
The estimation results are summarized in Table 3-6. The range of estimates for travel
costs per day for sites of different distances was quite narrow. The per mile total travel
costs ranged from 6.6 cents per mile per day for nearby sites (0 to 75 miles) to 4.4 cents
per mile per day as more distant sites were included in the sample (0 to 225 miles). The
estimates for only the oil and gas portion of travel costs were slightly less, ranging from
5.8 to 2.5 cents per mile per day.
3.3 TRAVEL COST MODEL ESTIMATION
Several different techniques were considered for use in estimating a relationship between
travel costs and fishing days. The data set available for use in this project is different
from the data sets typically used in travel cost models. To briefly review, the data set
contains information on individuals, the distances from the individuals' home to each of
the 24 sites, and the number of days that the individual spent at each of the 24 sites.
The fewest number of individuals visiting any site was 30. In estimating the site demand
function, the typical travel cost model would only use data on individuals that have
actually visited the site. This would result in observations on a sample of 30 individuals
being available for the least visited site. However, using data on only those individuals
that have actually visited the site ignores a substantial amount of information, namely
the travel distance to the site and characteristics of the individuals that did not visit the
site. For many of these individuals, the price in terms of travel costs to sites not visited
may have been too high relative to the costs of visiting other sites. This information is
pertinent to the analysis and should not be omitted from the estimation. As a result, it is
2
For example. Vaugan and Russell (1982) use the AAA estimate of 7.62 cents per mile.
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Energy and Resource Consultants, Inc.
Table 3-6
Summary of Kstimnted Kxpenditures per Mile1 jx^r Day
(t-values in parentheses, units are cents per mile per fishing day)
Kst imnted
Kstimnted
Kstimnted Totnl
Oil nnd Cns
Total Costs:
Distance to Site
Travel Costs
Travel Costs Only
Travel nnd Site1
0 to 75 miles
6.6
5.8
17.0
(8.11)
(7.84)
(0.1 r>)
0 to 150 miles
5.5
3.9
16.1
(9.78)
(9.71)
(8.03)
0 to 225 miles^
4.4
2.5
10.9
(10.1-1)
(8.58)
(9.20)
(1 renter thnn 225 miles
.05
-.003
4.6
i'M)
(.30)
(1.7)
* These travel cost estimates for trips of 0 to 225 miles were used in Chapter 5.0.
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desirable that the travel cost models for each site be estimated using the entire data
set. This would encompass those individuals in the sample that visited the site, as well as
those that did not.
A data set that contains observations on individuals who purchased the commodity (i.e..
made a trip to the site), as well as on individuals who did not purchase the commodity, is
termed a "limited" data set.-3 The data set is "limited" in that the dependent variable is
not observable over the entire range. In this case, the dependent variable is fishing days
at each site and is observable only when a trip to that site has been made. Therefore,
the dependent variable is observable only when it is greater than zero. The regression
mode1! is:
I) = BX + u; (:U)
where "D" represents the number of days spent at the site. D is observed only if D > 0.
Therefore, the model is:
D = BX + u if BX + u > 0. which implies u > - BX
or (H.2)
D = 0 if BX + u <_()
Applying ordinary least squares (OLS) regression techniques to only those observations
for which D > 0 results in biased estimates. The residuals in this equation will not satisfy
the OLS assumption that E(u) = 0. If some specific assumptions are made about the dis-
tribution of the residuals, then maximum likelihood techniques can be used to estimate
the parameters. If it is assumed that u has a normal distribution with mean zero and
variance then the joint distribution of the observations is:
L-11 £-f (¦*#-> T! F(^)
1 2.
^ This discussion follows Maddala (1977). pp. 1(52-KM.
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where f(*) is the standard normal density function and F(*) is the cumulative normal
density. The first term corresponds to those individuals for which Dj > 0 and therefore is
known. The second term corresponds to those individuals for which all that is known is
that D-5.0. The earliest application of this technique was by Tobin (1958).
The use of OLS techniques rather than the maximum likelihood techniques discussed
above will result in biased estimates of the coefficients. If OLS is applied to the data
and D- = 0 is used for those individuals who did not visit the site, there will be many non-
visitors with a resulting concentration of observations at Dj = 0. The absence of any
negative D-'s in the sample will tend to keep the estimated regression equation above the
zero axis over the relevant range of the X's. but it will also tend to flatten the estimated
curve. This results in the estimated number of days spent at the site being underesti-
mated for individuals with a low travel price (i.e., short distance between the site and
individual), and overestimated for individuals with a higher travel price.
A TOBIT procedure is recommended to correct for this bias. The TOBIT analysis takes
into account both the individual's likelihood of visiting a given site and the number of
days spent at the site, given that the individual decides to visit the site. These two
values taken together can be used to calculate the expected value of days at each site
for each individual. The TOBIT procedures also produce consistent estimates of the
regression coefficients in equation 3.1. In this analysis, both TOBIT and OLS estimates
of the regression coefficients are derived and compared.
A separate travel cost equation for each of the 24 sites was estimated. In each case, the
dependent variable is the number of days spent at the site. The independent variables
were the distance to the site, the individual's income, and the individual's years of fishing
experience. Distance to the site rather than an actual travel cost estimate was used as
an independent variable to allow for easy sensitivity analysis around the estimated per
mile travel cost. If information on the marginal value of time (e.g. wage rates) across
the individuals in the sample had been available, then it might have been desirable to
include an estimate of actual travel costs and actual time costs to determine relative
influence of each cost on the willingness to take a trip. Since both the out-of-pocket
value of time components of travel costs are expressed on a per mile basis in this analy-
sis. using distance in miles as the independent variable provides the most general formu-
lat ion.
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Crocker et al., 1981) have been very low, an estimate that is biased on the high side, if
still found to be low. should provide useful policy information.
3.3.1 TOBIT Procedures Applied to Total Fishing Days
The TOBIT procedure in the SHAZAM econometric software package was used to esti-
mate the model. Table 3-7 presents the estimated regression coefficients obtained by
using this TOBIT procedure and total fishing days at a site as the dependent variable.
Table 3-7 shows that the distance variable was highly significant in most of the equa-
tions. The coefficients on the distance variable were significant at the 1 percent level in
eighteen out of the twenty-three estimated equations. The distance variable was not
significant or had the wrong sign in the equations for sites 10. 16 and 20.^ Inspection of
these sites showed that the total number of fishing days at these sites was in the lower
half of the data set. The coefficients on the income and the years of fishing experience
variables were generally not significant. The R-squares were low, typically varying
between .01 and .10 for those equations where the distance variable was significant.
While low. these R-squares are not atypical for travel cost models/
The regression coefficients in the TOBIT model should be interpreted a little differently
than conventional OLS regression coefficients. In the TOBIT procedure, an index "I" is
created which is a function of the independent variables. I = XA; where A is a vector of
normalized coefficients:
In = Ao + Alxln + A2 x2n + • • • + Ak Xkn> O'M)
where Ip is the value of the index for the n**1 individual given the values of the X^'s for
that individual. These normalized coefficients can be transformed into estimates of
the regression coefficients - the Bi's - by multiplying the Ai's by the calculated
standard error of the estimate:
Also, the equation for site 13 was not estimated due to an error in the program that
merged the distance data and the site characteristics data, the distances to site 13 were
inadvertently entered as zeros. The merging of the data sets involved two extremely
large data bases and was expensive. It was decided not to correct this error until it was
determined to be significant.
^ For example, see Brown and Mendelsohn (1984) and Desvousges. Smith and McGivney
(198,']).
3-19
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Table 15-7
Travel Cost Model Using Total Days as the Dependent Variable and
Estimated with a TOBIT Procedure
(t-values in parentheses)
te #
Distance
1 ncome
Years Fishing
Constant
R2*
1
-.0727
-.2(5(51
-10.457
.08:5
(7.71)
(.19)
(1.20)
(1.25)
2
-2752
-.40:58
.1052
-1.5800
.077
(8.152)
(1.(57)
(.88)
(.2(5)
3
-.0780
. 1205
-.0:502
-24.1571
.0018
05.52)
(.7(5)
(-50)
(5.: 50)
4
-. 179-1
.0928
-.1008
-10.915
.0:55
((5.51)
(.55)
(.95)
(2.58)
5
-. 1772
-.1298
. 1254
-25.871
.0(5
(5.(515)
(.5(5)
(5.(515)
(4.152)
6
-.8122
.1 121
-.8122
1.4(510
.074
(7.92)
(.28)
(7.92)
(.11)
7
-.072(5
.084:5
-.072(5
-2(5.9:51
.009
(2.40)
(.5:5)
(2.40)
(5.22)
8
-.2:550
.09(59
-2:550
-25.51 1
.077
(5.72)
(.40)
(5.72)
05.59)
9
-2877
2:5:54
.4:559
-158.819
.079
((5.154)
(.99)
(2.90)
(5.415)
10
.12(5(5
-.5:579
. 1250
-515.252
.001
(2.(52)
(2. :5(5)
(1.14)
(7.4(5)
11
-.0777
-.o:?()4
.00:58
-1(5.99(5
.011
(:5.:58)
(.2(5)
(.05)
(4.80)
12
-.1(5:58
.2017
-.0:545
-41.044
.00(5
05.18)
(.84)
(.2:5)
(5.44)
H
-.1:504
.: 5 5 4 2
.1484
-151.192
.01:5
05.81)
(2.47)
(1.59)
(5.77)
15
-.0842
.090:5
.0:5(5:5
-18.249
.007
05.11)
(.87)
(.58)
(4.715)
2
*Note: R between observed and predicted values.
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Table :5-7
Travel Cost Model Using Total Days as the Dependent Variable and
Estimated with a TOBIT Procedure
(cent inued)
2
Site # Distance Income Years Fishing Constant R *
16
-.0024
-.2005
-.04:52
-19.0:5(5
.000(5
(.11)
(1.75)
(.7:5)
(5.5(5)
17
-.1915
-.07:51
-.0072
-2(5.19 1
.01 19
05.5:5)
(-55)
(.0(5)
05.(55)
18
-.2:501
.0944
-.0174
-r>r>. 70 1
.007
(:u>7)
(.28)
(.09)
(5.22)
19
-,:589:5
.(5(507
.0915
-9.91:59
.058
(10.24)
(4.75)
(1.04)
(2.21)
20
.054:5
-.190:5
.27(54
-(58.58(5
.004
(1.12)
(.(5(5)
(1.78)
(7.94)
21
-.1912
-.081(5
.1727
-27.:570
.0117
(4.25)
(.415)
(1.59)
(4.41)
22
-.:«52()
-.0584
-.0794
.2548
.0:58
((5.(52)
(-57)
(.90)
(.05)
2:5
-./If),™
-.1:574
.1884
1.(5:500
.098
(10.85
(.95)
(2-51)
(-58)
2 1
-.152(52
.0428
-.09:55
.1:5:51
.027
(10.04)
(-52)
(1.22)
(.0:5)
2
Note: R between observed and predicted values.
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Figure 3-1
Expected Relationship Between the OLS Estimates, TOBIT
Estimates, and the TOBIT Generated Expected Valuesl
Figure 4-la - Standard TOBIT, OLS
Relationship ******** Expected Value
Estimate
Days
at
Site
OLS Slope Estimate (BD)
TOBIT Maximum Like-
lihood Slope Estimate
(+) v
>>.
Distance
(-)
Figure 4-lb - Relationship when the probabilities of an individual visiting the site
are less than .5 for all distances
Days
at
Site
+ A
a
D Distance
(-)
"'"This figure is similar to Figures 3a and 3b in Tobin (1958).
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o Cis the standard error of the dependent variable;
o f (*) and F (*) are the marginal and cumulative normal density func-
I ions.
As is shown in Figure 3-1. this method of calculating the expected value locus results in a
nonlinear relationship. The expected value locus will always be above the TOBIT maxi-
mum likelihood equation (i.e.. segment AC). At the left where the probabilities of visit-
ing a site are high, the expected value locus will approach AC asymptotically. At the
right where the probability of visiting a site approaches zero, the expected value locus
will approach the line segment CD. which will be the horizontal axis in cases where the
limiting value is zero.
Given the above explanation, some further analysis of certain peculiarities of the TOBIT
regression results are possible. An examination of the coefficients estimated for site 1
in Table 3-7 shows that all of the coefficients are negative. This fact combined with the
realization that the values of all the independent variables are positive results in any
predicted number of fishing days from this model being negative. However, this result is
consistent with the TOBIT interpretation presented above. There are two factors that
must be considered when interpreting this outcome. First, the regression coefficients
are used to calculate an index that in turn is used to calculate the probability of an
individual taking a trip. This index is positive whenever the probability of taking a trip
exceeds fifty percent and is negative whenever the probability is less than fifty per-
cent.^ This result for site 1 indicates that the probability of any one individual taking a
fishing trip to that particular site is less than .5; however, the expected value for fishing
days will still be positive. This outcome is illustrated in Figure 3-lb.*® A second point
that should be considered when interpreting the TOBIT coefficients for site 1 is the large
standard errors of the coefficients on the non-distance variables. These make the actual
intercept in Figure 3-1 very uncertain.
^ See Tobin (1958). page 34 and Goldsmith (1983) footnote 19. page 39.
A similar result was found by Deegan and White (1976) where their TOBIT regression
coefficients only yielded negative values for the dependent variable over the entire range
of Xj, with the other Xj held constant at their means.
3-2/1
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3.3.2 Ordinary Least Squares Applied to Total Fishing Days
In spite of the fact that OLS estimates are biased, it was felt that applying OLS to the
data sets could provide useful information on the strength of the relationship between
fishing days and distance to the site. Also, the OLS estimates would provide a useful
point of comparison since there is an explicit theoretic prior expectation of the relative
magnitudes of the OLS and TOBIT regression coefficients.
The OLS estimates are presented in Table 3-8. As in the TOBIT analysis, only sites
requiring trips of less than 225 miles one way were included in the data set. The results
in Table 3-8 show that the distance variable was highly significant variable in most of the
equations. The coefficients on the distance variable were significant at the 1 percent
level in eighteen out of the twenty-three estimated equations. The distance variable was
not significant for sites 3, 10, 12, 16 and 20. The income and the years of fishing
experience variables were generally not significant. The R-squares were low. typically
varying between .01 and .06 for those equations where the distance variable was signifi-
cant.
Comparing the OLS results to the TOBIT results, the magnitudes of the coefficients con-
form to theoretic expectations. The absolute magnitudes of the TOBIT coefficients are
greater than the OLS estimated coefficients. Also, the calculated t-values and R-
squares were higher lor the TOBIT equations.
3.4 SECOND STAGE ANALYSIS OF THE CHARACTERISTICS OF FISHING SITES
The coefficients of a travel cost model using both TOBIT and OLS procedures were esti-
mated in Section 3.3. As was discussed in Chapter 1.0, these travel cost models do not
explicitly take into account site characteristics. Travel cost models do estimate the
travel and time costs that an individual is willing to pay to visit a site. These willing-
ness-to-pay amounts can be calculated from the coefficients on the independent var-
iables in the visitation equation for each site. It seems likely that sites with more
desirable recreational characteristics, such as fishing opportunities and catch rate, would
attract fishermen from further distances. This fact should show up in the relative mag-
nitudes of the estimated coefficients on the distance variable in the site equations. Also,
the participation models estimated in Section 3.1 showed the number of visitor days to be
positively related to site characteristics such as acres of ponds and total catch rate.
3-25
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Energy and Resource Consultants, Inc.
Table 3-8
Travel Cost Model Using Total Days as the Dependent Variable and
Estimated by Ordinary Least Squares
(t-values in parentheses)
Site #
Distance
Income
Years Fishing
Intercept
R2
1
-.0158
-.0066
-.0139
3.3441
.0468
(6.72)
(.41)
(1.48)
(6.86)
2
-.0178
-.0254
.0075
3.3922
.0445
(6.45)
(1.84)
(.93)
(6.77)
3
-.0012
-.0027
.0008
.4533
.0012
(1.02)
(.32)
(.16)
(1.73)
4
-.0076
.0036
-.0007
1.21
.033
(5.92)
(.52)
(.18)
(5.43)
5
-.0133
-.0074
.0114
2.0050
.0369
(6.06)
(.57)
(1.52)
(5.00)
6
-.0235
-.0047
.0082
3.4523
.0303
(5.60)
(.23)
(.69)
(4.91)
7
-.0104
-.0060
.0157
1.5810
.0155
(3.51)
(.25)
(1.89)
(3.23)
S
-.0347
-.0065
.0014
5.5683
.0436
(6.76)
(.25)
(.09)
(6.64)
9
-.0168
-.0082
.0174
2.0850
.0355
(5.82)
(.57)
(2.07)
(4.62)
10
.0052
-.0167
.0109
-.1924
.0044
(1.18)
(1.28)
(1.43)
(.36)
11
-.0040
(N
O
O
•
1
-.0016
.75
.0118
(3.38)
(.37)
(.49)
(4.13)
12
-.0064
-.0048
-.0076
1.4612
.0031
(1.59)
(.26)
(.70)
(2.46)
13
NA
NA
NA
NA
NA
14
-.0157
.0088
.0112
1.9952
.0172
(3.96)
(.58)
(1.27)
(3.33)
15
-.0091
.0050
-.0019
1.32
.0113
(3.40)
(.63)
(.41)
(3.83)
16
-.0010
0.0054
-.0005
.4222
.0014
(.58)
(1.00)
(.16)
(1.82)
3-26
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Energy and Resource Consultants, Inc.
Table 3-8
Travel Cost Model Using Total Days as the Dependent Variable and
Estimated by Ordinary Least Squares
(t-values are in parentheses)
(continued)
2
Site it Distance Income Years Fishing Intercept R
17
-.0182
00
o
•
1
.0058
2.4106
.0102
(2.94)
(.98)
(.61)
(3.38)
18
-.0229
-.0033
.0257
2.1425
.0126
(3.19)
(.13)
(1.68)
(2.35)
19
-.0439
.0717
.0335
3.9322
.0498
(6.63)
(2.44)
(1.94)
(4.23)
20
.0022
-.0093
.0126
-.1677
.0062
(1.08)
(.93)
(2.15)
(.55)
21
-.0137
-.0310
.0281
1.9496
.0152
(2.64)
(1.59)
(2.44)
(2.74)
22
-.0180
-.0153
-.0023
2.3041
.0291
(5.38)
(1.43)
(.36)
(5.79)
23
-.0486
-.0719
.0248
6.5822
.0579
(7.56)
(2.27)
(1.33)
(6.93)
24
-.0316
-.0155
-.0156
5.2824
.029
(5.52)
(.53)
(.91)
(6.15)
3-27
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Energy and Resource Consultants, Inc.
This section presents the results from regressing the coefficients from each site equation
on selected characteristics of that site. Two site characteristics were used: fishable
acreage and total catch rate. The equation that was estimated is shown below:
= Aq + Aj (Acres)j + A2 (Catch Rate)j
where B-. is the parameter (either a coefficient or intercept from the site equa-
tion. Two parameters were used as the dependent variable in this second stage. The
first was the coefficient on the distance variable (i.e., Bjj), the second was the inter-
cept. The demand curve intercept was defined as:
B2j (Mean Income Value) + B^j (Mean Experience Value) + B^j.
This composite variable represents the intercept of a demand equation relating fishing
days to distance, holding the other variables constant at their mean values. It would
have been possible to estimate each coefficient and intercept as a function of the site
characteristics; however, the income and experience variables were not significant in
most of the site equations. As a result, these coefficient estimates have large standard
errors and. at best, are imprecisely estimated. This would make statistically significant
estimates of the effects of the site characteristic levels on these coefficients unlikely
and the results hard to interpret. Given this situation, only the above composite inter-
cept was regressed against site characteristics.^ Since this intercept is the actual
demand curve intercept, this was felt to be appropriate.
The results of regressing both the coefficient on the distance variable and the intercept
against two site characteristics - net park areas and total catch rate - are shown in
Table 3-9a. In addition to that specification two other specifications were estimated.
The results of these are shown in Table 3-9b. The generalized least squares procedure
discussed in Chapter 1 was used in both instances. Table 3-10 presents similar GLS esti-
mated equations for the parameters from the OLS estimated travel cost equations.
In Tables 3-9 and 3-10, the site characteristics have t-values that are small. Still, a t-
value of 1.27 is significant at the 10 percent level for a one-tailed test and 20 percent
^ No attempt was made to regress the individual coefficients on income and experience
against the site characteristics. Only this composite intercept was regressed.
3-28
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Energy and Resource Consultants, Inc.
Table 3-9
Second Stage GLS Runs on the TOBIT Estimated Parameters
from the Total Fishing Day Equations
(t-values)
a. Base Equations
Dependent Net Total
Variable Park Acres Catch Rate Constant R
Coefficient on -.692 x 10"^ -.007 -.116 .161
Distance Variable (1.80) (1.01) (-1.27)
Intercept .597 x 10~3 4.81 45.01 .225
(1.27) (2.47) (10.15)
b. Additional Trial Specifications
Acres less Warm Two Total
Dependent than 1500 feet Water Story Catch
Variable Elevation Acres Acres Rate Constant R
Coefficient -.519 + 10"^ -.0056 -.129 .108
or Distance (1.36) (.2907) (1.89)
Variable
Intercept .623 x 10-3 .211 + 60-3 3.07 32.14 .134
(1.38) (.449) (1.13) (3.15)
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Table 3-10
GLS Runs on the OLS Parameters
from the Total Day Equations
Dependent
Variable
Net
Park Acres
Total
Catch Rate
Constant
Rz
Coefficient on
the Distance
Variable
Intercept
-.852 x 10"b
(1.91)
.135 + 10
(2 M)
.254 x 1Q-
(IM)
.253
(1.0#)
+.583 x 10
(.797)
-2
.7*0 x 10
(.072)
-1
.178
.235
3-30
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Energy and Resource Consultants, Inc.
for a two-tailed test. Although they are not significant at the highest levels (e.g. 1 per-
cent), these estimates represent the best information currently available and meet
modest statistical criteria.
3.5 TRAVEL COST MODEL ESTIMATES: CONCLUSIONS
The statistical results presented in this section show a strong relationship between visitor
days at a site and the travel distance to the site. The analyses performed to date provide
estimates that can be used to estimate the consumer surplus derived from each fishing
site; however, only the most basic specifications have been estimated and additional
analyses certainly would bo desirable.
There are several specific areas where additional analysis could prove beneficial. One of
these would be the examination of alternative functional forms including semi-log and
Box-Cox specifications. A second issue warranting additional analysis would be the
opportunity cost of time. To examine this second issue, an estimate of the individual's
marginal valuation of time is needed. Most often, the individual's wage1 rate1 is used as an
estimate of the value of time. Unfortunately, the Anglers' Survey does not include
information on the individual's wage1. It would be possible, however, to perform an analy-
sis similar to that contained in Section 7.4 of Desvousges. Smith and McGivney (1983).
Desvousges et al. used a model that predicts the wage rate given the individual's annual
income, occupation and related characteristics. Desvousges et al. found the variation in
1 ?
estimated wage rates from the mean wage level to be approximately 50 percent.
Given the potential magnitude of other errors in the model, the error due to not captur-
ing differences in individual's marginal valuation of time does not seem overwhelming,
but it also should not be minimized. The present formulation of the model where
distance rather than a specific travel cost is entered into the model allows alternative
cost per mile values to be calculated using varying travel and time costs.
1 0
The mean wage was $5.44 per hour. The low wage was $2.75 for female farmers and
the high was $7.89 for male professional workers.
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Another important issue concerns the current inability to estimate a separate model for
brook trout fishing days. The TOBIT procedures applied to brook trout fishing days failed
to converge on a set of coefficients for most of the sites because of too few non-zero
observations. This possibly could be remedied by redefining the sites and using alterna-
tive numerical techniques. Since the brook trout fish population is the fishery most
threatened by acid deposition, a separately estimated brook trout travel cost model could
be useful.
3-32
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Energy and Resource Consultants, Inc.
4.0 RECREATIONAL FISHING RESOURCE VALUATION
There are several procedures that can be used to provide estimates of the value of dam-
ages (i.e., reduced benefits) to recreational fishing in the Adirondacks from current
levels of acidification. Section 3.3 discussed the relationships between demand curves
based on OLS estimated regression coefficients, TOBIT estimated regression coeffi-
cients, and the expected value locus calculated from the TOBIT coefficients. A con-
sumer surplus estimate associated with each of the sites can be calculated using each of
these demand curves. Of these three options, the most appropriate curve to use for
estimating the consumer surplus is the TOBIT based expected value locus, since this
estimate takes into account both the probability of visiting the site and the estimated
number of days at a site given that a trip is taken. In addition to the travel cost model,
estimates of damages from acidification can be derived from the participation model
presented in Section 3.1.
The reduction in benefits due to the effects of acidification can be estimated by examin-
ing the difference between the consumer surplus estimates in the current state and the
pristine, pre-acidification state.* Figure 4-1 illustrates this benefits calculation. The
shaded area in Figure 4-1 is a measure of the dollar value of the damages that have re-
sulted from acidification.
4.1 ESTIMATE OF DAMAGES FROM ACIDIFICATION USING THE TRAVEL COST
MODEL
Estimates of the value of each site, using the travel cost model results, were obtained by
using the routine in the SHAZAM econometrics software package that produces the ex-
pected value locus. These expected value curves were estimated holding the values of
This consumer surplus measure is termed the Marshallian consumer surplus. It is not a
perfect welfare measure, but it is an adequate approximation for this application. Other
consumer surplus measures are available, but Freeman (1979) concludes that the differ-
ences among these measures are "small and almost trivial for most realistic cases."
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— Energy and Resource Consultants, Inc.
Figure 4-1
Measurement of the Reduction in Consumer Surplus
Resulting from Acidification
Quantity
(Fishing
Days)
Price
(Travel Cost)
p*
o Dc is the demand curve in the current situation where acidification has reduced the
fishing opportunities available at the site.
° Da is the demand curve given that there is no acidification.
o ACS is the change (i.e.. reduction) in consumer surplus due to acidification.
4-2
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Energy and Resource Consultants, Inc.
the income variable and fishing experience variable constant at the means of the sam-
ple. This resulted in a schedule for each site that shows the increase (decrease) in the
expected number of fishing days the "average" individual would spend at a site as his
distance from the site decreases (increases), other things held constant.
The estimated total willingness to pay and consumer surplus for each site is shown in
Table 4-1. These are based on an out-of-pocket travel cost estimate of 4.4 cents per
mile (from Table 3-6) and an opportunity of time cost of 9.06 cents per mile. The time
cost was based on an assumed average driving speed of 40 miles per hour, and the de-
flated mean hourly wage of a sample of fishermen from Desvousges et. al. (1983). The
time cost was calculated as being two thirds of the wage rate to reflect the fact that
some individuals may obtain some enjoyment from the drive and. therefore, time in tran-
sit should not be valued at the full wage rate. Table 4-1 shows the value for the current
recreational fishing experience in the Adirondack^ to be 261 million dollars per year.
The next step in the analysis is to obtain an estimate of the losses that may have resulted
from current levels of acidification. The second stage equations (shown in Table 3-9)
that regressed the TOBIT regression coefficient on the characteristics of the sites can be
used to show how the value of the resource has changed due to increased acidification.
These estimates are based on analyses conducted by Dr. Joan Baker as part of the
National Acid Precipitation Assessment Program (NAPAP). These estimates are based
on research that is still in progress.^ Table 4-2 shows some sites to have experienced
greater levels of acidification than other sites. This is due to a number of factors which
may include differing amounts of acid deposition and varying susceptibility of the lakes
in a site.
The reductions in fishing opportunities shown in Table 4-2 can be translated into an esti-
mated economic loss by using the site characteristic equations from Table 3-9. These
characteristic equations can be used to calculate how the TOBIT estimated regression
coefficients change as a result of these site characteristic changes. The new TOBIT
regression coefficients are then used to estimate a new expected value locus. New will-
ingness-to-pay estimates can be calculated from these new curves. The difference be-
2
Caveats to these estimates are presented in the Appendix.
4-',]
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Energy and Resource Consultants, Inc.
Table 4-1
Current Values Per Year For
Recreational Fishing in the Adlrondacks
Site
Expenditure*
Consumer
Surplus
Total
Willingness
To Pay
Total
Willingness
To Pay Per
Fishing Day
Consumer
Surplus Per
Fishing Day
1
7,294.5
3,033.0
10,327.5
107
31
2
8,483.8
2,912.6
11,396.4
104
26
3
4,157.5
1,267.5
5,425.0
118
27
4
3,228.4
1,489.8
4,718.2
97
31
5
5,870.5
2,510.4
8,380.9
98
29
6
6,586.6
4,038.1
10,624.7
105
40
7
7,784.2
4,373.6
12,157.8
107
38
8
13,615.6
6,334.5
19,950.1
96
30
9
5,679.1
2,934.3
8,613.4
96
32
10
(*)
(*)
(*)
(*)
11
2,415.6
1,147.1
3,562.7
75
24
12
6,569.0
3,698.7
10,267.7
103
37
13
N.A.
N.A.
N.A.
N.A.
N.A.
14
7,557.9
3,054.7
10,612.6
80
23
15
4,417.9
2,120.4
6,538.3
75
24
16
2,610.1
2,082.4
4,692.5
88
39
17
5,649.7
2,181.0
7,830.7
66
18
18
7,469.4
3,785.0
11,254.4
64
21
19
18,583.9
10,285.3
28,869.2
79
28
20
(*)
(*)
(*)
(*)
(*)
21
8,881.9
3,982.7
12,864.6
71
22
22
3,691.4
3,053.6
6,745.0
78
35
23
18,429.6
17,460.4
35,890.0
85
41
24
16,657.0
13,400.6
30,057.6
11
36
TOTAL
165,580.3
95,146.1
260,726.4
85
31
* Thousands of 1984 dollars per year
* These sites had a positive coefficient on the travel cost variable.
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Energy and Resource Consultants, Inc.
Table 4-2
Losses of Fishable Areas of Lakes Due to Acidification
Percent Reduction
Moderate Loss Estimate High Loss Estimate
Site Total Acreage (km2) Scenario 1 Scenario 2
1 27.023 0.0 0.0
2 (*) (used site 6 estimates)
3 61.510 .1% 4.3%
4 22.595 2.2% 32.0%
5 28.126 .1% .1%
6 7.008 53% 10.6%
7 145.445 .2% 8.6%
8 16.591 1.0% 19.5%
9 23.404 .3% .3%
10 55.165 0.0 16.7%
11 12.545 5.1% 10.4%
12 22.146 .2% 32.0%
13 71.019 17.7% 21.3%
14 25.750 7.5% 7.5%
15 39.235 .2% .2%
16 14.529 .2% 2.7%
17 36.319 .5% 3.4%
18 30.654 1.1% 3.3%
19 4.654 0.0 0.0
20 62.679 12.0% 27.7%
21 27.265 .6% 7.4%
22 17.411 20.2% 28.3%
23 125.79 0.0 0.0
24 (*) (used site 23 estimates)
* These sites lie outside the Adirondack Park boundaries. Dr. Baker's data set did not
have information on these sites.
4-5
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Energy and Resource Consultants, Inc.
tween the original willingness-to-pay or consumer surplus estimates represents the
change in the value of the experience due to the change in characteristics; in this case,
fishable acres of water.
Two site characteristics were incorporated in the TOBIT analyses presented in Section
3.4. They were net fishable acres and the catch rate in the remaining fishable acres at
•J
that site. It was assumed that the percentage change in net fishable acres due to acidi-
fication is the same as the percentage change in total fishable acres estimated by Dr.
Baker. How acidification at these levels influences the catch rate at a site is unknown.
As a result, several assumptions regarding the catch rate were made. Tables 4-3 and 4-4
show how the value of the recreational fishing resource changes assuming that the catch
rate is unaffected by whatever acidification has occurred. Tables 4-5 and 4-6 assume
that acidification reduces the average catch rate experienced by fishermen at the site by
the same proportion as fishable acres. The resource value changes presented in Tables
4-3 through 4-4 can be summarized as follows:
1) The estimated current value of the recreational fishing sites in terms
of total willingness to pay is 260.7 million dollars per year. The esti-
mated current consumer surplus is 9f).] million dollars.
2) Using the moderate acreage loss estimate and assuming no change in
catch rates, acidification is estimated to have resulted in a decline in
the resource value of 1.8 million dollars per year and reduced con-
sumer surplus of .7 million dollars per year.
3) Using the high acreage loss estimate and assuming no change1 in catch
rates, acidification is estimated to have resulted in a decline in the
resource value of 10.4 million dollars per year and a reduced con-
sumer surplus of 4.V) million dollars per year.
Estimates were available for the amount of lake area that would no longer support a
fish population, but catch rates at remaining fishable lake acreage might also be reduced
by acidification.
4-6
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Energy arid Resource Consultants, Inc.
Table 4-3
Valuation of Resource Losses Due to Acidification:
Moderate Acreage Loss Scenario
($ x 10^ per year, 1984 dollars)
Site
Current
Willingess
To Pay
Willingness
to Pay
Given No
Acidification
Losses
Current
Consumer
Surplus
Consumer
Surplus
Given No
Acidification
Losses
1
10,330
10,330
0
3,030
3,030
0
2
11,400
11,570
170
2,910
2,960
50
3
5,420
6,150
730
1,270
1,470
200
4
4,720
4,860
140
1,490
1,540
50
5
8,380
8,380
0
2,510
2,510
0
6
10,620
10,930
310
4,040
4,160
120
7
12,160
12,190
30
4,370
4,390
20
8
19,950
19,970
20
6,330
6,340
10
9
8,610
8,620
10
2,930
2,940
10
10
(*)
(*)
(*)
(*)
(*)
(*)
11
3,560
3,570
10
1,150
1,160
10
12
10,270
10,270
0
3,700
3,700
0
13
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
14
10,610
10,760
150
3,050
3,100
50
15
6,540
6,600
60
2,120
2,140
20
16
4,690
4,690
0
2,080
2,080
0
17
7,830
7,850
20
2,180
2,190
10
18
11,250
11,270
20
3,780
3,790
10
19
28,870
28,870
0
10,280
10,280
0
20
<*)
(*)
(*)
(*)
{*)
(*)
21
12,860
12,900
40
3,980
3,990
10
22
6,740
7,140
400
3,050
3,240
190
23
35,890
35,890
0
17,460
17,460
0
24
30,060
30,060
0
13,400
13,400
0
TOTALS
260,700
262,530
1,830
95,150
95,880
730
* These sites had a positive coefficient on the travel cost variable.
4-7
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Energy and Resource Consultants, Inc.
Table 4-4
Valuation of Resource Losses Due to Acidification:
High Acreage Loss Scenario
($ x 10^ per year, 1984 dollars)
Site
Current
Willing ess
To Pay
Willingness
to Pay
Given No
Acidification
Losses
Current
Consumer
Surplus
Consumer
Surplus
Given No
Acidification
Losses
1
10,330
10,330
0
3,030
3,030
0
2
11,400
13,030
1630
2,910
3,400
490
3
5,420
6,190
770
1,270
1,490
220
4
4,720
5,670
950
1,490
1,850
360
5
8,380
8,380
0
2,510
2,510
0
6
10,620
10,980
360
4,040
4,180
140
7
12,160
13,320
1,160
4,370
4,830
460
8
19,950
22,240
2,290
6,330
7,150
820
9
8,610
8,620
10
2,930
2,940
10
10
(*)
(*)
(*)
(*)
(*)
(*)
11
3,560
3,600
40
1,150
1,160
10
12
10,270
10,940
670
3,700
3,960
260
13
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
14
10,610
10,760
150
3,050
3,100
50
15
6,540
6,600
60
2,120
2,140
20
16
4,690
4,790
100
2,080
2,130
50
17
7,830
7,920
90
2,180
2,200
20
18
11,250
11,280
30
3,780
3,800
20
19
28,870
28,870
0
10,280
10,280
0
20
(*)
(*)
(*)
(*)
(*)
(*)
21
12,860
13,180
320
3,980
4,080
100
22
6,740
7,290
550
3,050
3,320
270
23
35,890
35,890
0
17,460
17,460
0
24
30,060
30,060
0
13,400
13,400
0
fALS
260,700
271,180
10,480
(4.0)
99,700
4,550(4.7)
* These sites had a positive coefficient on the travel cost variable.
4-8
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Energy arid Resource Consultants, Inc.
Table 4-5
Valuation of Resource Losses Due to Acidification:
Moderate Acreage and Catch Rate Loss Scenario
($ x 10^ per year, 198# dollars)
Site
Current
Willingess
To Pay
Willingness
to Pay
Given No
Acidification
Losses
Current
Consumer
Surplus
Consumer
Surplus
Given No
Acidification
Losses
1
10,330
10,330
0
3,030
3,030
0
2
11,400
13,410
2010
2,910
3,540
630
3
5,420
7,740
2320
1,270
2,080
810
4
4,720
5,210
490
1,490
1,870
380
5
8,380
8,390
10
2,510
2,520
10
6
10,620
11,740
1120
4,040
4,510
470
7
12,160
12,200
40
4,370
4,390
20
S
19,950
20,230
280
6,330
6,430
100
9
8,610
8,640
30
2,930
2,940
10
10
(*)
<*>
(*)
(*)
(*)
(*)
11
3,560
3,970
410
1,150
1,290
140
12
10,270
10,270
0
3,700
3,700
0
13
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
1#
10,610
22,430
710
3,050
3,230
180
15
6,540
6,620
80
2,120
2,150
30
16
4,690
4,720
30
2,080
2,090
10
17
7,830
7,870
40
2,180
2,190
10
IS
11,250
11,310
60
3,780
3,810
30
19
28,870
28,870
0
10,280
10,280
0
20
(*>
(*>
(*)
(*)
(*)
(*)
21
12,860
12,930
70
3,980
4,000
20
22
6,740
9,530
2,790
3,050
4,630
1,580
23
35,890
35,890
0
17,460
17,460
0
24
30,060
30,060
0
13,400
13,400
0
TOTALS
260,700
271,180
10,480
100,010
4,860
* These sites had a positive coefficient on the travel cost variable.
4-9
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Energy arid Resource Consultants, Inc.
Table 4-6
Valuation of Resource Losses Due to Acidification:
High Acreage and Catch Rate Loss Scenario
($ x 103 per year, 1984 dollars)
Site
Current
Willingess
To Pay
Willingness
to Pay
Given No
Acidification
Losses
Current
Consumer
Surplus
Consumer
Surplus
Given No
Acidification
Losses
1
10,330
10,330
0
3,030
3,030
0
2
11,400
15,770
4,370
2,910
4,320
1,410
3
5,420
8,140
2,720
1,270
2,280
1,010
4
4,720
7,760
3,040
1,490
3,200
1,710
5
8,380
8,380
10
2,510
2,510
0
6
10,620
12,910
2,290
4,040
5,060
1,020
7
12,160
13,520
1,359
4,370
4,920
550
8
19,950
22,860
2,910
6,330
7,400
1,070
9
8,610
8,690
80
2,930
2,940
10
10
(*)
(*)
(*)
(*)
(*)
(*)
11
3,560
4,400
840
1,150
1,470
320
12
10,270
13,280
3010
3,700
5,000
1,300
13
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
14
10,610
11,320
710
3,050
3,230
180
15
6,540
6,620
80
2,120
2,150
30
16
4,690
5,050
360
2,080
2,250
170
17
7,830
8,070
240
2,180
2,250
70
18
11,250
11,440
190
3,780
3,850
70
19
28,870
28,870
0
10,280
10,280
0
20
<*)
<*)
<*)
(*>
(*)
<*>
21
12,860
13,550
690
3,980
4,210
230
22
6,740
10,780
4,040
3,050
5,510
2,460
23
35,890
35,890
0
17,460
17,460
0
24
30,060
30,060
0
13,400
13,400
0
TOTALS
260,700
287,900
27,200
95,150
107,190
12,040
* These sites had a positive coefficient on the travel cost variable.
4-10
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Energy and Resource Consultants, Inc.
4) Using the moderate acreage loss estimate and assuming that the
catch rate declines proportionately, the estimated decline in the
resource value is 11.8 million dollars per year and the loss of con-
sumer surplus is <1.9 million dollars.
5) Using the high acreage loss estimate and assuming a proportionate
change in catch rate, the estimated decline in the resource value is
27.2 million dollars and the loss in consumer surplus is 12.0 million
dollars.
There are a number of factors that must be considered when interpreting these results.
First, the correct measure of benefits for use in a benefit-cost analysis of acid deposition
is the change1 in consumer surplus. Second, the data set used in the analysis only includes
information on visits to lakes. Streams in the Adirondack^ were not examined due to the
lack of data on the characteristics of the streams and uncertainty in the actual fishing
location. Data in the Anglers Survey indicated that approximately one third of fishing
trips listed a stream as the final destination.
Third, sites 10, 13 and 20 were not assigned a value. Site 13 was not valued due to an
error in the computer program that combined the data in the Anglers Survey and the
Ponded Waters Survey. There were not adequate resources available to go back and cor-
rect this error. Sites 10 and 20 had the wrong sign on the coefficients on the travel cost
variables. As a result, willingness-to-pay estimates for these sites were not available
from the statistical analysis. These sites certainly have some value. An examination of
the data presented in Table 4-2 shows each of these sites is susceptible to acidification
with the high estimates of fishable acreage losses being 16.7 percent. 21.3 percent, and
27.7 percent respectively. Thus, the exclusion of these sites in the value estimates con-
tained in this draft report biases the estimated effects of acidification downward.
Fourth, the travel cost model in its present version does not explicitly take into account
the substitutability of fishing sites. This will tend to result in estimates of losses that
are overstated. See Section 4.3 for a more complete discussion of this point.
Fifth, the travel cost analysis considered only trips that have a one-way distance of 225
miles or less. This was done to avoid including multi-purpose trips where fishing may not
have been the primary reason for the trip. The inclusion of these trips would have biased
/I-]]
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Energy and Resource Consultants, Inc.
the estimates and made the results uninterpretable. Still, these trips represent fishing
days spent at the site which have value. In scaling the sample estimates up to a popula-
tion estimate, it was assumed that fishing days from trips of distances greater than 225
miles resulted in the same consumer surplus as shorter trips. The actual consumer sur-
plus resulting from fishing days taken as part of a multi-purpose trip could be either
greater or smaller than that estimated from the shorter trips. Still, over 70 percent of
the fishing days were from trips of less than 225 miles.
4.2 ESTIMATING THE DAMAGES FROM ACIDIFICATION USING THE PARTICIPATION
MODEL
As a final piece of analysis, the participation model developed in Section 4.1 can be used
in conjunction with the resource value estimates from Table 4-1 to estimate the damages
from acidification. The participation model found a robust relationship between the
number of fishing days spent at a site and fishing opportunities measured by fishable
acreage and fishing success measured by the total catch rate. Equation 3 from Table 3-1
presents the estimated relationship between fishing days and a site's fishable acreage and
catch rate:
Fishing Days = .0978 (Net Park Acres) + 199.4 (Catch Rate) + intercept
(f).()()) (1.97)
The R-square for this equation was .615. The moderate loss due to acidification scenario
from Table 4-2 resulted in an average reduction in fishable acreage of 3.2 percent and
the high loss scenario resulted in an average acreage reduction of 10 percent. The mean
values across all sites for net park acres and catch are 7420 and 3.47 respectively. Using
these mean values to represent the average site, the effect of acidification on total fish-
ing days for this average site can be calculated. Then, the average willingness to pay
($85) and consumer surplus ($31) per fishing day from the travel cost model (see Table
4-1) can be used to calculate an estimate of damages. Four scenarios are evaluated.
Scenario 1 - Assuming moderate acreage losses and no change in catch
rate, a reduction of 56,000 fishing days across all site - is estimated.
Losses in terms of willingness to pay and consumer surplus is 4.8 and 1.7
million dollars per year respectively.
<1-12
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Energy and Resource Consultants, Inc.
Scenario 2 -- Assuming high acreage losses and no change in catch rate, a
reduction of 173,000 fishing days across all sites is estimated. Losses in
terms of willingness to pay and consumer surplus is 14.7 and 5.4 million
dollars per year respectively.
Scenario 3 -- Assuming moderate acreage losses and a proportionate change
in catch rate, a reduction of 109,000 fishing days is estimated. Losses in
terms of willingness to pay and consumer surplus is 9.3 and 3.4 million
dollars per year respectively.
Scenario 4 -- Assuming high acreage losses and a proportionate change in
catch rate, a reduction of 340,000 fishing days across all sites is esti-
mated. Losses in terms of willingness to pay and consumer surplus is 28.9
and 10.5 million dollars per year respectively.
4.3 COMPARISON OF PARTICIPATION MODEL AND TRAVEL COST MODEL
ESTIMATES OF DAMAGES
The damage estimates derived in terms of reduced consumer surplus from both the travel
cost model and participation model are presented in Table 4-7. The estimates derived
from the two models are quite similar in magnitude. There is no clear reason to prefer
one set of estimates over the other. The use of average values in the participation model
poses some problems, but are reasonable approximations for the modest changes in site
characteristics examined in this study. One favorable attribute of the participation
model results was the robust statistical relationship that was found between fishing days
and site attributes. The statistical relationship found in the second stage of the varying
coefficient travel cost model was less robust.
4-13
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Energy and Resource Consultants, Inc.
Table 4-7
Estimates of Damages Resulting from Acidification
($ x 106 per year; in 1984 dollars)
Assumed
Acidification
Scenario
Kst i mated
Consumer Surplus
Losses from the
Travel Cost Model
Kst i mated
Consumer Surplus
Losses from the
Participation Model
1. Moderate acreage losses ;i
no change in catch rate
ind
.7
1.7
2. High acreage losses and
no change in catch rate
4.(5
•r)./l
U. Moderate acreage losses a
proportionate changes in
catch rate
ind
4.9
:\A
A. High acreage losses and
proportionate changes in
catch rate
12.0
10. f)
AAA
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Energy and Resource Consultants, Inc.
9. Desvousges, Smith and McGivney, A Comparison of Alternative Approaches for
Estimating Recreation and Related Benefits of Water Quality Improvements. U.S.
Environmental Protection Agency. Economic Analysis Division. Washington. DC.
EPA-230-04-83-001. 1983.
10. Fisher. Ann and Raucher. R.. "Intrinsic Benefits of Improved Water Quality: Con-
ceptual and Empirical Perspectives," in Advances in Microeconomics, Vol. 3, V.
Kerry Smith and A. DeWitte, eds. JAI Press: Grenwhich, CT, 1984.
11. Freeman, A.M., III. The Benefits of Environmental Improvement: Theory and Prac-
tice, The Johns Hopkins University Press, Baltimore1, Maryland, 1979.
12. Goldberger, Econometric Theory. Wiley Pubs., New York, 1964 (Chapter 5).
1:5. Goldsmith, A., "Household Life Cycle Protection: Human Capital Versus Life
Insurance1," The Journal of Risk and Insurance. XL (March), 1983, /173-/18(>.
M. Greeson and Robison, "Characteristics of New York Lakes, Part 1 -- Gazatteer of
Lakes, Ponds and Reservoirs," Report of the New York Department of Environ-
mental Conservation, 1970.
IT). Grieg, P.J., "Recreation Evaluation Using a Characteristics Theory of Consumer
Behavior", American Journal of Agricultural Economics. 65 (1983): 90-97.
Hi. Kretser, W.A., and Klatt, L.E., "1976-1977 New York Angler Survey -- Final
Report," New York Department of Environmental Conservation, May 1981.
17. Maddalla, G.S.. Econometrics. McGraw-Hill, New York, 1977.
18. Men/, F.C. and Mullen, J.K., "Acidification Impacts on Fisheries", presented before
the Division of Environmental Chemistry, American Chemical Society, Las Vegas,
April 1982.
19. Morey, E.R., "The Demand for Site-Specific Recreational Activities: A Charac-
teristics Approach", Journal of Environmental Economics and Management, 8
(1981): 345-371.
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Energy and Resource Consultants, Inc.
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Adirondack Zone." FW-P142 (12/9). New York State Department of Environmental
Conservation. Albany. NY. 1979.
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R 3
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DRAFT
Modeling Recreational Demand in a Multiple Site Framework
Nancy E. Bockstael
W. Michael Hanemann
Catherine L. Kling
TO be presented at the AERE Workshop on Recreation Demand Modelling
Boulder, Colorado
May 1985
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Introduction
There is a large and growing literature on recreational demand modelling. A
topic which has, of late, received particular attention in this literature is the
modelling of the demand for systems of alternative sites, as compared with the more
traditional single site modelling approaches. The multiple site models are
frequently complex, diverging from simple intuitive extensions of the single site
model, They are also diverse, and this together with their complexity makes
assessment and comparison of models and results difficult. While problems in the
theory and application of single site models remain, most practitioners understand
these models and their inherent problems and can apply them with a cautious
confidence. In contrast, multiple site models are difficult to sort out, to
interpret and to estimate.
In this paper, we first explore the reasons why multiple site models have been
developed and outline a number of the approaches which have been used. We then
assess these models with a specific criteria in mind: how well do they account for
the specific nature of benefit changes in a multiple site framework? Using a common
data set, we demonstrate a few of the estimation techniques.
Why Multiple Site Modelling?
A Review of Approaches with Trip Allocation and Site Valuation Motivations
The long list of models which treat multiple sites can be subdivided into three
categories: (a) those which are used primarily to explain the allocation of visits
among alternative sites; (b) those which may explain allocation, but also value the
addition of a new site; and (c) those which focus on the valuation of site
characteristics. The models in (a) and (b) often include site characteristics as
explanatory variables but do not always facilitate the valuation of characteristics.
Some, but not all, of those in (c) also explain trip allocation decisions.
1
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One of the first treatments of multiple sites was in the context of zonal trip
allocation models. In 1969 Cesario suggested the use of these gravity models for the
specific purpose of explaining the allocation of trips from each zone to alternative
sites. In these models visits between a zone and a site were explained on the basis
of zonal and site characteristics and distance, with one set of parameters estimated
for all combinations of zones and origins. For the most part such models have been
used Simply to estimate demand and predict use rates. Freund and Wilson (1974)
provided one of the most careful applications of this approach in a study of
recreation travel and participation in Texas.
In their 1975 paper Cesario and Knetsch extended the gravity model so that the
trips equation for zone i visitors to site j included a factor reflecting "competing
opportunities" provided by all other sites, presumably this made more explicit the
substitutability among sites. These authors also introduced the possibility of using
gravity models for benefit measurement. Including travel cost (time and money costs)
instead of distance, Cesario and Knetsch proceeded to treat the zonal visits
equations as demand curves and take areas behind these curves as measures of consumer
surplus.
The use of gravity models for benefit estimation has been limited, culminating
in a rather complex paper by Sutherland published in 1982. Unlike his predecessors,
Sutherland obtained predictions of individual's behavior rather than simply zonal
aggregates. The model had four components which, while inextricably linked, were
estimated independently. Each zone's demand for trips to all sites (trip production
models), and each site's aggregate demand from all zones (attractiveness
models), T, were estimated, predicted values for these variables were combined
with variables reflecting distances in a trip distribution (gravity) model to predict
each zone's allocation of visits among all sites, T^j. It seems that results from
this gravity model were then used to estimate a demand function where predicted trips
by zone to each origin was regressed on travel cost (constructed from the distance
2
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data). The model, at best, seemed to overfit the demand system.
Sutherland's paper inadvertently exposed what is perhaps the most disturbing
aspect of the gravity models. They are simply statistical allocation models based on
no particular arguments about economic behavior. Consequently, when Sutherland used
a gravity model to "allocate trips from zones to sites," he did not have a model of
the requisite economic behavior to estimate benefits. He then was forced to re-
estimate a relationship between trips and cost to capture the economic behavior
implicit in a demand function. It is difficult to understand why one would wish to
estimate a gravity model for benefit estimation purposes a) if one does not believe
the gravity model is a demand function and b) if one believes that decisions are
driven by economic considerations.
Burt and Brewer (1971) were perhaps the first explicitly to specify multiple-
site demand models. Their motivation for going beyond the single-site model was that
they were interested in measuring the value of introducing a new recreational site.
For such a potential value to be measurable, one needs to admit the existence of at
least one other similar site. Once the existence of at least one alternative site is
recognized, it seems appropriate to estimate the system of demands for all existing
alternatives. Thus in deducing the value of the new site, Burt and Brewer set off to
estimate how patterns of demand for existing sites would change with its addition.
The Burt and Brewer model was a straightforward extension of the single site
travel cost model to a system of such demands
(1) = Pj_»P2»• • • ^ = 1 > • • • >m
where is the number of trips taken to site k, is the travel cost to site k, y
is income and m is the number of sites in the system considered. Any differences due
to the quality characteristics of sites simply showed up in the estimated
coefficients of the different demand functions. Unlike so many studies of this time,
3
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the authors used household rather than zonal data in their application - a study of
water based recreation in Missouri.
A similar model (with the omission of income and based on zonal data) was
employed by Cicchetti, Fisher, and Smith (1976) in their analysis of the Mineral King
project in California. Once again the motivation was the valuation of a proposed new
site. Similar to Burt and Brewer, the authors estimated a system of demands for
alternative sites or site groups as functions of prices (i.e. the costs of traveling
to each site). And, again, site characteristics were excluded from the model.
In each case the benefits from the introduction of the new site were assessed
by considering the benefits of a price change for the existing site most similar to
the proposed site. Thus, gains from the new site accrued from reduced travel costs
for some users.
Hof and King (1982) asked the very pertinent question - Why do we need to
estimate the system of demands in these cases? Why not just estimate the demand for
the similar site (as a function of all prices) and evaluate the benefits in that
market? In the context of the Burt and Brewer and the Cicchetti, Fisher and Smith
papers, their arguements are cogent. If there is only one price change, its effect
can be measured in one market (Just, Hueth, and Schmitz, 1982). Even if one expects
seemingly unrelated regression problems, ordinary least squares will achieve the same
results as generalized least squares when all equations include the same variables.
Hof and King further argued that Willig's results provide bounds on compensating
variation as functions of Marshallian consumer surplus. Thus, it is not necessary to
estimate the entire demand system so as to impose cross-price symmetry and ensure
path independence. In retrospect, this procedure of imposing symmetry (followed by
both the Burt and Brewer and the Cicchetti, Fisher and Smith papers) seems
inappropriate, since there is no reason for the Marshallian demands to exhibit such
characteristics. Additionally this path independence property is not worth worrying
about since the particular functional forms chosen for the systems of demand
4
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functions in these papers do not meet integrability conditions (LaFrance and
Hanemann, 1984). In any event, if we are interested in the effect of a single price
change, there would seem no especially compelling reason to estimate an entire system
of demands if they are to take the form suggested by Burt and Brewer or Cicchetti,
Fisher and Smith.
All of the models mentioned so far included multiple sites to capture allocation
of trips among substitute alternatives. Some of the gravity models attempted to
Capture the effect of site characteristics on this allocation, but were not concerned
with the valuation of characteristics. The demand systems models did not even
attempt to take explicit account of site heterogeneity.
Of the more recent and more sophisticated modelling attempts, only one has this
same type of motivation. While the multiple site models of Morey (1981, 1984a,
1984b) are more closely aligned in technique and conception to the models outlined in
the next section, their motivation is more akin to the earlier models discussed
above. They have been employed by the author both to explain the allocation of
visits among alternative sites (1981, I984a) and to value the introduction of a new
site (1984b). The approach nonetheless places heavy emphasis on site characteristics,
with characteristics contributing to the explanation of trip allocations, and there
is no reason why the approach could not be used to value characteristics. Because of
this, we will postpone discussion of this work until the next section.
Multiple Site Modelling and the Valuation of Site Characteristics
Of burgeoning interest in environmental economics is the valuation of improvements
in environmental quality. While valuation exercises have frequently taken place in
the context of contingent valuation models, economists have concurrently tried to
adapt recreational demand models to this task. This has given a new and more
insistent motivation for multiple site modelling. It was quickly realized that in
order to value characteristics one needed to estimate demand as a function of
5
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characteristics and this required observing variation in characteristics over
observations. This variation could, presumably, be found only by looking across
recreational sites.
In what follows we will be describing approaches which are currently being used
to model multiple site demand and which can be used to value environmental
improvements. The first approach we shall outline here has as its sole focus the
valuation of site characteristics. The hedonic travel cost model (Brown and
Mendelsohn, 1984; Mendelsohn, 1984) attempts to reveal shadow values for
characteristics by estimating individuals' demand for the characteristics. This
approach consists of two separate procedures. The first step entails regressing
individuals' total costs of visiting a site on the characteristics of the site.
Each individual is assumed to visit only one site and separate regressions are run
for individuals from each origin. The costs of visiting any given site and
characteristics of the site are identical for all individuals visiting the site from
the same origin, and variation in the data comes from variation in the sites visited
by those individuals from the same origin. The partial derivatives of cost with
respect to characteristics are then interpretted as the hedonic prices of the
characteristics. The hedonic prices are used as prices in a second stage where the
demand for characteristics is estimated.
Since chance and not markets provides the array of sites and their qualities, it
is unreasonable to expect costs of accessing alj_ possible sites for all individuals
to be an increasing function of even one characteristic. However the approach
requires including observations on costs and site characteristics only for those
sites which are actually visited by individuals in the regression subsample. It is,
of course, a logical result of constrained utility maximization that an individual
will only incur greater costs to visit a more distant site if the benefits derived
from the visit exceed those from a closer site. Nonetheless, it does not seem to
6
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follow that costs will be a single-valued, increasing function of each element of a
vector of site characteristics.
The conceptual validity of the hedonic travel cost approach depends on two
contentions which remain contestable and unproven. No attempt will be made to
resolve these particular issues here, as we are interested in other dimensions of
the multiple site modelling problem. However, we mention the problems in hopes of
stimulating discussion. The first contention worthy of debate is whether the
derivatives of the first stage regression legitimately reflect prices - the prices an
individual perceives himself to have to pay to increase the level of the
characteristics. If more than one characteristic is included in the function, or if
important characteristics are omitted - and especially if sites are not continuous,
it becomes quite possible for costs to be declining in at least one characteristic,
thus producing a negative "hedonic price."
Presuming for a moment that orderly prices for individual characteristics exist,
the second debatable contention is that true demand functions for the
characteristics can be statistically identified. This identification issue has been
debated extensively in the context of the hedonic property value technique for
valuing amenities, but many of the same points of controversy arise here. For a
sampling of the arguments, see Brown and Rosen (1982), Mendelsohn (1983), and
McConnell (1984).
The output of the final stage of the hedonic travel cost approach is a demand
function for each characteristic. The demand function, although not derived from a
utility maximizing framework, is interpretted to reflect the marginal willingness to
pay per recreation day for an increase in the quality of the characteristic. There
is an apparent inconsistency in the interpretation as we consider hpothetical
movements away from the observed point. The demand functions are associated with
characteristics and not sites and thus it does not seem possible to assess the value
of a specific change in quality (such as would be brought about by a regulation,
7
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etc.) Also these functions do not capture any information about how individuals'
behavior (participation and site choice) would change with a change in quality.
Without this latter information, it would not seem possible to assess the value of a
change.
A second approach which is both interesting and potentially fruitful is due to
Morey. This approach models shares of total recreational trips allocated to
alternative sites. Several techniques for statistically estimating shares which are
consistent with demand functions have been proffered by economists (see for example
Woodland, 1979, and Hanemann's cataloguing in Bockstael, Hanemann and Strand, 1984).
Morey chooses a share model based on the multinomial distribution which has the
appealing features that if the shares are assumed to follow such a distribution, then
the implied demands are "counts" and therefore non-negative integers.
The standard scenario underlying the multinomial distribution is that R
independent trials are held and, on each trial, N mutually exclusive outcomes may
ti
occur, with'ft.,- being the probability of the it'1 outcome where ITj > 0 = 1-
Let t.j be the number of times that the itf1 outcome occurs in R trials. The
probability of an outcome vector (x^,...,x^) is
T? »
(2) =
*1 ITO
IT fc0!
r1
Applications of the multinominal distribution (such as Morey's) equate the count
with the number of trips to site i, x^, and 1T^ with the share function s.,-(p,t>,yx).
The total number of trials, R, is equivalent to the total number of trips, X. The
density of the observed demands is then
(3) f(x1,...,xN) = — ¦ TT \
JJ
8
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parameters of the Sj(*) are then estimated by maximizing the likelihood function
M (* V Ji y .
l *
rn--»
where M is the number of individuals in the sample.
The logic of the statistical model is that the number of trials, R, is exogenous,
and, therefore, this parameter may be ignored in maximizing the likelihood function
to obtain estimates of theTT's. However, R equals x., the total number of trips, and
thus contains information on the coefficients to be estimated which should not be
ignored in estimating the likelihood function. Additionally, the approach provides
estimates of shares and not demands. The prediction of demands would require the
prediction of total number of visits as well. Interesting, the shares are consistent
with a system of demand functions which could be estimated to obtain information on
total trips as well as their allocation.
An alternative approach is to retain the multinomial model but interpret the
parameters, not as shares per se, but as choice probabilities arising from
some structural economic model. Variations of this appraoch can be found in Caulkins
(1982), Hanemann (1978), Feenberg and Mills (1980), and Bockstael, Hanemann, and
Strand (1984).
Recalling the expression for the multinomial distribution in (2) a different
interpretation is now employed. Rather than treat the allocation of total demand, we
are now concerned with the decision of what site to visit on each choice occasion.
Thus becomes the probability that alternative j is chosen on the given choice
occasion and tj equals 1 if j was chosen, 0 otherwise. In this way of structuring
the problem, the expression Rl/iTt,-! disappears, since the number of repeated trials
J
is 1. Finally, the likelihood function takes the form
9
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where m indexes individuals, j indexes alternatives , and g indexes individuals'
choice occasions. In this formul ationTT^ is still constrained to be strictly
positive but this does not preclude si equaling zero since is no longer a share but
instead the probability of choosing alternative i on a given choice occasion.
The probabilities, are determined by costs and characteristics of the
alternatives and the characteristics of the individuals in a utility maximizing
framework. On each choice occasion, the individual chooses one alternative site to
visit. In order to describe the solution, suppose that on the given choice occasion,
the individual has selected site i. Since the consumer selects the site which yields
the highest utility, the decision can be expressed in terms of conditional indirect
utility functions as
-I:
if vi(bi,yr-pi) > vj(bj,yr-Pj) all j
(6)
otherwi se
where is a choice index which equals 1 when the itl1 site is chosen, and is the
indirect utility function conditioned on the choice of visiting site i. Notice that
we have involved a weak complementarity assumption here by including only b-j, the
vector of quality characteristics associated with site i in the function. Here yr is
the income available per choice occasion.
For estimation purposes, it is necessary to introduce a stochastic element into
this demand model. If we assume that the random elements enter the utility functions
in such a way that they, too, are affected by weak complementary, then we can write
each conditional indirect utility function, v-jC*) simply as a function of a scalar
random element, The consumer's utility maximizing choice is still expressed in
terms of the conditional indirect utility functions, along the lines of (5), except
that the discrete choice indices d^,...d^ are now random variables with means E[d^] =
'ttj given by
10
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(7) = j~— P-j»^i^ ^ '^p-^for all j ^ »
To estimate the parameters of these indirect utility functions, one needs to
assume a tractable distribution for the £'s. At this point the various discrete
choice multiple site models diverge. A common assumption e.g. (Caulkins, Feenberg
and Mills, Hanemann) is that the random variables, are independently and
identically distributed extreme value variates, and that they are additive in the
indirect utility function, i.e.
u-j = v1(bi ,yr-p-j) +s, i =
This yields the logit model of discrete choices
(8) Iff = en/£.e>' i = 1,..., N.
In Bockstael, Hanemann, and Strand, the Generalized Extreme Value Distribution (of
McFadden, 1978) is employed such that
(9) <_ sx,...,£n £ sNJ= exp[-G(e H,...,e"S")]
where G is a positive, linear homogeneous function of N variables. When combined
with the indirect utility function with additive errors, this yields discrete choice
probabilities of the form
(10) = e ^Gjfe N)/G(e N) i =
where Gj(*) is the partial derivative of G(') with respect to its argument. In
either case, the formulas for the choice probabilities may be substituted into the
multinomial density for maximum likelihood estimation of the parameters in the v^*)
functions.
11
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The treatment of choice occasions is also different in the various models.
Caulkins considers each choice occasion to be each day of the year and Feenberg and
Mills each day of the recreational season, but both presume that on each day, the
individual decides both whether to participate in the recreational activity and, if
he participates, which site he visits.
To accomplish this, Caulkins first estimates a logit model on
the site choice decision:
V. V*:
(11) = e VI e J
j=l
and then defines an index which, although not completely consistent, is conceptually
similar to the inclusive value index of McFadden. This index, I, is a linear
function of the average price and quality characteristics of the alternative sites.
The probability of participation is estimated as the following binary logit
(ti) tfp = e^/eV° + e*
where vQ is the utility associated with not participating and is a function of income
(and potentially other characteristics of the individual).
Feenberg and Mills estimate the same type of first stage logit model in
analyzing site choices. Their model employs a similar inclusive value index
N v.
(13) I = In Z e J'.
j=l
The participation decision is once again a function of the inclusive value index and
vQ, but it is estimated using ordinary regression techniques.
The above studies have one characteristic in common: the total number of trips
taken in a season is determined indirectly by adding up the number of independent
occasions upon which the individual chooses to participate in recreation. Treating
the total consumption decision as the sum of totally uncoordinated micro decisions is
12
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not especially appealing. Bockstael, Hanemann and Strand offer an alternative
approach which on some grounds may be considered slightly more appealing but which
still fails to be rigorously derivable from a single utility maximizing framework.
The essence of this approach is that a logit model (in this case a slightly more
complex, generalized extreme value model) is estimated on site choices per choice
occasion. But rather than considering every day of the year (or season) to be an
independent choice occasion upon which the individual must decide whether to
participate, the participation decision (both whether to be a participant in this
activity at all and, if so, how much) is estimated as one discrete-continuous total
recreation demand decision. This macro decision of how many days in the season to
recreate is estimated using a discrete-continuous choice model which takes account of
the fact that decisions will be nonnegative but may be zero for a number of people.
Although of a different form from the other models, the decision is estimated as a
function of similar variables: the characteristics of the individuals and the
characteristics of the recreational opportunities available as captured through an
inclusive value index. The specific model used is presented in the estimation
section of this paper.
A comparison of this approach with the Feenberg and Mills and Caulkins models
exposes an important difference. In this model the probability that an individual is
not a recreationalist, i.e. he does not participate at all in the recreational
activity, is estimated directly. Either Tobit or Heckman procedures can be used to
estimate this equation. The later procedure is particularly appropriate if factors
such as old age, ill health or preferences for other activites causes an individual
never to recreate. In the other approaches where total visits are determined by the
summation of independent decisions on sequential choice occasions, nonparticipants
happen, in a sense, by accident. They are predicted to be those individuals who
happen to have a string of zero predicted responses to a sequence of N independent
13
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micro decisions. Modelling the macro allocation separately would appear to be a more
realistic and useful description of individual behavior. However, it does not offer
a consistent way to link independent site choice decisions and the demand for total
trips with a common underlying utility maximization framework.
Welfare Measurement Given The Nature of Recreational Decisions
One can certainly argue with features of all of the models outlined above. Here
we will be concerned with only one criteria, albeit an extremely important one, for
assessing alternative models. The criteria is how adequately each model captures the
appropriate benefits which accrue from an environmental change, given the nature of
recreational decisions in a multiple site framework.
It is important at this point to reiterate and to develop more fully what we
mean by the nature of recreational decisions. Suppose we are interested in valuing
an improvement in water quality, and we attempt to do this by looking at recreational
behavior over an array of recreational sites with different water quality in the
region of interest. Any sample of the relevant population will turn up a fair number
of individuals who do not participate in water recreation at these sites at all. Of
those who do participate in the activity, it will be unusual to find anyone who
visits aJJ sites. It will also be unusual if the entire data set consists of
individuals each of whom visit only one site. Additionally, we are interested in how
many trips an individual takes to each site. Thus we observe either that an
individual did not participate in the activity at all or that he participated but
took no trips to several sites and a positive number of trips to some subset of
sites.
Recreational behavior is complicated to model because of this mix of continuous
and discrete decisions and because decisions result invariably in corner solutions.
Nonparticipants are, of course, at a corner solution with respect to the total trips
decision, participants are even observed to be at corner solutions of a sort since
14
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they take zero trips to at least some sites. One of the drawbacks of the straight-
forward demand systems modelling of Burt and Brewer and Cicchetti, Fisher and Smith
is that they are predicated on the assumption of interior solutions to the utility
maximization process. Once we admit to corner solutions, the nature of demand
systems changes.
This criticism is in some ways applicable to the share models as well. The
share models treat the total number of trips as fixed. Additionally most of these
models implicitly presume a nonzero share (however small) for all sites. The share
models can be transformed into demand systems and estimated in that form, providing
predictions of total number of trips. However such models suffer from the same
problem as the Burt and Brewer type models in that they presume interior solutions.
Many of the discrete choice approaches get around the problem by estimating decisions
per choice occasion. This ignores interdependence across trip decisions and provides
estimates of total trips demanded only in an indirect and unsatisfactory way. The
final discrete choice model suggested above attempts to mitigate the second of these
criticisms, but does so in a way which is not completely consistent with a utility
maximization framework.
Given the complexities of the decision making process, a pertinent question at
this point is: How important is it to model behavior, if we are interested simply in
valuing changes in characteristics (e.g. environmental improvements)? The answer to
this question is critical. The costs of obtaining good models of behavior in this
context are high and we need to know whether they are worth it,
One can debate the importance of wholly consistent, utilitic theoretic models,
but what is much more certain is the importance of estimating effectively the complex
dimensions of recreational demand. There are two reasons for this. Estimation can
be biased if account is not taken of corner solutions (see for example the literature
on truncated and censored samples). More important for our purposes here, welfare
measurement in this context depends on the behavioral adjustments of individuals. In
15
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the next section, we will summarize some of the work on welfare measurement in a
discrete choice framework but this must await a more rigorous description of the
recreationalists' decision model. At this point, it is useful to present some
intuition.
Consider once again the water quality example. Suppose there are N sites and
water quality is improved at one of these sites, j. It is true that those who visit
site j will benefit, How much they benefit will be affected by how many trips they
take to site j - a decision which might change with the improvement of the site.
Additionally, recreationalists who did not previously visit site j may now find it
desirable and may move from corner solutions for visits to site j to positive
demands. Finally, we may find the improvement of site j attracting previous non-
participants into the recreational activity.
Now suppose more than one site's quality is improved, a more likely result of a
regional implementation of an environmental regulation. Then, depending on the
pattern of improvements, all sorts of re-orderings may take place. Some sites may be
improved but may generate no user net benefits because they actually lose visits to
other more improved sites. Clearly the welfare gains to an individual at any one
site are conditioned on his decision to visit that site and must be adjusted by the
probability of that site being visited. Models which do not take into account
changes in behavior can not accurately measure benefits.
Corner Solution Models and Welfare Evaluation
In this section we present an approach which takes account conceptually of all
aspects af the multiple site recreational decision. The "general" corner solution
model is extremely difficult to estimate, but we present its logic here for two
reasons. The approach incorporates in a consistent way all facets of the
recreational decision process and thus provides a standard by which to compare other,
more tractable, approaches. Also it facilitates a clear statement of appropriate
16
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welfare measures.
We make a distinction here between "extreme" and "general" corner solution
models. "Extreme" corner solutions arise when something in the structure of the
decision forces a corner solution in _a|l but one of the site demands (which we shall
denote x^). This can occur either because the sites are perfect substitutes or
because for some logical or institutional reason, the sites are mutually exclusive.
By contrast, a "general" corner solution arises when some, but no necessarily N-1, of
the x^'s are zero at the optimum.
For most recreation choices one finds evidence of a general rather than an
extreme corner solution. The total demand for the class of commodities is allocated
to more than one, but less than N, of the quality differentiated goods. However, the
analysis of extreme corner solutions is more straightforward and will set the stage
for the more general models.
Suppose for the moment, that the consumer has decided to consume only good i
(visit site i). His utility, conditional on this decision, can be written as
(14) un- = u(0,...,0,x1,0,...,0,D,z;£)
where x.j is the number of visits to site i, b is of vector of site characteristics, z
is a Hicksian good and £ is a random vector. The conditional direct utility function
can be written (if we assume weak complementarity between site characteristics and
visits) as
(15)
Given his selection of this site, he still must make a decision as to the number of
times he should visit it over the recreation season by solving:
(16) maximize u.,-*(x.,- .b^z;£.) s.t. p-jx.,- + z = y
x.j z x.j >_ 0, z 0.
17
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The solutions are
(17)
xi = hi*(p,b,y;t)
z = zi(pi,bi,y;t) = y - pihi*(pi .b,- ,y;L).
These demand functions are "conditional" ordinary demand functions, conditional on
an interior solution for (i.e. conditional on the decision to consume the
particular at a nonzero level and all other x's at a zero level). The conditional
indirect utility function obtained by substituting these functions back into
is v-j*(p.j ,b.j ,y;c). These functions are random variables from the point of view of
the econometric investigator, and their distribution may be derived from the assumed
joint density of c.,ffc(L).
All of the foregoing is conditional on the consumer's selecting site i. The
discrete choice of which site to select can once again be represented by a set of
binary valued indices where d.j = 1 if x.,- > 0 and d^ = 0 if x^ = 0. The
choice may be expressed in terms of the conditional indirect utility functions as
The "unconditional" demand functions can not be derived by applying the standard
calculus but are defined by the conditional ones together with the binary valued
indices:
0 otherwi se
1 if vi*{Pi ,bi ,y;b) >_ Vj-*(Pj,bj,y;£.), allj
where the expected value of d^ is
(20)
•^(p.b.y;*) = di(p,b,y;t)h1*(p1,bi,y;£) i = 1
N
18
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Additionally, the unconditional indirect utility function is given by
(21)
v(p,t>,y;£) = max[v1*(p1,b1,y;£),...,vN*(pN,bN,y;£)]
The practical application of extreme corner solution models rests on the ability
to devise specific functional forms for the conditional indirect utility functions
and the joint density f^(£) which yield reasonably tractable formulas for the
discrete choice probabilities and the conditional demand functions. Hanemann (1984a)
presents a variety of demand functions suitable for extreme corner solutions which
offer considerable flexibility in modelling price, income, and quality elasticities.
Unfortunately, it is "general" and not "extreme" corner solutions which
characterize most multiple site recreational decisions, and the general corner
solution is more difficult to estimate. Several approaches to treating this problem
are explored by Hanemann in Bockstael, Hanemann and Strand (Chap. 9). However, in
this paper we consider only one for exposition.
The generalized corner solution differs from the extreme corner solution in that
more than one alternative (site) is chosen and has a nonzero level of demand. One
estimation procedure appeals to the economic considerations underlying the solution to
the utility maximization problem embodied in the Kuhn Tucker conditions.
Substituting the budget constraint into the utility function, this problem may be
written
(22) maximize u(x,b,z;<) =
maximize u(x,b,yr -fpjXjjl) s.t. 0 £ x^ £ y/p-j i = 1
N
and the Kuhn Tucker conditions are
(23)
19
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Suppose one observes an individual who purchases quantities x^,...^ of goods
1 _ and y - 2 p^Xj of the Hicksian composite commodity, but nothing of goods
Q + 1,...,N. Define the N random variables by
(24) Hi = 1i(x,p,b,y;£)
-fr. t " P£ia '>L)
O f-b v Si
and let be their joint density derived from f£(t) by an appropriate
change of variables. The probability of observing this consumption event is given by
x, = x-j» i = 1 »•••»()
(25) Pr "
= 0, i Q+l
0, "i 1,...,Q
= Pr )
V^i £ 0, i = Q+1,...,N
t> o
j ••• j ^°»• • * »°»1q+1'• • * »"lt^dlQ+l dlN'
-oO
Given the entire sample of consumers located at different corner solutions, the
likelihood function would be the product of individual probability statements
each having this form.
Two general points emerge from this analysis which are worth emphasizing,
first, the probability expressions generally require the evaluation of an (N-Q)-
dimensional cumulative distribution function - i.e. a multiple integral whose
dimensionality corresponds to one less than the number of commodities not consumed.
In the recreation case, where the number of sites (N) may equal perhaps 20, but the
number of sites visited by an average individual (Q) will be 2 or 3, the evaluation
20
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of these integrals may be a daunting task unless one chooses the error structure and
utility function carefully.
The second point worth emphasizing is that there is a basic tradeoff between
achieving simplicity in the Kuhn-Tucker conditions and in the demand functions. In
order to appreciate the significance of this tradeoff, it is necessary to consider
the distinction between estimation and prediction as facets of the modelling
activity. Both involve probability statements - estimation, for the purpose of
forming likelihood functions; prediction, for the purpose of calculating the
expected demand for sites under different price or quality regimes. In conventional
demand analysis, including the share models described in the previous section,
estimation and prediction are both based on essentially the same thing - the system
of demand or share equations. Therefore, generally speaking, a stochastic
specification which facilitates the process of estimation will also facilitate that
of prediction, and conversely. This is not true when we deal with corner solutions,
where estimation can be based on the (perhaps simple) Kuhn-Tucker conditions, while
prediction is based on the (perhaps complex) demand functions. An alternative and
promising line of attack would be to begin with the conditional indirect utility
functions. This approach is outlined in Bockstael, Strand and Hanemann but not
explored here.
At this juncture we proceed to discuss how, when estimated, the multiple site
demand models can be used to derive money measures of the effect on an individual's
welfare of a change in the qualities (or prices) of the available recreation sites.
The task of performing welfare evaluations is more complex than the basic theory of
welfare measurement (Maler 1971, 1974) when one works in a discrete choice, random
utility setting. The theory of welfare measurement in this context has been
developed by Hanemann (1982c), and revised and extended in Hanemann (1984c). We will
provide a sketch of this theory here, leaving the reader to refer to these papers for
21
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a more detailed presentation. Both papers deal with extreme, rather than general,
corner solutions but these can involve either purely discrete choices as in the logit
models or mixed discrete continuous choices. After summarizing the methodology for
these extreme corner solution models we will indicate how it can be extended to cover
general corner solution models of the type discussed earlier. The compensation
required by the individual to offset a change in prices and/or qualities from (p',b')
to (p",b") are given by
(A similar expression exists for equivalent variation, which we shall ignore here to
save space.) The problem in the random utility context is that C is now a random
variable, since it depends implicitly on How then, do we obtain a single number
representing the compensating variation for the price/quality change?
Hanemann (1984c) presents three different approaches to welfare evaluations in
the random utility context, only one of which we present here. That approach is
based on the expectation of the individual's unconditional indirect utility function.
In terms of this function, the measure of compensating variation is the quantity C'
defined by
This measure has been employed by Hanemann (1978, 1982c, 1983a), McFadden (1981), and
Small and Rosen (1982). The formulas needed to calculate E[v(*)] for some common
logit and probit additive-error random utility models are summarized in Hanemann
(1982c) . For example, in the GEV logit model
which is simply the inclusive value index (apart from Euler's constant, 0.57722...).
(26)
v(p'',b'',y-C;£) = v(p',b',y;t).
(27)
E[v(p",b",y-C')] = E[v(p',b',y)].
(28)
22
-------
The important point is that we must take into account both the discrete and
continuous aspect of the decision problem and the stochastic nature of the decision.
One way of doing this is to calculate the compensation which equates the expected
values of the indirect utility functions. It is easy to see the implications of this
in the extreme corner solution context. Suppose we are concerned with evaluating the
benefits from an improvement in quality at an individual site - say, site 1. Thus,
bj changes from b^' to b^11 while b2»...,bjj and pp...,Pu remain constant.
If we knew for certain whether or not each individual would select site 1, these
welfare measures would be straightforward to calculate. They would be the sum of the
compensation over individuals who chose site 1, where the compensations are defined
on the conditional indirect utility functions such that
(29) v1(p1,bi" ,y-C) = v1(p1,b1,,y).
But some individuals will and some will not visit site 1 and we can only predict the
probabilities of site selection. And, of equal importance, these probabilities will
themselves be functions of the qualities (and prices). Equation (27) suggests that
we need to weight the conditional indirect utility functions by the probabilities of
choosing different sites. (Hanemann (1984) suggests the possibility of using,
instead, moments of the induced distribution on the compensating variation as a
useful welfare measure.)
The extension to the general corner solution model is intuitively, if not
analytically, clear. Here conditional indirect utility functions are defined for all
combinations of choices of sites. There will, for example, be an indirect utility
function conditioned on the individual choosing nonzero trips to sites 1,2,and 3, but
not 4 through N. This will differ for example, from the indirect utility function
conditioned on the choice of sites 1,2 and 4, but not 3, or 5 through N.
Additionally the conditional demand function for site 1 will differ depending on
which additional sites are chosen.
23
-------
By analogy to the above, welfare measures will require the assessment of the
probability of choosing each possible combination of sites as weights for the
indirect utility functions conditioned on site choices. This complexity stems from
the very nature of the recreational decision process. The benefits which an
individual derives from an environmental quality change at some site or group of
sites is dependent on whether or not, and at what level, he visits those sites. But
this latter mixed continuous-discrete choice is itself a function of quality
characteristics.
Some Estimation Examples
Our ultimate intent is to undertake the estimation of each of the above
described models (which is capable of valuing site characteristics) using a common
data set. The purpose is not to compare the benefit estimates which each approach
produces, for such comparisons can never be decisive in any way. Instead we hope
simply to demonstrate how each approach gets estimates - to reveal data requirements,
necessary estimation techniques, and the practical problems which arise in the
estimation process. Of most importance, we wish to determine how useful each
approach is in providing answers to policy questions.
Unfortunately we have not yet completed this portion of our task. Of the four
general approaches (hedonic travel cost, multinomial shares, discrete choice, and
general corner solution), we have completed only two and have estimated the first
stage of a third. In what follows we present the results of two versions of the
hedonic travel cost model (as presented in Brown and Mendelsohn, 1984, and in
Mendelsohn, 1984) and a rather elaborate discrete-continuous choice model (from
Bockstael, Hanemann and Strand). The fact that these two are the first to be
completed is no accident. They have in their favor one very important quality. Both
can be estimated from readily available economic computer software packages. The
hedonic travel cost approach is by far the simplest. The first version relies only
24
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on OLS estimation techniques, although the second adds a fairly complex Box-Cox
transformation. The discrete choice models of Caulkins and Feenberg and Mills
requires a multinomial logit and the more elaborate discrete-continuous choice model
estimated here requires access to a Tobit type routine (or a general maximum like-
lihood algorithm) as well.
The approach which is most preferred theoretically is by far the most difficult
to estimate. One way to handle the general corner solution model is to estimate the
parameters in the direct utility function by maximizing a likelihood function
composed of the Kuhn Tucker conditions. By choosing a utility function and error
structure, we were able to obtain significant parameter estimates with expected
signs. This gives us the direct utility function as a function of these parameters,
number of visits, quality of sites, characteristics of the individual and the error
structure. However, in a corner solution world, such information is not easy to
transform into demands functions for prediction or into indirect utility functions
for welfare analysis. While work is continuing in this area, we present the results
of our estimation of the other two models.
The data set we use was collected by EPA in 1975 and includes information on
recreational swimming at Boston area beaches. The data set contains information on
both participants and nonparticipants, as it is based on random household interviews
in the Boston SMSA. For each participant, a complete season's beach use pattern is
reported, including the number of trips to each beach in the Boston area. We have
objective measures of water quality for 30 beach sites. It should be noted that,
participants in this data set, like other data sets of its kind which we have
encountered, tend to visit more than one site but far less than all sites available.
1. Discrete-Continuous Choice Model
The multiple site recreational demand model estimated by Bockstael, Hanemann and
Strand has two components. The first is the macro-decision: does an individual
25
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participate in the activity of interest (swimming at beaches in the Boston-Cape Cod
area) and if so how many trips does he take in a season? The second component is a
site allocation decision: on each choice occasion, which site does he visit?
Because the micro decision generates information necessary for estimation of the
macro decision, we deal with the micro decision first.
The first part of the model involves the estimation of the household's choice
among sites. The indirect utility associated with choosing the site is some
function Of z.,-, a vector of attributes of the it'1 alternative,, so that v.,-* = v^z^)
The random component is additive and attributed to the systematic, but
unmeasurable, variation in tastes and omitted variables. If the £'s are
independently and identically distributed with type I extreme value distribution
(Weibull), then we have a multinomial logit model. However, the multinomial logit
implicitly assumes independence of irrelevant alternatives, i.e. the relative odds of
choosing any pair of alternatives remains constant no matter what happens in the
remainder of the choice set, Thus, this model allows for no specific pattern of
correlation among the errors associated with the alternatives; it denies - and in
fact is violated by - any particular similarities within groups of alternatives.
McFadden (1978) has shown that a more general nested logit model specifically
incorporating varying correlations among the errors associated with the alternatives
can also be derived from a stochastic utility maximization framework. If the Cs
have a generalized extreme value distribution then a pattern of correlation among the
choices can be allowed. Given the probabilistic choice model
e. *¦ ** . ,%e- >
(30) Pi= - „, ^
where G-j is the partial of G with respect to the i argument and G(e 1 . N e ) has
certain properties which imply that
26
-------
(31) = expJ -G(e ri)
vi
is a multivariate extreme value distribution. When G(e ,...,e N) is defined as
«r vi
Ze \ then the model reduces to the ordinary multinomial logit (MNL) desribed above.
However when
? (*r w/0-«\O
(32) G(Y) = \*rK '
W»l {*.
where there are M subsets of the N alternatives and 0
-------
To make the estimation process explicit, let us consider the following form of
vim
(33) vim = ^im + ^ tyn
where the Z's denote attributes associated with all sites and the W's are associated
solely with the salt water-fresh water choice, i indexes the site and m indexes the
salt or fresh water alternative. Also let us assume that G"m is identical within all
groups and equal to 0\ Define the "inclusive value" of group m as
(34) 1™ = ln(5j
NOW, the probability of choosing site i conditioned on the salt/fresh water choice is
(35) pi |m = ~
2. €-
and the probability of making the salt (or fresh) water choice is
tv' Wv* + tv-«OX^
&
(36) Wi »
.2. e.
These probabilities can be estimated using MNL procedures. First, the jm are
estimated with M independent applications of the multinomial logit (where M = 2 here
- one for salt water beaches and one for fresh water beaches). Note that at
this stage 9 is not recoverable, but can be estimated only up to a scale factor of
1-G*. From the results of (35), the inclusive prices (34) are calculated and
incorporated as variables in the second level of estimation (36). Here them's and
the
-------
In choosing among sites, the determinants of most interest are the site
characteristics which vary over alternatives and the costs of gaining access to
sites. The quality variables chosen for this model include environmental indicators
such as oil, turbidity, fecal coliform, chemical oxygen demand and temperature.
Three other variables are identified as potentially valuable in the site choice
model, each of which is a restricted variable of sorts. The variable "Noise" was set
to one for all beaches which were in particularly noisy, congested areas close to
freeways (zero otherwise). The variable "Ethnic" was set to one if the beach was
especailly popular with a particular ethnic group and the individual was not of that
group (zero otherwise). Several beaches were so designated in the study. Finally
"Auto" was set to one if a beach was not accessible by public transportation and the
household did not own a car.
Because of the nature of the logit model, variables which are present in the
indirect utility function but do not change across alternatives (i.e. individual
specific) tend to cancel out upon estimation - that is, their coefficients cannot be
recovered. This is true unless it is argued that an alternative specific variable has
a different effect depending on the value of a socioeconomic variable, in which case
the two variables could be entered interactively.
Income is a special individual specific variable because we know from utility
theory that income and price must enter the indirect utility function in the form
Y - p. Thus if Y - p^enters linearly into v.,-, income will cancel out upon
estimation, but the coefficient on price will be income's implicit coefficient as
well. This will be important in calculating benefits.
Estimation of the second stage of the model requires the calculation of
inclusive values from each of the first stage estimations, where the inclusive price
is as defined in (34). This "inclusive value" captures the information about each
group of sites in Stage I. Thus if water quality were to change at some sites, the
29
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inclusive values would change. Additionally, we postulate that other variables
besides the inclusive values may enter at this stage - variables which affect the
salt-fresh water decision but do not vary over alternatives within each group. Also,
since the fresh-salt water decision is dichotomous, it is straightforward to enter
individual specific variables which we believe may affect salt water and fresh water
decisions differently. Besides a constant term and the inclusive price, we include
the size of the household, the proportion of children and whether or not the
household has access to a swimming pool.
Table 1 presents the estimated coefficients and test statistics for the first
stage of the GEV model and Table 2 presents the second stage results. Goodness of
fit measures for logit models are not especially decisive. For each model we present
Chi-square statistics based on likelihood ratio tests. In each case the statistic is
significant at the 1% level of significance.
In the first stage of the GEV, the estimated coefficients on quality
characteristics all are significant at the 5% significance level and of the expected
sign (with the possible exception of temperature and turbidity in the fresh water
equation), Additionally, individuals (ceteris paribus) visit closer beaches, avoid
noisy areas and are discouraged by beaches heavily pospulated by ethnic groups
different from their own. Individuals who do not own cars are less likely to visit
beaches not serviced by public transportation.
From the first stage results the "inclusive" values were calculated and
introduced in stage two. The inclusive value term captures the effect of all of the
variables used to explain site choice. In our problem, 1 -5", equals .854 implying a
of .146, which is significantly different from both 0 and 1. This indicates fresh
and salt water sites are considered significantly different, but all fresh water sites
are not viewed as perfect substitutes for one another and neither are all salt water
sites. Thus we can expect that there are some gains from using the GEV
30
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TABLE 1: First Stage GEV
Model Estimates
of Choice Among Freshwater and
Saltwater Beaches
Boston - Cape Cod, 1975
Saltwater
Freshwater
Beach
Estimate
Estimate
Characteri sti c
(t-ratio)
(t-ratio)
011
-.036
-.100
(-10.01)
(-2.62) *
Fecal Coliform
-.049
-.486
(-4.12)
(-5.47)
T emperature
-.056
-.281
(-5.32)
(-3.58)
COD
-.022
-.169
(-17.67 )
(-14.31)
T u r b i d i ty
-.047
.273
(-8.48)
(9.10)
Noi se
-.109
-.938
(-9.90)
(-8.47)
Public Trans.
-1.103
-1.275
(-12.91)
(-4.07)
Beach Ethnicity
-1.784
-1.321
(-27.58)
(-5.51)
Trip Cost
-.572
-2.166
(-35.89)
(-26.61)
L i keVihood
. -10850.
-89b .
Chi-souared v/ith
9 degrees of freedom 4084.2
1804.7
-------
TABLE 2
Second Stage GEV Model Estimates of Choice
between
Saltwater and Freshwater Beaches
Boston - Cape Cod, 1975
Constant Inclusive No. of People % of Children
Price in Household in Household
Access
to Swim.
Pool
(1-*)
Estimated
Coefficient 16.520
(t-ratio) (22.9)
.854
(23.6)*
-.162
(-10.9)
(2.33)
.420
,861
(9.16)
Likelihood = -1780.
Chi squared with
5 degrees of freedom = 3421.0
* t-ratios in parentheses
** This t-ratio tests significant difference from zero. A more appropriate test
is significant difference from 1; the relevant t- ratio is -4.044.
-------
specification. Because of the way in which the constant term, household size,
percent children, and swimming pool are entered into the estimation, their
coefficients reflect the log of the odds of choosing a salt water site over a fresh
water site. Thus larger families tend to go to lakes but families with a larger
portion of children tend to go to salt water beaches. Those who have access to a
swimming pool are more likely to visit salt water beaches. The constant term
suggests that, ceteris paribus, people prefer salt water beaches.
The second part of the model is a single activity model of swimming
participation. While several discrete-continuous methods are available, we use the
Tobit model which presumes that individual's decisions can be described as
x,- = h(z.j) + S'1- if h(z.j) + &^ > 0
(37)
xn- = 0 if h{z.j) + £0.
and that the decision of whether or not to participate and how much to participate
are dictated by the same forces. The likelihood function for model is
(38) LT •= "IT 'IT
U* L\s
where s is the set of individuals who participate. It was determined that the
following household characteristics were most likely to affect this decision:
income
size and composition of household
education
length of work week of household head
ownership of water sports equipment.
Additionally, we would wish to include variables reflecting the cost and
quality of the swimming activities available. Herein lies one of the major
difficulties with this "second best," two part approach. How does one choose
appropriate variables for the cost and quality of swimming excursions, if those trips
are or can be taken to different sites with different costs and quality
characteristics? Ideally the decision of how much and where to go should be modelled
31
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simultaneously as in the corner solution model. However, the discrete choice models
are unable to handle these problems simultaneously and require some approximations.
Indeed, we wish to include variables which reflect the quality and costs of
the best alternatives for each individual, not necessarily the characteristics of the
closest site or the average characteristics over sites. The inclusive value concept
has an appealing interpretation since it represents, in a sense, the value of
different alternatives weighted by their probabilities of being chosen. Defining an
inclusive value from both stages of the GEV estimation gives us
<39»
where Js is the set of salt water sites, Jp is the set of fresh water sites and Vj =
9'Zj + ^1 Wj where the Z's are explanatory variables in the first stage and the W's
are explanatory variables in the second stage.
Inclusion of Ip in our macro allocation model is intuitively appealing but
not perfectly correct. Ip, after all, is defined on choice occasions and the macro
allocation decision is an annual or seasonal decision. In fact, there is no obvious
way to make this model, or any of the related models, perfectly consistent between
micro and macro decisions as well as economically plausible. Nonetheless we hope it
offers us a good, albeit ad hoc, reflection of the value of the swimming alternatives
available to the individual. It is, however, not consistent with a McFadden type
utility theoretic model, and as such, its coefficient is not theoretically bounded by
zero and one.
The model includes income, household size, household composition, a restricted
variable for ownership of specific water sports equipment and the inclusive value
variable discussed above. The results are presented in Table 3. Other variables
such as education and length of work week were not significantly different from zero
by any reasonable test in the models employed, nor did their exclusion significantly
32
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TABLE 3
Estimates of Tobit Model of Boston
Swimming Participation and Intensity
Variable Tobit Initial Value
Estimates (OLS estimates)
Constant
26.01
35.98
(2.57)*
(4.59)
"Inclusive Value"
.897
1.02
(1.86)
(2.74)
Income
-1.19
-.07
(-.56)
(1.79)
Size of Household
-24.10
-8.1
(-2.76)
(-2.08)
Percent Children
-6.18
-14.71
(-1.22)
(-2.02)
Water Sports Equipment
13.05
6.42
(3.44)
(2.05)
Chi-Squared statistic = 262.
* t-ratios in parentheses
-------
model are combined with site qualities, individuals' costs and other variables to
predict each household's probability of visiting each site. A predicted probability
can be interpretted as a predicted share of the household's total trips. Thus a
change in the quality at one or more sites can change a) the total number of tips
taken, (b) whether or not a household participates in the recreational activity, and
c) the allocation of trips among sites.
The ultimate purpose of the modelling effort however is to estimate the benefits
associated with improvements in water quality.
In our problem the expected value of the indirect utility function can be shown
to equal
(40)
where k is a constant.
Now consider a change in prices and quality from (p°,b°) to (p^,b^). The C'
measure defined earlier is given by
(41)
V(p°,t>°,y) = v(p1,t>1,y-C)
or
(42) m '
There is no closed form solution for compensating variation in this case, but
we can approximate the compensating variation of a change form (p°,b°) to (p^.b^) by
(43) CVfcC
34
-------
where m = 1,2 denotes the salt and fresh water alternatives, and
represent values of variables before and after the policy change respectively, arid
and Y2 are the implicit income coefficients in the salt and fresh water models.
The calculation of CV according to (43) yields an estimate of the expected
compensating variation per choice occasion for the household. To obtain annual or
seasonal benefit estimates this number must be multiplied by the predicted number of
trips the individual takes. One should note that even if the individual takes no
more trips in response to the quality change (either because he is constrained or
because a more substantial quality change is necessary to increment the number of
trips), the benefits of improvements are still measureable. That is, even if a
quality change is insufficiently large to prompt an individual to alter his behavior
in any way, the benefits he experiences if he is a user of the improved sites can be
calculated.
In Table 4 the estimated benefits (in 1974 dollars) of a series of hypothetical
water quality changes are reported. The hypothetical water quality changes
introduced include a 10% and a 30% reduction in each of the following water quality
parameters individually: oil, chemical oxygen demand (COD) and fecal coliform.
These reductions were introduced uniformly across all sites. Also in Table 4 is
reported the results of a 30% reduction at all sites in oil, turbidity, COD and fecal
coliform simultaneously. This figure can be compared to the same sort of pollutant
reductions if they affect only beaches in Boston harbor. Reductions in pollutants at
downtown Boston beaches (8 of the 30 sites) generate more than half the benefits
reported when all sites are uniformly improved.
These examples are offered to demonstrate the sorts of questions which can be
answered with a model such as the one estimated here. The model is admittedly a
"second best" model; it pieces together relevant aspects of the recreational
decision problem in a somewhat ad hoc way, not completely consistent with any
underlying story of utility maximization. While only an approximation, however, the
35
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TABLE 4
Average Compensating Variation Estimates of
Specific Reductions in Pollutants at Boston Area Beaches
(in 1 974 dollars)
1 0 % reduction
at all sites
per choice
occasion
o i I
COD
fecal
c o I i f o r m
$ .05
.12
.- 2
per
season
$ .96
2.65
. 1 9
30% reduction
at all sites
per choice per
occasion season
$ .20
.29
.12
$4.66
7.15
2.85
30% reduction
at all sites
perchoice per
occasion season
oil, turbidity, COD
and fecal coliform $.50
$12.04
30% reduction at
downtown Boston Beaches
per choice per
occasion season
$.27
$6.13
-------
model does attempt to capture all aspects of the individual's recreational decision.
2. The Hedonic Travel Cost Model
The only other approach for which we have completed estimation results is the
hedonic travel cost method. Unfortunately, we encountered several difficulties, some
of which may be associated with the nature of our data and the recreational activity
we are studying and some of which is no doubt due to our lack of experience with the
approach. Nonetheless we present our results, hoping to solicit some guidance and
stimulate some discussion.
We chose to estimate the model for the subset of saltwater, sites since it seems
more likely that good results could be obtained by excluding the 8 very different
fresh water sites. The first difficulty we encountered relates to the nature of the
observed site choice decisions in our data set and the implicit assumptions of the
hedonic travel cost model (HTC). Past HTC applications have implicitly assumed that
individuals visit only one site, yet about three-fourths of the participants in the
Boston survey visited more than one site. We skirted the problem, perhaps
Incorrectly, by including different site choices by the same individual in the
regressions as additional observations (in effect as though they were site choices by
different individuals). By doing this we gained the added benefit of more variation
in sites visited by individuals from the same origin.
Following the approach prescribed by Brown and Mendelsohn, we chose the two most
important environmental quality indices (oil and COD) and ran linear regressions of
costs on site characteristics for each of 25 origins. The site characteristics are
indexed here such that increasing values imply improving water quality to facilitate
interpretation. We initially attempted this on the 93 smaller origin zones but found
we had so little variation in site choices that regressions were infeasible.
Given the linear functional form of the Brown and Mendelsohn application, the
hedonic prices of oil and COD are the estimated coefficients of the regression,
36
-------
Ci ~&o 2D-j + 6-j
where = costs, 0-j = an index of the absence of oil and Dj = an index of the
absence of COD. The results of these regressions produced 50 "hedonic prices"
(coefficients) only 7 of which were positive and significantly different from zero.
In contrast, 23 of the 50 are negative and significantly different from zero,
The marginal value functions for quality characteristics are then estimated by
regressing these derived hedonic prices for individuals from each origin to each site
on the level of the quality characteristics at the relevant site and several
individual related variables. These variables included income and the ethnic dummy
variable which had turned out to be important in the discrete-continuous choice
model. We also included an instrumental variable for the number of trips the
indivdual took, since this variable was included in the Brown and Mendelsohn
application. As in that paper, trips were initially regressed on the other
individual-specific variables (ethnic dummy and income) as well as dummy variables
for origins. Then the predicted values were included in the following marginal value
functions for each characteristic
A
(45) P0i =^0 +°<101- +«2Di +*3yi +*4Ei 'h^5xi + ui
and
A
(46) PD-j =Yo + Vl°i +Y2Di +V3yi +Y4Ei +V5Xi + wi
where POj and PD-j are the derived prices of improvements in oil and COD levels, y.,- is
A
income, X-,- is predicted visits and the E-j is the ethnic dummy.
An important question arose at this point. Since not all hedonic prices from
the first stage were positive and even fewer were significant and positive, we were
uncertain as to whether observations on all prices should be included in the final
stage demand function. The results of two separate approaches are reported in Table
5. The first set of characteristics demand functions includes only those
37
-------
TABLE 5
Demand for Characteristics Using the Hedonic Travel Cost Approach
(Linear hedonic equation, inverse demand function)
Regressions include only positive prices:
o ^
Price Oil = .15 + .007 Oil* + .0004 COD* - .064 Ethnic.+ 2.9X10"° Inc - .011 Visits
(4.90)** (11.97) (2.46) (-6.28) (4.64) (-50.64)
Price COD = .007 + .00005 COD + .001 Oil - .004 Ethnic + 4.5x10 y Inc - .0007 Visits
(1.56) (2.12) (10.4) (-2.83) (4.74) (-22.33)
Regressions include all prices:
A
Price Oil = .06 + .0015 Oil + .0005 COD + .024 Ethnic + 2.19xl0~8 Inc - .0035 Visits
(1.77) (2.32) (3.17) (1 94) (3.05) (-15.98)
Price COD = -1624 - 89.4 COD + 485.1 Oil - 7311.7 Ethnic + 002 Inc. - 375.5 Visits
(-.97) (- 1 1.1 ) (15.26) (-11.75) (5.78) (-34.87)
* oil and COD denote indices which increase with declining levels of these pollutants.
** t statistics are in parentheses
-------
observations for which we have positive prices. The second set includes all
observations. The functions estimated on reasonable prices (the positive ones) did
not produce negative coefficients on own-prices. In both cases, both price
coefficients were significantly different from zero and positive. Only when negative
prices were included did we estimate a negative demand slope - and then only for COD.
Given the rather discouraging results using this form of the model, we chose to
follow the estimation procedures presented in Mendelsohn (1984). Here the first
stage regressions (i.e. the hedonic price equations) were nonlinear Box-Cox
transformations. We estimated
which allowed some flexibility in form as well as a "hedonic price" which was a
function of characteristic levels. Characteristics' prices can not be determined
directly from these results, but must be constructed from the derivation of equation
(47). There are, however, 25 price gradients for each characteristic. Only 11 of the
25 price gradients for COD produced positive prices and 16 of the 25 price gradients
for oil produced positive prices.
The next step of this procedure requires estimating instrumental variables for
characteristic prices (in addition to visits) before including these prices in the
characteristics demand function. Following Mendelsohn, the constructed prices were
regressed on income, the ethnic dummy and site dummies producing predicted prices.
This procedure did not appreciably increase the number of positive prices, however.
The final step of the procedure involves the estimation of characteristic demand
functions with quantity on the left hand side as opposed to price. The forms of
these functions are
(47)
A
A
A
0-j = U0 +*t' +<^3^i +<^4^i +*^5^i + ui
Di =yo +Ylpoi +Y2PDi +V3Yi + vf4Ei +V5Xi + wi
38
-------
Again we ran one set of regressions on observations which had only positive predicted
prices and a second set on all observations including negative prices. The results
are reported in Table 6.
Once again, those regressions which included only positive prices were
unsatisfactory. The own price coefficient was posiive and significant for oil and
insignificant (although negative) for COD. When both positive and negative prices
were included, however, both the oil and COD regressions behaved respectably. For
example, in the oil equation, the demand for cleaner water (less oil) decreased with
the "price" of cleaner water (in terms of oil) increased with the "price" of cleaner
water (in terms of COD), increased with income and decreased with total number of
trips taken. In the COD equation, the demand for less COD decreased with the price
of less COD and increased with the price of less oil. However the signs on income and
total (predicted visits) were reversed from the previous results.
There is an obvious difficulty in the above results. 'We are only able to
estimate negative demand slopes when we include nonsensical (negative) prices. One
can have little faith in the results of such regressions. Nonetheless we used the
one downward sloping demand function in the first set of results (linear hedonic
price and inverse demand function procedure) and calculated the consumer surplus (per
visit?) of a 10% change in COD. The result was an embarrassingly large number -
$39,529. Not trusting demand functions estimated from negative prices, we then
calculated welfare measures using the demand estimation which generated a negative
(albeit insignificant) price slope from the second procedure (Box-Cox hedonic
equation, quantity-dependent demand). The consumer surplus of a 10% change in COD
was calculated to be $450 (per visit?).
The application of the hedonic travel cost model to the Boston data set was far
from successful. The less than satisfactory results at each stage of the procedure
may result from our misunderstanding of the model. Alternatively, it could be that
39
-------
TA3LE 6
Demand for Characteristics Using the Hedonic Travel Cost Approacn
(Nonlinear hedonic equation, quantity dependent demands)
Regressions include only positive prices:
A a , *
Oil* = 36.30 + 7.93 Price Oil + 3.89 Price COD + 1.6x10° Inc + 1.3 Ethnic + .08 Visits
(43.94)** (8.29) ( 1.91) (5.26) (2.05) (6.1)
A ^ fi ^
COD* = 64.39 - .98 Price COD + 6.03 Price Oil - 4.8x10° Inc + 3.4 Ethnic - .206 Visits
(19.27) (-.12) (1.56) (-3.91) (1.32) (-3.98)
Regressions include all prices:
Oil = 44.54 - 1.17 Price Oil + 8.79 Price COD + 1.9xl06 Inc - 1.17 Ethnic - .11 Visits
(110.9) (-2.57) (6.68) (9.2) (-5.19) (-17.34)
COD = 24.05 - 17.06 Price COD + 4.33 Price Oil - 4.1xl06 Inc + 34.25 Ethnic + .37 Visits
(15.11) (-3.27) (2.40) (-5.01) (25.96) (14.62)
* oil and COD denote indices which increase with declining levels of these pollutants.
** t statistics are in parentheses
-------
the approach is appropriate only under very restrictive conditions which are violated
by many real world valuation problems.
40
-------
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(revised 5/3/85)
THE TOTAL VALUE OF WILDLIFE RESOURCES:
CONCEPTUAL AND EMPIRICAL ISSUES
by: Kevin J. Boyle
Department of Agricultural Economics
University of Wisconsin
Madison, WI 53706
and
Richard C. Bishop
Department of Agricultural Economics
University of Wisconsin
Madison, WI 53706
Invited paper, Association of Environmental and Resource Economists Workshop on
Recreational Demand Modeling, Boulder, Colorado, May 17-18, 1985.
The authors would like to thank Scott Milliman, Kathy Segerson and Mike Welsh
for their comments on earlier drafts of this paper. This research was
supported by the College of Agriculture and Life Sciences, University of
Wisconsin-Madison; the Rocky Mountain Forest and Range Experiment Station, U.S.
Forest Service; and the Bureau of Research, Wisconsin Department of Natural
Resources.
The work described in this paper was not funded by the U.S. Environmental
Protection Agency and therefore the contents do not necessarily reflect the
views of the Agency and no official endorsement should be inferred.
-------
THE TOTAL VALUE OF WILDLIFE RESOURCES:
CONCEPTUAL AND EMPIRICAL ISSUES
I. INTRODUCTION
A major issue in benefit-cost analysis is how to conceptualize the total
benefits from environmental assets in a consistent and usable manner. Many
practitioners seem to agree that these benefits can be roughly grouped under
the general headings of "use" and "intrinsic" values (see Fisher and Raucher
1983) . Use benefits are associated with the actual use of an environmental
asset and intrinsic benefits comprise a catch-all category for all nonuse
benefits such as option values and existence benefits. However, considerable
confusion exists regarding the exact distinction between these categories. In
addition, the components of the intrinsic benefit category have not always been
clearly defined in a way that is internally consistent.
Partly because of these conceptual problems, the valuation of resources
often focuses on consumptive uses such as hunting, fishing and trapping.
Esoteric benefits such as existence values have been almost completely ignored
and even nonconsumptive uses like viewing wildlife are rarely studied.-7' The
purpose of this paper will be to identify the components of total value and to
clarify the definitions of these various components in the context of wildlife
Recent studies by Brookshire, Eubanks and Randall (1983), Stoll and
Johnson (1984) and Walsh, Loomis and Gillman (1984) are exceptions to this
statement.
-------
valuation.— Specifically, the various types of use values will be discussed
and a theoretic definition of existence value will be proposed. Further, an
application to valuing two of Wisconsin's endangered species of wildlife will
be presented.
CONCEPTUAL FRAMEWORK
A TRADITIONAL NOTION OF VALUE
Early benefit-cost analyses focused merely on the user benefits associated
with environmental assets. Later theoretical analyses incorporated the concept
of option value which was first introduced by Weisbrod (1964). The option
value concept was subsequently refined and clarified (Bishop 1982; Freeman
1984; Graham 1981; Hanemann 1985; and Smith 1983 and 1984a). Option value is
an adjustment to the monetary measure of welfare to reflect the uncertainty
consumers face when future states of the world are unknown. Recent
developments indicate that option value may be either positive or negative.
Thus, the maximum that an individual would be willing to pay to insure that an
environmental asset will be available in the future is termed "option price"
and consists of the expected value of Hicksian surplus and option value, where
option value may be positive, negative or zero.
Consider the case of elk hunting. The choice problem faced by an elk
hunter, under conditions of certainty, can be stated as
max U(X,Z) 1.1
x, z
s.t. px + pz^i
X z
2/
— The conceptual approach developed in this paper is applicable to the
valuation of other types of nonmarket resources when the peculiarity of
the resource in question is taken into consideration.
-------
where U(-) is a utility function, X is elk hunting, Z is a vector of market
goods and services, Px is the price of elk hunting, is a vector of market
prices and I is income. The hunting argument is typically measured in some
3/
unit of time, e.g., trips, days, etc.— The cost of a unit of hunting is
interpreted as the price of hunting.
Assuming this maximization problem is well behaved and can be solved, an
indirect utility function can be derived:
¦u•
The reference level of utility is "0. The equivalent variation measure of the
total value of elk hunting (3 ) is given by
3.
V(w-V -
where P™ is the lowest price which is high enough that the individual would
choose not to hunt. All other prices are held constant at their existing
levels. The argument &a is the maximum that the individual would pay to
maintain the opportunity to hunt elk rather than give it up completely.
3/
The important consideration is that
hunting regardless of the units of
concerned with the units of measure
people do derive satisfaction from
measure. Thus, we are not overly
in the present discussion.
-------
The concepts of option price and option value arise when uncertainty is
4/
introduced into the valuation question.— Suppose that it is desirable to know
the value that elk hunters place on a hunt in a particular wildlife management
area. Individual elk hunters are certain that they will desire to hunt elk in
this wildlife management area, but that uncertainty arises as to whether this
area will be open to elk hunting due to an administrative snafu. This simple
example is equivalent to price uncertainty in a timeless world (see Bishop
1982). Option price in this simple model, under conditions of "supply-side"
uncertainty in a timeless world,'is defined by
V(P ,P ,I-B ) = irV(Py,P ,1) + (1-tt)V(P™,Pz,I) (1.5)
where 3 is a equivalent variation measure of supply-side option price and
0ps
IT is the probability that the wildlife area will be open for elk hunting. The
left-hand side of equation (1.4) can be substituted into equation (1.5) to
yield the following relation:
V(P »P ,i-B ) = T7V(P ,P ,1) + (l-TT)V(P ,P ,I-B ). l.C
xzop x z x z a
s
Using equation (1.6) and following Bishop (1982), supply-side option value is
defined as
3 = 3 - (1-ir) B > 0
ov op a
s s
4/
5/
Our intent is not to make this another paper on option value. This simple
example is merely intended to identify the option price concept and to
point out when option values occur. In the remainder of the paper we will
merely identify where uncertainty can enter the model giving rise to
notions of option price and option value.
The distinction between demand-side and supply-side uncertainty has been
made by Bishop (1982) and Freemen (1985).
-------
where 3
is supply option value and the other symbols are as previously
ov
s
defined. If some of the simplifying assumptions of the current model are
relaxed, the sign of supply-side option value is indeterminate (Chavas and
Bishop 1984). This result is consistent with the findings of Freeman (1985).
Now assume that elk hunters are uncertain as to whether they will desire
to participate in the hunt, but that it is certain that the wildlife management
area will be open to hunting. "Demand-side" uncertainty results in a slightly
different definition of option price. This is
is the probability that the individual will choose to participate in the hunt
at any price, i.e., hunting is not an argument in the individual's utility
function. The left-hand side of equation (1.4) can be substituted into
equation (1.8) to yield the following relation:
This relationship can be used to derive demand-side option value. We will not
derive demand-side option value here as it is slightly more complicated than
supply-side option value and the derivation is a relatively straightforward
application of previous work by Bishop (1982) and Smith (1983). These authors
is a equivalent variation measure of demand-side option price and it
iTV(Px,Pz,I-e
) + (l-ir)V(P ,1-B ) =
z op.
Q
uV(P ,P ,I-B ) + (l-u)V(P ,1).
x z a z
-------
have shown that the sign of option value is indeterminate when an individual's
demand is uncertain.
The current model summarizes the simple framework traditionally used for
considering consumptive use values for wildlife, e.g., hunting, fishing and
trapping. This model is not general enough in that it overlooks individuals
who are not hunters, but do participate in other types of uses of wildlife,
e.g., viewing, photographing, reading, etc. In addition, consumptive users may
also participate in these other activities. These other uses may need to be
incorporated specifically as arguments in the utility function as they may be
measured in different units than consumptive use or may have different per unit
prices, and they may also have different parameters in the utility function.
These other uses may also have complementary or substitute relations to
consumptive uses. Thus, a total valuation framework is needed which is much
broader. This is especially true for species of wildlife that are not hunted,
trapped or fished.
AN EXPANDED NOTION OF VALUE
Not only did early benefit-cost analyses focus merely on use benefits, but
only a subset of such benefits were actually considered for empirical
valuation. This was especially true in regard to the valuation of wildlife
resources (Brown and Nawas 1973; Gum and Martin 1975; and Davis 1964)Only
consumptive use values such as hunting and fishing were typically estimated.
There are also nonconsumptive use values associated with wildlife. For
—^ This is not to imply that these studies were poorly designed, but that
they merely reflect the state of the art of nonmarket valuation at the
time they were conducted.
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example, people visit National Parks and wildlife sanctuaries with the intent
of viewing wildlife. Bird watching is also an activity that some people enjoy.
People in the Northwest go out to watch the salmon runs, even if they never
plan to fish for salmon. These nonconsumptive uses may be at least as
important in value terms as hunting and fishing (see Fisher and Raucher 1983).
There is also a hazy area of use that is not associated with direct
contact with wildlife. Many people never come in contact with wildlife in its
natural habitat, but they do derive satisfaction from it. Among other
activities, they en]oy reading about wildlife, viewing pictures of wildlife,
watching television specials about wildlife, and visiting zoos. Another form
of indirect consumption arises when people benefit from some types of wildlife
research. These indirect users obtain satisfaction from wildlife via the
consumption of goods and services that are derived from wildlife.
The choice problem for the elk valuation example can be expanded to
incorporate all three categories of use. The new choice problem is
msx U(X^ (2.1)
x^,z
s.t. P X + P Z S I
x z —
where X^ is consumptive use (hunting), X^ is nonconsumptive use (viewing,
photographing, etc.), X^ is indirect use, and Px and X are now vectors that
reflect all three categories of use. The other symbols are as previously
defined. Any specific individual may participate in any one, or combination
these uses. We include all three here for expository purposes.
Consumptive uses were referred to as "use" in the preceding section.
Nonconsumptive use could involve merely viewing elk and, for a hunter, it could
-------
be scouting for elk prior to hunting season. Nonconsumptive use could be
measured in some unit of time spent participating in the activity, as is done
to measure consumptive use. Indirect use is more difficult to characterize and
measure. One approach might be to consider indirect use as a composite good
and aggregate the time spent in all types of indirect use. This is not an
entirely satisfactory procedure. For example, the consumption of the benefits
of wildlife research, very broadly defined, may not be amenable to a time
measure. This is an issue that requires further consideration. An additional
issue of concern is related to the durability of books, movies, photographs,
and the like. It is possible for some types of indirect use to occur even when
a species no longer exists. One might argue that the initial cost of durable
items fully covers the present value of future uses. If this is the case then
only new expenditures would need to be valued.
The total value of elk for an individual who participates in all three
types of use is defined as
''W-V ¦ v(p°'p,'«
where 3, is a equivalent variation measure and Pm is the vector of lowest
b x x
possible prices that are high enough that all three categories of use are
zero.-^ Similarly, the component use values are defined as
V(P ,P ,1-3,) = V(Pm ,P ,P ,P ,1)
x z' 1' v x^ x^ Z
V(P ,P ,I-3_) = V(P ,Pm ,P ,P ,1)
x z' 2 x^ x^ z
—^ It is important to realize that the following condition generally holds:
Pm 4 [Pm , Pm , Pm ]•
X *l x2 x3
-------
v(p ,p ,i-3,) = v(p ,p ,pm ,p ,i) :.c
x z 3 x x x z
1 2 3
where 3^ is the respective equivalent variation measure of value and the
superscript m indicates a price such that the respective category of use is
zero. Total value (3J is generally not the sum of the component use values.
b
This occurs because there may be complementary or substitute relations among
the use arguments.
This expanded model highlights the fact that only measuring consumptive
use value for a wildlife resource can result in an underestimate of total
value. That is, if ^ an^ ^3 are positive, then only considering consumptive
use value (6l) will yield an underestimate 6^. (There is not a direct relation
between 3 and 3, as they are each defined in a different context.) Thus, it
a b
is necessary to consider all categories of use when estimating total value.
Even if an estimate of consumptive use value is all that is desired, it is
still important to consider the status quo of the other categories of use.
Notions of option price and option value can be developed with respect to
each of the three use arguments. For example, uncertainty could arise with
respect to the price of any one use argument. Thus, it is not sufficient to
only ask whether the uncertainty is on the supply-side or the demand-side. I:
is also necessary to evaluate the source of the uncertainty. In turn, option
value is not merely a concept related to the potential for consumptive use of a
resource, but rather is the result of uncertainty wherever it occurs in the
choice problem.
Finally, this expanded notion of value may still not be sufficient to
conceptualize the total value of a wildlife resource. Values that are not
associated with use may also be present.
-------
A NOTION OF NONUSE VALUES
As an outgrowth of the option value discussion, Krutilla (1967) suggested
that people may value an environmental asset even though they are sure that
they will never personally use the resource in question. This is in direct
contrast to use values. Krutilla proposed two types of nonuse values. The
first is bequest value and is motivated by a desire to provide some of a
resource for future generations. The second category is existence value and
arises from the knowledge that a resource merely exists. That is, many people
might be willing to pay some positive amount to know that a resource exists,
even though they are sure that they will never personally use it. It is also
conceivable that users and potential users of environmental assets may possess
existence or bequest values over and above their use values. If this is the
case, the expected value of consumer surplus is not merely comprised of use
values.
Recent theoretical discussions have treated bequests and pure existence as
motivations for nonuse values and have referred to the entire category of
nonuse values as existence value (Bishop and Heberlein 1984; Fisher and Raucher
1983; McConnell 1983; and Randall 1984). On the other hand, a recent empirical
study attempted to differentiate between bequest values and pure existence
values (Walsh, Loomis and Gillman 1984).
Individuals who place a value on an environmental asset and are sure that
they will never use this resource must be motivated by some form altruism.
Bequest values reflect altruism toward future generations. The desire to know
that a natural environment merely exists reflects altruism towards nature.
Several authors have argued or assumed that the basis for existence value is
altruism (McConnell 1983; Randall 1984; and Randall and Stoll 1983). In
-------
contrast, Smith (1984b) has alluded that altruism may not be the only
motivation for existence values and appears to include indirect use as an
additional motivation. Randall (1984) and other authors who have considered
the components of total value either include indirect use as a use value as was
done in the preceding section or overlook it entirely. This discrepancy is due
to a fuzzy definition of the term existence value. The broad definition used
by Smith (1984b) answers the practical question of what types of values are
missing when valuation studies overlook individuals who are certain to never
come in contact with a resource. While this approach has some appeal the
narrower definition of existence value may be of more help in the development
of appropriate estimates of value.
We argue that the term existence value should be used to refer to nonuse
values that arise due to altruistic motives. Thus, existence is a pure public
good. Values that arise from indirect contact with a resource will be referred
to as indirect use values. We advocate these definitions due to their
intuitive and practical appeal. The names provide some insight into the
characteristics of the categories. More importantly, there is a theoretical
distinction that helps to clarify this definition of existence value. This is
the notion of weak complementarity (Freeman 1979; and Maler 1974). Weak
complementarity implies that people who do not demand a market good that is
dependent on the environmental asset being valued will not be willing to pay
any positive amount for the maintenance of the asset. Since there are not any
market goods that are related to existence motivations based on altruism,
methods of valuation utilizing weak complementarity cannot be used to measure
existence values. Furthermore, this definition of existence value will aid in
the development of appropriate estimates of value in empirical applications.
-------
That is, we believe that a careful
the motivation for values can lead
consideration of the components of value
to more precise estimates of value.
and
MOTIVATION FOR EXISTENCE VALUES
The concept of pure existence value requires careful consideration.
Randall (1984) argues that existence values require some type of use behavior
in order for individuals to have any knowledge or recognition of a resource.
This could be either current use or prior use. Of course, Randall is including
what we refer to as indirect use under the heading of use. McConnell (1983)
has suggested that information about a resource may come to an individual as a
pure public good. For example, environmental groups do a considerable amount
of public education to further their causes. State and federal resource
agencies also disperse information about the environment that has public good
characteristics. Therefore, information about wildlife may be available as a
public good. As a result, direct expenditures may not be a prerequisite for
pure existence values. On the practical side, and it does appear to be a
reasonable assumption that someone who places an existence value on a natural
resource will seek to learn more about the resource. At the very least it is
plausible that indirect use values may occur simultaneously with existence
values for many wildlife resources. In turn, one would expect that an
individual who has existence motivations toward a resource is also a current or
previous user of the resource in some sense.
Randall and Stoll (1983) have identified three types of altruism that
could motivate existence values. These motivations are: interpersonal
altruism, intergenerational altruism and Q-altruism. Interpersonal altruism
arises from feelings toward individuals in the current generation and
-------
intergenerational altruism reflects feelings about future generations.
Q-altruism arises from the knowledge of the pure existence of an environmental
asset and is not related to other people. Bishop and Heberlein (1984)
identified five similar categories of altruistic motives for existence values:
bequest motives, benevolence towards friends and relatives, sympathy for people
and animals, environmental linkages and environmental responsibility.
Bishop and Heberbein provided the following justifications for each of
their suggested altruistic motives for existence values.
(a) Bequest motives - As Krutilla (1967) argued many years ago, it
would appear quite rational to will an endowment of natural amenities as
well as private goods and money to one's heirs. The fact that future
generations are so often mentioned in debates over natural resources is
one indication that their well-being, including their endowments of
natural resources, is taken seriously by some present members of society.
(b) Benevolence toward relatives and friends. Giving gifts to
friends and relatives may be even more common than making bequests of
them. Why should not such goals extend to the availability of natural
resources?
(c) Sympathy for people and animals. Even if one does not plan to
personally enjoy a resource or do so vicariously through friends and
relatives, he or she may still feel sympathy for people adversely affected
by environmental deterioration and want to help them. Particularly for
living creatures, sympathy may extend beyond humans. The same emotions
that lead us to nurse a baby bird or stop to aid a run-over cat or dog may
well induce us to pay something to maintain animal populations and
ecosystems.
(d) Environmental linkages. A better term probably exists here.
What we are driving at is the belief that while specific environmental
damage such as acidification of Adirondack lakes does not affect one
directly, it is symptomatic of more wide-spread forces that must be
stopped before resources of direct importance are also affected. To some
extent this may reflect a simple "you've-got-to-stop-'em-somewhere"
philosophy. It may also reflect the view that if "we" support "them" in
maintaining their environment, "they" will support us.
(e) Environmental responsibility. The opinion is often expressed
that those who damage the environment should pay for mitigating or
avoiding future damage. In the acid rain case, there may be a prevalent
feeling that if "my" use of electricity is causing damage to ecosystems
elsewhere, then "I" should pick up part of the costs of reducing the
damage.
-------
Accepting the validity of these altruistic motivations is tantamount to
acknowledging the potential for existence values. A casual observation might
also lead one to suspect that existence values for a major wildlife resource
might be positive. In fact, the case studies cited by Fisher and Raucher
(1983) indicate substantial existence values for several types of environmental
assets, including wildlife.
THOUGHTS ON MODELING EXISTENCE MOTIVATIONS
Becker (1974) and Chavas (1984) have modeled altruism in a general context
by incorporating the utility of others as arguments in the utility function of.
an altruistic individual. This is a questionable procedure. First, the
altruistic individual does not know the utility functions or utility levels of
others. Alternatively, an altruist may not feel that it is appropriate to
evaluate the satisfaction of others in terms of his or her own utility
function. Finally, intrinsic altruism (Q-altruism) toward environmental assets
cannot be evaluated in terms of the utility of others.
McConnell has noted that it is only possible to recover a monotonic
transformation of an individual's utility function. This means that if a poor
person is better-off due to a food program an empirical investigator can only
identify that the altruist derives positive marginal utility from the food
consumption of the poor person. In turn, it may be sufficient for empirical
purposes that the poor person's consumption of food enters as an argument in
the altruist's utility function. No evaluation of the poor persons utility is
necessary for empirical purposes other than that marginal utility is positive.
A reasonable approach may be to assume that an altruist knows that an
altruistic action will lead to an increase in utility for others or will lead
-------
to an improvement in the environment. In terms of other people we are merely
stating that the marginal utility of an altruistic action is positive. For
this case the question becomes one of need and ability to contribute. Most
altruistic people probably can arrive at a conclusion regarding their ability
to contribute, but may struggle with the question of need of the recipients of
8 /
the altruistic gesture.— This question of need may be the reason why altruism
among individuals who are not closely associated is manifested in private and
public organizations. The organization can evaluate need and coordinate
altruists. In turn, altruists merely need to know that their actions, or an
organization's actions, will make a positive contribution. By positive
contribution we mean an increase in someone's utility level or an improvement
in the environment.
Consider an action by a public agency that improves elk habitat in Idaho.
The primary effect of this action is an increase in the population of elk.
Such an increase in population may be indicative of increased opportunities for
viewing elk, higher success rates for elk hunters, a stronger and more viable
elk population, and a larger elk population base for future users. In this
example the population of elk could enter as the altruistic argument in an
individual's utility function. Another example is water quality where the
quality level could enter as an argument in an altruist's utility function.
Recognizing that the average person is not entirely cognizant of water quality
indicies or wildlife population levels, a rough approximation to these measures
may be the best information that people use to make decisions. All the same,
Suppes (1966) discusses this type of choice problem in a game theoretic
framework.
-------
these types of considerations are extremely important if appropriate measures
9/
of value are to be obtained.—
A final issue on this topic is that existence is not simply a dichotomous
choice. Of course, a resource can either exist or not exist, but when a
resource exists there are various levels of existence. This fact is reflected
when existence is measured by variables such as a water quality index or
wildlife population levels. It seems reasonable to assume that people do
recognize that there are differing levels of existence.
All of the preceding discussion has contained the implicit assumption that
the marginal existence value of a resource is positive. This is also true of
other author's discussions of existence value (See McConnell, 1983). It is
possible that for some people the marginal existence value of certain resources
may be negative. Consider the case of coyotes in the western United States.
Some people may not like coyotes even though they will never come in contact
with one. An increase in the population of coyotes may irk these people,
thereby leading to a reduction in their level of utility. Alternatively, there
may be people who have relatives who are ranchers that are adversely affected
by coyotes. In this case, these people may be willing to pay some positive
amount just to know that their relatives (the ranchers) will not be bothered by
coyotes. Another example is the case of parents who have children who enjoy
back-country hiking in places like Yellowstone National Park. The parents
might be willing to pay some positive amount to know that grizzly bears do not
91
— A similar approach was used by Schulze, Brookshire and Thayer (1981).
These authors were trying to measure existence value for beauty in
National Parks and include a measure of visibility as an argument in their
utility specification.
-------
exist in the hiking area posing a threat to their children. These examples
suggest that pure existence values may not always be positive.
A MODEL OF TOTAL VALUE
The model developed in this section specifically incorporates
nonconsumptive use, indirect use and existence as arguments in an individual's
utility function. This model is somewhat similar to one developed by Smith
(1984b), but our model incorporates more than one category of use, gives a more
precise definition of the existence argument, and highlights an oversight in
Smith's development. Using the elk example once again, the choice problem
becomes
max U(X1,X2>X3,Z,y) (3.1)
x. ,z
1
s.t. P X + P Z < I (3 2)
X Z * • '
Xi 5 gi(Y) V 1 (3-3)
Y = Y (3.4)
where y is the elk population level (existence argument) and y is the current
population of elk.—^ The constraint on the use arguments [g^(*)] could take
the form
Xi " gi(Y) = c (3.5)
10/
Within this simple model the existence argument is represented in a static
framework. In reality, individuals probably desire that a resource exists
over a number of time periods. There are several ways that existence
preferences could be modeled in a dynamic framework. First, one could
consider the existence argument to be a vector with the components being
indexed over time. A second suggestion would be to index utility
functions over time periods. Finally, a third approach would be to
combine the first and second suggestions within one model.
-------
and
I±(Y) =
0 otherwise
1 if y 2 a.
(3.6)
where is an indicator function, C is an arbitrarily large constant and
is a constant that varies across use arguments. If the population (y) falls
All other symbols are as previously defined.
We will assume that the marginal utility of existence (y) is positive and
is increasing at a decreasing rate. A practical consideration is that the
existence argument enters the utility function so that utility is positive even
when existence is zero. Finally, existence will be treated as a pure public
good and therefore it is not a choice variable. Once again, a specific
individual may participate in any one, or combination of, the three categories
of the use. All three are included for expository purposes.
The total value (eTV) of elk is defined as:
Here we are comparing expenditures with and without the resource (elk). The
below a^, there are insufficient animals to support the ith category of use.
v(px.pz.7.i-6tv) - v(p^,p2,o,d
(3.7)
total use value (B
123
of elk is defined in a similar manner as was done in
equation (2.3):
-------
Likewise, the component use values can be defined for the present model:
V^.Pz.Y.Wi) = V
-------
where the vector does not enter as an argument because the person is not a
user of elk. This is not a typical case since it was argued in preceding
sections that a person who has existence motivations for a resource will
probably also be at least an indirect user of the resource although existence
value may be based on historical use alone.
Total existence value of a resource is not easily defined when a person is
both a user of the resource and also has existence motivations. This problem
can be portrayed in the context of the current example. That is, the
constraint specified in equation (3.5) is binding when the existence argument
(elk population) is very small or is zero. The following condition holds when
this constraint is binding.
3
Z
i=l
3U 3X.
1
3X. 3y
l
3U
+ (3.15)
As a result it is not conceptually possible to identify a definition for pure
existence value in this case. It appears that this result holds regardless of
the manner in which existence motivations are modeled as it is impossible to
use a resource when it does not exist or the level of existence is at some
minimal level. This is an issue that Smith (1984b) appears to have overlooked
in his definition of existence value.
This is not a severe limitation for applied policy research since the
researcher may only desire to measure marginal changes in existence values or
total value. An alternative is to measure a conditional existence value. This
value is defined by
- V(P° Ft.O,I) (3.16)
20
-------
where prices are such that all categories of use are zero. This conditional
existence value turns out to be merely total value (&^y) minus total use value
(8 ^
123 " The prospects for measuring an unconditional existence value are not
promising because of the one-way interaction between the use arguments and the
existence argument when the constraint in equation (3.5) is binding.
Option price and option value concepts can also be developed with respect
to the existence argument if individuals are uncertain as to whether they have
existence motivations for elk or if the population level of elk is uncertain.
The result, as was previously stated, is that option prices and option values
arise when uncertainty enters the valuation question. The important point is
that there is no single concept of option price or option value. It is
necessary to consider whether the uncertainty is demand-side or supply-side,
and consideration must be given to the source of the uncertainty within these
two categorizations.
The valuation question is even more complicated than presented here. Each
of the four components of value have various features. For example,
consumptive use of elk could involve bow hunts, gun hunts, antlerless-only
hunts, etc. It is likely that hunters will place different values on each type
of hunt and there may be substitute relationships. Nonconsumptive use may
involve going out with the intent of viewing elk or incidentally seeing an elk
while you are driving or hiking. The four crude groupings of value components
are used here to represent on an abstract level the complexity of the valuation
question. As noted before, only valuing consumptive uses of a wildlife
resource will in general result in an underestimate of total value. Now it is
clear that only measuring use values is not sufficient when existence
motivations are present. In fact, even if the objective is to measure only one
-------
component of value, it is still necessary to consider the other types of values
that individuals might place on the resource.
Finally, the discussion in this section was developed under the assumption
that the marginal existence value of elk is positive. Appropriate measures of
existence value can also be developed for the case where marginal existence
value is negative and the definitions would be parallel to the procedures used
for the case of positive marginal existence values.
III. EMPIRICAL ISSUES
The discussion in this section will focus on the practical question of
what values are relevant for public policy. We argue that separate measures of
option and existence values may be of interest only to economists. In a policy
context, the option value discussion has given economic credence to the fact
that potential users of a resource can place a monetary value on the resource.
The notion of existence value takes this argument one step further and includes
people who will never use a resource among those who might place a monetary
value on it. Policy makers may not be concerned with the names that economists
place on the various components of value, nor do they necessarily desire a
measurement of each component. Rather, policy makers hope that economists are
able to develop consistent and usable definitions of value, and are able to
provide relatively accurate estimates of total value relevant to a given change
in a resource. Bishop (1984) has concluded that the relevant concept for
applied policy research is generally option price. The equivalent concept in
the deterministic case is total value as defined in equation (3.7). That is,
3^ is just a special case of option price when the world is deterministic.
-------
Using the simple model with only a single use argument, $ will equal in
s
equation (1.7) when the world is certain since (1-n) will be unity. In the
case of uncertainty, option price includes total value (the expected value of
consumers surplus) as was shown in equations (1.6), (1.7) and (1.9).
Measurement of total value or option price leads to several empirical
questions. The elk valuation example will illustrate. An accepted tool for
measuring consumptive use values (hunting) is the travel cost method. The
problem in the context of the current model is that consumptive users may also
have existence motivations or may be nonconsumptive and indirect users. Weak
complementarity does not apply to existence motivations so that indirect
methods of valuation such as the travel cost method cannot be used to measure
existence values. The only available method for estimating existence value is
contingent valuation since weak complementarity is not a prerequisite to its
application.—^ Contingent valuation may also be the best tool available for
measuring indirect use values, if these types of values can be measured at all.
Although weak complementarity probably applies for qualitative changes in
indirect use, the diverse nature of indirect uses makes it difficult to apply
any indirect technique of valuation. Thus, the travel cost method is only
appropriate for estimating consumptive use values, and perhaps nonconsumptive
use values in some cases.
One approach to this problem would be to use the travel cost method to
estimate consumptive use values and nonconsumptive use values where
—^ The use of contingent valuation to measure existence values for
individuals who are users of a resource and have existence motivations for
the resource would be limited due to the previously mentioned problem of
precisely identifying existence value for a person with this type of
preference structure.
-------
that the payment card method and dichotomous choices may be superior to bidding
games. Our research leads us to conclude that contingent valuation, although
imperfect, is a reasonable tool for measuring the values that people place on
consumptive and nonconsumptive uses of environmental assets. Whether this
conclusion can be extended to contingent valuation measures of indirect use
12/
values, existence values and option values remains to be seen.—
I".". PRELIMINARY RESULTS PROM AN APPLICATION
In a recent contingent valuation experiment we estimated the value of
preserving two endangered species of wildlife in Wisconsin (bald eagles and
13 /
striped shiners).— The objective of this study was to test whether there are
significant values that are not derived from direct contact with these wildlife
resources. To facilitate this test, three types of values were estimated: a
total value for bald eagles (BETV), a conditional total value for bald eagles
(BETVl and a total value for striped shiners (SSEV). Striped shiner
e2
total value is existence value as there is not any current or anticipated use
associated with these fish in Wisconsin.
12/
— There have been some studies where attempts have been made to use
contingent valuation to estimate existence values (Brookshire, Eubanks and
Randall, 1983; and Walsh, Loomis and Gillman, 1984). These studies appear
to suffer from the vague definition of the term existence value, as was
discussed in earlier sections of the present paper.
13/
— The bald eagle is classified as a federally threatened species. The
striped shiner is a minnow whose primary habitat is in sections of the
Milwaukee River and it is not classified as a federally threatened or
endangered species.
-------
The values to be estimated are defined in a manner similar to the
definitions developed in section II. The definitions are
V(Pe,Pz,u,p,I-BETV) = V(P™,Pz,0,p,I) (4.1)
V(P® ,Pe ,P .u.p.I-BETVl -J = V(P°,P ,0,p,I) (4.2)
2 3 2 6
V(P .P.w,p,I-SSEV) = V(P.P ,5,0,1) (4.3)
e z © z
where Pg is a vector of market prices for the bald eagle use arguments, w is
the current population of bald eagles, p is the current population of striped
shiners, e^ and are nonconsumptive and indirect use arguments for bald
eagles, and all other arguments are as previously defined. There is not a
consumptive use argument for bald eagles (e^) due to their status as an
endangered species.
SURVEY PROCEDURES
The valuation questions for the present study were at the end of a mail
survey conducted by the Wisconsin Department of Natural Resources (DNR). The
purpose of the DNR's survey was to determine why Wisconsin residents do or do
not contribute to the State's Endangered Resources Donation (ERD) program.
Questionnaires were mailed to samples of individuals from three groups of
Wisconsin residents: (1) identified environmentalists who attended selected
DNR public meetings in 1984, (2) contributors to the ERD program in 1984, and
(3) noncontributors to the ERD program in 1984. These sample groups will be
referred to as Sample 1, Sample 2 and Sample 3, respectively.
26
-------
One half of the individuals in each sample were asked a bald eagle total
value question (BETV) and the other half were asked a conditional bald eagle
total value question (BETV[e _q). All respondents were administered the
^ 14/
striped shiner total value question.— The payment vehicle for eliciting
these valuation responses was a membership to a private foundation that would
conduct the necessary activities to preserve the species in question. This is
similar to the payment vehicle used by Stoll and Johnson (1984) in their study
of whooping cranes at the Aransas National Wildlife Refuge in Texas.
Two techniques were used to ask each valuation question. All respondents
were administered both question formats. The first question format was the
dichotomous choice technique which has been used in several contingent
valuation studies (Bishop, Heberlein and Kealy 1983; Boyle and Bishop 1984; and
Sellar, Chavas and Stoll 1983). Respondents were asked to accept or reject
fixed membership fees to the foundation to preserve the species in question.
Offers were even dollar amounts that were randomly selected within fixed
intervals on the range $1 to $100. The second technique was a type of
open-ended question. After respondents answered the dichotomous choice
question they were asked what the most was that they would actually pay.
Copies of the valuation questions are presented in Appendix A.
Given the finding of Randall, Hoehn and Tolley that contingent values for
an item may vary depending on the placement of the respective valuation
question in the valuation process, it would have been desirable to
alternate the order of the valuation questions in the questionnaires.
This was not possible due to certain research limitations. In turn, the
striped shiner valuation question was preceded by a bald eagle valuation
question in all questionnaires. It should be noted that there was not a
statistical difference between the striped shiner values that were
preceded by a bald eagle total value question and the striped shiner
values that were preceded by a conditional bald eagle total value
question. Even so, this result would not address the issue of whether
respondents bid most of their allotment for endangered species on bald
eagles.
-------
SURVEY RESULTS
A total of 1,162 questionnaires were mailed to individuals in the sample.
Five hundred questionnaires were mailed to individuals in Sample 2 and an
additional 500 were mailed to individuals in Sample 3. The remaining 162
questionnaires were sent to individuals in Sample 1. The overall response rate
was 81 percent. The within group response rates were 85 percent for Sample 1,
89 percent for Sample 2, and 72 percent for Sample 3.
VALUE ESTIMATES
Bald eagle values were split according to whether respondents were viewers
or nonviewers of bald eagles. This split was made on the basis of whether
respondents had ever made a trip where one of their intentions was to view bald
eagles. The information to make this classification was collected as part of
the survey. An example of this question is also presented in Appendix A.
Open-Ended Results
Values estimated with the open-ended question are presented in Table 1.
The estimated means show some obvious patterns when one looks across the rows
and down the columns. An interesting result is that all of the estimated means
are significantly different from zero, even the striped shiner existence value
for Sample 3.
We hypothesized that BETV would equal BETV| _ for nonviewers. This null
e2"°
hypothesis could not be rejected for any of the three samples. On the other
hand, if there are significant values associated with viewing bald eagles, then
BETV would be significantly larger than BETV| for viewers. The null
28
-------
TABLE 1. OPEN-ENDED VALUE ESTIMATES
Type
of Value
Sample 1
Sample 2
Sample 3
Mean
Median
Mean
Median
Mean
Median
BETV
- Viewer
40.S& ,
(5.92)—
24.95, ,
W1-'
31.39
(3.55)
20.25
27.65
(5.74)
15.25
- Nonviewer
25.27
(6.17)
24.63
20.42
(1.81)
15.05
(105)
12.47
(1.32)
9.85
(110)
BETV |
-Viewer
e2=o
44.25
(11.57)
24.60
28.25
(3.36)
20.20
21.38
(4.02)
15.60
- Nonviewer
21.06
(3.99)
15.25
21.93
(2.14)
10.43
(117)
12.62
(1.83)
5.19
SSEV
13.24
(1.45)
9.71
7.68
(0.65)
3.40
(340)
4.70
(0.71)
0.31
(255)
— Standard errors are presented in parentheses below the means.
—^ Sample sizes are presented in parentheses below the medians.
hypothesis that these two means are the same could not be rejected for each of
the three samples of viewers.
There are several reasons why this last hypothesis test resulted in a
conclusion which is contrary to expectations. Values associated with viewing
bald eagles could be very small with respect to indirect and existence values.
This may be plausible due to the bald eagles status as a symbol of freedom and
patriotism. Alternatively, individuals could have provided their total values
for bald eagles, or maybe even endangered species, regardless of the manner in
which the valuation question was asked. This could be due to a survey problem
in the questionnaire or it could be that individuals are not readily able to
provide estimates of component values. This is an issue that was discussed by
-------
Randall, Hoehn and Tolley (1981). There is no way to identify which
explanation is true in the present research. It should be noted, however, that
this result is reversed for two of the samples when the dichotomous choice
results are examined. We suggest that future research to test this type of
hypothesis be conducted with a resource that is not associated with the
symbolism that is attached to bald eagles.
An issue of concern to us was whether the fixed offers in the dichotomous
choice question influenced respondents answers to the open-ended question. The
survey design allowed a simple test that was used by Boyle, Bishop and Welsh
(1985) to test for starting point bias in bidding games. The statistical
results of this test are presented in Appendix B. The findings indicate that
eight of the open-ended means were influenced by the fixed offers in the
dichotomous choice question. Thus, this effect must be considered when
interpreting the open-ended valuation estimates presented in Table 1.
Dichotomous Choice Results
The dichotomous choice means are not simple averages, but rather, are
computed from estimated logit models.—^ The general form of the logit models
estimated for the present study is
tt = (1 + exp(-GY)) * 5.1
—^ The means reported in Table 3 are computed by truncating the range of
integration of the estimated logit models. This is a procedure that has
been used in several contingent valuation studies to cope with the large
tails that can occur with estimated logit models (Bishop, Heberlein and
Kealy 1983; Boyle and Bishop 1984; and Sellar, Chavas and Stoll 1983). A
simple rule of thumb discussed by Boyle and Bishop (1984) was used to
choose the point of truncation. This is, the range of integration was
truncated at the ninetieth percentile or the highest offer in the sample
($100 here), whichever was larger. The truncated models were normalized
so that the areas under the p.d.f.'s equaled one.
30
-------
where ir is the probability of a yes response to the fixed offer, 0 is a vector
of coefficients and Y is a vector of explanatory variables. The QY term takes
the following form
0Y = 0_ + 0..1n(offer) + 0OD (5.2)
0 1 2 v
where is a dummy variable that is equal to one when a respondent is
classified as a viewer of eagles. Of course, the dummy variable for viewing
does not enter the striped shiner equations.
The specification of equation (5.2) is not consistent with any
conventional utility theoretic framework, as has been discussed by Hanemann
(1984b). This conflict is due to the fact that income does not enter the
functional specification. On the other hand, empirical applications have shown
that specifications like equation (5.2) provide the best statistical fit to the
data and that income is often not a significant explanatory variable (Bishop,
Heberlein and Kealy 1983; and Boyle and Bishop 1984). This conclusion seems to
be supported in the present study in that the specification in equation (5.3)
fit the data better than a linear specification that is consistent with a
conventional utility framework.—''
The estimated logit equations are presented in Table 2. Only equation (a)
in Table 2 did not provide acceptable statistical results. The problem is
that the coefficient 0^ is not significant. It is not plausible to assume that
equation (a) would not have a constant term in the exponent. That is, a
—^ Specifications of the logit models with income as an argument were not
possible since the DNR choose not to ask respondents to report their
incomes on the questionnaires. We are currently trying to obtain
secondary data on income since the sample for the study was drawn from
Wisconsin Department of Revenue taxpayer records.
-------
TABLE 2. ESTIMATED LOGIT COEFFICIENTS
Equation
0
o
81
0_
2
2
X
Statistic
N
(a)
BETV
- Sample
1
1.410 .
(1.151)-
-0.642
(0.319)
**
1.212
(0.603)
8.84++^/
68
(b)
- Sample
2
2.234*-/
(0.567)
-0.903*
(0.173)
**
0.687
(0.302)
39.52+
222
(c)
- Sample
3
sfe
1.667
(0.584)
-0.978*
(0.190)
1.019
(0.444)
39.22+
182
(d)
BETV|e2-o
- Sample
1
3.649*
(1.222)
*
-1.124
(0.346)
—
14.10+
70
(e)
- Sample
2
2.991*
(0.635)
-1.008*
(0.183)
—
41.91+
216
(£)
- Sample
3
2.062*
(0.729)
•k
-1.134
(0.236)
**
1.137
(0.444)
33.22+
176
(g)
SSEV
- Sample
1
2.789*
(0.672)
•k
-1.269
(0.243)
—
39.32+
136
00
- Sample
2
—
-0.613*
(0.049)
—
245.36+
435
(i)
- Sample
3
—
-0.833*
(0.073)
—
274.54+
355
Numbers in parentheses are asymptotic standard errors.
Single asterisk denotes significance at the 1% level and double asterisk
denotes significance at the 5% level.
Single plus sign denotes significance at the 1% level and double plus sign
denotes significance at the 5% level.
32
-------
specification without a constant term in the exponent would imply that the
median response for nonviewers is $1. That would not be a reasonable result.
Given that 0q is not significant in equation (a), the viewer and nonviewer
values computed from this equation should be cautiously interpreted. However,
it is plausible that 0q is not significant in equations (h) and (i). It does
appear reasonable that the striped shiner medians might be only $1 for Samples
2 and 3.
An interesting result is that there was not a significant difference
between the way viewers and nonviewers responded to the conditional bald eagle
total value question for Samples 1 and 2. The ^ coefficient was not
significant in either of these equations [equations (d) and e)]. This is in
contrast to the open-ended result which indicated that there was a significant
difference between viewer and nonviewer conditional bald eagle total values in
each group. The dichotomous choice results were in agreement with the open-
ended results when this same comparison was made for Sample 3.
The estimated values are presented in Table 3. As in Table 1, the means
show some obvious patterns when one looks across the rows and down the columns.
A Comparison of Results
There are five open-ended means that could not be directly compared with
the dichotomous choice means. The bald eagle total value for nonviewers in
Sample 1 could not be tested due to a small sample size, i.e., the central
limit theorem does not apply. The other four open-ended means for which direct
comparisons could not be made are the conditional bald eagle total values for
Samples 1 and 2. This is because the dichotomous choice means are the same for
viewers and nonviewers, and the open-ended estimates are statistically
33
-------
TABLE 3. DICHOTOMOUS CHOICE VALUE ESTIMATES
Type of Value
Sample
1
Sample 2
Sample 3
Mean
Median
Mean
Median
Mean
Median
BETV - Viewer
181.43
59.5^
43.93
25.40
24.36
15.59
- Nonviewer
27.16
9.00
20.23
11.88
11.24
5.50
BETV|&2=o ~ Viewer
35.51
25.70
29.56
19.44
22.87
16.79
- Nonviewer
35.51
25.70
29.56
19.44
11.47
6.16
SSEV
14.38
9.01
5.67
1.00
4.17
1.00
Significance of the estimates is tested by testing the significance of the
estimated logit equations. See TABLE 2 for these results.
—^ It is stated in footnote (15) that the means were derived by truncating
the range of integration and normalizing the logit models so that the
areas under the p.d.f.'s would be one. The reported medians are for the
untruncated models. The medians from the untruncated models are presented
because a median is not sensitive to the mass in the tail of a
distribution.
different for viewers and nonviewers. In this context, the dichotomous choice
means for Samples 1 and 2 are not significantly different from the associated
open-ended means for viewers.
Treating the dichotomous choice means as parameters, and invoking the
central limit theorem, it is possible to test whether the means derived from
the two valuation techniques are statistically the same for cases where direct
comparisons can be made. There are ten pairs of means where a direct
comparison can be made. In seven of these cases there is not a statistical
difference. The cases where a statistical difference occurs are bald eagle
total values for viewers in Samples 1 and 2, and striped shiner existence value
for Sample 2. The difference for Sample 1 is not surprising given the
34
-------
statistical problems with the logit equation from which the dichotomous choice
means were derived.
Finally, as was previously noted, the bald eagle total values and
conditional total values are not significantly different for viewers in the
open-ended data, whereas the dichotomous choice results indicate that bald
eagle viewer total values and conditional total values are significantly
different in Samples 1 and 2. The dichotomous choice results do support the
open-ended results for Sample 3 with respect to this comparison, i.e.,
equations (c) and (f) are not significantly different.
I".". CONCLUSIONS
The valuation of nonmarketed natural resources is a complex conceptual and
empirical problem, as this discussion of, and application to, the valuation of
wildlife portrays. In this paper we attempted to clarify some of the
conceptual issues and discussed some of the empirical questions relevant to the
valuation nonmarketed resources. In particular, we pointed out that
consumptive use of a resource is merely one category of use. There are also
nonconsumptive and indirect users. Nonconsumptive use and indirect use are
likely to be associated with resources that have relatively attractive
aesthetic features.
We also proposed what we feel is an acceptable definition of existence
value. Hanemann (1984a) has said that, "...it is tempting to characterize the
burgeoning literature on option value as a label in search of contents." It
may be more than tempting to make the same statement about the existence value
literature. Nearly everyone would agree that some people who are sure they
will never come in contact with a resource may still place a monetary value on
35
-------
The disagreement arises with respect to what constitutes and motivates
such values. We have proposed in this paper that the existence value label be
used to refer only to values that are motivated by altruism.
On the practical side , we do not believe that it is necessary or desirable
to measure all of the individual components of total value. Economists are
concerned with these various components to avoid gaps in the conceptual
framework for valuation and to also avoid double counting. Estimates of
components such as option value and existence value can then be used to verify
the theoretical models that define such values. Measures of option value and
existence value as separate entities are generally irrelevant for policy
applications. Policy research generally requires estimates of the total value
associated with an incremental change in a resource.
In the context of valuing wildlife resources, contingent valuation is the
only tool available for measuring the total value. All other techniques of
valuation (indirect methods) require on the notion of weak complementarity to
measure qualitative changes in resources. These indirect methods of valuation
are not appropriate for measuring existence values. In addition, indirect
methods may not be operational for measuring indirect or nonconsumptive use
values, although the concept of weak complementarity may apply. Sufficient
research has been done to show that contingent valuation is a useful tool for
measuring consumptive and nonconsumptive use values, but more research is
needed regarding indirect use and existence values.
With respect to the empirical application we feel obliged to ask, can
contingent values, such as the estimates presented in this paper, be taken as
clear evidence that intrinsic values for wildlife species are positive? As was
previously discussed, there is a growing body of research that is contributing
-------
to a greater confidence that contingent valuation produces use values that are
sufficiently accurate to be acceptable in policy analysis (Bishop_et_al. 1984).
On the other hand, doubts have been voiced as to whether this conclusion
extends to more esoteric concepts like existence value (Cummings, Brookshire
and Schulze 1984) . This is an issue that requires more research. However, we
have previously concluded that altruistic motives leading to positive utility
from the existence of a wildlife resource are quite compatible with economic
theory. Furthermore, the present contingent valuation results indicate a
substantial willingness to pay that is not associated with direct contact with
both a well-known and an obscure species.
The bottom line is that we as economists must give careful consideration
to the components of total value, and to the motivation for the components,
before values are estimated. This is necessary to obtain accurate and
appropriate estimates of value even when total value is the desired end result
for public policy analysis. Smith (1984b) has stated that researchers should,
"...ask individuals first how they use the resources involved and how they
think about their values," before values are estimated. In addition, a
thoughtful application of empirical techniques for measuring values is needed.
Finally, the concepts discussed in this paper in the context of wildlife are
applicable to other resources when the peculiarities of each resource is
accounted for.
-------
BIBLIOGRAPHY
Becker, Gary S. 1974. "A Theory of Social Interactions." Journal of
Political Economy, Vol. 82 (Nov./Dec.):1063-1093.
Bishop, Richard C. 1982. "Option Value: An Exposition and Extension." Land
Economics, Vol. 58 (Feb.):1—15.
Bishop, Richard C. 1984. "Option Value or Option Price: Principles for
Empirical Resource Valuation Under Uncertainty." University of Wisconsin-
Madison, Department of Agricultural Economics, unpublished paper.
Bishop, Richard C., and Thomas A. Heberlein. 1984. "Contingent Valuation
Methods and Ecosystem Damages from Acid Rain." University of
Wisconsin-Madison, Department of Agricultural Economics, Staff Paper No.
217.
Bishop, Richard C., Thomas A. Heberlein, and Mary Jo Kealy. 1983, "Contingent
Valuation of Environmental Assets: Comparisons with a Simulated Market."
Natural Resources Journal, Vol. 23 (July):619-633.
Bishop, Richard C., Thomas A. Heberlein, Michael P. Welsh, and Robert M.
Baumgartner. 1984. "Does Contingent Valuation Work? Results of the
Sandhill Experiment." Invited paper, joint meetings of the AERE and AAEA.
Boyle, Kevin J., and Richard C. Bishop. 1984. "A Comparison of Contingent
Valuation Techniques." University of Wisconsin-Madison, Department of
Agricultural Economics, Staff Paper No. 22.
Boyle, Kevin J., Richard C. Bishop, and Michael P. Welsh. 1985. "Starting
Point Bias in Contingent Valuation Bidding Games." Land Economics,
Vol. 61(May):188-194.
38
-------
Brookshire, David S., Larry S. Eubanks, and Alan Randall. 1983. "Estimating
Option Prices and Existence Values for Wildlife Resources." Land
Economics, Vol. 59 (Feb.): 1-15.
Brown, William G., and Farid Nawas. 1973. "Impact of Aggregation on the
Estimation of Outdoor Recreation Demand Functions." American Journal of
Agricultural Economics, Vol. 55 (May):246-249.
Chavas, Jean-Paul. 1984. "Future Directions for Domestic Food Policy."
American Journal of Agricultural Economics, Vol. 66 (May):225-231.
Chavas, Jean-Paul, and Richard C. Bishop. 1984. "Ex Ante Consumer Welfare
Evaluations in Cost Benefit Analysis." University of Wisconsin-Madison,
Department of Agricultural Economics, unpublished paper.
Coursey, Don L. _et al. 1984. "Experimental Methods for Assessing Environmental
Benefits." Drafrt report to the U.S. Environmental Protection Agency,
CR-E11077-01-0, Washington, D.C.
Davis, Robert K. 1964. "The Value of Big Game Hunting in a Private Forest."
Transactions of the Twenty-ninth North American Wildlife and Natural
Resource Conference.
Fisher, Ann, and Robert Raucher. 1984. "Intrinsic Benefits of Improved Water
Quality: Conceptual and Empirical Perspectives." In Applied Micro-
Economics , Vol. 3, eds. V. Kerry Smith and Ann D. Witte. Greenwich, CT:
JAI Press.
Freeman, A. Myrick. 1979. The Benefits of Environmental Improvement.
Baltimore: The Johns Hopkins University Press.
Freeman, A. Myrick. 1984. "The Sign and Size of Option Value." Land
Economics, Vol. 60 (F eb.):1 — 13
-------
Freeman, A. Myrick. 1985. "Supply Uncertainty, Option Price, and Option
Value." Land Economics, Vol. 61 (May):176-181.
Graham, Daniel A. 1981. "Cost-Benefit Analysis under Uncertainty." American
Economic Review, Vol. 71 (Sept.):715-725.
Gum, Russell L., and William E. Martin. 1975. "Problems and Solutions in
Estimating the Demand for and Value of Rural Outdoor Recreation."
American Journal of Agricultural Economics, Vol. 57 (Nov.):558-566.
Hanemann, W. Michael. 1985. "Information and the Concept of Option Value."
Quarterly Journal of Economics (forthcoming).
Hanemann, W. Michael. 1984a. "On Reconciling Different Concepts of Option
Value." University of California-Berkeley, Department of Agricultural and
Resource Economics, working paper.
Hanemann, W. Michael. 1984b. "Welfare Evaluations in Contingent Valuation
Experiments with Discrete Response." American Journal of Agricultural
Economics, Vol. 66 (Aug.):332-341.
Just, Richard E., Darrell L. Hueth, and Andrew Schmitz. 1982. Applied Welfare
Economics and Public Policy. Englewood Cliffs, New Jersey: Prentice-Hall,
Inc.
Krutilla, John A. 1967. "Conservation Reconsidered." American Economic
Review, Vol. 57 (Sept.):777-786.
MSler, Karl G. 1974. Environmental Economics: A Theoretical Inquiry.
Baltimore: The Johns Hopkins University Press.
McConnell, Kenneth E. 1983. "Existence and Bequest Value." In Managing Air
Quality and Scenic Resources at National Parks and Wilderness Areas, eds.
Robert D. Rowe and Lauraine G. Chestnut. Boulder, CO: Westview Press.
40
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Suppes, Patrick. 1966. "Some Formal Models of Grading Principles." Synthese,
Vol. 16 (Dec.):284-306.
Walsh, Richard G., John B. Loomis, and Richard S. Gillman. 1984. "Valuing
Option, Existence, and Beguest Demands for Wilderness." Land Economics,
Vol. 60 (Feb.):14-29.
Weisbrod, Burton A. 1964. "Collective-Consumption Services of Individual
Consumption Goods." Quarterly Journal of Economics, Vol. 7 8
(Aug.):471-477.
42
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APPENDIX A
INTRODUCTION TO VALUATION QUESTIONS
THIS LAST SERIES OF QUESTIONS INVOLVES FIGURING OUT
THE ECONOMIC VALUE OF ENDANGERED SPECIES
When it comes down to what people think is important, wildlife often has a hard
time competing with other issues. We sometimes talk about things that are
important to us in terms of their dollar value (such as how many dollars a
building is worth) but it has been difficult to talk about what wildlife is
worth in terms of dollars. Researchers at the University of Wisconsin are
interested in these questions, and in cooperation with them, we are including
this section in our questionnaire.
Please keep in mind that the questions involve pretend situations. Even so,
you answers will still help us decide what amount of money should be spent for
endangered species programs, and how the money should be spent. Please
disregard your answers from the sections about the Endangered Resources
Donation program while answering the questions in this section. We are
interested in how much you personally value endangered species, no matter what
you think of the Endangered Resources Donation program.
A-l
-------
BALD EAGLE TOTAL VALUE QUESTIONS (BETV)
We would like you to pretend that all funding to preserve bald eagles in
Wisconsin is terminated. Assume that without funding, there will not be an
organized effort to preserve bald eagles in Wisconsin and bald eagles will
become extinct in our state. Suppose that an independent private foundation is
formed to preserve bald eagles in Wisconsin and to prevent the possibility of
extinction. The activities of the foundation will include maintaining and
restoring bald eagle habitats. Please assume that the foundation will be able
to save the bald eagle.
Pretend that the foundation is to be funded by selling supporting memberships.
All members will be provided with information, at no cost, on how to
conveniently view bald eagles in Wisconsin. Members who do not wish to view
eagles will have the satisfaction of knowing that they helped preserve the bald
eagle in Wisconsin. These people may have various resons for wanting to
preserve bald eagles. Some of these reasons might be: a gift to future
generations, a sense of responsibility for the environment, sympathy for
animals, and generosity towards friends and relatives.
If a supporting membership cost $ per year, would you become a member and
help to make sure that bald eagles will not become extinct in Wisconsin?
yes — I would become a supporting member at this amount. In fact, I
would even pay up to $ per year for a membership.
(WRITE IN THE HIGHEST DOLLAR AMOUNT THAT YOU WOULD PAY.)
no — I would not become a supporting member at this amount.
IF NOT: WHY NOT? (CHECK ALL THAT APPLY)
The membership costs too much, but I would pay $ per year.
(WRITE IN THE HIGHEST DOLLAR. AMOUNT THAT YOU WOULD PAY.)
I would like to see the bald eagle preserved in Wisconsin, but I
would let others pay for preservation.
The bald eagle is not worth anything to me.
I refuse to place a dollar value on bald eagles.
I object to the way the question was asked.
I felt that I didn't have enough information to answer yes.
Other, please explain
A-2
-------
BALD EAGLE CONDITIONAL TOTAL VALUE QUESTION (BETV| =Q)
We would dike you to pretend that all funding to preserve bald eagles in
Wisconsin is terminated. Assume that without funding, there will not be an
organized effort to preserve bald eagles in Wisconsin and bald eagles will
become extinct in our state. Suppose that an independent private foundation is
formed to preserve bald eagles in Wisconsin and to prevent the possibility of
extinction. The activities of the foundation will include maintaining and
restoring bald eagle habitats. Please assume that the foundation will be able
to save the bald eagle.
Pretend that the foundation is to be funded by selling supporting memberships.
However, bald eagles will be located in remote areas of Wisconsin so that it
will be extremely unlikely that you will ever see a bald eagle in the wild in
Wisconsin. Under these conditions, members of the foundation will still have
the satisfaction of knowing that they are helping to preserve the bald eagle in
Wisconsin. These people may have various reasons for wanting to preserve bald
eagles. Some of these reasons might be: a gift to future generations, a sense
of responsibility for the environment, sympathy for animals, and generosity
towards friends and relatives.
If a supporting membership cost $ per year, would you become a member and
help to make sure that bald eagles will not become extinct in Wisconsin?
y05 1 WUU1U UfcrLOIllt:
would even pay up to $
— I would become a supporting member at this amount. In fact, I
(WRITE IN THE HIGHEST DOLLAR
ar for a membership.
fT~THAT YOU WOULD PAY.)
no — I would not become a supporting member at this amount.
IF NOT: WHY NOT? (CHECK ALL THAT APPLY)
The membership costs too much, but I would pay $ per year.
(WRITE IN THE HIGHEST DOLLAR AMOUNT THAT YOU WOULD PAY.)
I would like to see the bald eagle preserved in Wisconsin, but I
would let others pay for preservation.
The bald eagle is not worth anything to me.
I refuse to place a dollar value on bald eagles.
I object to the way the question was asked.
I felt that I didn't have enough information to answer yes.
Other, please explain
A-3
-------
STRIPED SHINER EXISTENCE VALUE QUESTION (SSEV)
Now we would like you to assume that there is enough funding to preserve the
bald eagle in Wisconsin. That is, it will not be necessary to form a bald
eagle foundation and to ask for donations from the public. In the next few
questions, we are interested in finding out about the dollar value you place on
another one of Wisconsin's endangered species.
We would now like you to pretend that all funding to preserve the striped
shiner in Wisconsin is terminated. The striped shiner is an endangered
species of fish in Wisconsin that most Wisconsin residents will never see.
Assume that without funding to maintain habitat, the striped shiner will
become extinct in Wisconsin. Suppose that another independent private
foundation is formed to preserve striped shiners in Wisconsin. The
objectives of the foundation will be to recover and maintain striped
shiner habitat in Wisconsin. Please assume that this foundation will be
able to save the striped shiner.
Pretend that the striped shiner foundation is to be funded by selling
supporting memberships. It is highly unlikely that members of the
foundation will ever see a striped shiner in the wild. Even so, people
may choose to become members for various reasons such as a gift to future
generations, a sense of responsibility for the environment, sympathy for
animals, and generosity toward friends and relatives.
If a supporting membership in the striped shiner foundation cost $ per
year, would you become a member and help to make sure that striped shiners
will not become extinct in Wisconsin?
yes — I would become a supporting member at this amount. In fact I
would even pay up to $ per year for a membership.
(WRITE IN THE HIGHEST DOLLAR AMOUNT THAT YOU WOULD PAY.)
no — I would not become a supporting member.
IF NO: WHY NOT? (CHECK ALL THAT APPLY)
The membership costs too much, but I would pay $ per year.
(WRITE IN THE HIGHEST DOLLAR AMOUNT THAT YOU WOULD PAY.)
I would like to see the striped shiner preserved in Wisconsin,
but I would let others pay for preservation.
The striped shiner is not worth anything to me.
A-4
-------
I refuse to place a dollar value on striped shiners.
I object to the way the question was asked.
I felt that I didn't have enough information to answer yes.
Other, please explain
A-5
-------
BALD EAGLE VIEWING QUESTION
Do you ever take trips where one of your intentions is to try to see a bald
eagle?
regularly
sometimes
once
never have, but would like to
never will
A-6
-------
APPENDIX B
ESTIMATED COEFFICIENTS FOR OFFER EFFECT EQUATIONS
a /
Equation— N
**b /
BETV - Sample 1 - Viewer 22.2PP 0.547** 45
(9.423)— (0.217)
- Nonviewer 14.152 0.260 1:
(11.852) (0.237)
- Sample 2 - Viewer 11.4S5** 0.546* 90
(5.588) (0.125)
- Nonviewer 11.637* 0.263* 105
(2.725) (0.064)
- Sample 3 - Viewer 8.515 0.568** 31
(9.154) (0.222)
- Nonviewer 3.748* -0.020 110
(0.614) (0.048)
* * *
BETV|e„=o - Sample 1 - Viewer 10.269 -0.436 44
(5.543) (0.844)
- Nonviewer 21.851* -0.015 1:
(6.851) (0.153)
- Sample 2 - Viewer 21.715* 0.156 75
(6.009) (0.119)
- Nonviewer 10.153* 0.309* 11"
(3.384) (0.072)
- Sample 3 - Viewer 7.153* -0.525 34
(2.020) (0.328)
- Nonviewer 9.604* 0.086 51
(3.245) (0.077)
3-1
-------
ESTIMATED COEFFICIENTS FOR OFFER EFFECT EQUATIONS (CONT.)
g /
Equation— cx^
:i3) SSEV - Sample 1 9.519* 0.158 106
(2.179) (0.070)
1_ - Sample 2 5.445* 0.084* 340
a/
b/
c/
9.519*
0.158
2.179)
(0.070)
5.445*
0.084*
1.009)
(0.029)
•Jr -Jr -Jr
1.929
0.106*
1.082)
(0.032)
Sample 3 1.929 0.106* 255
The equations have the following functional form:
(open-ended bid) = + a^(offer).
The estimated equations have been corrected for heteroskedasticity if it
was identified as a problem.
Single asterisk denotes significance at the 99 level, double asterisk
denotes significance at the 95 level and triple asterisk denotes
significance at the 90 level.
Numbers in parentheses are standard errors.
B-2
-------
DRAFT
Exploring Existence Value
Bruce Madariaga and K. E. McConnell
Department of Agricultural and Resource Economics
University of Maryland
College Park, Maryland 20742
Prepared for AERE Workshop on
Recreation Demand Modelling
May 17-18, 1985
Boulder, Colorado
-------
This paper explores the role of existence value in benefit-cost analysis of
policies involving natural and environmental resources. Existence value is one of
several components of benefits, including option value and quasi-option value, which
may accrue to people who do not necessarily visit the resources. We tend to assume
that with the inclusion of intrinsic benefits, benefit-cost analysis Will be more
resource-conserving, though this assumption is being eroded by ambiguous results on
option and quasi-option value. Regardless of whether the inclusion of intrinsic
benefits makes benefit-cost analysis more resource conserving, it makes the analysis
less erroneous. There is no guarantee that the development of partial measurers of
benefits and costs will provide even a potential improvement of the allocation of
resources.
There are at least two perspectives on the development and use of existence
value. The simplest is to view such work as part of the continuing evolution of
benefit-cost analysis to include "intangibles," those benefits which are especially
difficult to measure. In the analysis of projects, rules and regulations, we tend to
focus our tools on those activities which by our prior notions are important but are
also measureable. When we grapple with the practical aspect of including existence
value in benefit cost analysis, we are making estimates of benefit more inclusive,
and in an incremental way, improving the tool. Viewed in this way, work on existence
value is simply another of the many positive developments which gradually improve
benefit-cost analysis and possibly the allocation of resources.
There is a second and more disturbing perspective on attempts to measure non-use
values such as existence value. In the analysis below we will give a more precise
definition of existence value, but for the moment, let us simply define it as an
individual's willingness to pay for a change (or to avoid a change) in the provision
of a resource with no prospects or no intention of enjoying in situ services from the
resource. This definition of value is quite elastic and is naturally appealling to
1
-------
those who wish that economics could be more holistic. In this aspect of existence
value we find both its promise and its danger. It allows us the temerity of
believing that we can do benefit-cost analysis, not of individual projects, but of
the economic order. For those of us educated in an era when questions about the
economic order were important, existence value and related concepts offer a larger
vision of economics than the one that the practical exigencies of benefit-cost
analysis force us to adopt. But here lies the danger. For if we utilize the
elasticity of these concepts in attempting to measure everything, we will most
certainly fail, and we may in the process undermine whatever faith is placed in
things we do well.
These ruminations about existence value are meant to motivate the paper.
Because of its potential, and because it is less susceptible to disproof than in
other sources of benefits, existence value should be subjected to careful and
thorough discussions of concept and substance. When dealing with existence value
more than other sources of value, we need to concern ourselves with the question
"what are we measuring" rather than "what is the measurement?"
Many of us find ourselves working on problems addressed by John Krutilla in the
elegant essay "Conservation Reconsidered." Thus it is no surprise that this essay is
the source of a fairly complete exposition of existence value. First Krutilla
recognized that "There are many persons who obtain satisfaction from mere knowledge
that part of wilderness North America remains even though they would be appalled by
the prospect of being exposed to it" (p. 781). Then he argued that market outcomes
are inefficient for resources which provide existence value, because this value is
surely a nondepletable service flow which cannot be appropriated. Hence, efficient
allocation of natural resources which provide existence value requires that this
value be added to the value of other service flows to calculate the total benefits of
preserving natural resources.
2
-------
Empirical evidence of existence value has been of two sorts. First we have
indirect evidence based on people's willingness to join organizations Such as the
Sierra Club, Aububon Society, etc., organizations which are active in resource
conservation. This sort of activity, not always based on use, seems to be an under-
utilized source of revealed preferences implying existence value. Second, most of
the more formal enquiries, using contingent valuation, are ably summarized by Fisher
and Raucher. They give evidence that intrinsic benefits (which include option value
as well as existence value) tend to be some fraction of the use value of resource
changes. Other research, for example Walsh, Sanders and Loomis and Schulze et al.
gives evidence that existence value is greater than use value, in the Schulze et al.
case, substantially greater.
The thrust of this review suggests that economists have accepted existence value
as a reasonable concept, and are now intent on applying contingent valuation
approaches to measuring existence value.
Conceptual discussions of existence value have focused on basically three
issues:
1) Should existence value apply to all but on-site "hands-on" uses of
the resource, or is it limited only to service flows which are not
connected with any other resource use?
2) Does the measurement of the resource from which existence value is derived
matter?
3) Do the motives which give rise to existence value matter?
4) Is existence value limited to natural resources, i.e. the "biological and
geomorphological variety" of which Krutilla speaks?
Some futher discussion of these issues will help in developing our understanding of
the proper role of existence value in benefit-cost analysis.
3
-------
The purpose of this paper is to explore the concept of existence value in some
detail. The first section repeats for convenience a fairly well known definition of
existence value. Section 2 will explore the implications of different definitions.
Section 3 will argue that motives matter and that existence value need not be limited
to any single type of good. Section 4 will provide some preliminary empirical
evidence, on the issue of motives and their implications,
1. The Accounting Definition of Existence Value
Before we discuss the breadth of the concept of existence value, it will be
useful to repeat the definition of this value as derived from the minimum cost or
expenditure function. We proceed in a framework of certainty. Details about the
following summary can be found in McConnell, Smith or Smith, Desvousges, and
Freeman, ch. 6. Let the preference function be U(x,R) where x is an n-
dimensional vector of commodities purchased at the price vector p, and R is the
resource whose existence may be valued. The minimal cost of obtaining utility level
u is given by the standard cost function
C(p,R,u) = min[x*p|U(x,R) = u] (1)
x
To define existence value, let x be partitioned such that x = (x*,x°) where x* is a
vector of commodities complementary to R. For example, for x* = Uj.Xg) ^ could be
visits to the resource and ^ purchases of a magazine which features news about the
resource. Let p* be the price vector which sets the Hicksian demands for x* to
zero.1 Then the existence value (EV) of a change in the resource from R-^ to R2 is
the change in the cost of obtaining utility u at prices p*.
EV = C(p*,Rl5u) - C(p*,R2,u) (2)
The change in use value from the change in the resource is the sum of the change in
the areas under the Hicksian demand curves for x* at the appropriately defined limit
4
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prices. At R^, the sum of the areas under the Hicksian demand curves, is given by
C(p*,R2,u) - C(p,R^,u). The change in this value, which we call UV for use value, is
given by
UV = C(p*,R2,u) - C(p,R2,u)
- {C(p*sRx,u) - C(p,R1,u)} (3)
By adding existence and use value we obtain the accounting identity that total value
equals use value plus existence valued
TV = C(p,Rj_,u) - C(p,R2,u)
= EV + UV (4)
We can use these definitions as we discuss various issues in defining and measuring
existence value.
2. Issues in Defining Existence Value
The first issue concerns the precise definition of existence value. At one
extreme is the notion that any complementarity with the resource and market
commodities connotes use. For example, when one reads a magazine article about
Yellowstone, then one is gaining use value from the resource. This view of existence
value is found in Randall and Stoll. The other perspective, see for example Smith,
would equate existence value to any use of the resource which does not utilize _in_
situ services. One may also find this view in Krutilla and Fisher (p. 124).
What difference does it make whether we define existence value as any offsite
enjoyment of the resource service flows, or require it to be enjoyment of the
resource not complementary to any marketed good? Aside from some technical issues
relating to the cost and utility function the answer is part pragmatic and part
substantive. The pragmatic part concerns measurement. If we define existence value
in its most broad sense, then we hold out the hope that we can measure at least part
5
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of the existence value from a resource change as changes in the areas under the
demand curves for commodities not connected with in situ use. For example, we
measure the existence value of the California condor by estimating the demand for
books and articles about the condor and show how these demands change with the
change in the stock of condors. The resolution of this issue is partly pragmatic.
If in fact one is able to estimate the demand for a good which is weakly.
Complementary to the resource, then it may be argued that we can use these links to
estimate the existence value. In effect, we replace the violation of weak
complementarity between onsite use and the resource with weak complementarity between
the resource and several offsite goods. In the process, one must be careful of
aggregating benefits across several goods.^ It seems most unlikely that one will be
able to estimate via the behavior-based techniques the individual values associated
with a change in the resource.^
Whether we should limit definitions of the use of the resource relates to the
number of elements in x*, the complementary vector. We assume that x*^ is onsite
use, and the rest of the x*'s are offsite uses. Let p-^* be the price that sets the
Hicksian demand for x-^ to zero. Then total existence value (TEV) is the change in
cost of obtaining utility u at the price vector P£, • •• Pn>:
TEV - C( P^*> P2> • * • Pp >>u) ~ C(p^*> P2> * * (®)
This expression equates existence value with any offsite use, and the principal
rationale for this is pragmatic. This definition mixes values from uses such as
reading magazines about a natural resource with values derived from the altruistic
motive of enjoying the pleasure of others who visit the site (and the pleasure of
others who read magazine articles about the resource?).
In concept, this broad definition causes no difficulty. It is merely an
accounting change, reclassifying benefits from use to existence in expression (4).
By manipulating the cost function, we can show that the total value of a resource
6
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change is
TV = TEV + (Change in area under Hicksian demand for x^) (6)
If there is only one use complementary to R^, then = x*, and there is no
difference between the two definitions, If we wish to ignore motives, then we can
lump all offsite uses into one category, call their value total existence value, and
add them to the change in onsite value for an accounting of total value. If motives
don't matter, and we feel confident that we can measure these offsites uses and
existence value together, then we may as well lump them all together. If we wish to
maintain some notion of existence value that is not connected with any other
commodity, or if we are perhaps interested in motives which induce such value, then
we would have to add up areas under the Hicksian demand curve for each element in x*.
The substantive aspect of the definition of existence value leads us to a
consideration of the question of motives. Suppose we take the narrow view, that
existence value is not connected with any other commodity. We will call this "pure
existence value". Defined in this way, pure existence value exerts no influence on
behavior, and we are led to ask "Why do people value resources which they cannot
enjoy directly or indirectly?" A plausible explanation is altruism. We may value
the existence of resources because they are valued by others of our own generation or
by future generations. Randall and Stoll further argue that we can distinguish among
various kinds of altruism.
These conceptual discussions of existence values have led economists into the
unfamiliar territory of motives. As Smith, Desvousges and Freeman observe, "This
discussion of the possible motivations for pure existence value is inconclusive...
Definitions can be considered in part as a matter of taste. A set of definitions can
be considered useful if it furthers the research objective and leads to useful
answers to meaningful questions and if the definitions are based on operationally
meaningful distinctions" (pp. 6-6 to 6-7). We agree in general with these comments,
7
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but will argue for operationally meaningful distinctions in section 3 below.
A second issue worth exploring is the nature of the resource, R. Typically R
has been treated as if it only influences behavior as an argument in the preference
function. The recent work by Smith and by Smith, Desvousges, and Freeman
investigates the question of welfare measurement for changes in R when R acts as an
implicit constraint.*5 We find many different measures of R, even in the context of
measuring existence value. For example, it can be an index of visibility (Schultze
et a I.), grizzly bears and bighorn sheep (Brookshire et a I.), an index of water
quality (Desvousges, Smith and McGivney) or the availability of wild and scenic
rivers (Walsh et al.). But there are two different ways of looking at measures of
resources in the context of discussions of weak complementarity and existence value.
Both views may be useful in understanding the nature of a resource change, but the
distinction of views appears to make little difference to the measurement of welfare. To
maintain some simplicity in the following arguments, we assume that R is weakly
complementary to only, and that there are no offsite uses. Hence, when x-^ is
zero, the only benefit from a change in R is existence value.
First, we can conceive of R as simply an index of quality, as it is most
frequently used. In that case R simply enters the preference function, and is not
part of any explicit or implicit production process. It merely enhances the
enjoyment of use. Second R can be viewed as derived from the production process. In
such a case we might think of minimum levels of R as being essential for x^. This
view of R in the preference function makes the link between and R a technical
link. Denote the critical minimum level of R as Rm, the level of the resource which
reduces use to zero, and suppose that R0 is less than Rm. We are interested in
changes in welfare induced by increasing the resource from its minimum level at RQ to
some level R^. This approach is similar in spirit to work by Smith and by Smith,
Desvousges and Freeman. In effect, we introduce a kind of symmetry in the preference
function. Weak complementary would give
8
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8U(0, x2,...xn,R)/9R = 0
while having R at R0 implies
xi = *i(p»R0)
= o
or
U(x,R) = U(0,X2,...xn,Ro).
The symmetry, perhaps not apparent, exists because when R is below some critical
minimum Ro, changes in x^ bring no net increases in utility. That is, when R = R0,
This symmetry also extends to the expenditure function. The classic result of Maler
concerning weak complementarity simply states that when the price vector reaches p*,
the expenditure function is stable with regard to the resource level. Specifying R
as an implicit but essential input gives us another condition in the absence of
existence value. For resource levels less than Rm, changes in the price of x^ have
no impact on the expenditure function.
when there is no existence value, broadly defined. Goes this additional link between
R and x^ provide any additional information? It suggests looking for existence value
in two ways. First, when individuals don't use a resource because they are priced
out, we can look for existence value. Second, when the resource level is so low that
the technical link involves no direct use, existence motives, that is, care about the
resource for reasons other than its direct use, will induce existence value:
3U(x,Rn)/3x1 = 0
(7)
C(p1°,p2...Pn,R0,u) - C(p,R0,u) = 0
EV = C(p,R0,u) - C(p,Rlfu)
(8)
9
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where R0,R^ are less than the critical minimum.
What is the practical significance of this distinction? It is clear from
earlier discussion of existence value that changes in R influence the choke price for
Xj, so that reductions in R can bring to zero without technical or implicit
production links. That is, the p^* that satisfies x^(p^*) = 0 depends on R, so that
with enough reductions in R, and the right complementarity between R and x^, p^* will
fall. The case of the technical link differs. When the link between and R is
purely technical, and R falls below the critical minimum or essential level, then no
other levels of (Pi • • • pn) will induce a positive level of x^ to be chosen. Thus, the
technical link influences behavior independent of the utility function and the budget
constraint.
An example can help illustrate the issues. Suppose utility is given by
U(x1,x2,R) = a Xj + In x2 + & (9)
where a and b are functions of R such that 9a/9R > 0, 9D/3R > 0. Suppose that a(Rm)
= 0, where R^ is the critical minimum level of the resource. This is a weakly
complementary link. Thus, when R = Rm, x^ = 0. The Hicksian demand for x^ is given
by
Xj = [u - b - ln(p1/ap2)]/a
and the Hicksian choke price is
Pj* = a p2exp(u - b) (10)
Now from this example it is clear that we can adjust R two different ways to get x^
to zero. First, from (9) we see that if R = Rm, a = 0 and will not be chosen
regardless of p. This most closely resembles the elimination of a wilderness area or
converting a beach to condominiums. Second, we can adjust R such that
10
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Pi > a(R)p2exp(u - b(R))
and the user spends his money on something else, even though he could technically
still enjoy the service of the site.
The important issue here is whether defining the resource as essential raises
any special problems in establishing measures of use and existence value. To address
this issue, we can imagine three kinds of policy changes, depending on whether the
resource is greater than or less than the critical minimum. Let R^ be the initial
resource level and R2 be the resource level after the implementation of a policy
change. Then we have the following cases:
a)
R1
<
r2
<
Rm
b)
R1
<
Rm
<
r2
c)
Rm
<
R1
<
r2
In case a, the policy induces only existence value, and in cases (b) and (c) the
policy brings use and existence value. Consider case (b). We can always use the
identity
TV = C(p,Ri,u) - C(p,R2,u)
= C(p,Rlsu) - C(p,Rm,u) + C(p,Rm,u) - C(p,R2,u) (11)
to define total value as in (4). The term Ctp.Rj^u) - C(p,Rm,u) is composed of
existence value only, since the resource levels less than Rm will not allow use. The
second term on the right hand side has both existence and use components, and can be
decomposed as in (2) - (4) or with more detail, as in McConnell, pp. 259-261. Case
c, when the resource is greater than the minimum level, is a special case of (11),
without the first two terms, and hence presents no special problems.
An example decomposing the welfare changes for case b is instructive. For the
preference function (9), the cost function is
11
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' p2exp(u - b) if p1 > p*j or Rm £ R
C(p,R,u)
=
(pj/aJCu - b + l/p2 - ln(p1/ap2)] p^ < p*j_ and. Rm < R
where the dependence of C on R is through a and b: a = a(R), b = b(R) and a'(R), b'(R)
> 0. The value decomposed as in (11) is
C(p,Rj^,u) - C(p,Rm,u) = p2exp(u)[exp(-b(R1) - expC-bCRjj,))] (12)
Cfp.Rm.u) - C(p,R2,u) = p2exp(u - b(Rm))
pi . . . 1 . h
- iTRp"C" " «»tR-2) + ln(a(K2)p2 )] (13)
The sum of (12) and (13) is the total value of the resource change, as given by (11).
Expression (12) is existence value, because use value is zero as long as R < Rm.
Expression (13) is both use and existence value, but it too can be decomposed using
the definitions of existence and use value in expressions (2) and (3). By (2), the
existence value component of (13) is
C(p*i»P2,Rm»u) - C(p*ltp2,R2,u) = p2exp(u)[exp(-b(Rm)) - exp(-b(R2))] (14)
The use value component of (13), based on the definition in (4), is the increase in
use value (area under the Hicksian demand curve) created by a change from Rm to R2.
Since use value is zero at Rm(because is zero at Rm), this change is use value is
simply the area under the Hicksian demand curve at R2:
UV = C(P*i»P2,R2,u) - C(p,R2,u)
= p2exp(u - b(R2)) -^Eu - MR2> +--1- - )] (15)
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Expressions (15) and (14) add up to total value; as given in (13), so that in
principal at least, the case where the resource is essential causes no difficulty in
the decomposition of total value into use and existence value.
This discussion of decomposing use and existence value for a resource change has
been based on the fact that when R = Rm, purchases of bring no utility and hence
any positive level of is a waste of money. What about the case where Rm reduces
to zero by a technical link, and not through the utility function? We will get
the same answer as we have above. With R ^ Rm, the expenditure function is
independent of Xj, and the welfare analysis of changes in R measures existence value
only. When the change is from to R£ where R^ < Rm < ^2 (case b), we can proceed
as we have in the example above.
We can summarize this result with an other example. Suppose that R is the depth
of water in a lake in feet. Let Xj be swimming and Rm = 3; i.e., when the depth is
less than three feet, swimming is impossible. Existence value is attached to R
because greater R means greater biological diversity. A change in R from two feet to
four feet can be decomposed as follows. We have the existence value of the change
from two feet to three feet. We have the total value from three feet to four feet,
which we can decompose into existence and use values.
Thus, while it is clearly possible that resource levels may constrain use just
as the level of use may constrain enjoyment of the resource, accounting for this
phenomenon with the expenditure function appears to present no special problems.
This conclusion, however, presumes knowledge of the expenditure function and the
critical minimum level of resource, a very optimistic presumption.
3. Do Motives Matter?
In previous sections, we flirted with a discussion of motives, but we have not
argued that motives matter. Here we extend our enquiry to considering motives more
carefully. Existence value, whether broadly or narrowly defined, cannot practically
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be linked to behavior, so that its estimation requires the use of contingent
valuation methods. We suggest that it is necessary to consider what motives underlie
existence value bids for proper design and interpretation of contingent valuation
experiments.
Consider the following categories of the motives that may underlie pure
existence value:
1) individualistic altruism - altruism in the sense that individuals gain
value from the enhanced income or well being of others without regard to
the manner in which the utility gains of others were achieved.
2) paternalistic altruism - altruism in the sense that individuals gain value
from the use of a particular good or resource by others.®
3) all other motives.
Whether individualistic or paternalistic altruism (or neither) underlies preferences
is an empirical question. At this point, our purpose is merely to suggest that both
kinds of altruism are possible.
In general, individualistic altruism could be directed toward heirs (bequest
value), or others of current or future generations. For simplicity, consider a 2-
person world where person A is a nonuser and person B is a user of the publicly
provided resource R.' Suppose that existence value accrues to person A from the
provision of R. If the underlying motive is individualistic altruism, then we could
envision persons A and B's preference functions as follows:
UA = UA(Ya,Ub(Yb,R)) (16)
UB = UB(Yb,R) , (17)
where U1 and are the utility and income levels, respectively, for person i = A,B.
3llA 3UB
A unit increase in R yields existence value to person A when —r- • ' 0. Note
31) 3R
that any good which yields value to person B, whether public or private, would yield
existence value to person A.
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Now suppose the motive behind existence value is paternalistic altruism. (The
notion of paternalistic altruism has been discussed in some detail by Collard.) If
person A has paternalistic altruism solely toward person B's use of R, then (16)
would be rewritten simply as
UA = UA(Ya,R) (18)
so that fjL > o, |^=0.
With these definitions we now argue that the motives which give rise to
existence value are important. Consider a proposed project that would tax A and B in
order to pay for an increase in R from to R£. Suppose we ask person A the
following stylized contingent valuation question:
Q* How much would you be willing to pay to have R increased
from R^ to R2?
We would expect person A's response to be positive if he is motivated by either kind
of altruism. Since A is not a user of the resource, the standard procedure would be
to interpret this response as his existence value from the increase in R. However,
depending on A's motives, this interpretation may be misleading.
Suppose person A's existence value stems, at least in part, from individualistic
altruism. Since he is not told the value of goods that must be sacrificed (other
than his own contribution) for the resource enhancement, he is not given the
opportunity to compute the change in well-being of person B. Hence, there is no
opportunity for a negative response. Suppose Q* is rephrased as follows:
q** How much would you be willing to pay to have a project undertaken
(postive $) or stop a project from, being undertaken (negative $)
that would tax person B and increase R from to R2?
The response to Q**, even if still positive, will very likely be lower than when no
opportunity cost is presented to person A. It may even vary depending on the type of
goods to be sacrificed by person B if A is motivated partly by paternalistic
15
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altruism. That is, person A's response may depend on whether person B pays in higher
taxes or reduced services of some other public good. Most likely, at some level of
opportunity cost, person A will become willing to pay some amount to keep the
resource change from occurring. Thus, if existence value bids are partially based on
individualistic altruism, contingent valuation attempts to estimate existence value
must give respondents information about the size and form of the costs that others
must pay when a resource enhancement project is undertaken.
In addition to altruism towards other people, it is possible that other motives
could underlie existence value. Randall and Stoll have used the term "Q-Altruism" to
represent altruism directed toward the resource itself. This seems plausible if the
resource in question is an advanced form of animal life, but less plausible if the
resource is an inanimate object. Alternatively, there may exist an underlying
"environmental ethic" which is totally independent of anyone's use of environmental
resources. We have no basis for judging which motives are operative. Both the
presence of environmental groups, and the observed positive responses to questions
eliciting existence value can be explained by altruism towards others, other motives
or indirect use values. In any case, it is sufficient for our purposes simply to
recognize that other motivations may exist and to note that the presence of other
motivations may also be relevant to the proper design and interpretation of
contingent valuation experiments.
Let us take the analysis one step further. Consider a project which increases R
from R^ to R2, and costs C, to be paid by B, the user. B's surplus from the change
(Sg) is given implicitly by
UB(YB - SB,R2) = UB(Yb,R1) (19)
Suppose that C > Sg, i.e. user benefits are less than costs. Now we ask, under the
payment scheme when B pays, how much surplus does A get from the project when he is
16
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motivated by individualistic altruism? a's surplus is given implicitly by
U%A - Sa,UB(Yb - C,R2)) = UA(Ya,UB(Yb,R1)) (20)
Since UB(Yg - C^) < UB(Yg,R^) = UB(Yg - Sg^), A must be compensated for the move
and hence SA (existence value) is negative. Thus, the aggregate benefits remain less
than costs after the inclusion of existence value
SA + SB < C (21)
because C > Sg, SA < 0. When individualistic altruism prevails, and the user pays
all costs, adding in the surplus from existence value from the nonuser does not
change the benefit-cost outcome.®
It is reasonable to ask whether a change in the distribution of costs will make
benefits exceed costs. If A is altruistic towards B, won't he help share costs? We
can rewrite (20), letting w be A's share of costs and (1-w) B's share:
UA(YA - SA - wC, UB(Yb - (l-w)C, R2)) = UA(Ya, UgfYg.R],)). (22)
Expression (20) has w = 0. Differentiating with respect to w and observing how SA
changes gives us
3SA/3W = [U]0' - 1]C (23)
where subscripts on U indicate partial derivatives with respect to arguments.
This algebraic result tells us what we should already know. A's willingness to
pay for the project will increase if he gets more utility by giving B a dollar
is the rate of A's utility change from B's income increase) than he gets from
having a dollar himself (U^A). While such a result can not be discarded completely,
it seems extreme. Thus, if the users can't pay for the project when w = 0, then
including individualistic altruism when nonusers share the cost, will not increase
the benefits.
17
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Let us now consider the question of whether any resource, good, action, risk or
regulation can provide or deprive an individual of existence value. This bears
directly on the issue of motives. Krutilla observed that historical and cultural
features and perhaps rare works of art can also provide service flows to those who do
not use them. This same conclusion is argued by Randall and Stoll, who suggest that
many different kinds of goods and services have potentially significant existence
value. Nevertheless, the prevailing view is that there is something special about
natural and environmental resources that makes existence value from these resources
more significant than existence value from most or all other types of goods. This
view has been based on the intuition that existence value is likely to be most
important for assets that are unique, irreplaceable, and long lived.
Unfortunately, there is no easy answer to the question of the extent of
existence value. The answer lies with the unobserved motives that give rise to
existence value. For example, if the only motive underlying an individual's
existence value is individualistic altruism, then all kinds of goods consumed by
others would provide existence value to the individual based on the extent of use
values provided by each good. Characteristics of natural assets such as uniqueness,
irreplaceability and longevity may account for large existence value, but only in as
much as these characteristics increase the potential for use value from
natural assets. In contrast, if the source of existence value is paternalistic
altruism, then existence value could be greater from natural versus man made assets,
though we know of no clear reason _a priori why it should be.
Motives other than altruism or an environmental ethic may account for existence
value. For example, it could be hypothesized that existence value from resource
preservation stems from an inherent desire to preserve the status quo. Even so, it
is not clear that ignoring existence value encourages too much conservation.
Consider a community where a major source of livelihood is timber harvesting, so that
conserving the forest means a drastic change in the structure of the community. If
18
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people have existence value for the status quo in their community, then ignoring
existence value might encourage too much conservation.
This section has explored the consequences of individualistic altruism. By
hypothesizing individualistic altruism as a plausible motive for existence value, we
have argued that existence value could accrue from any type of good. We have further
argued that individualistic altruism will not change the benefit-cost outcome. As
discussed above, there are other plausible motives for existence value. In cases
other than individualistic altruism, adding existence value to user benefits could
change the sign of a benefit-cost analysis. Thus, it is useful to ask if there is
any way to discover whether individualistic altruism is important in the sense that
many people are so motivated. Without more specific information, the role of
existence value in benefit-cost analysis is ambiguous.
4. Some Empirical Evidence
This section presents some preliminary results of a stylized contingent
valuation experiment designed to provide information about the motives behind
existence value. The study population was defined as adult (age 18 or over)
residents of the Washington D.C. and Baltimore Standard Metropolitan Statistical
Areas. A Random Digit Dialing Telephone Survey was used to contact 1057 indivduals
in the study area. Of those contracted, 741 agreed to fill out and return a brief
mail questionnaire regarding water quality in the Chesapeake Bay, and of these 741,
282 actually returned the questionnaires. The 282 respondents were grouped as users
or non-users. Users were defined as all respondents who thought they might use the
Bay. Respondents who felt certain that they would not use the Bay for recreation at
any time in the future were defined as non-users. Non-users accounted for 16.3% of
the respondents.
Because only about 70% of those contacted agreed to receive the mail
questionnaire, and because only 38% of those who agreed actually returned these
19
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questionnaires, these results should not be taken as representative of the population
sampled. Further, we are aware that the counterfactual nature of the questions
raises some doubt about the validity of the responses. But we are interested in
using the contingent valuation framework for gaining insights into motives, not
computing aggregate benefits and costs.
Respondents were asked to consider a series of situations concerning public
beaches surrounding the Chesapeake Bay. They were asked to assume that water quality
at these beaches had fallen below a level acceptable for swimming. They were told
that a clean-up project could be undertaken that would clean the beaches so that a
water quality level acceptable for swimming was achieved and maintained. Then
respondents were asked the following question under 4 different scenarios:
Q.1 Would you prefer that the clean-up project be undertaken?
Scenario 1. No additional information.
Scenario 2. Access to the beaches by the public is permanently denied so
that even if clean, the beaches will not be used.
Scenario 3. If the project is undertaken, taxes would be raised so much
that nearly everyone prefers that the project is not
undertaken. These taxes would be paid by individuals other
than the respondent.
Scenario 4. If the project is not undertaken, funds would instead be used
to improve hospital services in selected communities
surrounding the Bay. The respondent would never need to visit
any of the improved hospitals, and of all the people who care,
half want the beaches cleaned and half want improved hospital
services.
The proportion of yes responses for users and nonusers under each scenario is given
in Table 1.
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Table 1. Summary Results of Contingent Valuation Experiment
Scenario
Number
Proportion
Responses:
of Yes
Users3
Standard Error
of Difference0
Proportion
Responses:
of_y^s._ h
Non-users
Standard Error
of Difference0
1
.96
.83
2
.70
.032
.69
.088
3
.71
.032
.67
.088
4
.49
.035
.37
.091
a. The number of users is 236.
b. The number of nonusers is 46.
c. This number is the standard error of the difference between the proportion
in Scenario 1 and the proportion of the given Scenario.
Responses to Q.1 under Scenario 1 are used as a control to be compared with
responses under Scenarios 2 through 4. As expected, most respondents preferred that
the project be undertaken under Scenario 1. Non-user responses of yes indicate
positive existence value. The relatively high number of non-users exhibiting
positive existence value is consistent with the results of previous studies that have
estimated existence value. Note, however, that Scenario 1 is purposely ambiguous
about project costs. It appears that respondents, when not told of costs to
themselves or others, simply assume there are none.
With access to beaches denied under Scenario 2, the number of yes responses to
Q.1 predictably declined. Since the number of nonuser responses of yes declined when
access was denied, it appears that existence value, to at least some individuals, is
related to others' use. Thus, altruism may be one motive that underlies existence
value. However, even with access denied, most respondents preferred that the project
be undertaken. This may reflect the presence of indirect use value, an environmental
ethic, or any number of other motivations. Finally, it is interesting to note the
21
-------
closeness of user and non-user group responses under Scenario 2. Since with access
denied there can be no users, yes responses from the user group will also indicate
positive existence value. Thus, the proportion of users and non-users exhibiting
existence value was nearly identical.
Scenario 3 differs from Scenario 1 only in that respondents were told that
others would need to pay taxes to have the project undertaken. The reduced number of
yes responses under Scenario 3 indicate an underlying concern regarding the income or
well-being of others, i.e. individualistic altruism. Hence, the conceptual results
of section 3 appear to have practical significance. Unexpectedly, a greater
percentage of users changed their response than did non-users when told of the taxes.
Under Scenario 4 the number of yes responses fell dramatically compared with the
responses under Scenario 1. Since less than half of the non-users preferred that the
clean-up project be undertaken, it appears that existence value from improved
hospital services is at least as great as existence value from clean water in the
Bay. Preferences for the clean-up project or improved hospital services should not
be interpreted as stemming from individualistic altruism, since respondents were told
that an equal number of people preferred each project. Non-user preferences for one
project or the other could be based on paternalistic altruism or some other motive.
This result is not inconsistent with the hypothesis that existence value is not
confined to natural assets, even if the underlying motive for existence value is not
individualistic altruism,
To summarize, our results do not contradict the idea that individualistic
altruism is one of the motives underlying existence value and that existence value
accrues from at least some man-made goods, even if individualistic altruism is
ignored. Interpretation of this experiment must, however, be made with some caution
given the highly hypothetical nature of the questions posed. Nevertheless,
experiments such as this one may be our only means to provide information regarding
the underlying motives behind existence value.
22
-------
Footnotes
1 We take the Hicksian limit price as the appropriate price to evaluate welfare
changes. That is the p^* that sets to zero is the derived from the
following expression:
Using the Marshallian limit price will miss part of the welfare change. For more
details, see Hanemann.
In the case of certainty, option and quasi-option value will be zero.
Consider the problem of valuing changes in an asset R when and x2 are weakly
complementary to R. Suppose that SU(0,0,X3,...xn,R)/3 R = 0, but
8U(xpX2,X3,...,xn,R)/8R > 0 for x^ > 0 or x2 > I e., this is a slight
generalization of weak complementarity. The value of a change in R is given by
C(p,R^,u) - C(p,R2jU). To get this from areas under the demand for market
commodities, we can aggregate across x^ and x2 in the following way. Let
p* be (Pi*)P2>»**Pn^ '3e t'~ie current prices and the price that sets x^ to zero,
given the other prices, R and u. Let p** be (p^*,P2*»P3>«"Pn) be the current
prices and the prices that set x^ and x2 to zero, when p2* depends on pj*, the
other p's, u, and R. Then under weak complementarity 8C{p**,R,u)/9 R = 0.
Consider the value of a change in the price vector from p to p**.
rPi
C(p**,R,u) - C(p,R,u) =
* *
P2
^2(Pl*>P>P3> * * *Pn
C1(p,p2,...pn,R,u)dp +
'pl "P2
The areas on the right hand side represent, first the area under the Hicksian
demand for x^ given current prices for x2,...xn> and second the area under x2.
given p^*,p3....pn. When R-^ changes to R2 when compute
-------
UV = - [C(p,R2»u) - C(p,R^,u)] = change in area under x-^ .given P2»...pn
+ change in area under Qiven p^*,pg,...pn,
so that we can get the value of resource changes from commodity demand curves.
There are two implications of this result. First,, to get the use value from other
than in situ use, one must add values across all possible uses. Second, when
adding values, each successive value must be conditional on zero levels of all
previous uses.
^ Smith, Desvousges and Freeman suggest some of the difficulties in estimating
offsite demand. See pages 6-7.
® This issue is also investigated by Richard Bishop and Kevin Boyle in preliminary
work.
® These motives are labelled utility-related and commodity-related by Collard(p.7).
In an apt phrase, Collard also describes paternalistic preferences as
"meddlesome".
^ The principal results of this section have been shown to hold for any number of
users and nonusers, see Madariaga and McConnell (1984).
® This result may not hold in the case of N users if the nonuser is more altruistic
toward one group of the users than another group, see Madariaga and McConnell
p. 11.
-------
References
Brookshire, D., L. Eubanks, and A. Randall. 1983. "Estimating Option Prices and
Existence Values for Wildlike Resources," Land Economics 59, 1-15.
Collard, D. 1978. Altruism and Economy, Oxford Press: New York, New York.
Desvousges, W. H., V. K. Smith, and M. P. McGivney. 1983. A Comparison of
Alternative Approaches for Estimating Recreation and Related Benefits of Water
Quality Improvements, prepared for U.S. Environmental Protection Agency,
contract no. 68-01-5838.
Fisher, A. and R. Raucher. 1984. "Intrinsic Benefits of Improved Water Quality:
Conceptual and Empirical Perspectives," in V. K. Smith, ed., Advances in
Applied Microeconomics Vol. 3, JAI Press: Greenwich, Connecticut.
Hanemann, W. Michael. 1980. "Measuring the Worth of Natural Resource Facilities:
Comment," Land Economics 56:482-486.
Krutilla, J. V. 1 967. "Conservation Reconsidered," American Economic Review
57:777-86.
Krutilla, J. V. and A. C. Fisher. 1975. The Economics of Natural Environments:
Studies in the Valuation of Commodity and Amenity Resources, Johns Hopkins Press
for Resources for the Future, Inc.: Baltimore, Maryland.
Madariaga, B. and K. E. McConnell. 1984. "Some Implications of Existence Value,"
unpublished paper, University of Maryland.
Maler, K. G. 1974. Environmental Economics: A Theoretical Inquiry, Johns Hopkins
Press for Resources for the Future, Inc.: Baltimore, Maryland.
McConnell, K. E. 1983. "Existence and Bequest Values," in R.D. Rowe and L. G.
Chestnut, eds., Managing Air Quality and Scenic Resources at National Parks and
Wilderness Area's^ Westview Press: Boulder, Colorado.
Randall, A., and J. R. Stoll. 1983. "Existence Value in a Total Valuation
Framework," in R. D. Rowe and L. G. Chestnut, eds., Managing Air Quality and
Scenic Resources at National Parks and Wilderness Areas, Westview Press:
Boulder, Colorado.
Schulze, W. D., D. S. Brookshire, E. G. Walther, K. K. MacFarland, M. A. Thayer, R.
L. Whitworth, S. Ben-David, W. Malm, and J. Molenar. 1983. "The Economic
Benefits Of Preserving Visibility in the National Parklands of the Southwest,"
Natural Resources Journal 23:149-173.
Smith, V. K. 1985. "Intrinsic Values in Benefit Cost Analysis," unpublished paper,
Vanderbilt University.
Smith, V. K., W. H. Desvousges, and A. M. Freeman, III. 1985. Valuing Changes in
Hazardous Waste Risks: A Contingent Valuation Analysis, prepared for U.S.
Environmental Protection Agency under Cooperative Agreement no. CR-811075, Vol.
I, Draft Interim Report.
-------
A TIME-SEQUENCED APPROACH
TO THE ANALYSIS OF OPTION VALUE*
by
Theodore Graham-Tomasi**
May, 1985
^Prepared for the AERE Workshop on Recreation Modeling
Boulder, Colorado, May 17-18, 1985
**The author is Assistant Professor, Department of
Agricultural and Applied Economics and Department of
Forest Resources, University of Minnesota. Numerous
helpful discussions with Bob Myers are acknowledged.
This research partially was funded under Project 14-88
of the Agricultural Experiment Station, University of
Minnesota.
-------
A Time-Sequenced Approach to the
Analysis of Option Value
by
Theodore Graham-Tomasi
1. Introduction
Burton Weisbrod's 1964 seminal article on option value spawned a
large literature which addresses the following question: will an individual
who is uncertain about his or her future demand for a good be willing to
pay a premium, in excess of the expected value of use, for the right to
retain the option of future use? This difference between maximum sure
willingness-to-pay for the option of future use (option price) and the
expected value of future use (the mathematical expectation of Hicksian
consumer surplus) is option value.
It generally is conceded that when preferences are uncertain, option
value can be positive or negative (Smith, 1983, and Bishop, 1982, provide
overviews of this literature). These results are of dubious theoretical
interest, but of some practical importance.
They are of dubious theoretical interest because, given current
institutions, the option Value is the correct ex-ante measure of welfare
change under uncertainty (Anderson, 1979). If compensation for a change
in regime could be exacted ex-post, after uncertainty was resolved, then
the expectation of Hicksian equivalent variation would be an appropriate
ex-ante measure of welfare change. Alternatively, if contingent claims
markets exist, then the expected value of equivalent variation again is
appropriate (Graham, 1981). However, neither contingent claims markets
nor the ability to determine ex-post compensation exist. Therefore, it may
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-2-
be concluded that option tag is relevant to measuring welfare changes, under
uncertainty and expected consumer surplus is irrelevant. Why then should we
study option value?
The answer to this good question is that the sign and size of option
value is of considerable practical importance in project analysis. Individual
option prices may be assessed by contingent valuation techniques, but these
analyses are quite expensive to undertake. One-way tests for project accep-
tance based on expected surplus would be available if the sign of option
value is determinate. For, if a project passed (failed) a benefit-cost test
which uses expected surplus measures and it is known that option value always
is positive (negative), then the project could be accepted (rejected).
Naturally, this approach leaves a zone of indeterminancy, which may be
filled only if the magnitude of option value is known. As well, if the issue
is the optimal size of a project, then the magnitude of option value, and
not just its sign, must be known. Of course, this is equivalent to saying
that you need to know option price. This has led some investigators (Freeman,
1984, and Smith, 1984) to seek a bound for option value. Unfortunately, useful
analytical results along these lines have been difficult to obtain.
Most of ths option value literature has dealt with Weisbrod's original
notion of demand uncertainty. The difficulty that arises in establishing
a sign for option value is the need to compare the marginal utility of income
across states: with different utility functions in each state, nothing
definite can be said in this regard. This realization led Bishop (1982) to
consider supply-side options. That is, if demand for a resource is certain
but its stability is uncertain, then the problem of state-dependent marginal
utility of income is eliminated and the sign of option value can be established.
Freeman (1985) has pointed out that Bishop only studied one case of supply-side
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-3-
uncertainty and concluded that in the other cases, option value again is
indeterminate.
The assumption of the supply-side analyses that demand is certain, but
supply is not, seems relevant to many current resource policy issues. As
well, based on the positive analytical results obtained by Bishop (1982),
more work along these lines appears warranted. In this paper, we investigate
supply-side option value.
In the option value literature, analyses most often have been based on
static models and have used the common postulate that individual preferences
satisfy the von Neumann-Morganstern axioms and, hence, have an expected utility
representation. In these analyses, little attention has been paid to under-
lying choices and constraints. This is natural, given the well-known foundation
of expected utility analysis. However, we argue in this paper that this possi-
bly has led to a misrepresentation of actual choice situations of interest in
policy discussions.
In particular, it seems that inadequate attention has been paid to
temporal aspects of the risky choices at issue, and the timing of possible
olutions of uncertainty relative to the time of when choices must be made.
Consideration of temporal risk (in the sense of Dreze and Modigliani, 1972)
undermines the expected utility foundation on which previous research has
been based. Since most, if not all, actual choices involve temporal risk,
this appears to be a serious problem.
The issue of time sequencing has been raised in the option value litera-
ture in the guise of quasi-option value (Arrow and Fisher, 1974) . Here, the
central issue is the timing of choices relative to the timing of resolution
of uncertainty. Specifically, Arrow and Fisher and others (see Henry, 1974 ;
Epstein, 1980; Hanneman, 1983; and Grahm-Tomasi, 1983) seek to determine if
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-4-
the prospect of learning reduces the benefits of implementing irreversible
investments relative to the case when learning is ignored. The general result
is that, even under risk neutrality, there is a benefit to maintaining flexi-
bility (a quasi-option value of not undertaking irreversible investment-)
due to expected learning possibilities. In fact, Conrad (1981) suggests that
quasi-option value is equal to the expected value of information. Here, we
very briefly address quasi-option value (QOV)(Smith, 1983 calls this time-
sequenced option value) and its relationship to the time sequenced approach
taken here.
The paper is organized as follows. In the next two sections, we remind
ourselves using a certainty model of what we wish to measure in the stochastic
case and how these measurements can be used to select a project. Section 2
addresses individual welfare change measures, while Section 3 provides a
review of how a planner could use information on individual welfare change
to choose a project. In Section 4, we very briefly discuss possible sources
of uncertainty. Section 5 contains an analysis of supply-side option value
in a setting where there is no temporal risk and individuals have standard
von Neumann-Morganstern utility functions. We provide an alternative approach
to that used by Bishop (1982) and Freeman (1985) and are able to obtain some
positive results. In the sixth section, we study the problems introduced by
a move to temporal risk and derive several results from this literature in
terms of our model of supply-side uncertainty. The results here are quite
negative: temporal risk greatly, complicates the study of option value. The
next section shows in the case of uncertainty how the planner could use
individual welfare change measures to select a project. This section also
addresses quasi-option value. The final section provides a discussion and
points out some empirical implications.
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-5-
It should be stressed at the outset that this paper is exploratory in
nature. It represents an attempt to draw inferences from the general economic
literature on temporal risk for the modeling of option prices and option
values in the analysis of projects with uncertain environmental consequences.
There remains a great deal of work to be done. We seek here to illustrate the
kinds of difficult questions that arise when time is composed with uncertainty
in the study of welfare change and project appraisal.
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-6-
2. A Certainty Model: The Individual
In this section, we set out a simple model of a project in a dynamic
setting and study measures of welfare change. This will serve as a foundation
for the stochastic models to be analyzed in the sequel. It also has some
important implications for project analysis which carry through to the sto-
chastic case and, therefore, to the study of dynamic option prices.
The individual has preferences over alternative sequences of goods con-
sumed and environmental quality. Let e En (Euclidean n-space) be a vector of
consumption goods at date t. Included in are labor supplies (measured as
negative) as well as visits to recreation areas. Let c = (Cp . . . , Cj) be a
sequence of such consumptions; the individual's time horizon is date T. Prices
of consumption goods are given by the spot price vector e Ea. This includes
the prices of visits to recreation areas.
The level of environmental quality at various locations at date t is
in
given by a vector q^ e E • This vector is exogenous to the individual. How-
ever, as the individual has preferences over alternative quality vectors,
these have components measured in an "individual payoff-relevant" fashion.
The vector q^ will depend on the "output" of a "project" that is being
anticipated. I introduce this with some generality. A project is represented
by a sequence of points on the real line which may be thought of a "project
size." This is a sequence v = . . . VT)» Of course, the project may
outlive the individual; generally T * T. Often, we have a project represented
In the literature by
But this is not necessary and the more general approach allows alternative
"phasings" of projects, which as we will see below, may be important under
uncertainty.
0 if the project is not implemented
1 if the project is implemented
all t.
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-7-
The project affects payoff-relevant environmental quality variables
via a biological/physical process function. Thus, a project may affect fish
populations of relevance to recreationists by controlling amounts of a pollu-
tant which is detrimental to ecosystem functioning more generally. In a
dynamic model, the history of outputs of a project, as well as the history
of environmental quality will affect current environmental quality. This can
be captured by specifying a difference equation which governs the time path
of environmental quality which does not have a Markovian structure. Let
vt - (vx, v2, vt_1)
<1^ * » ^2' ^t—1^*
Then
qt+1 " f(*t» vt» qt» (i)
We now turn to individual preferences. We assume that all individuals
are finite-lived. Let z= (c^, q^) be a consumption goods/environmental
quality bundle at date t (zt e En x Em) and let z = (z^, . . . , z^,). For
notational convenience, we let Z = En^ x E^. The following a::ioms concern-
ing individual behavior are posited to hold.
Axiom 1.1: Each individual's choices from Z are
represented by a binary relation R
on Z where R is a weak order and R is
monotonic.
Axiom 1.2: Let § be the usual topoloqy on Z. Then
{z: z £ Z, z R y} e § and {z: z £ Z,
y R z} s § for every z, y £ Z.
We have the well-known representation theorem.
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-8-
Theorem 1.1: If individual preference orderings satisfy
axioms 1.1-1.2, then there exists a real-
valued utility function U(z), continuous
in the usual topology on Z, such that
z R y iff U(z) > U(y).
Proof: Fishburn (1970) theorems 3.1, 3.5, and Lemma 5.1.
We now turn to the individual's budget constraint. Let a £ (0,1) be
the (constant for convenience) one-period, riskless market rate of interest
at which individuals can borrow and lend. The Individual has an exogenous
T
sequence on non-wage incomes {w} Then the budget constraint may be
written
t"T t"T
B(pT,w,a) - {C e EnT I a*"1** • cr < £ at_1 w.; c e C }
t-1 ~ t-1 c
__rn
T ( x t-1 ) and C C E is the set of feasible
where p " vpj, ., Pj), w - (2,fco wc
consumptions.
It is natural to impose the following assumptions:
Al: B(.) is non-empty.
A2: wt £ v • for all t.
nT
Under assumption A2, it is clear that B(.) is compact in E
Let
T T T
v(p »w,q ,a) = sup (U(z) : c e B(p ,w,a)),
c
T 1 /
where q ¦ (q^, •••» q^)#—• Since u is continuous and B is compact and non-
empty, the supremum is attained.
In a world of certainty, we can define measures of welfare change using
this intertemporal indirect utility function. Let (p°^»q°^) be the initial
, 'T 'T
situation and let vp ,q be the situation subsequent to implementation of a
project. The compensating variation (cv) and equivalent variation (ev) are
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defined implicitly by
V(poT,w,qoT a) - V(p T, w-cv, q T, a) (1)
V(p'T, W, q'T, a) - V(poT, w+ev, qoT, a). (2)
An important special case of this arises when the utility function U is
separable. Here, we impose more structure on preferences by means of the
following axiom.
Axiom 1.3: (z : z e Z, z R y) and (z : z E Z, y R z)
both are open in the usual topology on Z
(continuity) and are convex.
To discuss separability and the existence of instantaneous utility
n m
functions, we reconsider the sequence z. Recall z^ E E x E ; we then con-
_n+in
structed z by considering the T-fold Cartesian product of E with itself
and considered z to be an element of this space. Now, we consider preferences
on each z^ individually. Thus, we let Z = Z^, where (Z^, is a
topological space for each t. Let £ = be the product topology for Z.
It is well known that if each (Zt, €t) is a connected and separable space,
then (Z, C) is connected and separable in the product topology. Therefore,
it makes sense to discuss properties of the instantaneous utility functions
which are similar to those of the overall utility function discussed above.
Let z_t = (Zj_» ..... zt+l* • • •/ ZT^ 'oe t'"ie consumPtion/quality
o
bundle at all dates other than date t. For fixed z = z , the preference
ordering R induces a preference ordering on Z^ given by R x x't if and
only if R ^ ^or an^ Xt* "'~n We ^ave the following
statement of a separability axiom.
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Axiom 1.4: For each t e (1, . . . , T) x R x
C -t
implies x„ R x' for all x s H Z.•
t x-t i*t 1
The following theorem provides a utility function representation for
separable preferences.
Theorem 1.2:
The preference ordering posited in Axioms 1.1
to 1.4 may be represented by a continuous,
quasi-concave function U: H + E which
may be written
U (z) = OCujCzj), Uj.(zT))
where u
Z„ + E and 0 : E E, and
G as well as each is increasing, continuous
(in the product topology and usual topologies
respectively) and quasi-concave.
Proof: The existence of a continuous utility function
taking the separable form is proved by
Katzner (1970). That the component functions
0 and u are quasi-concave if U is (which follows
from axiom 1.3) , is shown by Blackorby, et al.,
(1978), Theorem 4.1.
Let be income allocated to consumption at date t, and let =
(C£ : • C£ <_wt' C£ e C) . Define
Vt(pt,wt,qt)
= max (U(ct) : ct e Bt(.)).
Then
t-T t-T
v(Pt»w»q» °) " ""ax {0({V(pt>wt,qt^} ): I ot 1w£ <. w}«
{wt> t»l t-1
The instantaneous indirect utility functions can be used to define instantan-
eouc measures of welfare change, i.e.,
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-11-
vt - vpt,wt" cvqP
Vt(p;,w^,qp - Vt(p°,w° + e»t, q°), for t E [0,1].
Here, when the project is implemented, the consumer may respond by reallocating
income through time as well. This point is crucial, for it creates the follow-
ing inequality:
, t-T
V(p T, w T cv, q') - 0({V (p* w - cv , q')} ) <
c z z t«0
VCp T, 1 <*' 1(w - cv ),q T) - V(p T,w- I a* 1cv ,q T).
t-1 C t-1 C
This implies, since V is increasing in its second arguement, that
N. V t—1
cv 2. At a cvt*
Thus, if the present value of consumer surplus is non-negative, so is the
present value welfare change measure cv.
Similarly,
V t~l >.
lt a evt >. ev»
whence if the present value of equivalent variations is negative, so is the
true welfare charge measure. These give two one-way tests, but leaves a zone
of indeterminancy. Moreover, we have the following theorem.
Theorem 1.3: There is no U with U, t) and {u£} continuous,
increasing, and quasi-concave, such that the
present value of instantaneous cv^ or evfc is an
exact index of welfare change for all projects.
Proof: Blackorby, Donaldson and Moloney (1984).
Before turning to an assessment of how the equivalent variation measure
of welfare change for individuals can be used in making choices among projects
by a social planner, we introduce the intertemporal expenditure function and
discuss briefly the money metric measure of welfare change.
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Dual to the lifetime indirect utility function introduced above is the
lifetime expenditure function defined by
V(P^» w» °) * v° E(pT» *1" * a» V°) " w»
The money metric (see McKenzie and Pearce, 1982) is defined by
Y(v) = E(pT(0), qT(0), a, V(pT(v), w, qT(v), a))
T T
where p L(0) and q L(0) are prices and environmental quality in the absence
of the anticipated project. The definition of the expenditure function shows
that
ev(v) - Y(v) - w. (2)
The money metric gives minimum the cost of achieving the level of the utility
with the project, when the project has not been implemented. Since Y is a
monotonic increasing function of an indirect utility function, it is itself an
indirect utility function. Importantly, both the ev and the money metric are
invariant to increasing monotonic transformations of the underlying ordinal
utility function.
The money metric and equivalent variations possess an important property
that the compensating variation does not have. The cv is not an exact measure
of welfare change in that it may not correctly rank several projects relative
to a base project, although it will correctly make pairwise comparisons
(Hause, 1975; Chipman and Moore, 1980). Thus, we restrict our attention in
what follows to the ev and Y measures of welfare change.
To sum up the results of this section, the equivalent variation and
money metric are useful measures of individual welfare change due to the
implementation of a project. In a dynamic setting, these should be defined
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relative to the lifetime indirect utility or expenditure functions. This
would seem to underscore the usefulness of survey techniques in eliciting
willingness-to-pay since lifetime compensation measures (or their annualized
equivalent) can be directly assessed. However, the lifetime approach does
create a few difficulties for the definition of an appropriate criterion
for selection of a project by the planning authority. We address this
issue, at least partially, in the next section.
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3. Project Selection under Uncertainty
The difficulties of moving from individual to social valuations of
projects are of two kinds. The first is the much discussed possibility
of providing an axiomatic foundation for a social preference ordering or
welfare function which is based on individual orderings. We do not address
this issue here, and merely assert the existence of a preference ordering
for the planning authority which has certain properties. The second diffi-
culty derives from our focus on lifetime indirect utility functions in
Section II. In particular, if it is asserted that the planner has preferences
over indirect utilities, and we do not assume that each "generation" con-
sists of a single individual (see, e.g., Ferejohn and Page, 1978), then some
work is required to establish a benefit-cost foundation for social choices.
T T
The individual theory above used the sequences p and q , which are
sequences with terminal date corresponding to the individual's planning
horizon. These are subsequences of p^r = (P]_»• • • »P^") and = (q^ ,«•. >
where T is the horizon relevant to the planning authority. These price
and environmental quality sequences depend on the project that is imple-
mented. The environmental quality sequence depends on the project as repre-
«
sented by equation (1). In the sequel we write q^"(v) to denote this depen-
dence. Being purposely vague, we write P^(v) as well. We assume that both
of these functions are unique without specifying conditions under which this
will be true. Note that for t e(t, t)
"Wi " £((V °S)- °» Vs> v.1'
S 8
where 0 is the zero vector in E . Similarly, we let pfc = pfc(0) for
t e (t , 7).
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The set of possible projects is given by ACE, A = {v$E ; v is
feasible}. We say that an individual cares about a project if his/her.
lifetime indirect utility varies with changes in v. Formally, we say that
T x T
Agent i cares about the project set A if V(p (v), w, q (v), a) * V(p (v'), w,
T
q (v*), a ) when v * v' for some v, v', e A.
There are several ways in which an individual might not care about a
projfct. If the individual is not alive, then (presumably) V*" (•) = 0
for all v £ A. As well, some prices might not depend on the project and an
individual might not consume any of the goods (including recreation) with
project-sensitive prices. If V^" is independent of changes in environmental
quality when consumption of recreation is zero and the individual does not
care about price changes for goods (s)he does not consume, then (s)he will
not care about the project. This is the case of "weak complimentarity"
discussed in the valuation literature (Bradford and Hildebrandt, 1977) .
Let M* ¦ {t : i cares about A at t} , and let t(i) - inf {t : t e M*}.
To avoid mathematical complexities which are not of concern in this paper,
we impose
A3.1: The number of agents at each date t is
finite.
A3. 2: 7 < °°.
A3. 3: t(i) <_ T - T^" for all i.
Let CI = {i : t(i) = t}. We denote the power of by It« Individual i's
planning horizon is given by T^J purely to ease notational burden, we
assume that T* = T for all i.
The vector of lifetime indirect utilities is a vector in E^, where
T
I " H I". By A3.1 and A3.2, this is a finite-dimensional space. The planning
t
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authority is presumed to have preferences on E^ as given in the following axioms,
Axiom 3.1: The planner's preferences are represented
by a binary relation PCE^ E^ where P
is a weak order, which is monotonic and
continuous in the usual topology.
Under axiom 3.1, we can represent P by a real valued social welfare function.
Theorem 3.1: If the planner's preferences satisfy axiom 3.1,
then there exists W : E^ E, with W con-
tinuous and such that > W(V*,...V*)
if and only if V^) V^).
Proof: Fishburn (1970).
Theorem 3.1 establishes a social welfare function defined on sequences
of lifetime indirect utility profiles. However, a problem arises in this
approach. The arguments of W are individual utilities, which can be sub-
jected to an arbitrary monotonic transformation with affecting underlying
behavior. Undertaking such a transformation may drastically change the
social rankings involved. Clearly, this is an undesirable characteristic
for a social welfare function to have. Rather than dealing carefully with
specification of W, it is more convenient to measure the arguments of W
such that they are invariant to such monotonic transformations. The money
metric described in the previous section is an obvious candidate.
Furthermore, we are interested in deriving social rankings of alterna-
tive projects induced from this ranking of utilities. That is, we seek a
ranking p* defined by v P* v' if and only if g (v) P g(v'), where g: A -»¦ E*
given individual lifetime utility vectors as a function of projects. An
important special case for which this is straightforward and which will be
useful when uncertainty is introduced is where the social welfare function
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is linear. Thus, we impose
1 T imI .
A3.4: WCV1,..., VA) - I b.V .
i-1
The implementation of a project entails a cost and, therefore, the
central planner must devise some method of financing the effort. We assume
that lump-sum financing is possible. Let the spot expenditures required to
implement a project v be given by
k(v) « (kj^v), kT(v)).
The planner has several options for financing project v. A financing scheme
is a vector of payments s(v) = (s^(v), ..., s*(v)) which specifies s^(v),
the payment by agent i to finance project v. The set of feasible financing
schemes is given by
t-T , i-IC t-T ,
S(v) - {s(v) : I a I s (v) 2 1 <*
t-1 i-1 t-1
The central authority will choose a feasible project/financing scheme
pair so as to maximize social welfare. That is, it will solve
max b. Y*1, (v),
veA
where
Y*^(v) » Y^"(v,s*i(v)) ¦ Ei(pT(0),qT(0),wi,a> Vi(pT(v),wi-s*i(v),qT(v), a))
for
s*(v) e argmax b.Yi(v,si(v)).
s(v)eS(v)
It is interesting to point out that the following theorem governs a relationship
between choices of v and choices of lifetime indirect utility vectors.
Theorem 3.2: v P* v' if and only if
b± [evi(v) - evi(v')] > 0.
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IX
Proof: By theorem 3.1, VP V' iff W(¥)>W(V*), where v-(v ,
+ ¦¥
whence by A3.4, V P V' iff
l± b± [ViCv) - Vi(0) - (V^V) - Vi(0))] > 0.
Since Y*" is a utility indicator and Y^(0) = w*",
V P V' iff I ± bi[Yi(v) - wi - (Yi(v* ) - wi) ] > 0,
By definition of P* and by (2), the result follows.
The magnitude of ev^(v) will depend on the financing scheme used. It is
not possible to separate these decisions. McKenzie (1983, chapter 8) shows how
the ordinal properties of W can be used to determine losses due to use of non-
optimal financing schemes.
In this section, we have shown how to elicitation of equivalent variations
for lifetime utility can be used to make social choices among prjects. In
particular, for a planner with "welfare weights" given by a linear social
welfare function, a project will be selected based on the maximization of
the weighted sum of the equivalent variations for that project, given the
use of an optimal financing scheme.
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Uncertaintv
We now turn to possibilities for generalizing the framework developed in
the previous section to the case of uncertainty. As discussed in the introduc-
tion, it is critical that when uncertainty is addressed, that it is clear what
it is that uncertainty surrounds, who faces the uncertainty, and what that agent
can do about it. In this section we investigate individual uncertainty. In the
ne::t section we will discuss uncertainty on the part of the planner.
There are several ways that uncertainty can enter the model developed in
Section II of the paper. We identify here several that seem relevant in the
option value literature:
(i) Ecological uncertainty. Given a V e A it is not known what level of
environmental quality will obtain. This may be represented by making (1) a
random function. There are two ways to capture this, each representing a dif-
ferent source of uncertainty.
First, we could think of the function f itself as being unknown. That is,
we may not know how ecosystem function maps projects into environmental quality.
Second, even if the true f is known, the sequence of quality outcomes might be
stochastic. In fact, both of these are operating to make uncertainty relevant.
If the former operated without the latter, a simple experiment at date zero
would resolve all of this type of uncertainty. If the latter operated without
the former, then learning about ecosystem function would not be possible unless
it is interpreted as trying to discover the probability law driving the
stochastic process; clearly biological investigation seeks more than this.
(ii) Economic uncertainty. It seems plausible to assume that future prices
and incomes are risky.
(iii) Preference uncertainty. The majority of the literature, on option
value has investigated the implications of state-dependent preferences (demand
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uncertainty) where individual preference orderings are uncertain.
(iv) Political/Regulatory uncertainty. The project itself may be risky.
The project may entail some enforcement which may be applied at various levels
in the future or may no yield compliance.
(v) Social uncertainty. When confronted with a project which can be imple-
mented at alternative levels and where aggregate willingness to contribute to
funding the project is involved, individuals may hold uncertainty about the
contributions of other agents. This often is discussed in terms of strategic
bias in contingent valuation assessments of willingness-to-pay where the pre-
sumption is free-riding behavior, but this is a special case of more general
problems of social interdependence in provision of public goods.
(vi) Planning uncertainty. Even if agents know their own preferences, the
planning authority may not know them. Thus, the planning authority may have
uncertainty about preferences even if individuals do not.
The theoretical option value literature has focused on uncertainty of types
(1), (11), and (iii) above, though one analysis of time-sequenced option value
has examined uncertainty of type (iv) (Graham-Tomasi, 1983) . The ecological
uncertainty has taken a particular form in the literature on supply-side option
value (Bishop, Freeman, 1985), in which quality either is good enough to allow a
particular recreational activity or quality deteriorates to the point where the
activity no longer is available. Thus, just two states are possible. It is
common in this literature to see this uncertainty represented as price uncer-
tainty, with the entry fee for activity at the rate equal to some finite price
of the activity is available and an infinite price if it is not. we present a
generalization of this approach below. Usually, though not always (Hartman and
Plummer, Freeman, 1984) it is assumed that prices of other goods and income are
non-stochastic.
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5. Individual Uncertainty with an Expected Utility Representation
The majority of analyses of option value employ a static model and use an
expected utility representation of individual preferences. In this section we
take a similar approach to modelling preferences and investigate extensions of
the material developed above to the case here. We focus on ecological
uncertainty; that is, we focus on supply-side uncertainty. Given a project,
there is a probability structure on environmental quality induced by the proba-
bility structure on ecosystem functioning. To gain an expected utility repre-
sentation, we restrict ourselves to analysis of a static problem. In section
VII we consider a two-period problem.
Let ) be a probability space, We turn the function f defined in
(1) into a random function representing the two sources of ecological uncer-
tainty in the following fashion. Let
~ - { f; Em x E x SI * Em: f
is Borel measurable relative to^^for all fixed
(g,v) e Em x E and - integrable}.
We assume
A5.1: f e (f1, fF) f1 e i for all i,.
with iri • Prob [f ¦ f*l.
Then, the induced probability measure on environmental quality, conditional on
the project V and initial (non-random) enviornmental qualtiy qQ is
VV(Q,) - I u{w £ fl: f4(q , V, to) e Q,} ir1
i
for the Borel set of Em.
In this section we suppose that the individual has preferences on the space
of probability measures on CQX) which satisfy the non-Newmann and Morganstern
axioms. Formally, let L be the space of lotteries on environmental qualtiy,
i.e.,
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L - {yV(Q1): v e A}.
A::iom 5.1: The individual's choices from L are representable
by a binary relation R which satisfies
(j_) is a weak order
(11) (y1 R y2) -> ay1 + (1- a)y3 R ay2 + (1 -a)y3
too
for y , y , y e L and ae(0,l)
(iii) (y* R y2) and (y2 R y3) "> ay* + (1 - a)y3 R y2
2 1 3
and y R By + (1 - B)y for some a, B £ (0,1)
12 3
and y , y , y e L.
Then we can show
Theorem 5.1: For all yV, V £ A, let the sets {y R y°} and
{y £ L: y R y}open in the weak topology and let
the preference represented by y of the previous section
be strictly conve::. Then there e::ists a continuous
function V: E3n 2nrH + g such that
y R y° <-> IaV(* )dy > JnV(»)dy0»
where
sup
V(p0, Px, a w, Cq, q0, qx) - ^ e B(pQ, px> w, cQ)
U(cQ, q0, cx, qx, for B(-) - {cji aP^ <. Wj + a w2}.
Moreover, this supremum is attained, and
C, £ arg max U(*) is continuous.
Cl £ B(*)
Proof: The existence of the function V follows from Axiom 5.1 and
Fishburn (1970), Theorem 8.4. Continuity of V follows from
openness of the upper and lower contour sets (Varian, 1978).
That the supremum is attained derives from the Weierstrauss
Theorem, the continuity ofu and the compactness of B(#)«
*
Upper semi-continuity of C, follows from the ma::imum principle
* 1
of Berge (1963); but c, is unique due to the strict convexity
1 *
of the upper contour sets of y,and therefore is continuous.
We now are in a position to define welfare measures for changes in the
v o
measure y due to choices of V £ A. Let y be the measure induced by project
0 £ A. Similary, let F°(q1) and F be the probability distribution func-
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o v
tions for U and U • There is a one-to-one correspondence between U and F (Ash,
1970) . We define the compensating option price (COP) and equivalent price (EOP)
implicitly by
V(P> <1* o, w - COP(v))duV » /jj V(p, q, o, w)du°.
Jfl v(p» <1» °» w)duV - V(p, q, o, w + EOP(v))du.
These, of course, are natural analogs of the cv and ev measures of welfare
change defined in Section II. In most of the option value literature, the COP
measure is called the option price (e.g. Smith, 1983; Freeman, 1985). As
discussed in the introduction, considerable attention has focused in this
literature on the relationship between COP and the expected value of consumer
surplus. The motivation for this concern is two-fold. First, in the absence of
contingent claims markets, or the ability to extract e::-post compensation from
agents, it is though that COP is the proper measure of e::-ante WTP for the pro=
ject. Second, since consumer surplus measures are used to determine project
choice (as in Section III of this paper), investigators are interested in
whether use of consumer surplus over or under estimates true e::-ante WTP.
One difficulty with this discussion is that the COP measure only is an
appropriate inde:-: of welfare when binary choices among projects are being made.
This is for the same reason that the cv measure is inappropriate. Formally, we
have the following theorem.
Theorem 5.2: The COP(v) measure is not a valid measure of welfare
change.
Proof: Define certainty equivalent environmental quality levels
CEQ(p, w, a, cQ, y) by
/ v(p, w, a, cQ)dp - V(p, w, a, co> CEQ(»)).
Then by definition,
V(p, w - COP(v), a, cq, CEQ(p, w, a, cQ, yV)) ¦
V(p, w, a, Cq, CEQ(p, w, a, CQ, y°)).
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But, by arguments in Chipman and Moore (1980), COP(v) only
is a valid index for binary choices. If there is more than
one V e A other than V = 0, COP may not rank these correctly.
Thus, we suggest that attention be focused on the equivalent option price,
since, by a similar argument, EOF is a valid measure of welfare change. In
their analyses of option value, Schmalensee (1972) and Bishop (1982) uses the
EOF. Of course, whether EOF or COP is used will not matter if there are only
two possible projects.
As discussed above, much of the option value literature is concerned with
the relationship between an ex-ante measure such as COP or EOP and the expected
value of ex-post measures. Freeman (1985) has pointed out that the supply-side
of many of these analyses is a special case of the more general case of a change
in distribution that he (and we) consider. In particular, these analyses
presume that only type (iii) uncertainty, demand uncertainty exists, substitute
o v
two degenerate measures U and U on the supply side, and let m = 1.
Briefly, the formulation is as follows. Let V be the individual's indirect
utility function, a Borel measurable function of w e ft, and let be a probabi-
lity measure on the c-algebra on ft. On the supply side, assume that yV and
O V
U both are degenerate, assigning probability one to outcomes q and
q° respectively. Then, in state 3, the equivalent variation ev(fj) is
V0 (p» qV» a> V) " V0(p, q°, a, w + ev(0)),
and the expected equivalent variation is
Jev(p)dFD(0).
We have the following much-discussed result.
Theorem 5.3: With y° and yV degenerate and y^ non-degenerate, EOP
can be greater or less than expected equivalent
variation.
Proof: The proof follows that of Bishop (1982), where our definition
of ev is substituted for his.
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Note that in the formulation in Bishop and elsewhere (e.g. Andersen, 1981)
A O
it is assumed that under 0 £ A, q^ < q1nrtn» where q^n is the minimum quality
o
such that the site is not available. This is formalized as q^ => = 0 where
Cjj is visits to the site and is accomplished by a pricing function p(v) with
Plj(O) ¦ 00; Pjj(v) = Pjj < "• This formulation is not strictly necessary.
The literature which addresses ecological uncertainty in the absence of
preference uncertainty is somewhat confusing regarding definitions of equivalent
and compensating option price. In the definitions above, equivalent option
price (EOP) uses the situation without the project as a base adn asks how much
money must be given to the individual to forego the benefits induced by the pro-
ject. The compensating option price (COP) uses the situation with the project
as a base and asks how much can be taken away from the individual to return
him or her to the pre-project level of utility.
In the analyses by Bishop (1982) and Freeman (1985) of ecological uncer-
tainty, only two situations are compared; thus, the difficulty of ranking pro-
jects by the COP measure may not arise. However, it is important to note that
the proof of Theorem 5.2 used a certainty equivalent approach, when one defines
a welfare change measure for each state, then which measure is appropriate may
depend on whether the before-project or after-project probability is degenerate.
Both Bishop and Freeman study a model with only two possible outcomes, one
of which corresponds to a level of quality such that use of the site is zero.
They then define the e::-post compensation measure in the state in which the
resource is available by income change that equates indirect utility with and
without the resource. This is the natural approach. Here, we consider a model
with many possible states. Thus, our e::-post measure for each state is defined
relative to with and without project realizations of quality. That is, if
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q° e Q° is the realization without the project and qV £ QV is the realization
with project v£ A , then ev(q°, qV) and cv(qV, q°) are defined implicitly by
V(w - ev(q°,qV), q°) " V(w, qV)
V(w,q°) ¦ V(w - ev(qV, q°), qV)
In the most general situation in which there is risk about environmental
quality both with and without the project. Then expected values of ex-post
welfare measures are given by
/ J ev(q°,qV)dFV(qV)dF°(q°) « / J cv(qV,q°)dF°(q°)dFv(qV)
Q° Q Q Q
Having chosen a base outcome given by the first argument of the ev(.,.) and
cv(.,.) function (e.g., ev (q°, qV ) gives the ev of a move from outcome q°
V
without the project to outcome q with the project), both of these will correctly
compute the welfare change in each state. That is, conditional on outcome q°,
the L.H.S. measure will assign the same welfare measure to two indifferent with-
v
project outcomes q • The same is true for the R.H.S. where the conditioning
V
base event is the with-project event q •
Returning to the analyses of Bishop (1982) and Freeman (1985), we consider
two special cases. In the first, the situation without the project is risky,
while the project provides a desirable sure outcome, and in the second, environ-
mental quality without the project is given by a sure undesirable outcome, while
the project provides a risky quality. These correspond to Case B and Case C in
Freeman (1985), respectively; he notes that Bishop studies Case B.
Consider first Case B. Here, since the situation with the project is
fixed, it makes some sense to use the cv measure in each state. Then, a fixed
base is used for comparison to each of the risky outcomes without the project.
Then, it is easy to show that the COP is greater than the expected value of the
ex-post cv measures, at least for a finite number of states.
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Theorem 5.4: (Bishop, 1982) Let F° (q) be non-degenerate with
probability mass n°- (n°, ..., n°) and let FV(q)
V
be degenerate, with Prob [q = q ] = 1. Then, if V(«)
is strictly concave and increasing in income, the
COP is greater than the expectation of cv.
Proof: The cv measure in state i is defined implicitly by
V (w - cv1", qn) = V (w, q1).
Compensating option value is defined by
I± 1° V
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Theorem 5.5: Let F(q) be non-degenerate with probability mass
nv = (n^, . . . , n^), and let F°(q) be degenerate
with Prop [q=q°] = 1. Then, with V increasing
and strictly concave in income, the relationship
between COP and expected cv is not determinate.
A sufficient condition for COP - E(ev) to be
positive is that the marginal utility income is
the same for each state.
Proof: The cv in each state is defined by
VCw-cv1", q*) = V (w, q)
and COP is defined by
Iini V(w-COP,q1) = V(w,q°) .
By strict concavity of V in w,
V(w-cvi,qi) < V(w-COP,q1) + tCOP-cvi]V (w-COP.1*).
w
< = > V(w,q°) < V(w-COP,q1) + [COP-cvi]Vw (w-COP,q1)
<=> v(w,q°) < v(w-cop»qi)-^itcop-cvi]vw(w_cop^i)>
This holds for each i, whence by definition of COP,
0 < L E^[COP-cvi]V (w-COP, q1).
1 l w
The difficulty in establishing a sign for option value
is presented by the marginal utility of income. If
this Is the same at (w-COP) for each q1, then this
term can be factored out to yield
o < cop - cv1.
The value of an equivalent option price approach is that the marginal utility of
income term appears only with a fixed state. Thus, option value is positive.
Theorem 5.6: Assume the conditions of Theorem 5.5. Then EOP is
greater than E(ev).
Proof: The proof is exactly the same as for the proof of
Theorem 5.4 using EOP and ev1 defined by
VCw-ev^q0) = V (w, q^)
IjVCw.q^) = V(w-EOP, q°) .
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The discussion of the relationship between the ex-ante measures of COP and
EOP and the expected value of ex-post measure cv and ev is due to a desire to
determine if use of cv and ev in project evaluation systematically over or under
estimates true ex-ante WTP. We offer two observations on this. First and most
obviously, knowing that expected ev underestimates EOP is not particularly use-
ful if you don't know by how much. Thus, Smith (1984) tries to find a bound for
the size of the discrepancy. Unfortunately, Smith's approach requires a fairly
strong restriction on preferences and only works for two possible states.
Second, most analyses of projects do not use the expected ev or cv measure.
Rather, they ignore uncertainty altogether and presume that the expected outcome
is the true outcome. Thus, they calculate the Hicksian welfare measure at the
expected value. Formally, let
ev(q*) ¦ ev(/qdFV(g))
ev(q°) » ev(/qdF°(q)).
If ev(^) > evTq°), then the project is said to make the individual better off
and the analysis proceeds as in Section III. It may be possible to derive an
approximation to EOP based on readily observable variables and the deterministic
ev using expected values. The author will present such an approximation in a
future paper. The approach seems quite promising.
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c. Individual Uncertainty: Generalized Expected Utility
The model of the previous section, which predominates the option value
literature, is static. We captured the static nature of this in terms of our
model by assuming that Cq is fixed and concentrating on the relationship
between and As well, we assumed that could be chosen after observ-
ing Qj* When this assumption is dropped and the model becomes dynamic, there
are two difficulties that arise.
First, atemporal von Neumann-Morganstem (vN-M) utility theory applied
in a dynamic setting requires that preferences on income (or here, environ-
mental quality) be defined solely on income vectors. In the language of
dynamic programming, a plan for choosing actions given states induces a
probability distribution on the vector of payoffs. As optimal plan (if one
exists) is one that maximizes the expectation of vN-M utility function on
such vectors. As pointed out by Kreps and Porteus (1978), this rules out
the possibility that an individual may prefer earlier to later resolution
of uncertainty. They illustrate this by the following example. Suppose
the payoff vector is (5,10) with probability 1/2 and (5,0) with probability
1/2. Then under the vN-M axioms, since 5 is the first-period payoff for
sure, the individual should be indifferent between a flip of a fair coin
at t = 0 and a flip of the coin at t = 1 to determine which vector obtains.
In fact, individuals may prefer earlier resolution of uncertainty.
Kreps and Porteus (1978, 1979) derived a generalization of atemporal
vN-M theory, which they called temporal von Neumann-Morganstern utility
theory. In their theory, uncertainty is dated by the time of its resolution.
These entities are called temporal lotteries. They present axioms for prefer-
ences defined as these temporal lotteries which allow a temporal vN-M
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representation. Below, we will apply their framework to our problem
concerning environmental quality.
The second problem that arises concerns induced preferences when a
choice must be made before uncertainty resolves. Even if all uncertainty
resolves at a single date and the underlying preferences on consumption
have an expected utility representation, induced preferences will, in general,
not satisfy the independence axiom and will be "non-linear in the probabil-
ities." This has been observed by Markowitz (1959), Mossin (1969), Spence
and Zeckhauser (1972), and Dreze and Modigliani (1972). Kreps and Porteus
(1979) derive necessary and sufficient conditions for induced preferences
in the temporal case to take the temporal vN-M form. These are quite strong.
Machina (1982, 1984) has proposed an approximation approach called generalized
expected utility theory, which copes with this difficulty without sacrificing
the basic foundation of expected utility theory.
In this section, we develop these results in terms of our model of
ecological uncertainty.
Uncertainty is represented in same way as in the previous section. We
assume that the space of possible realizations of the "experiment" giving
rise to environmental uncertainty is compact. Let be the space of Borel
probability measures on We then have the following result:
Lemma 6.1: is a compact metric space.
Proof: By assumption, f is continuous function onto
for fixed By Theorem 3.5 in Kolmogorov and
Fomin (1970), is compact: e Em so it is a
metric space. The result follows from Parthasarathy
(1967), Theorem 6.4.
We endow with the weak topology. If g(q) is continuous, then the weak
topology is the weakest topology for which the functiona 1 / gCx)du(x) is
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continuous for U £ D. Alternatively, we could give D^ the Prohorov metric,
since convergence in the Prohorov distance of a sequence of measures on a
Polish space is equivalent to weak convergence of this sequence (Lukacs, 1975,
p. 74) .
Clearly, the probability measure on is conditioned on the realization
of
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Theorem 6.1: Axioms 6.1 to 6.4 are necessary and
sufficient for these to exist continuous
functions : Qq x Q| E and Uq : Qq E -~ E
with Uq increasing in its second argument
such that if Vq : Qq E is given by
V0^q0,wP " U0^q0' ^Vl^q0'ql^ ^1^*
then Uq R Uq if and only if
/ Vqo'Ml)dM0 > / V0(q0,yi) du£.
Proof: Kreps and Porteus, 1978, Theorem 2.
The relationship between temporal vN-M theory as given by Theorem 6.1 and
the atemporal theory studied the previous section is given by the following
result.
Theorem 6.2: If UQ(qQ,r) is affine in r, then the
temporal respresentation collapses to
the atemporal vN-M utility. This is
the case if and only if, in addition to
Axioms 6.1 to 6.4,
(q0»<*U1 + (1 - o)up I o(qQ,u1) + (1 - a)(q0,Uj)t
where I is the equivalence derived from R in the usual way.
Proof: Kreps and Porteus, 1978, Theorem 3
and its corollary.
Thus, we see that the kinds of analyses usually undertaken in the
literature of option value, where atemporal vN-M utility is assumed, can
be extended without modification if preferences satisfy the substitution
axioms and are neutral to the resolution of uncertainty. However, it is
highly unlikely that individuals are neutral with respect to the resolution
of uncertainty.
We now turn to the induced preference problem and the relationship
between the timing of choices of Cq and the timing of the resolution of
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uncertainty. As mentioned above, induced preference generally will not
have an expected utility representation. In fact, it generally will not
have a temporal vN-M represenation. Kreps and Porteus (1979) derive necess-
ary and sufficient conditions for the former to take on the latter form.
Note that in the above formulation, the first-period consumption
decision was not explicitly introduced. At date zero, after observing the
outcome of the temporal lottery Pq, the agent chooses Cq from B(*)» the
budget set. We note that it is possible to have uncertainty enter the
budget set (via income or price uncertainty), so that the constraint set
for time zero decisions depends on the realization of the date zero lottery,
as long as it does so continuously.
In the previous section, the conditions of Theorem 5.1 were stated
assuming xed. Alternatively, we could have assumed that the individual
chose after observing the outcome of We now uncouple
these. We continue to assume preferences representable by the expectation
of the continuous vN-M function V: Qq x Q^ x B + E, just as in Section V.
Here, however, after observing qQ, the agent chooses Cq maximize.
Q1(«) V(
-------
-35-
Induced preference can now be edfined on D0 by
"o *0 "i 1£ ^<8) v* duo > /qjW) > v* c<*o»wi> d uo-
Lemma 6.3: Rq is asymmetric, negatively transitive,
continuous, and satisfies the substitution
axiom for t = 0.
Proof: Kreps and Porteus (1979) Proposition 2.
Thus, induced preference satisfies axioms 6.1 to 6.3, and by Theorem 6.1,
induced preference is temporal vN-M if axiom 6.4 holds, i.e., if the
substitution axiom holds for t = 1. We have the following results from
Kreps and Porteus (1979).
Theorem 6.3:
Proof:
Theorem 6.4:
Induced preference is atemporal vN-
if and only if, for all
* *
and pj, CqCUj) » Cj^Cu,).
By Kreps and Porteus (1979) Lemma 1,
the C* : Qn x D, + B given by
*
C*(q0,Ui) - arg max V(q0,q1,W0,W1,C0,C1)dp1,
CQ e B(* )
is an upper-semicontinuous correspondence.
By Proposition 2 and Corollary 1, induced
preference is atemporal vN-M if and only if
= 0. Theorem 6.3
follows from this result and the fact that
C*(q0, UL) is si ngleton-valued under the
assumption of that upper and lower contour
sets on Dq under R are strictly convex sets.
Induced preference is temporal vN-M if and
only if
(i) (qO.Uj^) I (
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-36-
Proof: Kreps and Porteus (1979), Proposition 4.
Provide a statement for non-singleton C*.
The result is immediate.
These results are quite strong and not easily checked. Sufficient con-
ditions take the form of a restriction on the form of the utility function.
The following result generalizes one in Kreps and Porteus (1979).
Theorem 6.5: Suppose that
A
V(qQ, q1§ wQ, w, cQ, - *iCqQ, cQ) +
*2Cqo» co)A*3Cqo» ql» Cl)f let
Ul(qo' ql* co* H *3 aQd let uo(qo'
= max ^ for 6 e T^0^» where
c eB
o
T(qo) - {e e E: 8 - Jq (q) )du1 for ^ e Dx}.
Then if U is strictly increasing in 8,
o
induced preference Is temporal vN-M with
and representing induced preference.
Proof: It suffices to verify the substitution
axiom for t =1; the result then follows
from Theorem 6.1. This is obvious from
the fact that V is linear and increasing
in 8 and 8 is linear In By hypothesis,
maxOj^ + 2 BCVj)) - max + 28Cp)>0« But,
max I1+28Cotu1+Cl-o)yp)]-Iniax((j)1+(j)28Cy[+Cl-a)up]
¦ maxC^ + 2 a8(V]_) + ~ <*)8(v'P
- maxC^ + 2 o8(uJ) - "j>2^1 ~
« maxC^ + 2 oSCu^)) - maxC^ + 2 a8(u{) > 0.
While this condition is straightforward, it is restrictive. Kreps
and Porteus (1979) develop an approximation to induced preference which is
temporal VN-M, but do not claim that theirs is a "best" approximation in any
sense. Machina (1982, 1984) makes use of "generalized expected utility
theory," which does make use of a best approximation under the assumption
that induced preferences are Frechet differential.
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-37-
Before embarking on this approximation procedure, let us summarize
what the issues are. The agent is assumed to have a vN-M utility function
defined on (<1q» Cq, , C^)» When is chosen, everything else is known.
Maximizing out provides the function V(qQ, , Cq). Given some qQ» the
distribution on q^ is known, based on the function f. First period consump-
tion Cq is chosen after qQ is observed, but before q^ is. Thus, we can use
C*(q0, V*1 | V) as this optimal choice and define
V(q0) -/v(q0, qx, C*(q0, FJ.(q1 | q0)))dFl^l I <*()).
A
Overall rankings of temporal lotteries Fq on Qq are made on the basis
of J(Fq) = / V(q0) dF°(q0).
Now, it is clear that preferences on temporal lotteries are linear in
the probabilities given by Fq, However, the induced preferences on F^ are
not linear in the probabilities; Kreps and Porteus show that they are convex.
Machina's (1982, 1984) insight uses intuition from ordinary calculus: a
differential of a non-linear function is the best linear approximation to
that function at that point. Thus, the best linear approximation to the
non-linear preference functional is provided by differentiation provided it
is smooth. The appropriate concept of differentiation here is Frechet differ-
entiation .
We begin our application of Machina's analysis to the option value problem
by converting the above analysis to the use of distribution functions. For
i i *
each y. e 1). there is a unique distribution function F. in the space D. of
j J J J
A
distribution function on We endow the space with the weak topology,
as with the space Machina uses the notion of the Frechet derivative of
the value functional. This requires that we define a norm on the space
AD. - {X(F* - F) | F, F* e D. , X e E} .
J J
Then we have the following result.
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-39-
concave, then overall choices will exhibit risk aversion. Thus, we would expect
results that rely solely on risk aversion to carry over to the generalized case.
Unfortunately, this is not so for Bishop's proof of the non-negativity of
supply-side option value. The reason is familiar: Establishing the sign of
option value for supply-side uncertainty requires a singly utility function.
Here, the utility function corresponding to F° is different than the utility
• v v
function corresponding to F if F° and F are sufficiently different. Thus, for
projects which significantly will affect environmental quality, the assumption
Of one utility function cannot be used when there is temporal risk. Formally,
we state
Theorem 6.6: Under temporal ecological risk, the sign of supply-
side option value is indeterminate, if F° and FV
differ "significantly."
The main result of this section, Theorem 6.6, is a negative one. The sign
of supply-side option value is indeterminate when risk is temporal under con-
ditions that allow its determination when risk is timeless. However, Machina
(1984) derives a numberof useful results concerning monotonicity and concavity
of the induced utility function V(qQ,q^ C*(*)) and distribution that are ordered
by stochastic dominance differ by increases in risk. We will not repeat these
here; the results generally are not surprising given that most propositions in
the timeless setting relying on risk aversion carry over to the temporal setting
if all of the local utility functions exhibit risk aversion. While many of his
results could rule out from consideration certain projects in A, it is apparent
that a total ordering on A usually would not be forthcoming based on these
A
results. For example, if a project 0 induces a distribution which differs by a
o :
A
mean preserving increase in risk from the distribution induced by v, then V P* V
never would hold if individual utility functions are concave in q^» But cer-
tainly most projects of interest will give rise to changes in mean as well as
-------
-40-
increases or decreases in risk.
Of course, this does not mean that welfare evaluations cannot proceed
when individual's face temporal risk. As with the static option price, we know
what we wish to measure nad we have techniques available to us, contingent
valuation methods, to obtain it. The relevant measure is EOP defined by
J(F^(q), w) « J(F°(q), w-EOP(F^, F°, w)),
where J(F^, • ) is defined as above an alternative temporal lotteries, where
v
Fq is the temporal lottery induced by project v e A and 0 £ A is the "project"
which is defined by the status-quo. What we are unable to obtain in this frame-
work is teh sign of option value. This seems to be an elusive quest.
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-41-
Project Choice Under Uncertainty
As in the case of certainty, it is up to the central planner to select a
project from A, based on individual willingness-to-pay for them. Three issues
arise here. First, suppose that there is no planning uncertainty. That is, the
planner is able to obtain the EOP (F°, FV, w) resource for each individual and
for each v e A. The analysis proceeds exactly as in Section III; based on the
weights of the social welfare function, the planner selects v e A such that
the weighted EOP is maximal, after incorporating a feasible financing scheme for
the project.
The second question that arises concerns the possibility that the planner's
preferences or utilities can be formulated over projects such that the planner's
preferences satisfy the von Neumann-Morganstern axioms. Clearly this will only
be the case if individual utilities satisfy these axioms. Thus, in this section
we consider a static model. The answer to this question, based on Wilson's
(1968) analysis of the theory of syndicates, demonstrates the appeal of the
linear welfare function. This is undertaken below.
The third question concerns the assumption, maintained throughout the paper
so far, that uncertainty is exogenous. As Bishop (1982) points out, there is a
connection between supply-side option value. The literature on quasi-option
value (Arrow and Fisher, 1974), in which learning may take place.
Regarding the question of project selection, we now incorporate into the
risky choice problem the financing decision, and determine a relationship bet-
ween group and individual payoffs as functions of the project and outcomes of
the random event.
Suppressing dependence of a previous quality, if project V e A is imple-
mented and event U) e obtains, realized environment quality is f(v,U))«
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-42-
Individual i's assumed von Newmann-Morganstern utility function is
V^"(q, u) = Vi(f(v,0))w) and equivalent variation is defined by
Vi(f(0,u)wi - ev"*"(v ,u) ) - ,u),w).
As in Section III, under financing scheme s(v) e S(v), i pays s" L(v).
The payoff
to person i from implementationof project V is m*(v,u>) = ev^(v,u>) - s^(v)«
Since environmental quality is a public good, the group payoff from imple-
menting project v is
g(v,w) = - £ev^"(v ,u>) - k(v).
i i
To develop a tie to the linear welfare function of section III, we begin by sup-
posing that the planner seeks to implement a financing scheme that is Pareto
efficient.
We denote the expected utility of the ith agent under porject v by
F3-) = /oV^fCv.w), w - si(v))dFx(0)).
The standard proofs of the following lemmata are omitted.
Lemma 7.1: The set t(v) defined by t(v) = {J^(v : s^" e S(v)}
is convex.
Lemma 7.2: If s(v) is Pareto efficient then there Is a set of
weights {b^(v), i = 1, .... 1} with b^"(v) _>. 0 such
that s(v) solves
max. I b^v)
s(v )es(v) i
The following result is stated by Wilson (1968).
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-43-
Theorem 7.1: s(v) is Pareto efficient if and only if there exist
non-negative weights {biCv)} and a function X(v,w)
such that
(i) s(v) e S9v)
(i i ) (• ) t^Cw) = X (v ,w) X = i,
for almost all w E ft for which bi(v)hi(d)> > 0, where
h* = F^(* ), i.e., h^" is the density corresponding to
i's subject probability measure on u>.
"Proof": By Lemma 7.2 the planner wishes to solve a constrained
minimization problem, with weights defined by the
tangent hyperplane to x[v). This hyperplane exists by
Lemma 7.1. The function X(v,u>) can be thought of as
the Lagrange multiplier in the constrained maximization
problem, where the constraint is given by (i) . Thus,
s(v) and X(v ,(i)) can be found as by finding (pointwise)
a paddle-point of the Lagrangean, i.e., by solving
sup inf L(b^, h^",k)
s X
where
L(* ) = /{I bi(v)V(f(v,(D),w-si(v))hi((D) - si(v)X(v,d))}
i
This theorem concerns the choice of a Pareto efficient financing scheme.
The central question of this analysis concerns the overall problem faced by the
planner, which includes the choice of a feasible project. We wish to determine
if there exists some overall utility function such that, in choosing a Pareto
efficientproject, the planner will maximize the expectation of this function.
The answer to this question is stated in the next proposition.
Theorem 7.2: There exists a group utility function V°(q,w) such
that the choice of a Pareto efficient project involves
solving
max /V°(f (v ,u>),w)dw.
veA
if b*(v) are independent of v.
-------
-44-
Proof: Given Theorem 7.1, the overall problem is to solve
sup / inf {Xk + I sup [b1 V1 h1 - Xs1]} du>.
veA X i seS
Define the "rent" measure
4»i(di) = sup[Vi(q,x) - djx].
x
Then the above problem can be simplified to read
sup / inf {lib* h* ^ .)] ~ Xk}daj.
veA X i b h1
Define
V°(f(v ,o)),w,v) = inf {£ [bi(v)hi ~ Xk}.
X i bh1
Then the preferred project solves
sup / V°(f (v ,u)),w,v)da>.
veA
This V° will depend on v only through the transition
equation on environmental quality if the weights
bi(v) are independent of v.
The theory of syndicates, applied here to the analysis of provision of a
public good, concerns the relationship between individual preference represen-
tations and group preference representations. The key result is that if the
social welfare function is linear (as in Section 3), then there is a "utility
function" for the planner such that choice of efficient projects amounts to
maximization of the expected value of this function.
It is important to note that the only source of uncertainty in the model is
ecological uncertainty. There is no planning uncertainty (in the language of
Section 4) since the planner is assumed to know the individual vN-M utility
functions and the individual probability density functions. With planning
uncertainty, the planner does not know these individual preferences.
-------
-45-
The case of pure planning uncertainty raises a number of interesting
problems of analysis. The first concerns the form of the planner's objective
function. Anderson (1979) has proposed that planner's preferences in this
situation be assumed to take an expected utility form. This approach might be
considered to be controverial. Second, since uncertainty gives rise to possibi-
lities for learning, there is a possibility that the planner can devise a mecha-
nism to discover the true preferences of individuals. This issue is the topic
of the large literature on incentives. That is, can a principle (in this case
the planner) design an incentive scheme which induces an agent (individuals in
society who care about the project) to act in accord wtih the principle's goals
(reveal their preferences for a public good). The theory of incentives has been
reviewed recently by Laffont and Maskin (19820. They study particularly simple
forms of individual utility functions (quasi-linear) planner choice rules which
are similar to those posited here where the individual "weights" are the same
for all individuals. While it appears that the literature abounds with impossi-
bility theorems, these are often seeking incentive schemes with quite strong
properties. It would seem possible for the planner to learn something of indi-
vidual preferences which will be of use.
The third issue is that raised by the literature on quasi-option value.
Until now, all of hte timing of resolution of uncertainty relative to the timing
of choices in projects and consumption has been assumed exogenous. The QOV
literature seeks to deduce the effect of possibilities for learning on
willingness to undertake projects which are irreversible.
In terms of the current model, let A = Aq A^> where Afc = [0,1] . Suppose
that Int A^ = for t = 0,1, and that projects are irreversible in that
Vq = 1 => = 1, while = 0 is consistent with = 0 or = 1. The QOV
literature then compares two decision frameworks. In one framework it is
-------
-46-
assumed that no new information will become available. Thus, the planner
chooses immediately from A one of (0,0), (0,1) or (1,1). In the other decision
scheme a sequential decision is possible, i.e., conditional on vq, and the out-
come of an experiment y e Y that provides information, the planner chooses
* *
vx
-------
-47-
uncertainty for the case = [0,1] in which the concept of "quasi-option ta::"
(QOT) is presented. Although his model is very different than that considered
here and so the details of the analysis are not relevant, his QOT is an adjust-
ment to initial development benefits in the learning case that would lead to the
same level of initial development as in the non-sequential case. Moreover, QOT
is a potentially estimable number, given bythe expected present value of the
second period loss if an irreversible decision is implemented at the myopically
profitable level, where the loss is averaged over the possible states of nature
under which the decision-maker would reverse the decision if he/she could.
-------
-48-
:. Discussion
In this paper, we have attempted to explore the foundations of supply-side
option value and project appraisal under uncertainty. The key result is the
following: when temporal risk is present, the analysis of option prices and
option values significantly is complicated. Since almost all situations dis-
cussed in the option value literature involve temporal risk, the analyses of
this literature seriously are called into question. However, this is not
really a significant insight since most of the analyses of option value have
a negative result: option value is not determinate in sign. The key insight
for the analytical option value literature is the following: existing studies
in which positive results have been obtained, e.g., Bishop's (1982) result
on supply-side option value and our own Theorem 5.6 in the same area, do not
hold in an obvious way under temporal risk. As well, Freeman's (1984) and
Smith's (1984) bounds on option value would need to be reexamined under
temporal risk using an extension of Machina's (1984) generalized expected
utility analysis to the case of state dependent preferences. An alternative
is the use of the restriction of Kreps and Porteus (1979) to obtain temporal
von Neumann-Morgenstern utility representations. The use of atemporal vN-M
representations undoubtedly is too strong.
Another alternative to all of these machinations is to explicitly model
the intervening choices, as in Drege and Modigliani (1972) . This is the
approach taken in the QOV literature. While a complete analysis along these
lines is likely to result in too much detail so that analytical tractability
is lost, for some decisions (or under separability assumptions) this may
prove useful.
Regarding empirical studies, it is clear that the use of contingent
valuation techniques to measure option price holds the key to correct
-------
-49-
project appraisal under uncertainty. It may turn out that empirical regular-
ities exist. My own feeling is that this will not be the case, and such an
approach is similar to the search for a single discount rate for use in the
analysis of public projects. It is likely that decisions will differ suffic-
iently that regularities will not exist.
Regarding the conduct of these empirical studies to determine option
prices, two important points emerge. When setting the context of the
questions in the survey, it is crucial that respondents understand the tem-
poral aspects of the choices being made. It is our feeling that inadequate
attention has been given to this issue in existing studies. Can individuals
change their minds? Will a reassessment be made as learning takes place?
Need payments be equal annual payments, or can WTP lump-sum payments be
allocated through time in any fashion?
A second point concerns the existence of local utility functions. The
utility functions depend on initial probabilities and on all probabilities
in a global analysis. This may prove to be important in the assessment
procedure, particularly regarding specification bias in regressions explaining
wi llingness-to-pay.
While the overall results of this paper seem quite negative, this is
not the actual intent of the analysis. Rather, it is to suggest that much
work remains to be done. But, this is not surprising given the difficulty
of analyses involving both time and risk.
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-50-
REFERENCES
Anderson, J. 1979. "On the Measurement of Welfare Cost Under Uncertainty,"
Southern Economic Journal, 45:1160-1171.
Arrow, K. and A. Fisher. 1974. "Environmental Preservation, Uncertainty,
and Irreversibility," Quarterly Journal of Economics. 88:312-319.
Ash, R. 1972. Real Analysis and Probability, New York: Academic Press.
Berge, C. 1983. Topological Spaces, Translated by E. Patterson,
Bishop, R. 1982. "Option Value: An Exposition and Extension,"
Land Economics. 58:1-15.
Blackorby, C., D. Donaldson and D. Moloney. 1984. "Consumer's Surplus
and Welfare Change in a Simple Dynamic Model," Review of Economic
Studies 51:171-176.
Bradford, D. and G. Hildebrandt. 1977. "Observable Preferences for
Public Goods," Journal of Public Economics 8:111-131.
Chipman, J. and J. Moore. 1980. "Compensating Variation, Consumer's
Surplus,- and Welfare Change," American Economic Review, 70:933-949.
Conrad, J. 1980. "Quasi-Option Value and the Expected Value of Informa-
tion, "Quarterly Journal of Economics, 94:813-820.
Dreze, J. and F. Modigliani. 1972. "Consumption Decisions Under Uncertainty,"
Journal of Economic Theory, 5:308-335.
Epstein, L. 1980. "Decision Making and the Temporal Resolution of
Uncertainty," International Economic Review, 21:269-283.
Ferejohn, J. and T. Page. 1978. "On the Foundations of Intertemporal
Choice," American Journal of Agricultural Economics, 60:269-275.
Fishburn, P. 1970. Utility Theory for Decision Making, New York: John
Wiley and Sons.
Freeman, A. M. 1984. "The Size and Sign of Option Value," Land
Economics 60:1-13.
. 1985. "Supply Uncertainty, Option Price, and Option
Value," Land Economics, forthcoming.
Graham, D. 1981. "Benefit-Cost Analysis Under Uncertainty," American
Economic Review, 71:715-725.
Graham-Tomasi, T. 1983. "Uncertainty, Information, and Irreversible
Investments." Draft manuscript, University of Minnesota.
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Hartman, R. and M. Plummer. "Option Value under Income and Price Uncertainty,
Unpublished manuscript, University of Washington.
Hause, J. 1975. "The Theory of Welfare Cost Measurement," Journal of
Political Economy, 83:1145-1182.
Henry, C. 1974. "Investment Decisions Under Uncertainty: The 'Irreversi-
bility Effect,'" American Economic Review, 66:675-681.
Katzner, D. 1970. Static Demand Theory, London: MacMillan and Sons.
Kolmogorov, A. and S. Fomin. 1970. Introductory Real Analysis, Translated
and edited by P.. Silverman, New York: Dover Publications.
Kreps, D. and E. Porteus. 1978. "Temporal Resolution of Uncertainty and
Dynamic Choice Theory," Econometrica, 46:185-200.
197 9. "Temporal vonNeumann-Morganstern and Induced
Preference," Journal of Economic Theory, 20:81-109.
1979a. "Dynamic Choice Theory and Dynamic Programming,"
Econometrica, 47:91-100.
Laffont, J. and E. Maskin. 1982. "The Theory of Incentives: An Overview."
In W. Hildebrand, ed., Advances in Economic Theory, Cambridge:
Cambridge University Press.
Lukacs, E. 1975. Stochastic Convergence, 2nd edition, New York: Academic
Press.
Machina, M. 1982. "Expected Utility Analysis without the Independence
Axiom," Econometrica, 50:277-323.
. 1984. "Temporal Risk and the Nature of Induced Preferences,"
Journal of Economic Theory, 33:199-231.
McKenzie, G. 1983. Measuring Economic Welfare: New Methods, New York:
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Markowitz, H. 1959. Porfolio Selection: Efficient Diversification of
Investments, New Haven: Yale University Press.
Mossin, J. 1969. "A Note on Uncertainty and Preferences in a Temporal
Context," American Economic Review, 59:172-174.
Parthasarathy, K. 1967. Probability Measures on Metric Spaces, New York:
Academic Press.
Schmalensee, R. 1972. "Option Demand and Consumer Surplus: Valuing
Price Changes under Uncertainty," American Economic Review,
62:813-824.
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APPENDIX
AGENDA
-------
AERE WORKSHOP ON RECREATION DEMAND MODELING
May 17-18, 1985
Hilton Harvest House, Boulder, Colorado
Sponsored By:
THE ASSOCIATION OF ENVIRONMENTAL AND RESOURCE ECONOMISTS
With The Support of The:
U.S. Environmental Protection Agency
-------
AGENDA
AERE WORKSHOP ON RECREATION DEMAND MODELING
May 17-18, 1985
Hilton Harvest House, Boulder, Colorado
Sponsored By:
THE ASSOCIATION OF ENVIRONMENTAL AND RESOURCE ECONOMISTS
With The Support Of The:
U.S. Environmental Protection Agency
FRIDAY, MAY 17, 1985
8:00-8:30 am SIGN-IN PERIOD AND DISTRIBUTION OF WORKSHOP PAPERS
8:30-8:45 am WELCOME AND INTRODUCTION. V. Kerry Smith, Vanderbilt
University and AERE President
8:45-12:00 am SESSION I. THE TREATMENT OF SITE ATTRIBUTES IN THE MODELING
OF RECREATIONAL BEHAVIOR
V. Kerry Smith, Chairperson
8:45-9:45 am "The Logit Model and Exact Expected Consumer's Surplus Measures:
Valuing Marine Recreational Fishing"
Edward R. Morey, the University of Colorado and Robert D. Rowe,
Energy and Resource Consultants, Inc.
9:45-10:00 am Break
10:00-11:00 am "The Varying Parameter Model: In Perspective"
William H. Desvousges, Research Triangle Institute
11:00-12:00 am "Valuing Quality Changes In Recreation Resources"
Elizabeth A. Wilman, The University of Calgary
12:15-1:30 pm LUNCH Patio Grounds or Century Room depending upon weather.
LUNCH TICKET REQUIRED.
1:40-5:00 pm SESSION II. MODELING RECREATIONAL DEMAND IN A REGIONAL SYSTEM
OF SITES
Edward R. Morey, Chairperson
1:40-2:40 pm "Modeling The Demand For Outdoor Recreation"
Robert Mendelsohn, Yale University
2:40-3:40 pm "A Model To Estimate the Economic Impacts On Recreational
Fishing In the Adirondack.s From Current Levels of Acidification"
Daniel M. Violette, Energy and Resource Consultants, Inc.
-------
AGENDA
Page 2
3:40-4:00 pm BREAK
4:00-5:00 pm "Modeling Recreational Demand in a Multiple Site Framework"
Nancy E. Bock.stael, The University of Maryland, W. Michael
Hanemann, The University of California at Berkeley, Catherine
L. Kling, The University of Maryland
5:15- pm No-Host Coctail Party. Century Room.
SATURDAY MAY 18, 1985
8:30-12:00 am SESSION III. The Definition and Estimation of Intrinsic
Values Associated with Recreation Resources
Robert D. Rowe, Chairperson
8:30-9:30 am "The Total Value of Wildlife Resources: Conceptual and
Empirical Issues" Kevin J. Boyle and Richard C. Bishop
The University of Wisconsin, Madison
9:30-9:45 am BREAK
9:45-10:45 am "Exploring Existence Value"
Bruce Madariaga and R.E. McConnell, The University of Maryland
10:45-11:45 am "A Time-Sequenced Approach to the Analysis of Option Value"
Theodore Graham-Tomasi, The University of Minnesota
11:45- am WORKSHOP WRAP-UP
V. Kerry Smith, Vanderbilt University
-------
APPENDIX B
LIST OF PARTICIPANTS
-------
PARTICIPANTS LIST
AERE WORKSHOP ON RECREATION DEMAND MODELING
May 17-18, 1985
Hilton Harvest House, Boulder, Colorado
Sponsored By:
THE ASSOCIATION OF ENVIRONMENTAL AND RESOURCE ECONOMISTS
With The Support Of The:
U.S. Environmental Protection Agency
Richard Aiken
Department of Agricultural and
Natural Resource Economics
Colorado State University
Fort Collins, CO 80523
Curt Anderson
Dept. of Economics
University of Minnesota-Duluth
Duluth, MN 55812
Glen Anderson
Dept. of Resource Economics
University of Rhode Island
Kingston, RH 02881
Ross Arnold
Rocky Mtn. Forest & Range Exp.
Station
3825 E. Mulberry, Rm 4252
Ft. Collins, CO 80524
Richard Bishop
Dept. of Economics
University of Wisconsin-Madison
Madison, WI 53706
Nancy E. Bockstael
Dept. of Agricultural & Resource
Economics
University of Maryland
College Park, MD 20742
Kevin Boyle
Taylor Hall, Rm 321
University of Wisconsin-Madison
Madison, WI 53706
Edward Bradley
Dept. of Agricultural Economics
University of Wyoming
Laramie, WY 82071
Thomas C. Brown
Rocky Mountain Forest & Range Exp.
Station
240 W. Prospect
Ft. Collins, CO 80524
Margriet F. Caswell
Environmental Studies
University of California
Santa Barbara, CA 93106
Peter Caulkins
U.S. EPA
Benefits Branch - PM 220
401 M Street, S.W.
Washington, DC 20460
Lauraine G. Chestnut
Energy and Resource Conslt., Inc.
207 Canyon Blvd., Suite 301A
Boulder, CO 80306
William Desvousges
Center of Economic Research
Research Triangle Institute
P.O. Box 1294
Research Triangle Park, NC 27709
Dennis M. Donnelly
USDA Forest Service
Rocky Mtn. Forest & Range Exp.
Station
240 W. Prospect
Ft. Collins, CO 86525
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Ronald A. Dutton
Hammer, Siler, George Associates
1638 Pennsylvania
Denver, CO 80203
Steven Edwards
Marine Policy Center
Woods Hole Oceanographic Inst.
Woods Hole, MA 02543
Scott Farrow
Dept. of Eng. & Public Policy
Carnegie-Mellon University
Pittsburgh, PA 15213
Carol Gilbert
General Motors Research
Societal Analysis Dept. (Dept. 12)
Warren, MI 48090
Ted Graham-Tomasi
Dept. of Agricultural & Applied
Economics
University of Minnesota
St. Paul, MN 55108
Rhonda Hageman
Dept. of Economics
San Diego State University
San Diego, CA 92182
Michael Hanemann
Dept. of Economics
University of California-Berkeley
Berkeley, CA 94720
John Hoehn
Dept. of Agricultural Economics
Michigan State University
East Lansing, MI 48824
John Hof
Rocky Mountain Station
USDA Forest Service
240 W. Prospect
Ft. Collins, CO 80523
Suzanne Holt
University of California-Santa Cruz
Crown College
Santa Cruz, CA 95046
Donn Johnson
Department of Agricultural and
Natural Resource Economics
Colorado State University
Fort Collins, CO 80523
James P.. Kahn
Dept. of Economics
SUNY - Binghamton
Binghamton, NY 13901
John E. Keith
Dept. of Economics, UMC 35
Utah State University
Logan, UT 84322
David A. King
School of Renewable Nat. Res.
University of Arizona
Tucson, AZ 85721
Catherine L. Kling
Dept. of Economics
University of Maryland
College Park, MD 20742
Vernon P.. Leeworthy
NOAA, Ocean Assessment Division
Strategic Assessment Branch
Rockwall Building, Rm 652
11400 Rockville Pike
Rockville, MD 20852
Jay E. Leitch
Dept. of Agricultural & Res. Econ.
North Dakota State University
Fargo, ND 58105
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John Loomis
Dept. of Economics
Colorado State University
Ft. Collins, CO 80523
Kenneth E. McConnell
Dept. of Agricultural & Res. Econ.
University of Maryland
College Park, MD 20742
John McKean
Department of Agricultural and
Natural Resource Economics
Colorado State University
Fort Collins, CO 80523
Bruce Maderiaga
Dept. of Agricultural & Res. Econ.
University of Maryland
College Park, MD 20742
Norman Meade
NOAA, Ocean Assessment Division
11400 Rockville Pike
Rockville, MD 20852
Robert Mendelsohn
School of Forest & Env. Studies
Yale University
205 Prospect Street
New Haven, CT 06511
Edward P.. Morey (Coordinator)
Dept. of Economics
University of Colorado
Boulder, CO 80309
Glenn E. Morris
Research Triangle Institute
P.O. Box 1294
Research Triangle Park, NC 27709
Wesley N. Musser
Dept. of Agricultural & Res.
Oregon State University
Corvallis, OR 97331-3601
Michael Naughton
Research Triangle Institute
P.O. Box 1294
Research Triangle Park, NC 27709
James J. Opaluch
Dept. of Resource Economics
University of Rhode Island
Kingston, RH 02881
George Parsons
U.S. EPA
Benefits Branch - PM 220
401 M Street, S.W.
Washington, DC 20460
George Peterson
USDA Forest Service
Rocky Mtn. Forest & Range Exp.
Station
240 W. Prospect
Ft. Collins, CO 80526
Raymond Prince
Dept. of Economics
James Madison University
Harrisburg, VA 22807
Raymond Raab
Dept. of Economics
University of Minnesota-Duluth
Duluth, MN 55812
Donald H. Rosenthal
U.S. Forest Service
240 W. Prospect
Ft. Collins, CO 80526
Larry Sanders
Department of Agricultural and
Natural Resource Economics
Colorado State University
Fort Collins, CO 80523
William Schulze
Dept. of Economics
University of Colorado
Boulder, CO 80309
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Robert D. Rowe (Coordinator)
Energy and Resource Conslt., Inc.
207 Canyon Blvd, Suite 301A
Boulder, CO 80302
W. Douglas Shaw
Dept. of Economics
University of Colorado
Campus Box 526
Boulder, CO 80309
Michael L. Smith
W.B. Lord & Associates, Inc.
1722 14th Street, Suite 250
Boulder, CO 80302
V. Kerry Smith (Coordinator)
Dept. of Economics
Vanderbilt University
Nashville, Tenn 37235
Cindy F. Sorg
Rocky Mtn. Forest & Range Exp.
Station
240 W. Prospect
Ft. Collins, CO 80523
David T. Taylor
University of Wyoming
Box 3354
University Station
Laramie, WY 82071
Daniel Violette
Energy and Resource Conslt., Inc.
207 Canyon Blvd., Suite 301A
Boulder, CO 80302
Richard G. Walsh
Dept. of Agricultural & Nat. Res.
Economics
Colorado State University
Ft. Collins, CO 80523
Thomas C. Wegge
Jones and Stokes Associates, Inc.
2321 P Street
Sacramento, CA 95816
Elizabeth A. Wilman
Dept. of Economics
The University of Calgary Calgary,
Alberta Canada T2N 1N4
Robert A. Young
Department of Agricultural and
Natural Resource Economics
Colorado State University
Fort Collins, CO 80523
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