United Slates Policy, Planning, EPA 230-05-90-078
Environmental Protection And Evaluation November 1989
Agency (PM-221)
Contingent Valuation Assessment
Of The Economic Damages
Of Pollution To Marine
Recreational Fishing
A
Printed on R*cycbdPmp*r
-------
EPA-230-05-90-078
Contingent Valuation Assessment of The Economic
Damages of Pollution to Marine Recreational Fishing
Submitted to:
Mary Jo Kealy
Office of Regulatory Management and Evaluation
U.S. Environmental Protection Agency
Washington, D.C. 20460
Submitted by:
Trudy A. Cameron
Department of Economics
University of California, Los Angeles
405 Hilgard Avenue
Los Angeles, Ca. 90024
November, 1989
The information in this document has been funded in part by the
United States Environmental Protection Agency under Cooperative
Agreement No. CR 814656020. It has been subject to the Agency's
peer and administrative review, and it has been approved for
publication as an EPA document. Mention of trade names or
commercial products does not constitute endorsement or
recommendation for use.
-------
CONTINGENT VALUATION ASSESSMENT OF THE ECONOMIC DAMAGES
OF POLLUTION TO MARINE RECREATIONAL FISHING
(EPA Cooperative Agreement # CR-814656-01-0)
Trudy Ann Cameron
Executive Summary
The research performed under this cooperative agreement is summarized in
the contents of four papers. These are described in the following sections.
1. "The Determinants of Value for a Marine Estuarine Sportfishery: The
Effects of ffater Quality In Texas Bays," (also Vorking Paper #523, Department
of Economics, University of California at Los Angeles).
This paper gives a detailed description of the data collected in the
socioeconomic portion of the Texas Parks and Wildlife Creel Survey of over
10,000 recreational anglers between May and November of 1987. It also
summarizes the auxiliary data sources used to augment these data, which
include gamefish abundance estimates we have calculated from the data
collected in the Texas Parks and Wildlife Resource Monitoring Program, water
quality data from the Texas Department of Water Resources, and five-digit zip
code sociodemographic averages from the 1980 Census.
The objective in this first paper is to formulate special statistical
models that produce estimates of each individual survey respondent's
willingness to pay for access to the recreational fishery in the eight major
bays along the Texas Gulf Coast. In this paper, no attempt is made to force
these models to conform with formal economic theories. Instead, minimally
sophisticated discrete choice econometric models are used in an attempt to
establish the apparent systematic relationships between willingness to pay and
whatever explanatory factors are available. These factors include:
characteristics of the individual, their current catch, location and time of
the interview, typical gamefish abundance, and coarse measures of several
dimensions of water quality by time and location collected both by survey
personnel and separately by the Department of Water Resources.
The econometric methods used in this analysis are specially designed to
accommodate the "limited dependent variable" nature of the data. The paper
describes the method by which maximum likelihood logit estimates can be
transformed to yield the implied parameters of an approximation to the demand
function for recreational fishing access. In particular, we are interested in
-------
price and income elasticities of demand. But we also focus in this study on
the extent to which water quality, geographical and seasonal dummy variables,
socioeconomic and other variables act as shifters of this demand function.
For this portion of the study, there are mixed findings concerning the
effects of water quality on the value of the recreational fishery. A wide
variety of meteorological data and data on water quality is available. In
most cases, however, it was necessary to aggregate these data up to the level
of each of the eight major bays and for each month of the sample period. For
example, we know about average temperature, dissolved oxygen, turbidity, etc.,
as well as nitrogen nitrate levels, phosphate levels, non-filterable residues,
oil and gas in bottom deposits, and a wide array of other qualities.
While several of our water quality variables appear to make
statistically significant contributions to explaining willingness to pay for
fishing access, many of them have counter-intuitive signs. It can be inferred
that water quality probably varies inversely with other unmeasured attributes
of anglers and the fishing resource that directly affect the value of the
fishery. For example, if there are fewer substitute recreational
opportunities in the Houston area, recreational fishing opportunities may be
valued very highly, but simultaneously, the water quality may be very low.
The reverse may be true in more remote areas of the coast. If we include
water quality, but omit alternative recreational opportunities (for lack of
data), then, it will appear that lower water quality implies higher social
values of the fishery. I suspect that something like this is precisely what
is happening.
This study represents an heroic effort to assemble the most appropriate
water quality data for the Texas Gulf Coast available from many different
sources. Countless hours went into matching and merging all of this
information with the survey responses. Unfortunately, it is an empirical
issue whether or not the anticipated relationships will show up in these data.
This paper concludes that it will be necessary to control for other important
determinants of value before the residual variation attributed to measured
water quality can be unambiguously identified. However, there is definite
evidence that respondents perceptions regarding environmental quality are more
immediate determinants of value than the actual measured quality of the water.
While water quality apparently cannot be considered in this much detail
with the current dataset, other coarser sociodemographic variables, such as
income, appear to have strong and intuitively plausible effects on values.
The apparent price elasticity of demand for fishing days (if a market existed)
appears to be roughly -2.2, meaning that if access cost anglers 1% more,
demand would decrease by 2.2%. The income elasticity appears to be just less
than unity, implying that recreational fishing opportunities are borderline
between being necessities and luxuries.
There are other implications of these models, also conditional on the
quality of the data. For example, geographical heterogeneity in the demand
for recreational fishing days does seem to exist. The water quality
variables, collectively, seem to explain quite a lot of this geographic
variation, even if multicollinearity among these variables limits our ability
to attribute value differences to specific individual dimensions of water
quality.
-------
The Vietnamese, as opposed to other cultural groups, seem to have
markedly different preferences for fishing than the population as a whole.
Money spent on associated market goods, once thought to be a reasonable proxy
for the non-market value of a fishery, is positively related to the value of a
fishing day (but typically completely unrelated to catch rates). Importantly,
many other explanatory variables make strong contributions to explaining the
annual value of fishing day access; reliance solely upon market expenditures
could severely misstate resource values.
The preliminary specifications explored in detail in this paper produced
results that were sufficiently provocative to warrant further analysis of
these data. It was decided that placing a little more structure on the model
might help. Hence the next paper.
2. "Combining Contingent Valuation and Travel Cost Data for the Valuation of
Non-market Goods," (a retitled major revision of Working Paper #503,
Department of Economics, University of California at Los Angeles).
This second paper takes advantage of the general sense of the data
derived from the extensive exploratory modeling described in the first paper.
It has been determined that there are several apparently robust systematic
relationships between willingness to pay for access to the fishery and other
measurable variables. Vith this established, one can be more confident that
it is worthwhile to undertake further modeling that is more solidly founded
upon neoclassical microeconomic principles.
I am very pleased with the quality of this paper. It develops a new
methodology, employing novel and very sophisticated econometric techniques
appropriate to the special features of the data. The analysis is particularly
careful and rigorous and many tangential issues are considered thoroughly.
The simplest model of consumers' utility maximization posits that
consumers have preferences defined over two types of commodities: the good in
question (sportfishing days) and a composite of all other goods and services.
More of both of these things makes them happier, but they are constrained by
their budgets. They must trade off other goods and services in order to
consume an additional fishing day, and vice versa. They allocate their
limited budgets between fishing days and other things so as to maximize their
level of happiness.
All models of this type are, of course, dramatic simplifications of the
real world, but they frequently provide very useful insights into the
essential features of consumer behavior. Individuals with different
sociodemographic characteristics, under different resource conditions, will
make different consumption decisions. This type of variation allows us to
calibrate a model which can then be used to simulate the likely responses of
particular types of individuals if their decision making environment changes.
While these models cannot be expected to do very well in predicting the actual
response of a specific individual to some change, they can perform fairly well
in the aggregate.
-------
Earlier research employing these "utility-theoretic" models for the
valuation of a non-market good such as sportfishing access occasionally used a
technique known as the travel cost method. If fishing days can be considered
as a single homogeneous good, information on the cost of a single trip and the
number of trips taken can be combined to yield a model of demand for fishing
days. This is the relationship between the implicit price of access and the
number of days demanded, with accommodation for whatever shift factors
(income, resource quality, etc.) can be quantified.
Other attempts to value recreational fishing days have relied upon
"contingent valuation" survey techniques, where survey participants are
queried about the decisions they think they would make if a hypothetical
market for fishing days existed (i.e. if they had to pay a per-day entrance
fee or purchase a season's pass to fish). The discrete choice form of
contingent valuation question was posed on the Texas Parks and Wildlife Creel
Survey. Respondents' answers about whether or not they would be willing to
pay an arbitrarily selected annual fee to continue fishing were analyzed in ad
hoc models in the first paper discussed above.
In the paper being described here, however, the mathematical form of the
discrete choice model is carefully selected to conform to an underlying family
of consumer preference functions with desirable properties from the point of
view of economic theory. By doing this, the calibrated models can ultimately
be solved to yield corresponding estimates of the formal welfare measures of
value, including equivalent variation and compensating variation.
The primary methodological innovation in this paper is to combine both
travel cost and discrete choice contingent valuation data in one comprehensive
model. Both methods of eliciting valuation information from survey
respondents should provide insights regarding the same preference structure.
We can combine the two different perspectives for a more thorough
characterization of consumer behavior.
In the basic model in this paper, all fishing days are treated as
homogeneous and consumer choices regarding fishing access depend only upon
their taste for fishing, their incomes, and the price of access to a fishing
day. When this model is explored thoroughly and shown to be relatively
successful, the assumption that all fishing days are identical is relaxed.
The illustrative generalization explored in this paper is to allow
preferences for fishing days (versus all other goods and services) to vary
systematically with the zip code proportion of people reporting Vietnamese
heritage on the 1980 Census. This is an imperfect measure of the respondent's
own sociodemographic category, but we anticipate at least some correlation.
The proxy turns out to be a significant shifter of preferences. The higher
the proportion Vietnamese, the less willing is a representative consumer to
trade off fishing days for other goods. Likewise, the greater will be their
demand for fishing days at any relative price and the greater would be the
cost to them of having to forgo some or all of their fishing access.
The paper provides detailed empirical estimates of the welfare values
associated with changes in fishing access. However, these dollar values are
conditional upon the extent to which the data we are using actually capture
the concepts prescribed by the microeconomic theory underlying the
-------
specification. The data are far from ideal. Consequently, it would not be
appropriate in this summary to uphold the dollar values as unambiguous. The
Texas data are by far the best I had encountered up until that time. But it
is crucial that this set of papers be regarded as demonstrations of the types
of analyses that can be conducted. If results as satisfying as these can be
achieved with mediocre ingredients, then subsequent surveys can be conceived
and implemented to take maximum advantage of the methodological framework.
These future studies will undoubtedly produce final empirical value estimates
which can more confidently be used as a basis for policy making.
With these qualifications, and others described carefully in the paper,
some of the welfare estimates can be mentioned. For example, according to the
basic model, if fishing days were curtailed by 10%, the average survey
respondent would lose an amount of satisfaction roughly equivalent to the loss
of $35 of income per year (although individual losses range from $19 to $52).
A 20% curtailment would match an income loss of $139, on average. Simulating
a complete loss of access is riskier and less realistic, but the model
suggests that the average respondent would be hurt by about $3400.
Generalizing the model to accommodate sociodemographic heterogeneity
(proportion Vietnamese in zip code) shows how the fitted preference function
is markedly different (for an otherwise typical respondent) when this
proportion ranges from 0 to 2%. Plots of the estimated "indifference curves"
and budget constraints make these differences particularly obvious.
The paper also breaks new ground by freeing up certain parameter
restrictions within the jointly estimated model so that the travel cost and
contingent valuation data are allowed to imply different preferences. A
scheme is also developed for allowing differential weightings in the pooling
of these data, according to the perceived relative reliability of these two
types of information.
3. "Using the Basic 'Auto-Validation' Model to Assess the Effect of
Environmental Quality on Texas Recreational Fishing Demand: Welfare
Estimates," (also Vorking Paper #522, Department of Economics, University of
California at Los Angeles)
The initial exploratory study described above (which employed all of the
available data and used ad hoc models) suggested that measured objective
dimensions of water quality did not always have clear cut and intuitively
plausible effects on willingness to pay for access to sportfishing
opportunities. An alternative possibility is that people's preferences for
sportfishing are affected by their perceptions of environmental quality, not
by what is actually out there. (What you don't know won't hurt you?) The
creel survey asked respondents' subjective opinions about whether they were
able to enjoy "unpolluted natural surroundings." Answers were recorded on a
scale of one to ten. In this supplemental paper, we allow preferences to take
on systematically different configurations depending upon these answers.
Various welfare implications can be derived from the fitted model, again
with the same caveats mentioned in the above two summaries. The amount of
income loss that would be equivalent to a 10% cutback in access to the fishery
is roughly $29 per year at the mean level of the subjective variable (8.07).
-------
If environmental quality is perceived to be a 10, the loss would be about $37
per year. In contrast, if the quality is only 6, the loss of access would be
only $23. For a complete loss of access, the decrease in value at the mean,
at 10 and at 6 would be about $2400, $3000, and $1900 respectively. (Note
that only a smaller subsample of the data could be used for these models,
since not all respondents were queried regarding environmental quality.)
Thus, we find that perceptions of environmental quality do affect
preferences for fishing days as opposed to all other goods and services, and
thus the value of access to the fishery will almost certainly be influenced by
perceptible variations in water quality. Furthermore, we can show that
respondents' answers to the "unpolluted natural surroundings" questions are
statistically related to several of the measured water quality attributes
examined in the first paper described above. However, it is clear that more
research will be necessary to establish how objective water and environmental
quality data can be translated into individual perceptions.
With infinite and free computing resources, it would be desirable to
allow preferences to differ systematically according to the levels of a whole
range of shift variables. At present, however, there was no budget for such
an elaborate model, so we were limited to exploring single shift variables
independently. (Each shift variable adds five new unknown model parameters to
be estimated.)
4. "The Effects of Variations In G&mefish Abundance on Texas Recreational
Fishing Demand: Welfare Estimates."
Keeping in mind the limitations on complexity, a second supplemental
paper was also developed. Whether or not the value of this recreational
fishery is dependent upon the abundance of gamefish is another question of
vital interest to policy makers. Ideally, one would measure all of the major
gamefish species (there are seven or eight, described in the first paper,
above). For this illustration, however, we opt to concentrate upon red drum.
As a measure of red drum abundance, we could have used each individual's
reported catch of red drum on the fishing trip when they were surveyed, but
this catch is dependent upon skill levels, which will be related to the
individual's resource value. This is undesirable. Consequently, we rely upon
data produced by the Parks and Wildlife Resource Monitoring program. We used
data from the thousands of official samples collected by this program and
aggregated up to average abundance measures by bay system and by month. These
data are only proxies for the actual local abundance of red drum experienced
by recreational anglers in each area and month, but they are completely
unrelated to angler skill. Thus we hope to avoid simultaneity bias in the
resulting estimates.
This model, augmented to control for red drum abundance, lets us explore
the likely changes in the social value of access to the fishery when the
abundance of red drum changes. Again subject to extensive caveats, we find
that the income loss that would be equivalent to a 10% reduction in fishing
access is roughly $35 at mean abundance of red drum. If abundance was higher
by 20%, the same reduction would hurt anglers by an average of $40. If
abundance was lower by 20%, the decrease in access would be equivalent to
-------
about a $32 decrease in income. A total loss of access would imply a loss of
about $2800 at mean abundance, a loss of $3200 if abundance was 20% higher and
of $2600 if abundance was 20% lower. If red drum abundance went to zero, a
complete loss of access would still imply a loss of about $1800, presumably
because there are several other gamefish species which can be sought.
If anglers do not care directly about water quality, except to the
extent that it affects catch rates of their preferred species, this type of
model may be the most fruitful to pursue. Future studies might rely upon
expert biological opinion regarding the expected effects on gamefish of
changes in different attributes of water quality. Calibrated utility models
such as those used in this series of studies could then be used to simulate
the ultimate effects of these changes on social welfare.
Again, all of these studies do undertake to provide point estimates of
the dollar value of changes in consumer welfare corresponding to limitations
on their access to recreational fishing or to changes in the quality of the
fishing experience. However, due to the tenuousness of the data's ability to
capture the theoretical concepts employed in these models, I elect not to cite
all of these specific numbers outside the context of the papers, where the
full range of caveats is laid out. Conditional upon the data available, I am
confident of the validity of the findings. However, extensive detailed
simulation sensitivity analyses would be required to put "true" confidence
bounds on these estimates. The simple statistical precision of the estimates
reported in the paper (as is usual in empirical work) presume that the data
are exact measures of the desired quantities.
-------
Work in progress
Not for citation
without permission
5/18/88
The Determinants of Value for a Marine Estuarine Sportfishery:
The Effects of Water Quality in Texas Bays
by
Trudy Ann Cameron
Department of Economics
University of California, Los Angeles
* We would like to thank the Texas Department of Parks and Wildlife for
allowing us to use their survey. Jerry Clark and particularly Maury Osborn
have been extremely helpful in overseeing the assembly and cleaning of the
data. John Stoll contributed to the design of the survey. David Buzan and
Patrick Roque at the Texas Department of Water Resources volunteered
considerable effort in assembling water quality data from DWR records. David
Brock at the Texas Water Development Board generously provided disks and
documentation covering additional water data.
-------
Work in progress
Not for citation
without permission
5/18/88
The Determinants of Value for a Marine Estuarine Sportfishery:
The Effects of Water Quality in Texas Bays
by
Trudy Ann Cameron
Department of Economics
University of California, Los Angeles
* We would like to thank the Texas Department of Parks and Wildlife for
allowing us to use their survey. Jerry Clark and particularly Maury Osborn
have been extremely helpful in overseeing the assembly and cleaning of the
data. John Stoll contributed to the design of the survey. David Buzan and
Patrick Roque at the Texas Department of Water Resources volunteered
considerable effort in assembling water quality data from DWR records. David
Brock at the Texas Water Development Board generously provided disks and
documentation covering additional water data.
-------
EPA-230-05-90-078
Contingent Valuation Assessment of The Economic
Damages of Pollution to Marine Recreational Fishing
Submitted to:
Mary Jo Kealy
Office of Regulatory Management and Evaluation
U.S. Environmental Protection Agency
Washington, D.C. 20460
Submitted by:
Trudy A. Cameron
Department of Economics
University of California, Los Angeles
405 Hilgard Avenue
Los Angeles, Ca. 90024
November, 1989
The information in this document has been funded in part by the
United States Environmental Protection Agency under Cooperative
Agreement No. CR 814656020. It has been subject to the Agency's
peer and administrative review, and it has been approved for
publication as an EPA document. Mention of trade names or
commercial products does not constitute endorsement or
recommendation for use.
-------
2
The Determinants of Value for a Marine Estuarine Sportfishery:
The Effects of Water Quality in Texas Bays
by
Trudy Ann Cameron
ABSTRACT
We use a large number of responses to an in-person creel and contingent
valuation survey of recreational anglers collected in the bays along the Texas
Gulf Coast between May and November of 1987, supplemented by concurrent and
independently gathered water quality data and 1980 Census data. Using
empirical techniques recently developed by this author (censored logistic
regression by maximum likelihood), these data are employed to fit implied
(non-market) demand functions for fishing days which incorporate shift
variables for water quality, perceived pollution levels, ethnic heterogene icy,
expenditures on related market goods, and catch rates. The price elasticity
of demand for fishing days (if a market existed) appears to be roughly -2.2;
the income elasticity appears to be just less than unity. Geographical
heterogeneity in the demand for recreational fishing days is partially
explained by water quality variables. The Vietnamese seem to have markedly
different preferences for fishing than the population as a whole. Money spent
on associated market goods, once thought to be a reasonable proxy for the non-
market value of a fishery, is indeed positively related to the value of a
fishing day (but typically completely unrelated to catch success).
Importantly, many other explanatory variables make strong contributions to
explaining the annual value of fishing day access; reliance solely upon market
expenditures could severely misstate resource values.
-------
3
The Non-market Value of Water Quality Attributes:
Estimates for Texas' Marine Estuarine Sportfishery
by
Trudy Ann Cameron
1. Introduction
Decisions regarding the expenditure of public funds to enhance or
restore environmental assets have frequently been made on the basis of purely
normative arguments. Until recently, the non-market benefits enjoyed
collectively by the consumers of environmental resources have been difficult
to determine. The objective in this paper is to quantify the effects of
variations in water quality upon the non-market value of the marine
recreational fishery along the Texas Gulf Coast. Knowing how water quality
affects the social value of this fishery will allow us to simulate changes in
that value as a consequence of policies which improve water quality (or as a
result of decisions to allow water quality to deteriorate).
The "travel cost" method (TCM) for valuing non-market resources has been
widely used but is frequently inappropriate for a marine sportfishery because
the point-to-point distance for these fishing trips is often poorly defined.
Destinations are diffuse and true opportunity costs for access are difficult
to measure. These problems with the travel cost method have made hypothetical
or "contingent" market surveys popular for eliciting resource values.
In contingent valuation (CV) surveys, it seems to be particularly
difficult for respondents to state the precise value they would place on the
resource. Consequently, a variety of value elicitation techniques are
employed. Different strategies are suitable depending upon whether the
investigation relies upon personal interviews, telephone interviews, or mailed
questionnaires.
-------
One method is verbal "iterative bidding." An elaboration of this
method, useful for in-person interviews or mail surveys, is the "payment
card," where the respondent is merely asked to scan a card and to indicate the
highest amount willingly paid (or lowest compensation willingly accepted) for
access to the resource. An extreme form of the iterative bidding strategy
involves only the first iteration: a single randomly assigned value is
proposed and the respondent decides whether to "take it or leave it," much as
in ordinary day-to-day market transactions. This "closed-ended CV" or
"referendum" question format economizes greatly on respondent effort and
minimizes strategic bias, but reduces estimation efficiency. The single
offered sum is varied across respondents, which allows the yes/no responses to
these questions to imply both the location and the scale of the conditional
distribution of valuations. Many more responses are required to generate
equally statistically significant parameter estimates for the valuation
function, but it is suspected that this value elicitation technique minimizes
the wide array of biases which have been argued to plague the other CV
elicitation methods.
At present, contingent valuation investigations are probably the most
practical way to quantify the economic benefits to a recreational fishery of
pollution control activities. CV questions can often be appended quite easily
to regular creel survey instruments, so the marginal cost of gathering CV data
is relatively modest.
In CV valuation models, respondents' valuations of the resource are
presumed to depend upon (a.) characteristics of the respondent and (b.)
attributes of the resource (in this case, including the level of pollution and
indirect manifestations of pollution levels such as the degree of urbanization
and catch rates). A calibrated CV model can be used to simulate both (a.) the
-------
5
direct effects of changes in pollution levels--by imposing counterfactual
changes in the quantities of pollutants and recomputing the fitted individual
valuations; and (b.) indirect effects of changes in pollution levels--for
example, by imposing predicted changes in catch rates and recomputing
individual valuations. The difference in the population weighted sums of
these individual valuations before and after the simulated reductions in
pollution levels is a measure of the social benefit of the hypothesized clean-
up program. This overall change in social value can be added to estimates of
other relevant benefits (i.e. for market activities) and the total can be
compared to the costs of the program in order to determine its economic
advisability.
For our Texas fishery, there is some concern at present about the
proposed widening and deepening of the Houston Ship Channel, which is
anticipated to have a substantial negative environmental impact. If
statistically discernible effects of water quality upon the value of this
recreational fishery can be found, our fitted models can simulate the changes
in value resulting from changes in water quality due to projects such as this.
Section 2 of this paper reviews the intuition and the details of the
statistical model which we will use to fit valuation functions. Section 3
outlines the data. Section 4 considers "naive" specifications of the
"valuation function" and explains how implied demand functions can be
extracted from the estimated models. Section 5 presents some preliminary
empirical results. Section 6 digresses to evaluate the determinants of catch
success, an issue which is important to our ability to assume exogeneity of
the explanatory variables in the valuation function. Section 7 examines
respondents' claimed motivations for going fishing and their subsequent
satisfaction levels, issues which are fundamental to the form of the basic
-------
6
utility functions which underlie the demand for fishing days. Section 8 takes
advantage of explicit questions regarding perceived pollution levels to
address whether pollution levels enter directly or indirectly into people's
utility functions. We conclude with some tentative findings and a preliminary
set of recommendations for improving subsequent surveys which might be used to
assess the effects of water quality on the non-market value of recreational
fishing.
2. Censored Logistic Regression Models for Referendum Valuation Data
Before addressing this specific empirical project, it is helpful to
outline the econometric estimation procedure which will be used to calibrate
our model of valuation for this fishery. In Cameron and James (1987) , and in
a forthcoming paper (Cameron, 1988) I have made the argument that initial
estimates of utility-theoretic models of valuation in the spirit of Hanemann
(1984) (or even entirely data-driven ad hoc valuation models) using referendum
data can be obtained quite simply using packaged logit or probit maximum
likelihood algorithms. Since the numbers of observations in the models
explored in this study are large, and since the specifications involve a wide
array of potential explanatory variables, I opt here to perform initial
estimations using censored logistic regression models. The computations
necessary to optimize the likelihood function underlying these models does not
involve myriad evaluations of the non-closed-form integral for the cumulative
normal density function. The optimization is faster and cheaper than it would
be for a censored normal regression model. Furthermore, since the parameters
of the censored logistic regression model can be solved-for from the parameter
estimates produced by conventional packaged maximum likelihood logit models,
and the SAS computer package provides ML logit routines in its MLOGIT module,
we find it expedient to pursue initial trial specifications in the context of
-------
7
the SAS package. This also allows us to take advantage of the superior data-
manipulation capabilities of this program.
Based my earlier studies, the implicit valuation function parameter
estimates produced by either the censored normal (probit-type) or censored
logistic (logit-type) estimation procedures are very similar. The slight
differences in the shape of the conditional density function for the
regression errors makes only modest differences in the fitted values of the
ultimate "regression" model. Hence it is safe to presume that explanatory
variables which make a statistically significant contribution to the valuation
function in the context of a simple logit specification will also be important
under alternative distributional hypotheses.
2.1 Review of Censored Regression Models for Referendum Data
Since the censored logistic model is not yet in the public domain, I
will briefly reproduce the derivation of the model.
"Referendum" survevs have recently become very popular as a technique
for eliciting the value of public goods or non-market resources. Numerous •
applications of these methods now exist. (For comprehensive assessments of
these survey instruments and detailed citations to the seminal works and
specific applications, the reader is referred either to Cummings, Brookshire,
and Schulze (1986), or to Mitchell and Carson (1988).
The referendum approach first establishes the attributes of the public
good or the resource, and then asks the respondent whether or not they would
pay or accept a single specific sum for access. (It is crucial that the
arbitrarily assigned sums be varied across respondents.) This questioning
strategy is attractive because it generates a scenario for each consumer which
is similar to that encountered in day-to-day market transactions. A
hypothetical price is stated and the respondent merely decides whether to
-------
8
"take it or leave it." This is less stressful for the respondent than
requiring that a specific value be named, and circumvents much of the
potential for strategic response bias. The challenge for estimation arises
only because the respondent's true valuation is an unobserved random variable.
We must infer its magnitude through an indicator variable (the consumer's
"yes/no" response to the offered threshold sum) that tells us whether this
underlying value is greater or less than the offered value.
In formulating appropriate econometric methodologies for analyzing these
data, it is important to begin by imagining how valuation might be modeled if
we could somehow readily elicit from each respondent their true valuation. If
valuation could be measured like other variables (i.e. continuously), we would
simply regress it on all the things that we suspect might affect its level.
The econometrically interesting complication with referendum data arises from
the fact that we don't know the exact magnitude of the individual's valuation;
we only know whether it is greater than or less than some specified amount.
2.2 Log-likelihood Function for Censored Logistic Regression
Referendum data are not discrete choice data in the conventional sense
(see McFadden, 1976, or Maddala, 1983). The procedure developed below is
based upon the premise that if we could measure valuation exactly, we would
use it explicitly in a regression-type model.1 The censoring of valuation to
be "greater than or less than" a known threshold is a mere statistical
inconvenience to be worked around.
1 Here, we would be using it explicitly in a "non-normal" regression model,
namely, a regression model incorporating a two-parameter logistic density
function. But that would be nothing special--econometric researchers have for
several years been using maximum likelihood methods to explore Poisson
regression, Weibull regression, and a host of other distributional assumptions
as alternatives to the familiar normal model.
-------
9
Assume that the unobserved continuous dependent variable is the
respondent's true willingness-to-pay (WTP)2 for the resource or public good,
Y . We can assume that the underlying distribution of Y. , conditional on a
vector of explanatory variables, xi (with elements j-l,...,p), has a logistic
(rather than a normal) distribution, with a mean of g(xi,^) - xi'/3.
In the standard maximum likelihood binary logit model, we would assume
that:
(1) - x.'0 + ut
where Y is unobserved, but is manifested through the discrete indicator
variable, I , such that:
(2) It - 1 if Yt > 0
- 0 otherwise.
If we assume that ui is distributed according to a logistic distribution with
mean 0 and standard deviation b (and with alternative parameter k - bjl/n,
see Hastings and Peacock (1975)), then
(3) Pr(Ii - 1) - Pr (Yt > 0) - Pr(Ui > -x.'£)
- Pr(u1A > -x^^/k)
- 1 - Pr(V>1 < -x.'7) ,
where 7 - 0/k and we use ip to signify the standard logistic random variable
with mean 0 and standard deviation b - n/J3. The formula for the cumulative
density up to z for the standard logistic distribution is
(4) F(z) - 1 - {1 + exp[z]}.
2 1
These models can be adapted very simply to accommodate willingness-to-accept
(WTA).
-------
10
Therefore the log-likelihood function can be written as:
(5) log L - 2 - log{1 + exp[ -x. ' 7])
+ (1 - I.) log{exp[-x. '7]/(1 + exp[-x.'7])}.
Simplification3 yields:
(6) log L - 2 (1 - I.)(-xi,7) - log[l + exp(-x.'7)].
It is not possible in this model to estimate £ and k separately, since they
appear everywhere as /3/k. The model must therefore be evaluated in terms of
its estimated probabilities, since the underlying valuation function, x. '/3,
cannot be recovered.
With referendum data, however, each individual is confronted with a
threshold value, t . Earlier researchers have included t as one of the x,
1 1 i
variables in the conventional logit model described above. In our new model,
we conclude by the respondent's (yes/no) response that his true UTP is either
greater than or less than t1. We can assume a valuation function4 as in (1)
with the same distribution for u^ but we can now make use of the variable
threshold value t. as follows--in a new model which might be described as
special form of "censored logistic regression":
(7) It - 1 if Yt > t.
- 0 otherwise,
so that
3 Note that many textbooks (e.g. Maddala, 1983) exploit the symmetry around
zero of the standard logistic distribution to simplify these formulas even
further. We simplify this way to preserve consistency with the next model
where we estimate k explicitly.
* However, it is now straightforward to make the mean of the conditional
distribution any arbitrary function g(x. ,/?).
-------
11
(8) Pr(Ii - 1) - Pr(Y. > t.) - Pr(u. > t. - xt'0)
- Pr(u.//c > (ci - x.'/3)/*)
- 1 - Pr(il>i < (t. - x.'£)/*).
With this modification, the log likelihood function can now be written as:
(9) log L - £ - I. log{l + exp[(ti - x.'£)/*]}
+ (1 - I.) log{exp[(t1 - x. '0)/k]/(1 + exp[(t. - x.'/3)/k])}.
As before, this can be simplified to yield:
(10) log L - Z (1 - - x.^0)/*] - log{l + exp[(ti - xl'/3)/k)).
The presence of ti allows k to be identified, which then allows us to isolate
0 so that the underlying fitted valuation function can be determined. Note
that if t - 0 for all i, (10) collapses to the conventional logit likelihood
function in (6).
The log-likelihood function in (10) can be optimized directly using the
iterative algorithms of a general nonlinear function optimization computer
program5 and this is undeniably the preferred strategy when the option is
readily available. There exist function optimization algorithms which will
find the optimal parameter values using only the function itself (and numeric
derivatives). However, analytic first (and second) derivatives can sometimes
reduce computational costs considerably. See Appendix I for a description of
5 We used a program called GQOPT - A Package for Numerical Optimization of
Functions, developed by Richard E. Quandt and Stephen Goldfeld at Princeton
University (Department of Economics). Roughly optimal parameter values are
first achieved using the DFP (Davidon-Fletcher-Powell) algorithm; these values
are then used as starting values for the GRADX (quadratic hill-climbing)
algorithm to achieve refined estimates (i.e. to a function accuracy of 10~10) .
We understand that the programs GAUSS and LIMDEP can also be adapted to
optimize arbitrary functions.
-------
12
the gradient and Hessian components helpful in nonlinear optimization of this
log-likelihood function.
Maximization of the log-likelihood function in (10) will yield separate
estimates of 0 and /c (and their individual asymptotic standard errors).
However, estimates of -\/k and 0/k can, in the case of g(x.,/3) - x.',9, be
obtained quite conveniently from conventional maximum likelihood "packaged"
logit algorithms, although we emphasize that this is merely a handy "short-
cut" to be used if a general function-optimization program is not available.
If we simply include the threshold, t , among the "explanatory" variables in
an ordinary (maximum likelihood) logit model (as has typically been done by
earlier researchers using referendum data), it is easy to see that:
(11) - (t,x')
¦1/K
0/*
- -x*'7*,
The augmented vectors of variables, x* and coefficients, 7*, may be treated as
one would treat the explanatory variables and coefficients in an ordinary
logit estimation. From 7*, it is possible to compute point estimates of the
desired parameters fi and k. If we distinguish the elements of 7* as (a, 7) -
(-l//e, 0/k) then k - -1/a and 0^ - - 1^/ot, j - l,...,p. However, accurate
asymptotic standard errors for these functions of the estimated parameters are
not produced automatically. If the conventional logit algorithm used allows
one to save the point estimates and the variance-covariance matrix estimates
for subsequent calculations, there are some alternative, relatively simple,
methods for calculating approximate standard errors using only the information
-------
13
gleaned from a conventional logit model. (See the second portion of Appendix
I.)
3. Data
The Texas Parks and Wildlife Coastal Fisheries Branch has conducted a
major creel survey of recreational fishermen from the Mexican border to the
Louisiana state line during the period of May to November, 1987. The survey
records detailed catch information, and appends a list of "socioeconomic"
questions which make up the contingent valuation portion of questionnaire.
Over 10,000 responses were collected; our admissibility criteria reduce the
usable sample to 5526, which is still a very large number of responses.
Hydrological data are collected simultaneously at each investigation sit£
along with the CV investigation. We merge these survey data with an
assortment of data drawn from other sources, notably the Texas Department of
Water resources and the 1980 Census. Extensive documentary information on
variable construction is contained in Appendix II. The reader is referred to
that section for details.
A. Specifications
4.1 "Naive" Models
As always, the very simplest model of fisheries valuation could presume
that we only wish to know the marginal mean of the value of a year's fishing.
If we include only the offered threshold as an explanatory variable in a logit
model to explain the yes/no response, the fitted model will yield the marginal
mean and marginal standard deviation of values (ignoring heterogeneity among
respondents). This number is valuable if we can safely assume that the
interview sample is a truly random sample of the "use" population, and if we
know the size of the sample relative to the entire population. Under these
-------
14
limited circumstances, we can extrapolate from these per-person estimates to
the total fitted "use" value of the fishery at the time of the survey and
under the current conditions of the fishing population and the resource
itself.
If we were not concerned with forecasting the effects of changes in the
fishing population or changes in resource attributes, this single point
estimate and its standard deviation would tell us most of what we need to
know. However, resource valuation models can be extremely useful for
forecasting the anticipated effects upon resource values of changes in
resource attributes. In this study, we are primarily concerned with changes
in species abundance and changes in water quality. We will control for cross-
sectional heterogeneity in anglers and in resource attributes. Having
calibrated a model acknowledging this heterogeneity, we will have a fitted
model which will be useful for predicting the effects on the value of the
resource of a wide range of policy-induced changes in our explanatory
variables.
Where resource values are sensitive to water quality "parameters," we
can determine the effect of a change in the level of each parameter on the
social resource value of the resource. Comparing the social benefits of
pollution control, for example, with the social costs of a cleanup program can
provide a useful assessment of the economic efficiency implications of cleanup
proposals. If resource values are sensitive to species abundance or size
(either overall or by individual species), there will be important
implications for fisheries management. Likewise, if access values are
sensitive to the day of the week interacted with respondent characteristics,
these valuation models could indicate how fishing licenses and closures could
-------
15
be decided in order to optimize both the resource base and the aggregate
social value of access.
One initial problem observed in the data concerns the distinction
between willingness to pay and actual ability to pay. "Demand" in the
economic sense might be limited to "effective" demand, not just wishful
thinking. This distinction is unresolved at present, but must be addressed at
some point during this study.
The reason for raising this issue is that we observe in our sample that
many of the people who claim to be willing to pay $20000 to continue fishing
over the year come from zip codes where $20000 exceeds the median household
income. While it may be that the respondent's household income is
substantially larger than their zip code median, these responses cast some
doubt on the accuracy of "effective" demands implied by responses to the
$20000 referendum value. Fortunately, however, we have a very large sample,
by contingent valuation standards. The referendum threshold values were
assigned randomly to different respondents. Therefore, we will lose little
except some estimation efficiency by dropping all respondents who were offered
this extremely high threshold. It is quite possible that many of the
respondents who respond that they would be willing to pay $20000 for a year's
access to the recreational fishery are responding strategically, rather than
realistically. Strategic biases from these responses can be quite high, so
the results reported here exclude the $20000 offers, regardless of their yes
or no response. (Current plans for the continuation of the survey call for
this threshold to be dropped anyway. All specifications will eventually be
estimated with the full sample, with $20000 threshold respondents deleted, and
with thresholds exceeding $500, 2000, and $1500 deleted. This allows us to
-------
16
assess che sensitivity of the valuation function parameter estimates to survey
design.)
4.2. Derivation of "Demand Functions" Underlying the Valuation Data
In this survey, the underlying continuous dependent variable Y is the
respondent's total valuation of a full year's access to the fishery, which we
will designate as "total willingness to pay," TWTP. We can still estimate
models for TWTP using censored logistic (or censored normal) regression
implicitly via an ordinary MLE logit (or probit) algorithm. We can manipulate
the estimated discrete choice coefficients to uncover the individual
coefficients (/9) for any arbitrary underlying linear-in-parameters fitted
total TWTP relationship, 0. However, the TWTP function must then be solved
to yield the corresponding implicit demand function.
To illustrate, suppose that our explanatory variables included only the
number of fishing days per year, q, and other shift variables which we will
denote by the "generic" variable X. Then the fitted quantity log(2¥TP) will
be log(q) + X, where the parameters are now their estimated values
and we ignore the stochastic component. The price willingly paid for a year's
access is the total amount willingly paid for all trips. To determine the
marginal WTP for one additional trip, we need to find the expression for the
derivative: dTWTP/dq. Since 31ogTWTP/31og(q) is just 0Z, dTWTP/dq can be
assumed to be 02 times the ratio of fitted TWTP (- expf/Sj + /92 log(q) + X])
to q. (To be strictly correct in treating this exponentiated fitted value of
log(TWTP) as the fitted conditional mean of TWTP, we would scale this quantity
by r(l+/c)T(l-/c) , but this term affects only the intercept of the resulting
demand expression, so will will suppress it for simplicity of exposition.) If
we consider dTWTP/dq to be p(q), the presumed demand relationship can be
expressed as:
-------
17
(12) log p(q) - log 02 - log(q) + + 02 log(q) + 03 X.
- (^ + log 02 + 03 X) + (0Z - 1) log(q)
We can rearrange these formulas to isolate log(q) on the left-hand side:
(13) log(q) - [(^ + log(02))/(l-02)] - [1/(1-j92) 1 log p(q)
+ [p3/a-fi2)\ x
- a:* + a2* log p(q) + a3* X.
We have thus arrived at point estimates for the implicit demand function
corresponding to a log-log functional form for TWTP. The coefficients on
log(p) have the straightforward interpretation of price elasticities of demand
for fishing trips. If the X variables contain the logarithm of income, then
the corresponding coefficient in the a3* vector gives the income elasticity of
demand. Other variables making up the X vector will include respondent and
resource attributes which shift the demand function.
Of course, the p parameters in the above formulas are transformations of
the original MLE logit parameters. It will certainly be possible to •
"automate" the computation of all of the a* parameters of the implied demand
function if we use software which allows us to save the fitted logit
parameters to be used in subsequent computations (e.g. SHAZAM). Our initial
exploratory models focus on the estimation of the 0 parameters, indirectly via
the ordinary MLE logit approach. However, once promising specifications have
been identified, and if one is willing (and able) to estimate a censored
regression log-likelihood function directly, using non-linear optimization
algorithms, it would be straightforward to reparameterize the censored
regression likelihood function described above so that the elasticity
parameter a2* and the other a3* parameters could be estimated directly. Note
that 01 - - log[a2*/(l+a2*) ] - a:*/a2* (plus an additional term in T functions
-------
18
of k) and 02 - (1+a*)/a* and 03 - -a*/a*. The expression x.'/3 in che
likelihood function should therefore be replaced by:
(14) g(x.,£) - - log[a2*/ (l+a2*) ] - at*/a*
+ (l+a2*)/a2* log (q.) + X
- g(a1*,Q2*,a3*,q1>X.) .
The log-likelihood function to be optimized will now be:
(15) log L - S (1 - Ii)((ti - g(a1*,Q2*)a3*)qi,X.))//c]
- log(l + exp[(t. - g(a1*,a2*,a3*,qi,X.))/«]) .
Since the individual parameters c^*, a2*> an<* a3* are identified, the
nonlinear function optimizing program will produce the desired results. (The
analytical gradient and Hessian formulas will be different and much more
complicated, but as noted, many programs will compute their own numeric
derivatives.) This model would produce not only direct point estimates of the
demand elasticities, <*2*, and the other demand function derivatives, but also
their directly estimated asymptotic standard errors. By the invariance
property of maximum likelihood, the point estimates should be identical, so
extremely accurate starting values for these nonlinear algorithms can be
generated by transforming the ordinary logit point estimates. The nonlinear
optimization of the likelihood function in (15), however, will yield
asymptotic standard error estimates (and therefore t-ratios for hypothesis
testing) which could only be approximated with considerable difficulty from
the asymptotic variance-covariance matrix produced automatically for the
ordinary logit parameter estimates.
-------
19
5. Preliminary Empirical Results
5.1 Unspecified Geographic Heterogeneity in Demand
If we assume geographic homogeneity to begin with and estimate a TWTP
model in log form simply as a function of the log of the total number of
fishing trips (LTRIPS), the log of median zip code household income (LINC),
and market expenditures (MON), we get the ordinary logit point estimates in
Table la. To determine whether there exists systematic geographical variation
in the demand function for fishing days, we then extend this model to include
a set of qualitative dummy variables, one for each major bay system:
MJ1 - Sabine-Neches
MJ2 - Trinity-San Jacinto (Galveston Bay)
MJ3 - Lavaca-Tres Palacios (Matagorda Bay)
MJ4 - San Antonio-Espiritu Santo
MJ5 - Mission-Aransas
MJ6 - Corpus Christi-Neuces
MJ7 - Upper Laguna Madre
MJ8 - Lower Laguna Madre
Since the Galveston Bay area accounts for Houston, we arbitrarily make MJ2 the
omitted category when we enter sets of major bay dummy variables.
Coefficients on the other dummies therefore represent shifts in the dependent
variable relative to the values for MJ2.
Individually, several of these dummy variables are statistically
significant. Collectively, a likelihood ratio test for the incremental
contribution of the complete set of dummy variables indicates that
geographical variation in demand is statistically significant at the 10%
level.
If we take the ordinary logit parameter estimates from Table lb and
transform them to yield the parameters of the log-log demand function
corresponding to this TWTP function (shown in the last column of Table lb), we
find that the price elasticity of demand for a fishing day, controlling for
qualitative geographical variation via the set of major bay dummy variables,
-------
Table la
Extremely Simple Model: Geographic Homogeneity of Demand
Variable Est. Coeff. Asy. t-ratio
LOFFER
-0.5608
-24.631
LTRIPS
0.3077
12.05
LINC
0.2488
2.316
MON
0.001734
6.167
constant
1.718
1.625
max LogL - -2550.6.
Table lb
Augmented Simple Model: with Geographic Heterogeneity (dummies)
Variable Est. Coeff. Asy. t-ratio Demand fn q
LOFFER
-0.5638
-24.68
-
LTRIPS
0.3095
12.08
-
LINC
0.1278
1.058
0.5024
MON
0.001801
6.234
0.0071
MJ1
-0.1827
-0.7526
-0.7185
MJ3
-0.2589
-1.796
-1.018
MJ4
-0.03043
-0.1706
-0.1197
MJ5
-0.1167
-0.9230
-0.4587
MJ6
-0.3405
-2.819
-1.339
MJ7
-0.2878
-2.149
-1.131
MJ8
-0.3184
-2.478
-1.252
constant
3.119
2.563
-
log(p)
-
-
-2.217
max LogL - -2544.2 (LR test statistic for the set of seven
major bay dummy variables is 12.8. x2(.05) critical value -
14.07; x2(-10) critical value - 12.01.
-------
20
is -2.217. The income elasticity of demand is 0.5024. the change in the log
of fishing days for a one dollar increase in market expenditures is 0.0071.
The seven bay dummies shift the log of fishing days by -0.72, -1.02, -0.12, -
0.46, -1.34, -1.13, and -1.25, respectively.
5.2 Quantifying Geographical Heterogeneity in Demand
The evidence therefore suggests that geographical variation exists in
the demand function for recreational fishing days in Texas. But in the model
in the last section, the reasons for this geographical variation are non-
specific. Demand could differ by bay system for a variety of reasons. First,
systematically different types of people, with different preferences or
constraints, might be utilizing each different bay system. (This is suggested
by the drop in significance of the LINC variable when bay dummies are
included.) The quality attributes of the resource could also vary across bay
systems. If fish abundance affects TWTP, then variations in species abundance
across bays could be captured by these dummy variables. If fishing conditions
(weather and water conditions) vary systematically across bays, this effect
could also be manifested in the dummy coefficients. In particular, however,
we are curious to see whether measurable variations in water quality
"parameters" exert any statistically discernible influence on TWTP. In lieu
of a set of simple bay dummy variables, then, we begin to consider
specifications employing variables which quantify the inter-bay differences in
resource attributes.
Table 2a augments the model in Table la by including a variable, TOTAL,
for the total number of fish actually caught on the interview day. (In
subsequent models, we will consider exogenous measures of abundance for
individual species, by month and bay.) TOTAL current catch is not
statistically significant, but it bears the anticipated sign, so we will
-------
Table 2a
Simple Model with Current Total Catch, No Water Quality
Variable
Est. Coeff.'
Asy. t-ratio
LOFFER
-0.5617
-24.64
LTRIPS
0.3064
11.99
LINC
0.2504
2.331
MON
0.001735
6.156
TOTAL
0.003109
1.090
constant
1.718
1.625
max LogL - -2549.9.
Table 2b
Augmented Model: Geographic Heterogeneity in Water Quality
Variable Est. Coeff. Asy. t-ratio Demand fn q
LOFFER
-0.5637
-24.63
-
LTRIPS
0.3132
12.19
-
LINC
0.2299
1.888
0.9177
MON
0.001675
5.953
0.00669
TOTAL
0.003603
1.243
0.01438
RESU
0.005401
2.138
0.02156
PHOS
1.076
2.685
4.296
CHLORA
0.02313
2.725
0.09233
LOSSIGN
0.005420
1.359
0.02163
CHROMB
-0.009027
-0.969
-0.03603
LEADB
-0.006231
-1.160
-0.02487
constant
3.119
2.563
-
log(p)
-
-
-2.250
max LogL - -2536.9 (LR test statistic for the set of six
water quality variables is 26.0. x2(.05) critical value -
12.59.
-------
21
retain it in the model as a rudimentary control for "catch success." TOTAL
will vary with individual fishing skill or effort, but it will also vary
across major bays as species abundance varies. Of primary interest for the
purposes of this study, of course, is the potential influence of water quality
measures on TWTP, and hence on the demand function for recreational fishing
days.
Our supplementary data from the Texas Department of Water Resources
provides sufficient sample on several common water quality parameters to allow
us to generate monthly averages for each bay system. For others, however, the
limited number of samples only allows reliable estimates of annual averages
for each bay system. (This is particularly true for metals found in bottom
deposits. We are awaiting further supplementary data on bottom deposits from
the shellfish division of the Health Department.) In our first pass through
the data, we examined pairwise correlations between species abundance and a
wide range of water quality measures and selected several which seemed to have
an obvious relationship to species abundance. (We have tangentially explored
regressions of actual catch and monthly abundance of each species on all
reliably measured water quality attributes, described in Section 6.)
To illustrate the potential for water quality to affect TWTP for fishery
access, we display in Table 2a some preliminary results for a rudimentary
model incorporating a selection of water quality variables. (We emphasize
that this model is by no means our last word on the subject. We have barely
"scratched the surface" of a wide variety of potential specifications.)
The water quality variables we include in Table 2b which are available
as monthly averages for each bay system are RESU (total non-filterable
residue, dried at 105C, in mg/1), PHOS (phosphorous, total, wet method, mg/1
as P), and CHLORA (chlorophyll-A, Mg/1. spectrophotometry acid method).
-------
22
Variables which can at present only be used as annual averages for each bay
system are LOSSIGN (loss on ignition, bottom deposits, scaled to g/kg),
CHROMB (chromium, total, in bottom deposits, mg/kg, dry weight), and LEADB
(lead, total, in bottom deposits, mg/kg as PB dry weight).
Transforming the ordinary logit parameter point estimates in Table 2b
according to the formulas suggested above for solving such a model for the
corresponding log-log demand function yield the demand parameters given in the
last column of Table 2b. The price elasticity of demand for fishing days is
now -2.250. The income elasticity of demand is now 0.9177. (The increase is
probably attributable to the fact that we are not longer implicitly
controlling for geographic income variation via the set of major bay dummy
variables, so that this measure is probably more reliable.) A one dollar
increase in market expenditures corresponds to a 0.0067 increase in the log of
the number of fishing days demanded, suggesting that market goods associated
with the fishing day (if typical) are complementary goods. An extra fish
caught on the interview day affects demand by increasing the log of days
demanded by 0.0144. Demand is higher where non-filterable residues are
higher, where phosphorous concentrations are higher, where loss on ignition is
greater, and where there are greater concentrations of chlorophyll-A.
However, the presence of metals in bottom deposits, such as chromium and lead,
corresponds to lesser demand for fishing days.
5.3 Controlling for Demographic Heterogeneity Among Respondents
Having determined that there will be some water quality measures which
appear to have a statistically significant impact upon the value of access to
this recreational fishery, we now introduce three variables designed to
control for interregional variations in demographics. We use PSPN0ENG,
PVIETNAM, and PURBAN. To the extent that the demographic characteristics of
-------
23
anglers are correlated with the water quality in the areas where they fish, it
will be important to allow for demographic effects in any attempt to identify
the distinct effects on resource values of water quality measures.
Table 3 gives the ordinary MLE logit parameter estimates with these
additional explanatory variables. The last column of the table gives the
point estimates of the parameters of the corresponding log-log demand function
(and its shift variables). None of these three variables make statistically
significant contributions to explaining resource values, but this may be an
artifact of collinearity among the variables, so we retain them out of
interest in determining point estimates of their effects on the demand
function.6 The proportion of unassimilated Hispanic residents in the
respondent's zip code (PSPNOENG) tends to decrease the log of fishing days
demanded by about 1.5; the proportion of Vietnamese (PVIETNAM) has a dramatic
effect on values (which persists through a variety of alternative
specifications)--this variable increases the log of fishing days demanded by
31.8! People from relatively more urbanized areas apparently demand fewer
fishing days.
5.4 Introducing Variations in Species Catch Rates, Species Abundance
The total number of fish caught on the interview day has been included
as an explanatory variable in several of the specifications discussed above.
6 Bear in mind that just because a particular variable is not statistically
significantly different from zero for a particular sample of data does not
imply that it is zero. We retain variables for which the coefficient
estimates are stable across alternative specifications. With better data
(e.g. with a more equal distribution of "yes" and "no" responses) there might
have been enough information in this sample to reduce the sizes of the
standard errors. Likewise, the error distribution may have an apparent
dispersion larger than the actual dispersion because we are using group
averages as proxies for several of our explanatory variables, including
income. What could be an excellent "fit" with the true data could be
converted to a poorer "fit" by the use of group averages.
-------
Table 3
Augmented Model: Demographic Variables
Variable Est. Coeff. Asy. t-ratio Demand fn q
LOFFER
-0.5637
-24.63
-
LTRIPS
0.3132
12.09
-
LINC
0.2281
1.512
0.9068
MON
0.001632
5.731
0.006488
PSPNOENG
-0.3915
-0.5880
-1.556
PVIETNAM
8.000
1.237
31.80
PURBAN
-0.1190
-1.400
-0.4732
TOTAL
0.003624
1.250
0.01441
RESU
0.005333
2.106
0.02120
PHOS
1.142
2.819
4.541
CHLORA
0.02235
2.631
0.08884
LOSSIGN
0.007762
1.686
0.03085
CHROMB
-0.01300
-1.194
-0.05169
LEADB
-0.004626
-0.8354
-0.01839
constant
1.404
0.9377
-
log(p)
-
-
-2.241
max LogL - -2534.9
-------
24
Given that we have a wealth of data on the catch and on overall abundance, by
individual species, it seems worthwhile to experiment with valuation models
which discriminate among the effects of individual species on the annual value
of access to the fishery.
Perplexing results emerge as we include variables relating to the catch
of individual species. There are seven major species in our working data set:
REDS, TROUT, CROAK, SAND, BLACK, SHEEP, and FLOUND (See Appendix II for
detailed descriptions). We have experimented with:
a.) actual current day catch rates;
b.) monthly average actual catch rates by bay system;
c.) "annual" average actual catch rates by bay system;
d.) monthly average abundance indexes by bay system from the TPW resource
monitoring program;
e.) annual average abundance indexes by bay system from thr TPW resource
monitoring program
For all of these measure; of catch rates, we find that for at least some
species, often important ones, the coefficients in MLE logit models imply that
greater catch rates or greater abundance decreases the value of the resource.
This seems highly implausible, and points to the existence of important
unmeasured variables, negatively correlated with catch rates, which are
positively correlated with resource values and (by their omission) leave the
catch rate variables with counterintuitive signs.
Logically, since we are asking respondents to value a year's access to
the fishery, it should b^ expected annual catch which influences their values.
But anglers may be myopi-.. Actual average catch rates or abundance may be
discounted in favor of current perceptions of catch rates. A variety of
models have been estimated, but for illustration, we report our findings for
one which uses monthly bay average catch rates. It is our inclination that
average catch rates should be preferred to individual current catch rates
because the latter does not control for individual expertise or fishing
-------
25
intensity. The monthly averages reflect the catch of the "average" angler,
abstracting from individual differences in skill or enthusiasm.
Results for a specification which replaces the TOTAL current catch
variable with the full set of monthly catch averages for each bay system are
presented in Table 4. The coefficients on MATROUT, MASAND, and MABLACK are
negative, and the point estimate for the coefficient on MABLACK is relatively
large. The set of catch variables collectively results in an improvement of
only 3.0 in the log-likelihood function, which is not sufficient to reject by
an LR test the hypothesis that the catch data should be excluded from the
model. But perhaps we are not measuring the desired variables correctly.
It is unfortunate that the survey did not collect information from post-
trip respondents regarding their target species. If you only ever fish for
one particular species, then the abundance if other species will not affect
your value of access to the resource. In fact, of other species compete for
the same biological niche as your preferred species, their abundance might
detract from your value of the fishery. This angle will need to be explored.
At one point, we made the heroic assumption that observed target proportions
in each bay and month for pre-interview respondents carry over to the
population as a whole (which is tenuous). Including these target proportions
directly in a logistic regression model had no discernible effect, however,
probably because the information was not specific to individual anglers (a
severe errors in variables problem).
Further investigation of the observable (and unobserved) correlates of
catch rates is clearly warranted. At the time of this writing, we have not
yet uncovered and explanation for these counterintuitive findings. The
following section addresses catch rates explicitly, and describes the search
-------
Table 4
Augmented Model: Monthly Average Catch Rates (by bay system)
Variable Est. Coeff. Asy. t-ratio Demand fn q
LOFFER
-0.5636
-24.62
-
LTRIPS
0.3129
12.09
-
LINC
0.2158
1.432
0.8604
MON
0.001647
5.725
0.006566
PSPNOENG
-0.3705
-0.5479
-1.477
PVIETNAM
7.421
1.142
29.58
PURBAN
-0.1149
-1.343
-0.4580
MAREDS
0.05111
0.4234
0.2037
MATROUT
-0.02823
-0.6157
-0.1125
MACROAK
0.001740
0.05004
0.006935
MASAND
-0.02808
-0.5756
-0.1119
MABLACK
-0.2094
-0.6973
-0.8346
MASHEEP
0.4165
1.331
1.660
MAFLOUND
0.06694
0.5238
0.2669
RESU
0.006257
2.328
0.02494
PHOS
1.185
2.671
4.723
CHLORA
0.02056
2.244
0.08195
LOSSIGN
0.006621
1.289
0.02639
CHROMB
-0.009143
-0.7001
-0.03645
LEADB
-0.005987
-0.9940
-0.02387
constant
1.5419
1.030
-
log(p)
-
-
-2.247
max LogL - -2532.7
-------
26
for potential reasons for the results in Table 4 (and similar results for
other models not reported in this paper).
6. Actual Current Catch versus Species Abundance: Regr^sjon Models
It is not intuitively obvious whether exogenously measured species
abundance, or actual catch rates by the respondent, should be the more
appropriate determinant of valuation for the fishing season. Unfortunately,
it is rarely easy to extract from respondents a reliable (retrospective) total
of each species caught over the past year. We only have the current day's
catch of each species in our present survey data. But exogenously measured
abundance of each species is not necessarily a good predictor of variations in
expected catch from the point of view of the individual who is being asked to
value a year of access to the fishery. One reason is that Parks and Wildlife
Resource Monitoring controlled samples are not "caught" using the same
technology available to recreational fishermen. If fish are present, but are
not "biting," they may still be swept up in the nets used by the Monitoring
Program. Ideally, we would like to know the success rates (for each species)
for a "standardized" recreational angler (with given skills and effort level).
If we use individual respondents' actual catch rates, unobservable differences
in skill will potentially bias the coefficients on the catch rate in the
valuation equations.
To determine what factors affect individual respondents' current catch
rates, we ran a set of ordinary least squares regressions of each respondent's
actual catch of each species (REDS, TROUT, CROAK, SAND, BLACK, SHEEP, and
FLOUND) against the corresponding monthly and annual abundance indexes for
that species, current market expenditures related to the fishing day (MON),
specific fishing experience (SITETRIP, the annual number of trips to the site
where the respondent was interviewed), non-specific fishing experience
-------
27
(NSWTRIP, annual trips to other saltwater fishing sites in Texas), and a
number of demographic variables. The demographic variables reflect zip code
average or median data drawn from the 1980 Census, so they do not necessarily
capture concurrent demographics, but we will assume they are close. We
include PRETIRED (the proportion of people in your zip code who are retired),
PSPANISH (the proportion of people of Hispanic origin), PSPNOENG (the
proportion speaking Spanish at home and little or no English--unassimilated
immigrants), PVIETNAM (the proportion indicating Vietnamese origin, PURBAN
(the proportion living in areas designated as urban), PTEXNATV (the proportion
born in Texas--reflecting familiarity with the fishery or the environment),
PFFFISH (the proportion working in forestry, fishing, or farming), and HHLDINC
(median household income).
These variables may affect catch rates for several reasons. First,
demographic differences may influence the target species chosen.
Alternatively, these variables may serve as proxies for fishing experience or
skill. They may also proxy whether or not the objective of the fishing trip
is purely recreational, or whether the catch is a significant supplement to
the angler's diet. Demographic measures may also covary systematically with
geographical regions and therefore with species abundance.
Table A.l (at the back of this paper) displays the results of the seven
OLS regressions. Interestingly, the exogenous abundance indexes (MMxxxxx and
Axxxxx, computed from the Resource Monitoring data) are frequently
significantly negatively related to the actual catch. Only for sand seatrout
(SAND) do both abundance indexes enter positively. This result requires
further investigation. In any event, if the fish are there, but you cannot
catch them using legal recreational fishing gear, they may contribute
considerably less to your value of the resource.
-------
23
For several species, money spent on market goods related to the fishing
day is negatively related to the catch. (And it is interesting that MON is
markedly uncorrelated, at 0.03, with zip code median household income.) Site-
specific fishing experience (SITETRIP) significantly increases one's catch of
red drum (REDS), spotted seatrout (TROUT), and black drum (BLACK). Non-
specific fishing experience (NSWTRIP) significantly increase one's catch of
sheepsheads (SHEEP) and southern flounder (FLOUND), but significantly
diminishes one's catch of croakers (CROAK).
PRETIRED insignificantly decreases the TROUT, CROAK, BLACK and SHEEP
catch, significantly decreases the SAND catch, but has an insignificant
positive effect on the FLOUND catch. People from zip codes with relatively
large numbers of Vietnamese catch significantly (and substantially) fewer of
several species, notable REDS, and SAND, but they catch dramatically larger
numbers of CROAK. People from urbanized areas catch fewer REDS, but more
CROAK, SAND, and FLOUND. Texas natives (or at least people from areas where
relatively more people are Texas natives) catch significantly fewer REDS, but
more TROUT, CROAK, BLACK, and FLOUND. If more of your neighborhood is
employed in fishing, farming or forestry, you tend to catch significantly more
REDS, SAND, and SHEEP, but significantly fewer CROAK. Higher neighborhood
incomes mean higher REDS catch, but significantly lower CROAK and SAND catch
rates. These differing results undoubtedly reflect the "sport" versus "food"
values of different species.
These tendencies might still reflect regional variations in fishing
location, which might be correlated with demographic factors. To identify
non-specific geographical and seasonal variations in catch rates, we also
estimate OLS regressions of actual catch rates on a set of major bay dummies,
MJ1 - MJ8, and a set of monthly dummies, MN5 - MN11 (where MN5 is May 1987,
-------
29
etc.). The results of these regressions are displayed in Table A.2. Clearly,
there is considerable qualitative geographical and seasonal variation in catch
rates for all species. Table A.3 therefore includes the quantitative
variables from Table A.l (with the exception of Axxxxx, which takes on only
one value per bay system), as well as the set of dummy variables MJ1 - MJ8.
Geographical variation in resource stocks does not seem to explain completely
the observed variations in catch rates. Tastes (demographics) still seem to
matter in many cases.
Since the abundance indexes derived from the Resource Monitoring data
set do not seem to be a very good proxy for expected annual catch, we revert
to using the information present in the contingent valuation sample. With
over 5000 usable responses, we can average the actual current catch data for
each respondent across all fishing trips to a particular bay system in a
particular month. Likewise, we can generate annual average actual catch rates
in each bay system. Tables A.4a through A.4c describe catch data based on the
CV sample information. Table A.4a displays the differences in mean catch
rates across bay systems for each species (AAxxxxx). Table A4.b explains the
actual individual catch for each species using both monthly average catch
rates and "annual" (May through November) catch rates, plus a variety of
demographic variables. The monthly average catch is clearly the preferred
indicator when both are included. (Its coefficient is always near one and
highly significant.) However, if only annual catch rates are included, as in
Table A.4c, these do an excellent job of explaining current individual catch.
But sociodemographic, "experience," and market expenditure variables still
contribute significantly to explaining individual catch rates for several
species. In words, you don't just catch what everybody else catches--who you
are makes a difference too.
-------
30
In subsequent work, we will contemplate using regression models like
these to generate fitted reduced form estimates of individual catch to be used
as explanatory variables in the logistic regression models for the demand
equation. Purging catch rates of components which might be correlated the
error term may improve the accuracy of the estimated coefficients.
7. Explicit Trio Motivation. Trip Goal Satisfaction
The main objective of this project is to determine whether water quality
has any statistically discernible effect upon the value of access to a
recreational fishery. For a subset of respondents--those who were interviewed
prior to embarking on their fishing trip--respondents were actually asked
explicitly about how important it was to them to be able to "enjoy natural and
unpolluted surroundings" on a fishing trip. The responses warrant
investigation.
In the pre-trip interviews, the TPW survey actually asked direct
questions about a whole variety of potential motivations for going fishing.
All respondents were asked to respond on a 10-point Likert scale (with 10
being "extremely important" and 0 being "not at all important") the importance
they place upon recreational fishing as a way to:
A - Relax (PRERELX)
B - Catch Fish (PRECAT).
The third motivation question was drawn at random from a selection of
alternatives, including:
C - Get away from crowds of people (NOPEOPLE),
D - Experience unpolluted natural surroundings (NOPOLLUT),
E - Do what you want to do (DOWHTWNT) ,
F - Keep the fish you catch (KEEPFISH),
G - Have a quiet time to think (QUIETIME),
H - Experience good weather (GOODWTHR),
I - Spend time with friends or family (FRNDFMLY), and
J - Experience adventure and excitement (ADVNEXCT).
-------
31
Since the latter eight goals were not asked of everyone, it was
necessary to focus on the subsamples to which each question was posed. For
pre-trip interviews which were not matched with post-trip interviews of the
same anglers, we have a very limited amount of information. It is not
possible to include demographic data, because zip codes were not collected.
We therefore rely on whether the professed target species was red drum, trout,
or flounder (TARGR, TARGT, or TARGF), upon major bay dummies, monthly dummies,
and upon a dummy variable for weekend days. We use OLS regression of the
recorded Likert scale response on these variables in an effort to detect
factors affecting angler's objectives in going fishing. The results are
contained in Table A.5.
From Table A.5, we see that target species, geographic dummies, and
seasonal dummies do not help at all to explain the NOPOLLUT motivation for
going fishing. However, the target species do affect the NOPEOPLE motivation,
the KEEPFISH motivation (red drum anglers seem to fish for sport; flounder
anglers fish for food), and the GOODWTHR motivation (trout anglers enjoy the
weather more; red drum and flounder anglers are less inclined to go out for
the nice weather... they must be more serious). Red drum anglers are less
likely to go fishing for its social aspects (FRNDFMLY).
More weekend anglers claim to be strongly motivated by the desire for
adventure and excitement (ADVNEXCT). Geographical and seasonal dummies
occasionally make significant differences in the objectives of anglers.
However, the values of the F-test statistics corresponding to these regression
suggest that none of the models have particularly good explanatory power.
Unfortunately, people who were interviewed prior to their fishing trips
were not a random sample of anglers. Interviewing personnel did not begin to
collect data until 10:00 a.m. in general, so pre-trip interviews sample
-------
32
individuals who do not embark on fishing trips until relatively late in the
day. These are probably less avid fishermen. Consequently, what we learn
from this sample cannot be reliably extrapolated to the entire sample. (It
would have been helpful if the pollution question, in particular, had been
posed to everyone, both pre- and post-trip.) Nevertheless, with this caveat
in mind, we can examine the apparent relationships between attitudes and other
variables.
For the pre-trip interview sample which could be matched with
corresponding post-trip interviews, we have both the attitudinal variables and
the crucial zip code data which allow us to splice in data (by zip code) on
our primary Census variables: median household income (HHLDINC), proportion
of the population over 65 (PRETIRED), proportion of the population with
birthplace in Texas (PTEXNATV), the proportion living in urban areas (PURBAN),
the proportion of the population reporting Vietnamese origin (PVIETNAM), and
proportion of the population speaking Spanish at home and speaking English not
well or not at all (PSPNOENG). If we assume that zip code areas are
relatively homogeneous, we can use median household income and these
demographic proportions to control for a certain extent for the respondents
demographic characteristics. To determine the extent to each motivation
depends upon the characteristics of the respondent, we can attempt to
interpret a number of OLS regressions. Other included explanatory variables
are: number of fishing trips to the interview site over the last year
(SITETRIP), number of saltwater fishing trips to other sites (NSWTRIP), and
money spent on market goods during this fishing trip (MON). The results are
presented in Table A.6.
In the post-trip interviews, the TPW survey asked some direct questions
concerning respondents' ability to achieve certain goals in going fishing.
-------
33
Again, all respondents were asked to respond on a 10-point Likert scale (with
10 being "completely" and 0 being "not at all") the extent to which they were
able to achieve the same set of goals (A through J). All respondents were
offered the first two goals, and one question from the remaining eight was
asked of each respondent.
In subsequent research, we may devote attention to the other attitudinal
questions in the post-trip surveys, but for the present we will focus on the
NOPOLLUT question, since this is most relevant to the issue at hand. For
post-trip respondents' answers to the question "To what extent were you able
to experience unpolluted natural surroundings," we obtained the regression
results summarized in Table A.7. This OLS regression demonstrates that who
you are (the demographic variables) has little to do with your perception of
your ability to enjoy unpolluted surroundings. The only exception may be the
PVIETNAM variable. On the other hand, geographic and seasonal dummies
occasionally make a statistically significant contribution to explaining
peoples responses. Anglers do seem to have differing perceptions of the level
of pollution, especially across bay systems. The northern bays are perceived
to be more polluted than are southern bays.
It is unfortunate that this attitude question (NOPOLLUT) was not asked
of the entire sample, so that this variable could be employed as a potential
explanator for annual resource values. Nevertheless, we can experiment will a
logistic regression specification based upon the 830 respondents who were
posed both the NOPOLLUT question and the contingent valuation question. Table
5 summarizes the results of an ordinary logit model (without water quality
variables or catch data) which includes the Likert scale value for the
NOPOLLUT variable as a potential shift variable for the demand function.
-------
34
Since only a tiny subsample of the full dataset is being used in this
case, we might expect some differences in the implication of the fitted models
(especially if there was anything non-random regarding the choice of whom to
ask each of the trip satisfaction questions--a factor which has not yet been
investigated). However, the implied demand derivatives in Table 5 are highly
consistent with those derived using the full dataset, except for the fact that
the coefficient on PSPNOENG changes sign. The price elasticity of demand is
typical, at -2.66; the income elasticity of demand is somewhat higher than in
the full sample, at 1.589. However, in this subsample, the level of
significance of LINC has dropped somewhat.
Of particular interest is the coefficient on NOPOLLUT. This variable is
statistically significant at the 10% level in the logit model. Adjustments in
aspects of environmental quality (including water quality) which would
increase a respondents' Likert scale choice by 1 unit (on the scale of 1 to
10) would therefore seem to increase the log of fishing days demanded by 0.28.
Since the mean Likert scale value is approximately 8.2, this implies that the
"elasticity of fishing day demand with respect to environmental quality" is
roughly 2.2--an elastic response.
8. Perceptions of Pollution versus Measured Water Quality
When we choose to specify a resource valuation model using water quality
measures as explanatory variables, we are not being specific about whether
water quality affects valuation of the recreational fishery direcdy or
indirectly. For example, anglers may have no conscious perception of the
dimensions of water quality when they go fishing, but water quality may be
closely related to fish abundance and therefore to catch rates, so that water
quality variables are proxies for other variables which do enter directly into
-------
35
individuals' utility functions. (At present, we are exploring OLS regression
models for catch rates which include water quality variables.)
To determine whether perceptions of environmental quality reflect actual
levels of measured dimensions of water quality, we can select the subsample of
respondents who were queried regarding their ability to enjoy unpolluted
natural surroundings. We can then regress the NOPOLLUT variable on a range of
water quality variables to see whether any statistically significant
relationships emerge. If anglers appear to perceive water quality directly,
then we can argue that water quality probably enters directly into their
utility functions as a detectable resource attribute. If not, we would be
inclined to say that appreciation of water quality variables is implicit,
acting through other variables which are manifestations of water quality.
Results for this experiment are given in Table A.8. There are 695
observations for which complete data exist for the initial set of explanatory
variables we use here. Once again, monthly or annual averages for each bay
system are used for the water quality variables, rather than conditions
actually existing in the area on the specific day when the NOPOLLUT survey
response was collected. This averaging process may considerably obscure an
underlying close relationship between the date- and site-specific values of
the water quality variables, had we been able to collect this information
simultaneously with the creel survey. Consequently, the standard error for
the parameter estimates may well be larger than they would be with more
accurate data. Therefore t-tests for the statistical significance of
coefficients are probably not conclusive.
Table A.8 shows that several water quality measures bear estimated
coefficients with t-values greater than unity. The two different measures of
dissolved oxygen, MDO and DISO (from different data sources) enter oppositely
-------
Table 5
Alternative Strategy: Use Reported Pollution Perceptions to Explain Value
(n - 830)
Variable Est. Coeff. Asy. t-ratio Demand fn q
LOFFER
-0.6639
-10.22
-
LTRIPS
0.4145
5.946
-
LINC
0.3966
0.9774
1.590
MON
0.004663
3.901
0.01869
TOTAL
0.003468
0.2962
0.01390
PSPNOENG
0.2828
0.1820
1.134
PVIETNAM
4.228
0.2686
16.95
PURBAN
-0.2009
-0.8602
0.8051
NOPOLLUT
0.07043
1.753
0.2823
constant
0.08104
0.02007
-
log(p)
-
-
-2.661
max LogL - -357.53
-------
36
and relatively significantly. Water transparency (TRANSP) significantly
improves perceptions of low pollution. NH4 and PHOS and CHLORA are positively
correlated with these perceptions; NITR is negatively related. CHROMB and
LEADB detract from perceived environmental quality. (Other specifications
reveal the consequences of the high correlations between OILGRS and LEADB:
one or the other used alone is strongly negatively significant, but not both.)
A tentative conclusion from these initial models is that people do seem
to have perceptions of environmental quality that are somewhat related to
actual measured dimensions of water quality. Loosely, then, policy actions
designed to change the levels of arguments which probably figure significantly
in regressions like that in Table A.8 will change anglers' perceptions of
pollution levels. The censored logistic regression reported in Table 5 could
then be used crudely in a "second stage" to infer the effects of such policies
on the demand for fishery access and on the total social value of the fishery.
9. Tentative Findings and Directions for Continuing Research
At this stage, of course, the results we have obtained reflect only our
"first pass" through the data, to determine whether statistically discernible
relationships among the variables of interest will assert themselves. Having
achieved some success, it is now necessary to go back over all the data to
verify the plausibility of the observed values and to "clean" the sample of
additional influential observations which may be causing varying degrees of
mischief in the estimation process. Occasional questionable values emerged
during the work thus far. Usually, the statistical fit of the models is
improved by correction of these problems.
Some remarkable outliers among the water quality data on bottom deposits
from the Department of Water Resources need to be examined before these
"parameters" are included in the model. We also need to splice in the water
-------
37
quality data obtained from the Texas Water Development Board. Due to the
absence of a crucial map, we are not able at present to distinguish accurately
between the data for the Upper and Lower Laguna Madre areas. With that
problem resolved, we will have at our disposal a number of other important
dimensions of water quality.
With tighter data, we will be able to employ the more refined
econometric methods described in sections 2.2 and 4.2 of the paper. For now,
we have been satisfied to obtain point estimates of the demand function
parameters and to rely upon the statistical significance of the underlying MLE
logit parameters to imply the significance of the corresponding demand
function parameters.
As is typical with survey analyses, the process of utilizing a data set
reveals many ways in which the questionnaire could be improved from the point
of view of using its results for particular tasks. We find that these data
would have been much more useful if the range of offered threshold values had
been manipulated during the course of the survey to ensure that fairly even
proportions of "yes" and "no" responses were elicited. The efficiency of the
estimation process is greater when one is better able to discriminate the
shape of the distribution in the vicinity of the marginal mean of the
distribution of implicit valuations. This sample has a disproportionate
number of "no" responses, which means that the information we have frequently
concentrates on the upper tail of the distribution, which is less helpful.
For the pollution aspect of this study, our objectives would have been
helped by asking all respondents direct questions about their water pollution
perceptions and explicitly whether these perceptions affect their enjoyment of
the fishing day (today or over the course of the year).
-------
38
It would have been desirable to elicit retrospective information from
respondents on their approximate total annual catch of each species, their
self-assess fishing ability, and especially, their target species (this was
only asked in pre-trip interviews).
We need to know more about the econometric literature on utilization of
group means in lieu of individual values for explanatory variables. Since
some of our earlier work with San Francisco Bay area data (Cameron and
Huppert, 1988a, 1988b, and 1988c) has implied that individual income, for
example, is correlated with Census median zip code income only at a level of
roughly 0.3 to 0.4, much information may be lost by using these medians as
proxies. On the other hand, there may be some valid arguments for treating
zip code median income as a reasonable measure of "permanent income," or the
operational level of total consumption for the individual relative to
neighbors. This methodological issue still need to be explored. As we have
pointed out in the paper, if information is being obscured by the use of group
means or medians, the standard errors of the point estimates in our models
could be artificially amplified, making parameters appear to be statistically
insignificant at any of the typical (arbitrary) levels. With "real" data, the
proxied variables might be strongly statistically significant. We don't know.
A major unresolved issue, which has confounded us for some time, is the
apparent negative effect of catch rates for some species on resource values.
This is counterintuitive, since we have strong priors that better catch rates
should imply a more desirable resource. We are confident that some
explanation can be found. Certainly, five thousand Texans cannot be wrong.
Effort thus far has been focused on determining the parameters of the
demand functions corresponding to the fitted total valuation functions for a
year of fishing access. The basic implications of microeconomic theory for
-------
39
the parameters of a log-log demand specification are readily satisfied. The
price elasticity of demand for fishing days (if a market existed) appears to
be roughly -2.2; the income elasticity appears to be just less than unity,
implying that recreational fishing is borderline between being a necessity and
a luxury. It is unfortunate that the lack of specific demographic data on our
respondents prevents us from unambiguously identifying respondent
characteristics which would let us segregate the sample and estimate separate
demand functions for each group. We must content ourselves with using zip
code averages as "shift" variables for a common demand specification.
Geographical heterogeneity in the demand for recreational fishing days
does seem to exist. Water quality variables seem to explain quite a lot of
this geographic variation. The Vietnamese seem to have markedly different
preferences for fishing than the population as a whole. Money spent on
associated market goods, once thought to be a reasonable proxy for the non-
market value of a fishery, is positively related to the value of a fishing day
(but typically completely unrelated to catch success). Importantly, many
other explanatory variables make strong contributions to explaining the annual
value of fishing day access; reliance solely upon market expenditures could
severely misstate resource values.
-------
40
APPENDIX I
NONLINEAR OPTIMIZATION OF THE CENSORED LOGISTIC REGRESSION MODEL
a.) Gradients and Hessian Elements for Nonlinear Optimization
For the simplest version of the model, with g(x. ,/9) - x. ' f3, we can write
out these derivatives by first defining the following simplifying
abbreviations:
(1) 0i - (tj_ - xt'P)/ k RA - l/(l+exp(-^)) Si - R^expC-^)
The gradient vector for this model is then given by:
(2) dlog L/d/3r - Z (x^A) {(Ii - 1) + R1 } r - 1 p
dlog L/3k - Z (^/k) { (Ii - 1) + Rt }
The elements of the Hessian matrix are:
(3) 32logL/&l3vd0s - -(1 A2) Z xltXi> S. r,s-l p
d2logL/d0rdK - -(1 A)2 Z xlr { (I1 - 1) + R4(l + <£,) } r - 1 p
d2logL/dK2 - -(1A2) Z (2*t) ( (Ii - 1) + Ri } + Vi2Si
The expectation of IA is [ l/Cl+expC^)) ] . The negatives of the
expectations of the Hessian elements are as follows:
(4) - E(d2logL/d/9r30s) - <1A2) 2 x.rxis St r,s - l,...,p
- E(d2logL/d0rK) - (1A2) 2 xir^ S1 r - 1 p
- E(d2logL/8K2) - (1A2) 2 ^2 St
For models with more general forms of the valuation function, gCx^/9) ,
the gradient vector and Hessian matrix will have different formulas. In these
-------
41
situations, it may prove easier to substitute computing time for programming
effort by using numeric derivatives in the optimization process.
b.) Standard Error Estimate for Logistic Regression Parameters from Ordinary
MLE Logit Algorithms
One alternative is to use Taylor series approximation formulas for the
variances of the desired parameters (Kmenta (1971, p. 444)):
(5) Var(»c) - Var(- 1/a) - [1/a2]2 Var(a)
Var (/9 ) - [7/a2]2 Var(a) + [-1/a]2 Var(7 )
J J J
+ 2 [7/a2] [-1/a] Cov(a,7 )
J J
A second possibility is to use the analytical formulas for the Hessian matrix
given in (3) in conjunction with the optimal values of 0 and k derived from
7*. The negative of the inverse of this matrix can be used to approximate the
Cramer-Rao lower bound for the variance-covariance matrix for and k.
Alternately, the expected values of the Hessian matrix elements are sometimes
used in this process.7
Whichever way the point estimates are obtained, and by whatever method
the asymptotic standard errors are determined, these ingredients are necessary
for hypothesis testing regarding the signs and sizes of individual
parameters. These can frequently be interpreted as derivatives (or as
elasticities) of the inverse demand function (or ad hoc "valuation" function),
and assessments of their probable true values are can be an important
objective in many empirical investigations.8
7 The outer product of the gradient vector evaluated at the optimum is also
sometimes used. However, since the expectation of the Hessian has simple
formulas, it is probably preferred in this application.
8 Of course, if estimates are achieved by optimization of (10), hypothesis
testing regarding the 0s (individually or jointly) is the same as in any
maximum likelihood context: by likelihood ratio tests.
-------
42
APPENDIX II
CONSTRUCTION OF ESTIMATING SAMPLE DATA
I. Observations from the Texas P'arks and Wildlife Survey
The "high use" season data set from the survey covers primarily the
period from May 1987 to November 1987, although a few observations are
included for December, 1987 and for January and February, 1988. We begin our
analysis with the 9413 responses collected in post-trip interviews alone.
Relatively fewer respondents were interviewed before their outings, since
survey interviewers arrived later in the morning than most anglers leave for
fishing trip. Also included are the 1094 respondents who were interviewed
both before and after their fishing trip. These respondents were also posed
the contingent valuation question; they will also be systematically different
types of individuals because all are characterized by departing typically
later in the day. This may be related to their implicit resource values.
Variables from the survey which are available for use in this study
include the following:
MAJOR which of eight major bay systems (1 -north; 8-south)
HOLIDAY whether the survey day was a holiday
DAYTYPE 1st digit (holiday) 2nd digit (day of week)
MONDAY year/month/day
MINOR code identifying minor bay where survey was conducted
STAT numerical code identifying survey site
ID boat ID number
INTTIME interview time
TRIP
ACT activity- recreational fishing or partyboat fishing
PEOPLE number of people in the party
COUNTY code for county or state of residence
MINBAY minor bay where most fish were caught
GEAR type of fishing gear used by party
BAIT type of bait which caught the majority of fish
REDS number of red drum landed
LRED largest specimen landed and measured
MLRED average length of <-6 specimens landed and measured
TROUT number of spotted seatrout landed
LTROUT
-------
43
MLTROUT "
CROAK number of croakers landed
LCROAK
MLCROAK
SAND number of sand seatrouc landed
LSAND
MLSAND
BLACK number of black drum landed
LBLACK
MLBLACK
SHEEP number of sheepshead landed
LSHEEP
MLSHEEP
FLOUND number of South Atlantic flounder landed
LFLOUND
MLFLOUND
TOTAL total landed, all species
LTOTAL
MLTOTAL
SWTRIP number of saltwater fishing trips made in the
last 12 months
SITETRIP number of trips to the survey sight in last 12 months
FWTRIP number of freshwater fishing trips in last 12 months
SATISFY overall grade given to the fishing trip (0-10)
POSTRELX answer to the post-trip question on extent person
was able to relax
answer to the post-trip question on extent person
was able to catch fish;
answer to alternating questions on other dimensions
of fishing trip
five-digit zip codes which will be used to merge survey
data with census tract information on zip code areas
for the approximately 90% of the sample with Texas
residency implied. "What is the zip code where you
currently live?"
dollars spent on the fishing trip for non-capital
market purchases: "How much will you spend on this
fishing trip from when you left home until you get
home ?"
conveys the arbitrarily assigned threshold value
proposed to each respondent and their yes/no response
to the question: "If the total cost of all your
saltwater fishing last year was dollars more,
would you have quit fishing completely?" A "no"
response therefore implies that the resource value
is greater than the threshold.
While the data set was quite well checked for consistency prior to our
receipt of it, several unusable observations had to be deleted. Criteria for
deletion were:
POSTCAT
POSTVAR
ZIP
MON
CONTVAL
-------
44
- missing data on the contingent valuation question;
- erroneous codes for the relaxation or catch satisfaction questions;
- inadmissible codes for the post-trip varying satisfaction-oriented
questions;
- inadmissible levels for the relaxation or catch satisfaction
questions;
- inadmissible values for the response to the contingent valuation
question;
- more than 365 reported saltwater or freshwater fishing trips reported
over the last year;
- fractional numbers of salt- or freshwater fishing trips reported;
- negative or greater than 365 trips per year;
- satisfaction Likert scale values outside the 0-10 integer range;
- trout catch greater than 300, total catch greater than 300;
- zip codes greater than 99999;
- no average abundance figures for this month or bay system.
If preliminary specifications on this data set indicate that certain
variables appear to have no statistically discernible effect on valuations,
the presence or absence of valid values for these variables will be
irrelevant, and some of these observations can be reinstated.
Initial specifications do not incorporate sampling weights to offset any
bias in estimated valuations which could result from systematic deletions of
observations upon criteria which are correlated with resource values. If
necessary, weights will be incorporated in subsequent specifications.
2. Controlled Catch Rate Data: Resource Monitoring Data Set
Another requirement of this study is some measure of "expected" catch
rates by time and location. Actual catch associated with the fishing
excursion during which the survey responses were collected are at best an
imperfect indicator of catch expectations. Contemporaneous catch effects are
also confounded by the possibility that the angler's expertise is unmeasured,
and this expertise will simultaneously affect both their valuation of the
resource and their current catch. This will result in misleadingly large
estimates of the impact of catch rates on the total value of the year's access
-------
45
to Che sporcfishery if expertise, catch and resource valuation are all
positively correlated (which seems likely).
In order to avoid the omitted expertise variable's biasing effect on the
catch rate coefficient, we take advantage of a supplementary data source which
can be merged with the survey data. The Texas Department of Parks and
Wildlife regularly collects information on individual species abundance,
sizes, tagging, and other information. We elect to use this resource
monitoring data for the period 1983 to 1986, for which 23,729 samples are
available. Since we seek to reproduce a proxy for anglers' expectations about
catch rates, the 1983-86 period would seem to provide a proxy for recent
experience.
Each observation in this large data file conveys information collected
during a particular controlled harvest. Variables include, gear type (3
kinds), location, date, effort (which depends on gear type), meteorological
data (including winds, cloud cover, rain, fog, water temperature, water depth,
turbidity (TURB), salinity (SAL), dissolved oxygen (DO), barometric pressure,
tide information, and wave height. The gear is applied to the fishery for a
measured period of time. At the end of the sample period, the gear is removed
and a count is taken of each type of organism collected. Mean lengths are
also available. We focus on information for the major recreational target
species of finfish: red drum (REDS), croaker (CROAK), black drum (BLACK),
spotted seatrout (TROUT), sheepshead (SHEEP), sand seatrout (SAND), and
southern flounder (FLOUND).
In distilling this information into a catch expectation variable for
each species, several manipulations are required. First, we standardize the
catch using each of the three gear types to the mean number of effort units
for each gear type. This controls for variations in catch rates due solely to
-------
46
differing sampling durations, yielding catch per unit effort (CPUE) for each
type of gear, for arbitrary effort units.
Once these "catch per unit effort" (CPUE) figures have been obtained, we
compute overall means and standard deviations in CPUE for each species by gear
type. We then use these means and standard deviations to "standardize" the
individual CPUE figures for each species and each gear type. The resulting
quantities are "indices" of CPUE. The different gear types do not necessarily
yield additive estimates of catch rates, since they differ in effectiveness
for any given number of hours of application. Therefore, we must resort to
the standardized indices, which are unit-free (i.e. we subtract the overall
mean CPUE for each gear type, and divide through by the overall standard
deviation in CPUE for that gear type).
The next step is to aggregate these indices across gear types to come up
with a weighted average (across gear types) of the three indices of
standardized CPUE. Our objective, initially, is to create indices of expected
catch rates for each major species for each sample month and each major bay
system along the Texas Coast.
The weights we use are therefore the proportion of samples collected by
each type of gear in each month and each major bay system. This implies that
if one type of gear was only infrequently used in a given month or bay system,
the CPUE index for this type of gear will receive a very low weight in the
aggregation across gear types. Averages CPUE indices derived from large
numbers of samples are presumed to be more reliable, and therefore receive
larger weights. (DATA.CTCHIND2)
In addition to the weighted average abundance indices by major bay and
month, we also computed annual average catch rates for each major bay.
(DATA.ANCATCH2) Since the survey of recreational anglers asked whether they
-------
47
would have given up fishing encirely if the access cost had been a particular
specified amount, it will also be important to consider whether annual average
expected catch is a better explanatory variable for resource valuation than
actual catch on the current fishing trip or even monthly expected catch around
the time when the survey response was elicited. However, various different
measure of catch rates will be included in the valuation models, to determine
which measure, statistically, seems to have the greatest effect of resource
value.
Bear in mind that the constructed abundance variables (MMxxxxx for
monthly averages by bay system; Axxxxx for annual averages by bay system) are
measured in standard deviation units. When these variables are used in
regressions or logit an. yses, the coefficient reflects the consequences of a
one standard deviation change in abundance.
We may also take advantage of some of the dimensions of water quali ty
collected along with the resource monitoring data. The 23,729 observations
provides a rich quantity of information on turbidity, salinity, and dissolved
oxygen. We compute average values of these measures for each month and each
bay system, MTURB, MSAL, and MDO (DATA.TURSALDO), to be employed in
regressions of pollution perceptions on measured water quality levels.
3. Texas Department of Water Resources Water Quality Data
Dave Buzan and Patrick Roque of the Texas Department of Water Resources
were kind enough to allow us to utilize information on the characteristics of
a large number of water samples taken at diverse locations throughout the
Texas estuarine/bay system for the purpose of monitoring water quality.
We use only those observations on water quality measures for which a
precise quantity is given. We excluded all observations for which it was only
recorded that the amount of the substance was greater than a certain amount.
-------
48
For a few hundred observations, it was reported that the measured amount was
less than a certain amount. For these cases, the threshold amount was very
small, so we opted to record "zero" for these measures, so as not to bias
upwards the mean quantities of these substances.
While occasional water samples were taken on an incredible variety of
water quality "parameters," consistent sampling focuses on transparency
(TRANSP), dissolved oxygen (DISO), nonfilterable residues (RESU),
nitrogen/ammonia (NH4), nitrate nitrogen (NITR), total phosphorous (PHOS), and
chlorophyll-A (CHLORA). There were from 816 to 3884 observations on these
quality measures; the other parameters all had fewer than 100 measurements, so
that monthly averages by bay system were deemed to be less reliable. For
these other water quality measures (having from 90 to 100 observations), we
generate annual average levels for each bay system. These measures include
"loss on ignition, bottom deposits" (L0SSIGN), oil and grease (OILGRS), and
organic nitrogen (ORGNITR). In bottom deposits, a few records are available
for each bay system on phosphorous (PHOSB), arsenic (ARSENB), barium
(BARIUMB), cadmium (CADMIUMB), chromium (CHROMB), copper (C0PPERB), lead
(LEADB), manganese (MANGANB), nickel (NICKELB), silver (SILVERB), zinc
(ZINCB), selenium (SELENB) and mercury (MERCURB). These metals contamination
data can be employed investigate whether amounts or perceptions of metal
contamination appear to be statistically related to resource values.
Locational information for these samples is recorded at the level of
"stations," which we identified on maps and aggregated into each of the eight
major bay/estuary systems along the Texas gulf coast. Subsequent research may
disaggregate further, but for now, we rely on the presumption that each bay is
a reasonably isolated aquatic system. There is considerable variation across
bay systems in the average levels of these "parameters." [Early models use
-------
49
only those "parameters" which do not seem to involve questionable "outliers"
among the samples. Further investigation of these outliers will be necessary
before we can be confident about using bay average levels of contamination as
accurate measures of true levels.]
In siom, we have determined average levels for each of these basic water
quality parameters for each bay system and for each month (DATA.DWRPARM). We
also aggregate to determine annual averages for each bay system.
(DATA.ANDWRPAR) For the metals and other parameters for which there are fewer
observations, we have only eight observations, by major bay system.
(DATA.HVYMETAL).
4. Hvdroloyical and Meteorological Data Collected at Survey Sites
For each day at each survey site, TPW personnel recorded fairly detailed
information about weather and surface conditions in the vicinity of the survey
site. Both beginning of "day" and end of "day" values were recorded. We
begin by considering only the beginning conditions (bearing in mind that this
was approximately 10:00 a.m.). These data can be merged with the actual
survey responses according to major bay, date, minor bay, and station numbers.
Information from this data set which may prove pertinent includes:
BWINDSP - beginning wind speed;
BCLOUD - midpoints of cloud cover categories;
BARO - beginning barometer reading;
BRAIN - whether it was raining (0 - no, 1 - yes);
BFOG - whether there was fog (0 - no, 1 - yes);
BTEMP - temperature in Celsius;
The temperature data contained obvious reporting errors, where temperatures
had clearly been recorded in Farenheit instead of Celsius. Fortunately, there
is very little potential for overlap in the two scales. We discredited any
supposedly Celsius temperature over 40, presumed it was Farenheit, and
converted it to the corresponding Celsius measure. Consistency checks
-------
50
confirmed that the corrected data were feasible, give the location and times
of year.
We merged these data (DATA.MDMETEOR) directly with the survey response
records, based on day and location. We also constructed mean monthly levels
of each of these weather and sea condition variables for each bay system
(DATA.MMETEOR), as well as annual average levels for each bay system
(DATA.AMETEOR).
5. Texas Water Development Board Water Quality Data
David Brock of the Texas Water Development Board has been very helpful
in providing us with some of his agency's data on water quality. At the time
of this writing, we are still seeking additional information necessary for
merging this information with the other data sets. The original merge
criteria contained an error.
The TWDB data measures many of the same water quality "parameters" as
does the DWR data, plus some additional ones. The included data are:
Water temperature (C)
Turbidity (jksn ju)
Transparency (secchi cm)
Conductivity field @25 C-mmh
Conductivity lab @25 C - micromh
Dissolved oxygen mg/1
pH su
Ammonia NH3-N mg/1
Nitrite N02-N mg/1
Nitrate N03-N mg/1
NitrogenT kjeldl mg/1
Phos-T P-wet mg/1
Phos-D ortho mg/1
Organ, carbon toe mg/1
Sulfate S04 mg/1
Chlorophyll-A mg/1
These data will be incorporated with the main data set as soon as the
geographical definitions can be conformed accurately.
-------
51
6 . Health Department Data
In February 1988, during a visit to Austin to confer with the other
agencies mentioned in this Appendix, I met with Texas State Health Department
data management personnel with Maury Osborn of the TPW Coastal Fisheries
Branch. The Health Department maintains detailed historical records of water
contamination, in particular for the purpose of determining shellfish
"closures." We were informed that if a request for this data was issued by
Jerry Clark of TPW directly to the Health Department, these data could be
released to us. This formal request was made, but as yet, no data have
materialized. We are not sure what accounts for this lack of cooperation, but
we will persist.
7. Census Data (1980) for Texas, bv 5-Dlgit Zip Code
The Inter-University Consortium for Political and Social Research
(ICPSR) provided at nominal cost a tape containing detailed information about
Texas residents aggregated to the level of 5-digit zip codes. Since all post-
trip interviews attempted to collect the respondent's home zip code, we have a
rich source of supplementary demographic data which we can exploit to reduce
(to a certain extent) heterogeneity in valuation responses.
By far the majority of respondents (over 90% of the sample) gave zip
codes within Texas. For these respondents, then, we can augment our array of
potential explanatory variables for the valuation models with Census
information. It is extremely important to keep in mind that zip code
proportions or medians for these variables are by no means identical to the
respondents' actual characteristics. At best, we might assert that since 5-
digit zip codes are very small areas, geographically, it is more plausible to
use zip code demographic averages than, say, county or state averages, to
control for demographic heterogeneity.
-------
52
The Census data which we suspect may be relevant to explain valuation
responses were extracted from the Census tape and assembled in a file called
DATA.TEXCENS1. Our variables are:
HHLDINC - median household income in 1980 (TABLE69);
FAMINC - median family income in 1980 (TABLE74);
MEDINC - median individu.; income in 1980 (TABLE82) ;
PURBAN - proportion inside urbanized areas (TABLE1);
PRETIRED - proportion of individuals in zip code over the age of 65
(computed from TABLE15);
PSPANISH - proportion of individuals in zip code claiming hispanic
background (computed from TABLE13);
PSPNOENG - proportion of over-18 individuals in zip code claiming to speak
Spanish at home and to speak little or no English (computed from
TABLE27);
PVIETNAM - proportion stating "race" as Vietnamese (TABLE12);
PFFFISH - proportion of individuals in zip code reporting to work in
"forestry, fishing, or farming" sectors (TABLE66);
PTEXNATV - proportion of individuals in zip code reporting birthplace
outside Texas (TABLE33).
We anticipate that household income (HHLDINC) will be the most
appropriate explanatory variable reflecting income levels, although the other
income measures will be explored. Since retired persons' opportunity costs of
time for going fishing are smaller, we expect that if you come from a
community with a large proportion of retired persons (PRETIRED), your
likelihood of being retired yourself is larger, and your valuation of the
fishery may be systematically different. The proportion of people in your zip
code living in a designated urban area may also affect your motivations for
going fishing, and hence your value of access.
Cultural differences in tastes and preferences (for different species of
game fish, or for recreation in general) may affect valuations. Especially
since some people significantly supplement their diets with "game" fish, we
would like to control for these differences. The PSPANISH variable includes
people who have lived in the US or Texas for several generations; the PSPNOENG
variable is intended to capture the proportion of recent immigrants from
Mexico, since this is by far the most prominent immigrant group in the state.
-------
53
If PSPNOENG is significant where PSPANISH is not, this may reflect
assimilation of the immigrant group, at least in terms of preferences
regarding fish and recreation. Although this is 1980 Census data, significant
numbers of Vietnamese immigrants had already settled in Texas by that time.
PVIETNAM will be slightly outdated, but may nevertheless be important.
Unfortunately, the Census tapes do not seem to identify individuals which
consider themselves to be a member of the prevalent "Cajun" ethnic group.
PTEXNATV is the proportion of the community which reports being born in Texas,
versus elsewhere. This variable ignores the cultural background of
individuals, and simply discriminates the proportion of the community which
may have less familiarity with Texas recreational resources, fish species,
angling techniques, etc.
-------
54
REFERENCES
R.C. Bishop and T.A. Heberlein, Measuring values of extramarket goods: are
indirect measures biased? Amer. J. Agr. Econom. 61, 926-930 (1979).
R.C. Bishop, T.A. Heberlein, and M. J. Kealy, Contingent valuation of
environmental assets: comparisons with a simulated market, Natural
Resources J. 23, 619-633 (1983).
T.A. Cameron, "A New Paradigm for Valuing Non-Market Goods Using Referendum
Data: Maximum Likelihood Estimation by Censored Logistic
Regression," forthcoming, Journal of Environmental Economics and
Management, 1988.
T.A. Cameron and D.D. Huppert, "OLS Versus ML Estimation of Non-Market
Resource VAlues with Payment Card Interval Data," forthcoming,
Journal of Environmental Economics and Management, 1989.
T.A. Cameron and D.D. Huppert, "The Relative Efficiency of 'Payment Card'
versus 'Referendum' Data in Non-market Resource Valuation," mimeo,
Department of Economics, University of California, Los Angeles, 1988.
T.A. Cameron and D.D. Huppert, "Measuring the Value of a Public Good:
Further Remarks," mimeo, Department of Economics, University of
California, Los Angeles, 1988.
T.A. Cameron and M.D. James "The Determinants of Value for a Recreational
Fishing Day: Estimates from a Contingent Valuation Survey,"
Department of Economics Discussion Paper #405, University of
California, Los Angeles (1986).
T.A. Cameron and M.D. James, Efficient estimation methods for use with
'closed-ended' contingent valuation survey data," Rev. Econom.
Statist. (May 1987).
R.G. Cummings, D.S. Brookshire, and W.D. Schulze (Eds.) "Valuing
Environmental Goods: An Assessment of the Contingent Valuation
Method," Rowman and Allanheld, Totowa, New Jersey (1986).
W.M. Hanemann, Welfare evaluations in contingent valuation experiments with
discrete responses, Amer. J. Agr. Econom. 66, 332-341 (1984).
N.A.J. Hastings and J.B. Peacock, "Statistical Distributions," Wiley, New York
(1975).
J. Kmenta, "Elements of Econometrics," Macmillan, New York (1971).
G.S. Maddala, "Limited-dependent and Qualitative Variables in Econometrics,"
Cambridge University Press, Cambridge (1983).
D. McFadden, Quantal choice analysis: A survey, Ann. Econom. Soc. Measure. 5,
363-390 (1976).
-------
55
R.C. Mitchell and R.T. Carson, "Using
Contingent Valuation Method,"
D.C. (forthcoming, 1988).
C. Sellar, J.R. Stoll and J.P. Chavas,
welfare change: a comparison
61, 156-175 (1985).
Surveys to Value Public Goods: The
Resources for the Future, Washington,
Validation of empirical measures of
of nonmarket techniques, Land Econom.
C. Sellar, J.P. Chavas, and J.R. Stoll, Specification of the logit model: the
case of valuation of nonmarket goods, J. Environ. Econom Management
13, 382-390 (1986).
-------
SUPPLEMENTARY TABLES
-------
Table A.l - Regressions of current catch on monthly and annual
abundance measures for the species, market expenses, trip
frequencies, and demographic variables by zip code.
DEP VARIABLE: REDS
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T FOR HO:
PARAMETER-0
INTERCEP
0.55995251
0.30007121
MMREDS
0.36847595
0.23700779
AREDS
-0.10965756
0.04224035
MON
-0.000016971
0.000118226
NSWTRIP
0.000788784
0.000874304
SITETRIP
0.005368462
0.000797330
PRETIRED
0.85482835
0.72060800
PSPANISH
0.75937497
0.26831368
PSPNOENG
0.65719318
0.83394446
PVIETNAM
-9.52181432
4.10336572
PURBAN
-0.18475126
0.06936814
PTEXNATV
-0.69407659
0.27218848
PFFFISH
4.39061789
1.80245578
HHLDINC
0.000012134
0.0000073043
1.866
1.555
-2.596
-0.144
0.902
6.733
1.186
2.830
0.788
-2.320
-2.663
-2.550
2.436
1.661
DEP VARIABLE: TROUT
PARAMETER STANDARD T FOR HO:
VARIABLE ESTIMATE ERROR PARAMETER-0
INTERCEP 0.32098798 0.96852747 0.331
MMTROUT 0.46025045 0.55181825 0.834
ATROUT -0.10727163 0.08659900 -1.239
MON 0.000344210 0.000391106 0.880
NSWTRIP 0.000856360 0.002804431 0.305
SITETRIP 0.008488526 0.002555053 3.322
PRETIRED -2.23625648 2.31717300 -0.965
PSPANISH 2.50439916 0.90968459 2.753
PSPNOENG -4.76702938 2.65016291 -1.799
PVIETNAM -10.54180776 13.22176053 -0.797
PURBAN 0.007574193 0.22341404 0.034
PTEXNATV 1.61013946 0.92900808 1.733
PFFFISH 4.43354471 5.80127597 0.764
HHLDINC 0.000016170 0.000023415 0.691
-------
Table A.l, continued
DEP VARIABLE: CROAK
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
3.30401254
0.98231253
3.364
MMCROAK
-1.23508097
0.45744060
-2.700
ACROAK
0.08828395
0.09482006
0.931
MON
-0.001526458
0.000391878
-3.895
NSWTRIP
-0.006019254
0.002894183
-2.080
SITETRIP
-0.001736803
0.002636454
-0.659
PRETIRED
-3.96485185
2.37842920
-1.667
PSPANISH
-9.44617850
0.91612331
-10.311
FSPNOENG
16.61375283
2.78349049
5.969
PVIETNAH
34.13699452
13.59965826
2.510
PURBAN
1.00645150
0.22970427
4.382
PTEXNATV
4.46549691
0.89550728
4.987
PFFFISH
-26.83794821
5.96099955
-4.502
HHLDINC
-0.000175471
0.000024158
-7.263
EP VARIABLE:
SAND
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
2.60203861
1.27890185
2.035
MMSAND
0.13525806
0.62965032
0.215
ASAND
0.34725560
0.12388076
2.803
MON
0.003049747
0.000506331
6.023
NSWTRIP
0.000772157
0.003762673
0.205
SITETRIP
0.002321740
0.003427697
0.677
PRETIRED
-6.69928574
3.10020622
-2.161
PSPANISH
-5.55781967
1.15362653
-4.818
PSPNOENG
8.36237511
3.52678402
2.371
PVIETNAH
-37.14203944
17.67071748
-2.102
PURBAN
1.00236870
0.29815854
3.362
PTEXNATV
1.47548162
1.15738569
1.275
PFFFISH
18.26459246
7.73754036
2.361
HHLDINC
-0.000122238
0.000031442
-3.888
-------
Table A.l, continued
DEP VARIABLE: BLACK
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
-0.21504911
0.15372003
-1.399
MMBLACK
-0.03098885
0.11983304
-0.259
ABLACK
0.02454022
0.01586489
1.547
MON
-0.000098978
0.000060809
-1.628
NSWTRIP
-0.000610036
0.000452134
-1.349
SITETRIP
0.000872498
0.000411767
2.119
PRETIRED
-0.51376786
0.37191902
-1.381
PSPANISH
-0.88597982
0.13901951
-6.373
PSPNOENG
2.70210744
0.42860428
6.304
PVIETNAM
-0.11057677
2.12731804
-0.052
PURBAN
0.04845612
0.03601018
1.346
PTEXNATV
0.66908968
0.13901599
4.813
PFFFISH
0.23180632
0.93050578
0.249
HHLDINC
-.0000017218
.00000377165
-0.457
EP VARIABLE:
SHEEP
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
0.06836968
0.21828737
0.313
MMSHEEP
0.12234247
0.15810969
0.774
ASHEEP
-0.04147377
0.03175789
-1.306
MON
0.000139507
0.000087330
1.597
NSWTRIP
0.002547533
0.000636643
4.002
SITETRIP
0.000655088
0.000579990
1.129
PRETIRED
-0.22178639
0.52319454
-0.424
PSPANISH
0.06904953
0.19867934
0.348
PSPNOENG
-0.55274431
0.60979506
-0.906
PVIETNAM
-2.34572452
3.01854217
-0.777
PURBAN
0.02545117
0.05043334
0.505
PTEXNATV
-0.002006479
0.20671267
-0.010
PFFFISH
2.93979145
1.31880893
2.229
HHLDINC
-.0000027911
.00000531521
-0.525
-------
Table A.l, continued
•P VARIABLE:
FLOUND
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
-0.01970803
0.32426667
-0.061
MMFLOUND
-0.61281021
0.20575268
-2.978
AFLOUND
-0.15836960
0.03617201
-4.378
MON
-0.000077295
0.000129670
-0.596
NSWTRIP
0.007868546
0.000943887
8.336
SITETRIP
-0.000819604
0.000860134
-0.953
PRETIRED
1.13867584
0.78206752
1.456
PSPANISH
-0.98520829
0.30517406
-3.228
PSPNOENG
2.04588931
0.91854214
2.227
PVIETNAM
1.06771366
4.44847267
0.240
PURBAN
0.16953815
0.07518352
2.255
PTEXNATV
0.63002837
0.30251588
2.083
PFFFISH
-1.23657529
1.94501820
-0.636
HHLDINC
-.0000037847
.00000789691
-0.479
-------
Table A.2 - Regressions of current catch on major bay and
monthly dummy variables
DEP VARIABLE: REDS
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
0.05034214
0.07581144
0.664
MJ1
0.09586074
0.16287253
0.589
MJ3
0.47034606
0.09943735
4.730
MJ4
0.41556795
0.12293509
3.380
MJ5
0.19918153
0.08094287
2.461
MJ6
0.19034190
0.07985535
2.384
MJ7
0.39698000
0.09674908
4.103
MJ8
0.87774944
0.08008518
10.960
MN5
0.04357481
0.09756501
0.447
MN6
0.04480128
0.09810146
0.457
MN8
0.20531995
0.08224176
2.497
MN9
0.38649084
0.08346977
4.630
MN10
0.39501347
0.08322912
4.746
MN11
0.26375298
0.10148514
2.599
:p VARIABLE:
TROUT
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
2.02945978
0.24217103
8.380
MJ1
-0.30959043
0.52027779
-0.595
MJ3
0.60509801
0.31764131
1.905
MJ4
1.48200534
0.39270218
3.774
MJ5
-0.45785320
0.25856281
-1.771
MJ6
-0.23295552
0.25508884
-0.913
MJ7
1.81081777
0.30905394
5.859
MJ8
0.77603162
0.25582300
3.033
MN5
-0.19569724
0.31166034
-0.628
MN6
-0.61720332
0.31337396
-1.970
MN8
-0.37767862
0.26271195
-1.438
MN9
-0.51615104
0.26663468
-1.936
MN10
-0.43755749
0.26586596
-1.646
MN11
-0.08592488
0.32418277
-0.265
-------
Table A.2, continued
DEP VARIABLE: CROAK
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
1.80420655
0.25440856
7 .092
MJ1
0.15435967
0.54656879
0.282
MJ3
-1.44501071
0.33369255
-4.330
MJ4
-0.96835590
0.41254645
-2.347
MJ5
-1.22670089
0.27162867
-4.516
MJ6
0.12211734
0.26797915
0.456
MJ7
-0.80625121
0.32467124
-2.483
MJ8
-1.77502414
0.26875041
-6.605
MN5
-0.52584969
0.32740935
-1.606
MN6
-0.52478913
0.32920957
-1.594
MN8
1.30543161
0.27598747
4.730
MN9
0.54887768
0.28010843
1.960
MN10
0.24721955
0.27930087
0.885
MN11
-0.73844884
0.34056457
-2.168
EP VARIABLE:
SAND
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
1.49360615
0.32742378
4.562
MJ1
-1.75665494
0.70343395
-2.497
MJ3
-1.55240358
0.42946227
-3.615
MJ4
-1.25885186
0.53094723
-2.371
MJ5
-1.05708742
0.34958605
-3.024
MJ6
-1.56950545
0.34488913
-4.551
MJ7
-2.36323791
0.41785184
-5.656
MJ8
-1.87517327
0.34588174
-5.421
MN5
0.39706249
0.42137579
0.942
MN6
-0.32002563
0.42369266
-0.755
MN8
0.63333692
0.35519583
1.783
MN9
0.43997674
0.36049951
1.220
MNIO
0.84778208
0.35946017
2.358
MN11
2.84404560
0.43830655
6.489
-------
Table A.2, continued
DEP VARIABLE: BLACK
PARAMETER STANDARD T FOR HO:
VARIABLE ESTIMATE ERROR PARAMETER-0
INTERCEP 0.20731884 0.03932264 5.272
MJ1 -0.02152089 0.08448036 -0.255
MJ3 -0.12508682 0.05157716 -2.425
MJ4 -0.12285552 0.06376521 -1.927
MJ5 -0.15597693 0.04198426 -3.715
MJ6 -0.11956589 0.04142017 -2.887
MJ7 -0.13773178 0.05018278 -2.745
MJ8 -0.15204360 0.04153938 -3.660
MN5 -0.07209143 0.05060600 -1.425
MN6 -0.04345460 0.05088425 -0.854
MN8 -0.01226179 0.04265798 -0.287
MN9 0.02200455 0.04329494 0.508
MN10 0.14766722 0.04317011 3.421
MN11 0.05904913 0.05263933 1.122
DEP VARIABLE: SHEEP
PARAMETER STANDARD T FOR HO:
VARIABLE ESTIMATE ERROR PARAMETER-0
INTERCEP 0.12359373 0.05514031 2.241
MJ1 -0.19739614 0.11846289 -1.666
MJ3 -0.01479838 0.07232426 -0.205
MJ4 -0.06177563 0.08941499 -0.691
MJ5 -0.07825227 0.05887258 -1.329
MJ6 -0.14568843 0.05808159 -2.508
MJ7 -0.24692556 0.07036899 -3.509
MJ8 -0.15689291 0.05824875 -2.693
MN5 0.05152056 0.07096245 0.726
MN6 -0.007780611 0.07135262 -0.109
MN8 0.03604168 0.05981731 0.603
MN9 -0.004137654 0.06071048 -0.068
MN10 0.05014380 0.06053545 0.828
MN11 0.47535803 0.07381370 6.440
-------
Table A.2, continued
IP VARIABLE:
FLOUND
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
0.82159657
0.08199456
10.020
MJ1
-0.31496533
0.17615627
-1.788
MJ3
-0.30390463
0.10754737
-2.826
MJ4
-0.63615308
0.13296157
-4.784
MJ5
-0.79315402
0.08754450
-9.060
MJ6
-0.79126378
0.08636828
-9.162
MJ7
-0.73886256
0.10463985
-7.061
MJ8
-0.63585291
0.08661686
-7.341
MN5
0.06951967
0.10552233
0.659
MN6
0.13816270
0.10610253
1.302
MN8
0.15535632
0.08894932
1. 747
MN9
0.05658948
0.09027749
0.627
MN10
0.23391866
0.09001721
2.599
MN11
0.78029069
0.10976219
7.109
-------
Table A.3 - Regressions of current catch on monthly
abundance index, demographic variables, and major bay
dummy variables
DEP VARIABLE: REDS
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
0.08249090
0.30620085
0.269
MMREDS
0.31460321
0.24591373
1.279
MON
-0.000126631
0.000119475
-1.060
NSWTRIP
0.000997362
0.000871506
1.144
SITETRIP
0.005338593
0.000792004
6.741
PRETIRED
0.40792992
0.72216553
0.565
PSPANISH
0.94774237
0.29027646
3.265
PSPNOENG
-1.92730218
0.94335117
-2.043
PVIETNAM
-6.30008634
4.13511627
-1.524
PURBAN
-0.17926668
0.06960719
-2.575
PTEXNATV
-0.35985526
0.28079594
-1.282
PFFFISH
4.06562241
1.79684467
2.263
HHLDINC
0.000014557
.00000727471
2.001
MJ1
0.22117083
0.16308096
1.356
MJ3
0.41258319
0.10128207
4.074
MJ4
0.29340746
0.11918553
2.462
MJ5
0.11045001
0.08697339
1.270
MJ6
0.14403815
0.08637686
1.668
MJ7
0.36564235
0.09914413
3.688
MJ8
0.80571613
0.09778452
8.240
DEP VARIABLE: TROUT
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T FOR HO:
PARAMETER-0
INTERCEP
0.32926072
0.98058040
MMTROUT
0.72672191
0.51692313
MON
0.000418306
0.000383818
NSWTRIP
0.001301984
0.002790464
SITETRIP
0.009021724
0.002535271
PRETIRED
-1.40101257
2.31274943
PSPANISH
2.38954617
0.93836731
PSPNOENG
-6.87307423
3.02935838
PVIETNAM
-5.11369468
13.24493296
PURBAN
-0.08751728
0.22300185
PTEXNATV
1.51843888
0.90477954
PFFFISH
1.66646879
5.76057977
HHLDINC
0.000014731
0.000023296
MJ1
-0.12522173
0.51372014
MJ3
0.46603374
0.32238217
MJ4
1.42956747
0.38169115
MJ5
-0.73896336
0.29216032
MJ6
-0.56608140
0.27586664
MJ7
1.58614179
0.30245190
MJ8
0.62707082
0.32306103
0.336
1.406
1.090
0.467
3.558
-0.606
2.546
-2.269
-0.386
-0.392
1.678
0.289
0.632
-0.244
1.446
3.745
-2.529
-2.052
5.244
1.941
-------
Table A.3, continued
EP VARIABLE:
CROAK
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
2.66756373
1.00525808
2.654
MMCROAK
-3.98638283
0.40759600
-9.780
MON
-0.001477013
0.000392887
-3.759
NSWTRIP
-0.006107054
0.002860786
-2.135
SITETRIP
-0.001945570
0.002599357
-0.748
PRETIRED
-2.84572618
2.37166305
-1.200
PSPANISH
-10.44237560
0.96981335
-10.767
PSPNOENG
21.96652769
3.12265143
7.035
PVIETNAM
42.50799742
13.57571203
3.131
PURBAN
0.88205153
0.22857272
3.859
PTEXNATV
4.60465670
0.92367915
4.985
PFFFISH
-25.60229589
5.90128326
-4.338
HHLDINC
-0.000159420
0.000023899
-6.671
MJ1
-1.32428223
0.52467711
-2.524
MJ3
-1.26997939
0.32994369
-3.849
MJ4
-1.09222587
0.39260972
-2.782
MJ5
-0.23015884
0.28546340
-0.806
MJ6
2.96516199
0.32860335
9.024
MJ7
-0.10117965
0.31440281
-0.322
MJ8
-0.30969034
0.32172324
-0.963
EP VARIABLE:
SAND
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
3.49528262
1.33092771
2.626
MMSAND
0.72768171
0.58049126
1.254
MON
0.003208116
0.000516215
6.215
NSWTRIP
0.000111362
0.003769108
0.030
SITETRIP
0.002300422
0.003424049
0.672
PRETIRED
-6.18159589
3.12377497
-1.979
PSPANISH
-4.92447442
1.25551174
-3.922
PSPNOENG
8.32102379
4.07928230
2.040
PVIETNAM
-43.08458320
17.88205173
-2.409
PURBAN
0.98033470
0.30113908
3.255
PTEXNATV
1.59438668
1.21376362
1.314
PFFFISH
20.77898656
7.76855507
2.675
HHLDINC
-0.000125297
0.000031474
-3.981
MJ1
-1.26918171
0.70113740
-1.810
MJ3
-1.80970744
0.44122254
-4.102
MJ4
-1.69999347
0.55660418
-3.054
MJ5
-0.93288233
0.41761009
-2.234
MJ6
-1.51242967
0.37264711
-4.059
MJ7
-1.47083745
0.46585384
-3.157
MJ8
-1.88560063
0.44713447
-4.217
-------
Table A.3, continued
i? VARIABLE:
BLACK
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
-0.06527348
0.15959629
-0.409
MMBLACK
-0.03127245
0.12061281
-0.259
MON
-0.000069184
0.000062054
-1.115
NSWTRIP
-0.000675180
0.000452805
-1.491
SITETRIP
0.000844350
0.000411388
2.052
PRETIRED
-0.38407660
0.37526227
-1.023
PSPANISH
-0.81824332
0.15091174
-5.422
PSPNOENG
2.86581250
0.49012528
5.847
PVIETNAM
-1.20317407
2.14842043
-0.560
PURBAN
0.04742877
0.03617276
1.311
PTEXNATV
0.58276254
0.14602230
3.991
PFFFISH
0.39924427
0.93388199
0.428
HHLDINC
-.0000024413
.00000378035
-0.646
MJ1
-0.04210067
0.08343432
-0.505
MJ3
-0.12673404
0.05401686
-2.346
MJ4
-0.15692987
0.06429929
-2.441
MJ5
-0.11390689
0.04643952
-2.453
MJ 6
-0.06697295
0.04542878
-1.474
MJ7
-0.10752456
0.04999241
-2.151
MJ8
-0.21494500
0.05137572
-4.184
EP VARIABLE:
SHEEP
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
0.18397633
0.22424085
0.820
MMSHEEP
0.19706534
0.16868340
1.168
MON
0.000146931
0.000087682
1.676
NSWTRIP
0.002501075
0.000638205
3.919
SITETRIP
0.000654810
0.000579796
1.129
PRETIRED
-0.10899880
0.52896178
-0.206
PSPANISH
0.18634607
0.21297531
0.875
PSPNOENG
-0.98841053
0.69064803
-1.431
PVIETNAM
-3.18386372
3.02844868
-1.051
PURBAN
0.02463802
0.05097815
0.483
PTEXNATV
0.03107763
0.20624852
0.151
PFFFISH
2.90768177
1.32049588
2.202
HHLDINC
-.0000038586
.00000532886
-0.724
MJ1
-0.11879970
0.11723539
-1.013
MJ3
-0.08906114
0.07379417
-1.207
MJ4
-0.18881993
0.09180317
-2.057
MJ5
-0.11501370
0.06391136
-1.800
MJ6
-0.16932811
0.06321095
-2.679
MJ7
-0.21894058
0.06971473
-3.141
MJ8
-0.22701709
0.08198620
-2.769
-------
Table A.3, continued
:P VARIABLE:
FLOUND
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
0.21204966
0.33183132
0.639
MMFLOUND
-0.49321815
0.21939866
-2.248
MON
-0.000066724
0.000129246
-0.516
NSWTRIP
0.007551138
0.000943757
8.001
SITETRIP
-0.000819620
0.000857429
-0.956
PRETIRED
1.36027395
0.78225188
1.739
PSPANISH
-0.71324691
0.31584173
-2.258
PSPNOENG
0.81296362
1.02514679
0.793
PVIETNAM
0.52069004
4.47714546
0.116
PURBAN
0.16554232
0.07538672
2.196
PTEXNATV
0.93747057
0.30394040
3.084
PFFFISH
-0.37430053
1.94690673
-0.192
HHLDINC
-.0000050267
.00000787969
-0.638
MJ1
-0.35044016
0.17397636
-2.014
MJ3
-0.43350722
0.10925459
-3.968
MJ4
-0.80589558
0.12901976
-6.246
MJ5
-0.65223380
0.10370180
-6.290
MJ6
-0.63117761
0.09957913
-6.338
MJ7
-0.55085946
0.10597766
-5.198
MJ8
-0.42631471
0.10855894
-3.927
-------
Table A.4a - Average "Annual" Actual Catch Rates by Sample Respondents
(for May-Nov 1987); by Major Bay System
MAJOR AAREDS AATROUT AACROAK AASAND AABLACK AASHEEP AAFLOUND
1
2
3
4
5
6
7
8
0.35000
0.21942
0.70226
0.57912
0.42059
0.45898
0.62898
1.16386
1.44286
1.68155
2.34292
3.36027
1.29244
1.45691
3.56847
2.48221
1.63571
1.92039
0.46612
0.99663
0.75575
2.21288
1.31051
0.33708
0.75714
1.93689
0.19713
0.36364
1.05586
0.63344
0.15446
0.23034
0.214286
0.219417
0.117043
0.090909
0.062432
0.115265
0.057325
0.086142
0.064286
0.172816
0.119097
0.060606
0.118291
0.055036
0.007962
0.014045
0.785714
0.982524
0.603696
0.202020
0.205915
0.236760
0.340764
0.331461
Table A.4b - OLS Regressions of Actual Individual Catch Rates on
Average Rates for Sample Anglers (for each bay and month, MAxxxxxx,
and for each bay, AAxxxxxx).
DEP VARIABLE: REDS
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
-0.12266561
0.29823802
-0.411
MAREDS
0.95085659
0.08092220
11.750
AAREDS
-0.05043007
0.12278424
-0.411
MON
-0.000092812
0.000115702
-0.802
NSWTRIP
0.000923382
0.000857973
1.076
SITETRIP
0.005093002
0.000781527
6.517
PRETIRED
0.45725770
0.70551913
0.648
PSPANISH
0.72133204
0.26179804
2.755
PSPNOENG
-1.22854525
0.82771249
-1.484
PVIETNAM
-4.92451856
4.04183705
-1.218
PURBAN
-0.18016933
0.06794174
-2.652
PTEXNATV
-0.34731022
0.26481849
-1.312
PFFFISH
2.72013126
1.76799000
1.539
HHLDINC
0.000013987
.00000716232
1.953
-------
Table A.4b, continued
DEP VARIABLE:
VARIABLE
INTERCEP
MATROUT
AATROUT
MON
NSWTRIP
SITETRIP
PRETIRED
PSPANISH
PSPNOENG
PVIETNAM
PURBAN
PTEXNATV
PFFFISH
HHLDINC
TROUT
PARAMETER
ESTIMATE
-1.36523478
0.98197610
0.006042790
0.000286035
0.001863515
0.008918273
-1.43720691
1.43940886
-3.82852658
-2.07403981
-0.07554478
1.53446304
-1.98870119
0.000010671
STANDARD
ERROR
0.94998077
0.10033556
0.14070736
0.000370669
0.002757012
0.002511557
2.26629296
0.84354198
2.58495718
12.94627157
0.21864170
0.84795042
5.68333396
0.000023018
DEP VARIABLE:
VARIABLE
INTERCEP
MACROAK
AACROAK
MON
NSWTRIP
SITETRIP
PRETIRED
PSPANISH
PSPNOENG
PVIETNAM
PURBAN
PTEXNATV
PFFFISH
HHLDINC
CROAK
PARAMETER
ESTIMATE
1.81057461
0.83774972
0.11396771
-0.001215592
-0.005338101
-0.001572947
-1.90685717
-8.60976875
18.04502300
31.27438550
0.82502684
3.72817129
-21.13769899
-0.000159098
STANDARD
ERROR
0.97371072
0.06864557
0.13693499
0.000383033
0.002844955
0.002590113
2.34453169
0.88171963
2.73232498
13.34679054
0.22594926
0.87567771
5.86344930
0.000023783
T FOR HO:
PARAMETER-0
-1.437
9.787
0.043
0.772
0.676
3.551
-0.634
1.706
-1.481
-0.160
-0.346
1.810
-0.350
0.464
T FOR HO:
PARAMETER-0
1.859
12.204
0.832
-3.174
-1.876
-0.607
-0.813
-9.765
6.604
2.343
3.651
4.257
-3.605
-6.690
-------
Table A.4b, continued
DEP VARIABLE: SAND
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
1.04106408
1.26437786
0.823
MASAND
0.98233478
0.07436923
13.209
AASAND
0.11303100
0.18715312
0.604
MON
0.003017771
0.000497673
6.064
NSWTRIP
-0.001733434
0.003701859
-0.468
SITETRIP
0.000968215
0.003369551
0.287
PRETIRED
-5.89965190
3.04239513
-1.939
PSPANISH
-4.58440729
1.14376694
-4.008
PSPNOENG
7.47884232
3.46885734
2.156
PVIETNAM
-46.01016400
17.40831290
-2.643
PURBAN
0.91626869
0.29301929
3.127
PTEXNATV
1.94350416
1.13489728
1.712
PFFFISH
18.23397447
7.61793262
2.394
HHLDINC
-0.000110765
0.000030901
-3.585
SP VARIABLE:
BLACK
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
-0.29092946
0.15268688
-1.905
MABLACK
0.96665317
0.09114036
10.606
AABLACK
-0.09573732
0.25278827
-0.379
MON
-0.000071042
0.000060670
-1.171
NSWTRIP
-0.000674880
0.000447214
-1.509
SITETRIP
0.000671392
0.000407375
1.648
PRETIRED
-0.26273281
0.36938636
-0.711
PSPANISH
-0.61890961
0.14299078
-4.328
PSPNOENG
2.06309845
0.43075110
4.790
PVIETNAM
-0.74833926
2.10625389
-0.355
PURBAN
0.04133539
0.03551921
1.164
PTEXNATV
0.53988053
0.13864906
3.894
PFFFISH
0.35225404
0.92028645
0.383
HHLDINC
-5.35967E-07
.00000374053
-0.143
-------
Table A.4b, continued
DEP VARIABLE:
VARIABLE
INTERCEP
MASHEEP
AASHEEP
MON
NSWTRIP
SITETRIP
PRETIRED
PSPANISH
PSPNOENG
PVIETNAM
PURBAN
PTEXNATV
PFFFISH
HHLDINC
SHEEP
PARAMETER
ESTIMATE
-0.09047019
0.99441736
0.04962667
0.000051587
0.002201864
0.000382545
0.05006948
0.01381854
-0.32208556
-3.32365172
0.04434566
0.04907053
2.55337512
-.0000014707
STANDARD
ERROR
0.20353089
0.03670434
0.31134446
0.000080557
0.000597400
0.000544200
0.49119093
0.18550590
0.55982006
2.82850803
0.04734667
0.18406197
1.22902375
00000499508
DEP VARIABLE:
VARIABLE
INTERCEP
MAFLOUND
AAFLOUND
MON
NSWTRIP
SITETRIP
PRETIRED
PSPANISH
PSPNOENG
PVIETNAM
PURBAN
PTEXNATV
PFFFISH
HHLDINC
FLOUND
PARAMETER
ESTIMATE
-0.61623401
0.97594742
-0.02153132
-0.000030626
0.006652809
-0.001277307
1.44956602
-0.43520381
0.72106186
-1.86240792
0.09270761
0.70903598
-0.33088056
-4.07689E-07
STANDARD
ERROR
0.31048537
0.05182762
0.10986631
0.000124319
0.000914079
0.000831043
0.75447296
0.29352799
0.88677081
4.30327459
0.07250692
0.28266255
1.87895111
00000763403
T FOR HO:
PARAMETER-0
-0.445
27.093
0.159
0.640
3.686
0.703
0.102
0.074
-0.575
-1.175
0.937
0.267
2.078
-0.294
T FOR HO:
PARAMETER-0
-1.985
18.831
-0.196
-0.246
7.278
-1.537
1.921
-1.483
0.813
-0.433
1.279
2.508
-0.176
-0.053
-------
Table A.4c - OLS Regressions of Actual Individual Catch Rates
on "Annual" Average Catch Rates (by bay system, AAxxxxxx)
DEP VARIABLE:
VARIABLE
INTERCEP
AAREDS
MON
NSWTRIP
SITETRIP
PRETIRED
PSPANISH
PSPNOENG
PVIETNAM
PURBAN
PTEXNATV
PFFFISH
HHLDINC
DEP VARIABLE:
VARIABLE
INTERCEP
AATROUT
MON
NSWTRIP
SITETRIP
PRETIRED
PSPANISH
PSPNOENG
PVIETNAM
PURBAN
PTEXNATV
PFFFISH
HHLDINC
REDS
PARAMETER
ESTIMATE
-0.17221294
0.88499989
-0.000142307
0.001071111
0.005384716
0.33591552
0.82939290
-1.50245838
-6.08247392
-0.17038106
-0.32388801
4.01044819
0.000014969
TROUT
PARAMETER
ESTIMATE
-1.46919676
0.97625433
0.000416560
0.001431302
0.009029381
-1.53660877
2.05603824
-5.21985591
-4.62037204
-0.07380018
1.39479051
1.56510528
0.000015985
STANDARD
ERROR
0.30189259
0.09463395
0.000117054
0.000868480
0.000790784
0.71415935
0.26486900
0.83760654
4.09055782
0.06877599
0.26808275
1.78637790
00000725031
STANDARD
ERROR
0.95805247
0.10071020
0.000373599
0.002780255
0.002533030
2.28566892
0.84838605
2.60313817
13.05445151
0.22051315
0.85508754
5.72027055
0.000023209
T FOR HO:
PARAMETF.R-0
-0.570
9.352
-1.216
1.233
6.809
0.470
3.131
-1.794
-1.487
-2.477
-1.208
2.245
2.065
T FOR HO:
PARAMETER-0
-1.534
9.694
1.115
0.515
3.565
-0.672
2.423
-2.005
-0.354
-0.335
1.631
0.274
0.689
-------
Table A.4c, continued
DEP VARIABLE: CROAK
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
2.28572714
0.98589955
2.318
AACROAK
0.91638532
0.12171787
7.529
MON
-0.001416135
0.000387781
-3.652
NSUTRIP
-0.006336075
0.002881682
-2.199
SITETRIP
-0.001620966
0.002624632
-0.618
PRETIRED
-2.73498544
2.37478506
-1.152
PSPANISH
-10.42514263
0.88066463
-11.838
PSPNOENG
22.06274250
2.74857122
8.027
PVIETNAM
35.64921090
13.51980165
2.637
PURBAN
0.87878673
0.22891726
3.839
PTEXNATV
4.15492950
0.88664122
4.686
PFFFISH
-26.48857430
5.92496424
-4.471
HHLDINC
-0.000177231
0.000024053
-7.368
EP VARIABLE:
SAND
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
1.41489731
1.28379481
1.102
AASAND
1.08298286
0.17483291
6.194
MON
0.003137767
0.000505358
6.209
NSWTRIP
0.000235592
0.003756601
0.063
SITETRIP
0.002220311
0.003420799
0.649
PRETIRED
-6.59692145
3.08942598
-2.135
PSPANISH
-4.84730866
1.16144683
-4.174
PSPNOENG
7.61299788
3.52299589
2.161
PVIETNAM
-43.06236011
17.67862787
-2.436
PURBAN
0.98954192
0.29754040
3.326
PTEXNATV
1.73664712
1.15250486
1.507
PFFFISH
20.49016673
7.73491401
2.649
HHLDINC
-0.000123535
0.000031368
-3.938
-------
Table A.4c, continued
DEP VARIABLE:
VARIABLE
INTERCEP
AABLACK
MON
NSWTRIP
SITETRIP
PRETIRED
PSPANISH
PSPNOENG
PVIETNAH
PURBAN
PTEXNATV
PFFFISH
HHLDINC
BLACK
PARAMETER
ESTIMATE
-0.26300398
0.84957965
-0.000073271
-0.000649917
0.000826483
-0.40638490
-0.70453147
2.21811495
-1.10922521
0.04450246
0.59054447
0.35238792
-.0000025102
STANDARD
ERROR
0.15420014
0.23893440
0.000061280
0.000451707
0.000411208
0.37285190
0.14419906
0.43483440
2.12716746
0.03587531
0.13996088
0.92954552
00000377348
DEP VARIABLE:
VARIABLE
INTERCEP
AASHEEP
MON
NSWTRIP
SITETRIP
PRETIRED
PSPANISH
PSPNOENG
PVIETNAM
PURBAN
PTEXNATV
PFFFISH
HHLDINC
SHEEP
PARAMETER
ESTIMATE
-0.03535211
1.14481671
0.000147038
0.002511729
0.000648276
-0.16218767
0.14164609
-0.72252764
-3.27210423
0.03013284
0.01242447
2.98360822
-.0000038444
STANDARD
ERROR
0.21662870
0.32859181
0.000085663
0.000635759
0.000579156
0.52276013
0.19738974
0.59566819
3.01068062
0.05039299
0.19591140
1.30807122
00000531597
T FOR HO:
PARAMETER-0
-1.706
3.556
-1.196
-1.439
2.010
-1.090
-4.886
5.101
-0.521
1.240
4.219
0.379
-0.665
T FOR HO:
PARAMETER-0
-0.163
3.484
1.716
3.951
1.119
-0.310
0.718
-1.213
-1.087
0.598
0.063
2.281
-0.723
-------
Table A.4c, continued
DEP VARIABLE: FLOUND
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
-0.59237667
0.32028494
-1.850
AAFLOUND
0.92591610
0.10075174
9.190
MON
-0.000037291
0.000128243
-0.291
NSWTRIP
0.007522444
0.000941733
7.988
SITETRIP
-0.000864638
0.000856981
-1.009
PRETIRED
1.39301161
0.77828601
1.790
PSPANISH
-0.65905648
0.30254645
-2.178
PSPNOENG
1.15633766
0.91445592
1.265
PVIETNAM
-0.40499133
4.43841383
-0.091
PURBAN
0.16577954
0.07468882
2.220
PTEXNATV
0.77931103
0.29156099
2.673
PFFFISH
-0.12527303
1.93823814
-0.065
HHLDINC
-.0000051086
.00000787083
-0.649
-------
Table A.5 - Precrip Motivation Questions: OLS Regressions
DEP VARIABLE: N'OPEOPLE
F-TEST 0.943
OBS 603
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T FOR HO:
PARAMETER-0
INTERCEP
TARGR
TARGT
TARGF
MJ1
MJ3
MJ4
MJ5
MJ 6
MJ7
MJ8
MN5
MN6
MN8
MN9
MN10
MN11
WKND
7.59185247
0.52836370
-0.34403082
0.47487337
0.64433020
0.84117457
0.23616653
0.34060028
0.27210277
0.27241992
0.46534192
-0.04077979
-0.04905820
-0.37063712
0.32841948
-0.19742662
-0.09581740
-0.01828012
0.44738621
0.24653310
0.24382515
0.47290029
0.41974765
0.46032060
0.44200330
0.46624780
0.50602718
0.54607083
0.41754746
0.38895224
0.34417911
0.35045962
0.39216770
0.36166775
0.44172970
0.21044572
16.969
2.143
-1.411
1.004
1.535
1.827
0.534
0.731
0.538
0.499
1.114
-0.105
-0.143
-1.058
0.837
-0.546
-0.217
-0.087
DEP VARIABLE: NOPOLLUT
T-TEST
C 791
OBS
429
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
9.28862007
0.32744825
28.367
TARGR
-0.06010503
0.19483745
-0.308
TARGT
0.02721384
0.18658810
0.146
TARGF
-0.18077773
0.37549661
-0.481
MJ1
0.13636153
0.30518053
0.447
MJ3
0.06243266
0.36528564
0.171
MJ4
-0.18281956
0.27396226
-0.667
MJ5
-0.40245959
0.35735465
-1.126
MJ6
-0.14210375
0.33100665
-0.429
MJ7
0.02401744
0.32870964
0.073
MJ8
0.08025961
0.27896454
0.288
MN5
-0.007657418
0.31921439
-0.024
MN6
0.08823009
0.32933579
0.268
MN8
0.19207957
0.25276985
0.760
MN9
0.25429200
0.27247807
0.933
MN10
-0.39582402
0.27040307
-1.464
MN11
-0.28337536
0.32430722
-0.874
WKND
0.10035740
0.19787569
0.507
-------
DEP VARIABLE: DOWHTWNT
F-TEST
OBS
1.385
503
VARIABLE
INTERCEP
TARGR
TARGT
TARGF
MJ1
MJ3
MJ4
MJ5
MJ 6
MJ7
MJ8
MN5
MN6
MN8
MN9
MN10
MN11
WKND
PARAMETER
ESTIMATE
7.70993748
-0.19641401
0.10541805
0.26082970
0.80886667
1.33626023
0.77824468
0.80050893
0.48155068
1.08142499
0.89569917
0.50210737
0.09873351
0.60081590
-0.13628211
0.002551616
0.19458545
0.14459588
STANDARD
ERROR
0.44125530
0.21523229
0.21296736
0.39672252
0.48840354
0.43315279
0.43810012
0.42618053
0.40874203
0.43207201
0.44663572
0.40968952
0.31592841
0.37690952
0.31189957
0.35379013
0.39803834
0.25298011
T FOR HO:
PARAMETER-0
17.473
-0.913
0.495
0.657
1.656
3.085
1.776
1.878
1.178
2.503
2.005
1.226
0.313
1.594
-0.437
0.007
0.489
0.572
DEP VARIABLE: KEEPFISH
F-TEST
OBS
2.619
536
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T FOR HO:
PARAMETER-0
INTERCEP
TARGR
TARGT
TARGF
MJ 1
MJ3
MJ4
MJ 5
MJ 6
MJ7
MJ8
MN5
MN6
MN8
MN9
MN10
MN11
WKND
8.09163143
-0.63493893
-0.03000512
1.16005118
-0.67785857
-0.89785739
-0.21607825
-1.01361087
-1.04931986
-0.41688883
-0.25730722
-0.14119910
0.22085293
-0.63595454
1.45515992
0.18826575
-0.67293081
0.21160550
0.39754566
0.28813687
0.28608262
0.51360011
0.48409302
0.42731459
0.51354355
0.52192311
0.49730779
0.45091149
0.45696247
0.54846485
0.39028515
0.36390967
0.48851570
0.36217584
0.44317159
0.26132905
20.354
-2.204
-0.105
2.259
-1.400
-2.101
-0.421
-1.942
-2.110
-0.925
-0.563
-0.257
0.566
-1.748
2.979
0.520
-1.518
0.810
-------
DEP VARIABLE: QUIETIME
F-TEST
OBS
1.579
482
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T FOR HO:
PARAMETER-0
INTERCEP
TARGR
TARGT
TARGF
MJ1
MJ3
MJ4
MJ5
MJ6
MJ7
MJ8
MN5
MN6
MN8
MN9
MNIO
MN11
WKND
8.33047553
-0.14268653
•0.18754912
0.03336624
•0.73609622
•0.70451833
•0.56445054
•1.14804492
•1.34006483
¦0.29360849
0.04573877
¦0.81118400
¦0.09321641
0.08157845
•0.10180406
0.22701246
•0.45980224
•0.05979884
0.
0.
0.58638878
0.29999957
0.30534004
0.48896232
0.69983581
.71501660
.70372958
0.69315901
0.68904331
0.69167542
0.74465338
0.47981448
0.41382943
0.44580404
0.53428439
0.40778226
0.53274809
0.32476937
14.206
-0.476
-0.614
0.068
-1.052
-0.985
-0.802
-1.656
-1.945
-0.424
0.061
-1.691
-0.225
0.183
-0.191
0.557
-0.863
-0.184
DEP VARIABLE: GOODWTHR
F-TEST
OBS
2.759
381
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T FOR HO:
PARAMETER-0
INTERCEP
TARGR
TARGT
TARGF
MJ1
MJ3
MJ4
MJ5
MJ 6
MJ7
MJ8
MN5
MN6
MN8
MN9
MNIO
MN11
WKND
7.09707233
-0.48646878
0.51229235
-1.49302896
0.40571747
1.09149043
0.72597107
0.48019072
1.23645655
-0.26498057
0.22708658
-0.31701387
1.28035717
0.14411618
1.14428728
0.49489729
0.57428481
0.34439790
0.43106770
0.32599391
0.33760558
0.49194356
0.49441812
0.56904719
0.44476911
0.58953742
0.46327764
0.44679878
0.46512018
0.38871104
0.60295514
0.46022680
0.46974240
0.43572265
0.45843956
0.25591639
16.464
-1.492
1.517
-3.035
0.821
1.918
1.632
0.815
2.669
-0.593
0.488
-0.816
2.123
0.313
2.436
1.136
1.253
1.346
-------
DEP VARIABLE: FRNDFMLY
F-TEST
OBS
1.233
406
VARIABLE
INTERCEP
TARGR
TARGT
TARGF
MJ1
MJ3
MJ4
MJ5
MJ6
MJ7
MJ8
MN5
MN6
MN8
MN9
MN10
MN11
WKND
PARAMETER
ESTIMATE
8.54110823
-0.59800573
0.15487751
0.46287229
0.20963175
0.66950705
0.25996020
0.46650183
0.60614119
-0.09825039
0.17366924
-1.35708719
0.35442366
0.09749444
0.15200115
0.45811705
0.19319351
0.13095893
STANDARD
ERROR
0.46254806
0.25565774
0.25328885
0.40689201
0.44760664
0.46462665
0.42541605
0.43289498
0.55775904
0.43264822
0.40604008
0.70293279
0.34017854
0.32599378
0.39173057
0.33971443
0.47315411
0.23814544
T FOR HO:
PARAMETER-0
18.465
-2.339
0.611
1.138
0.468
1.441
0.611
1.078
1.087
-0.227
0.428
-1.931
1.042
0.299
0.388
1.349
0.408
0.550
DEP VARIABLE: ADVNEXCT
F-TEST
OBS
1.267
443
VARIABLE
INTERCEP
TARGR
TARGT
TARGF
MJ1
MJ3
MJ4
MJ5
MJ6
MJ7
MJ8
MN5
MN6
MN8
MN9
MN10
MN11
WKND
PARAMETER
ESTIMATE
7.25608143
0.23528665
-0.26195517
-0.14838342
0.03723037
-0.92314231
-0.04891245
1.01363017
-0.83621541
0.03118484
0.49056525
-0.01289834
0.04472742
-0.34816497
-0.55696234
-0.20256002
0.49999921
0.44184453
STANDARD
ERROR
0.61347890
0.31342257
0.30524996
0.47233401
0.54138594
0.71890424
0.51960706
0.56859825
0.60606846
0.49129926
0.53133745
0.53358967
0.49114189
0.46015875
0.54623163
0.52433722
0.52655699
0.26438608
T FOR HO:
PARAMETER-0
11.828
0.751
-0.858
-0.314
0.069
-1.284
-0.094
1.783
-1.380
0.063
0.923
-0.024
0.091
-0.757
-1.020
-0.386
0.950
1.671
-------
Table A,5, continued
DEP VARIABLE: PRERELX
F-TEST 1.585
OBS
3722
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
8.78987067
0.13274228
66.218
TARGR
-0.08702046
0.08311952
-1.047
TARGT
-0.02271869
0.08253455
-0.275
TARGF
-0.05306643
0.14142803
-0.375
MJ1
-0.009755689
0.13606929
-0.072
MJ3
-0.25145705
0.14111326
-1.782
MJ4
-0.36764056
0.13622517
-2.699
MJ5
0.03227412
0.14489392
0.223
MJ6
0.008712145
0.14303434
0.061
MJ7
0.05884559
0.13821775
0.426
MJ8
-0.003183858
0.13112852
-0.024
MN5
0.01144559
0.12708450
0.090
MN6
-0.02560113
0.11183769
-0.229
MN8
0.13506010
0.10587769
1.276
MN9
0.01645299
0.12161881
0.135
MN10
0.12827553
0.10739298
1.194
MN11
0.08320163
0.13371926
0.622
WKND
-0.01423466
0.06462206
-0.220
DEP VARIABLE: PRECAT
F-TEST 2.063
OBS 3722
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T FOR HO:
PARAMETER-0
INTERCEP
6.56236349
0.17428059
37.654
TARGR
0.09004818
0.10912966
0.825
TARGT
0.12237258
0.10836163
1.129
TARGF
0.52153433
0.18568432
2.809
MJ1
0.15331075
0.17864870
0.858
MJ3
-0.17609374
0.18527106
-0.950
MJ4
0.17431650
0.17885337
0.975
MJ5
0.15514299
0.19023478
0.816
MJ6
0.54007251
0.18779330
2.876
MJ7
0.15005384
0.18146947
0.827
MJ8
0.30449474
0.17216185
1.769
MN5
-0.10320669
0.16685235
-0.619
MN6
-0.22755882
0.14683444
-1.550
MN8
0.04694627
0.13900941
0.338
MN9
-0.14802188
0.15967631
-0.927
MN10
-0.10164869
0.14099887
-0.721
MN11
0.05654611
0.17556329
0.322
WKND
0.11237509
0.08484389
1.324
-------
Table A.6 - For sample interviewed both before and after
fishing trip; demographic, geographic, and seasonal variables
and their effects on extent to which "unpolluted natural
surroundings are a motivation for going fishing.
DEP VARIABLE: NOPOLLUT
F-TEST 1.569
OBS
85
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
19.31015380
26.92078701
0.717
HHLDINC
-0.000493022
0.000514831
-0.958
PRETIRED
-42.07217646
41.08032759
-1.024
PTEXNATV
-1.35518067
28.42559659
-0.048
PSPNOENG
6.58063295
39.05040280
0.169
PVIETNAM
-109.12039
406.35400
-0.269
PURBAN
0.18671766
5.03175573
0.037
SITETRIP
0.04004085
0.01082416
3.699
NSWTRIP
0.02132592
0.10230115
0.208
MON
0.005535399
0.01279516
0.433
MJ1
-4.17274793
8.79692225
-0.474
MJ3
-9.84498903
9.81685770
-1.003
MJ4
1.22590283
8.62253424
0.142
MJ5
-2.43125737
8.03930377
-0.302
MJ6
4.13690974
6.64660300
0.622
MJ7
-5.69727465
6.63558981
-0.859
MJ8
-15.01756379
8.27448287
-1.815
MN5
9.44642008
7.95520190
1.187
MN6
4.20898200
7.25488897
0.580
MN8
8.30827846
6.19106440
1.342
MN9
4.44008039
6.2385 3464
0.712
MN10
0.94326577
5.99986399
0.157
MN11
11.91217331
6.72034145
1.773
WKND
2.07968018
4.75885531
0.437
-------
Table A. 7 - Extent to which respondents were able to
"Experience Unpolluted Natural Surroundings." (n-858)
IF VARIABLE:
NOPOLLUT
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
8.42190686
1.00903630
8.346
HHLDINC
-0.000011214
0.000022673
-0.495
PRETIRED
1.58102890
1.96850152
0.803
PTEXNATV
-0.61188444
0.85289639
-0.717
PSPNOENG
-1.28938826
1.51495547
-0.851
PVIETNAM
19.42599903
11.87295215
1.636
PURBAN
0.08369006
0.19819351
0.422
MJ1
-0.86422020
0.36986443
-2.337
MJ3
0.32246599
0.38965319
0.828
MJ4
0.64005519
0.25369335
2.523
MJ5
1.01771109
0.35532066
2.864
MJ6
0.10662209
0.31278854
0.341
MJ7
0.46076012
0.29608459
1.556
MJ8
0.88094389
0.32441647
2.715
MN5
0.22148059
0.35923225
0.617
MN6
-0.69695574
0.29829741
-2.336
MN8
-0.02393900
0.22370082
-0.107
MN9
-0.18379131
0.27529979
-0.668
MN10
-0.02430656
0.26243870
-0.093
MN11
0.45402552
0.35517060
1.278
WKND
-0.16900558
0.19266161
-0.877
-------
Table A.8 - OLS Regression of "Ability to Enjoy Unpolluted
Natural Surroundings" on Measured Water Quality Variables
DEP VARIABLE: NOPOLLUT
F-TEST 4.192
OBS
695
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
7.65156764
1.88693837
4.055
MTURB
0.000064889
0.01043748
0.006
MSAL
0.01185356
0.01791982
0.661
MDO
-0.22131054
0.13894215
-1.593
TRANSP
0.02299990
0.01366888
1.683
DISO
0.26350825
0.10926245
2.412
RESU
0.009595514
0.007438127
1.290
NH4
3.99552741
3.69437706
1.082
NITR
-1.40780844
1.18960581
-1.183
PHOS
0.14529883
1.41691553
0.103
CHLORA
0.009712722
0.02752364
0.353
LOSSIGN
-0.01482662
0.02449996
-0.605
CHROMB
-0.003165001
0.01881366
-0.168
LEADB
-0.04634034
0.01468208
-3.156
-------
Combining Contingent Valuation and Travel Cost Data
for the Valuation of Non-market Goods
by
Trudy Ann Cameron
Department of Economics
University of California, Los Angeles
ABSTRACT
Contingent valuation (CVM) survey methods are now being used quite
widely to assess the economic value of non-market resources. However, the
implications of these surveys have sometimes met with a degree of skepticism.
Here, hypothetical CVM data are combined with travel cost data on actual
market behavior (exhibited by the same consumers) to internally validate the
implied CVM resource values. We estimate jointly both the parameters of the
underlying utility function and its corresponding Marshallian demand function.
Equivalence of the utility functions implied by the two types of data can be
tested statistically. Respondent and/or resource heterogeneity can be
accommodated readily. A sample of Texas recreational anglers illustrates the
technique.
* This project has benefited greatly from helpful comments and suggestions
provided by E.E. Learner and by B.C. Ellickson, W.M. Hanemann, J. Hirshleifer,
D.D. Huppert, K.E. McConnell, R.E. Quandt, M. Waldman, and seminar
participants at UCLA, the 1988 SEA meetings, the University of British
Columbia, and Simon Fraser University. J. Clark and the Texas Department of
Parks and Wildlife generously provided the results of the survey (designed in
consultation with J.R. Stoll of Texas A&M). M. Osborn at TPW prepared the
data. The Inter-university Consortium for Social and Political Research
provided Census data. This research is supported in part by EPA cooperative
agreement # CR-814656-01-0.
-------
Revised: April 21, 1989
Combining Contingent Valuation and Travel Cost Data
for the Valuation of Non-market Goods
Economists have long been skeptical about the reliability of consumers'
stated intentions, as opposed to their actions in the marketplace. The notion
that "actions speak louder than words" underlies much of the criticism of
survey methods as a basis for demand forecasting. In some situations,
however, market demand activity cannot be directly observed. Surveys and
other indirect methods are the only glimpses of demand relationships we have.
In these circumstances, it is valuable to explore methods by which researchers
can combine survey responses and other available information to formulate the
best possible characterization of demand when actual market observations "in
the field" are unattainable.
For a wide variety of environmental resources and public goods, the
absence of markets makes it extremely difficult to establish a monetary value
for access to these commodities. Whenever a proposed change in policy affects
the quality or availability of these non-market goods, either explicit or
Implicit cost-benefit analysis must be undertaken at some point in the
decision process. For some time, economists have experimented with
alternative methods of eliciting or inferring the social value of these non-
market goods.
The familiar travel cost method (TCM) popularized by Clawson and Knetsch
(1966) has been widely applied in an extensive array of empirical studies.
This method interprets variation in travel costs to a particular site where a
-------
non-market good is consumed as equivalent to the effect of a per-trip entrance
fee to the same location. Subsequent research has provided numerous
extensions and qualifications to the original travel cost method.
A somewhat newer, competing approach to valuation involves directly
asking individual consumers of the non-market good about its value. A
hypothetical market scenario is described to each respondent and their
professed behavior under that scenario is recorded. To avoid the connotations
of hypotheticality, this has been dubbed the "contingent valuation method"
(CVM). Despite the potential for a variety of biases in poorly designed CVM
surveys (described in detail in surveys by Cummings, Brookshire, and Schulze,
1986, or Mitchell and Carson, 1988) there are still many situations where more
realistic methods (such as market simulations or actual market experiments)
are prohibitively difficult, and where some of the other potential methods,
such as hedonic housing price models or hedonic wage models, are
inappropriate. In these cases, it has generally been conceded that CVM
surveys, when interpreted cautiously, can provide useful information about the
characteristics of demand for a good not presently priced and traded in a real
market. The CVM technique has also been widely applied.
Despite the semantic care in naming the CVM, the data it produces have
still been criticized as "hypothetical answers to hypothetical questions."
Consequently, "external validation" of empirical applications of CVM has
received considerable attention in the literature. Some of these compare CVM
and TCM; others compare CVM with other valuation methods.
For example, Bishop and Heberlein (1979) and Bishop, Heberlein and Kealy
(1983) pit CVM estimates against TCM and the results of simulated market
experiments. They conclude that CVM mechanisms produce "meaningful--albeit
inaccurate --economic information." CVM and TCM are also compared by Sellar,
-------
3
Stoll and Chavas (1985), who conclude that the two methods do provide
comparable estimates of consumer surplus, and that whenever possible, both
methods should be used in future studies as a validity check on the results.
Schulze, d'Arge, and Brookshire (1981) determine that "all evidence
obtained to date suggests that the most readily applicable methodologies for
evaluating environmental quality--hedonic studies of property values or wages,
travel cost, and [CVM] survey techniques--all yield values well within one
order of magnitude in accuracy. Such information...is preferable to complete
ignorance." Brookshire, Thayer, Schulze, and D'Arge (1982) compare CVM
estimates with a hedonic property value study. Regarding CVM, they conclude
that "[a]lthough better accuracy would be highly desirable, in many cases
where no other technique is available for valuing public goods, this level of
accuracy is certainly preferable to no information for the decision-making
process."
Brookshire and Coursey (1987), on the other hand, compare hypothetical
non-market CVM responses with market-like elicitation processes (Vernon
Smith's public good auction experiments in the laboratory and in the field).
Compared to CVM, the marketplace appears to be "a strong disciplinarian" in
terms of limiting the tendency for certain types of inconsistencies in
valuation responses.
In all these previous studies aimed at external validation of the values
for non-market goods produced by CVM, the alternative measures of value were
obtained either by indirect methods (the travel cost approach or hedonic wage
or rent functions) or by small simulated market experiments. The point
estimates of value produced by each technique are generated by completely
separate models which are sometimes even applied to completely separate
-------
samples of data. This makes rigorous statistical comparisons of the different
value estimates impossible.
The new joint models introduced in this paper also appeal to the
marketplace to "discipline" contingent valuation estimates, while at the same
time, the CVM information provides insights into the probable behavior of
respondents under conditions which are far removed from the current market
scenario. The innovation is that the validation occurs in the context of a
single joint model applied to a single sample of respondents. Since we
collect both CVM and TCM information from each respondent, the joint model can
be estimated both with and without restrictions, allowing the consistency of
the CVM information and TCM information to be tested in a statistically
rigorous fashion. 1
The new joint models described in this paper will be appropriate for a
whole spectrum of non-market resource valuation tasks wherever CVM or TCM have
been used separately before. For concreteness in this paper, however, we
concentrate on an empirical application concerning the non-market demand for
access to a recreational fishery. The U.S. Fish and Wildlife Service
estimates that economic activity associated with recreational fishing
generated $17.3 billion in 1980 and $28.1 billion in 1985, and there are at
least 60 million Americans who fish regularly (reported in Forbes, May 16,
1988, pp. 114-120). Recreational fisheries valuation has therefore attracted
considerable policy-making interest over the past few years.2 There are many
1 The conceptual framework for the econometric implementation is similar to
models of discrete/continuous choice employed by Hanemann (1984) and by Dubin
and McFadden (1984), but in the present case, the discrete choices are purely
hypothetical.
2 Among current related policy issues, for example, is the quantification of
the social costs of acid precipitation (which kills fish and decreases the
consumer surplus associated with recreational fishing). These costs are
-------
3
theoretical examinations and empirical attempts at valuation extant.3 One
factor accounting for the proliferation of empirical analyses is the
availability of vast quantities of survey data collected regularly for
fisheries management purposes.
Section I of this paper develops the logic whereby a discrete-choice
direct utility function can be modified into an indirect utility difference
function (defined over fishing days and a composite of all other goods). Then
this function and the corresponding Marshallian demand function for fishing
access days can be modeled jointly. Section II describes a sample of CVM and
TCM data used to demonstrate this technique. Section III describes
alternative stochastic specifications. Section IV provides a general outline
of the types of results these models generate. Section V goes into detail
regarding the specific empirical results for a basic model and some useful
extensions.
I. THE JOINTNESS OF CONTINGENT VALUATION AND TRAVEL COST RESPONSES
A rigorous utility-theoretic tradition in the analysis of "discrete-
choice" CVM data was initiated by Hanemann (1984b), who elaborated
substantially upon earlier estimation procedures used by Bishop and Heberlein
(1979). The discrete choice (or "referendum") format for CVM survey questions
is often argued to be less subject to some of the usual CVM biases than are
other formats. Rather than asking the respondent to place his own specific
generally considered to be one of the most substantial components of acid rain
damages.
3 To cite only a few of the more recent recreational fisheries studies:
McConnell, 1979, Anderson, 1980, Samples and Bishop, undated, McConnell and
Strand, 1981, Vaughn and Russell, 1982, Morey and Rowe, 1985, Rowe, Morey,
Ross, and Shaw, 1985, Samples and Bishop, 1985, Donnelly, Loomis, Sorg, and
Nelson, 1985, Morey and Shaw, 1986, Cameron and James, 1986, 1987, Thomson and
Huppert, 1987, Cameron 1988a, Cameron and Huppert, 1988, 1989, Agnello, 1988,
and McConnell and Norton, undated.
-------
6
dollar value on access to the resource, a single threshold value is offered
and the respondent is asked to indicate whether his personal valuation is
greater or less than this amount.
For the survey available for this study, the referendum CVM question
seems most easily interpreted as asking whether the respondent would entirely
cease to use the resource if the annual access fee ("tax") were equal to T.4
Let Y be the respondent's income, let q be the current number of trips per
year to the recreation site, and let M be the respondent's typical travel
costs (i.e. market cost of access and incidental expenses on complementary
market goods associated with one trip).5
With cross-sectional data, it is convenient to begin by assuming a
common utility function wherein access to the recreational resource can be
traded off against a composite of all other goods and services, z, for which
the price can be normalized to unity. If market goods (travel, etc.) are
consumed in fixed proportions with the number of recreation trips, then only
the number of trips appears separately in the utility function: U(z,q) - U(Y-
Mq.q).
Suppose a respondent to the CVM question indicates that he would
continue fishing under the hypothetical two-part tariff with fixed tax T and
marginal price M. This implies that his maximum attainable utility when
paying the tax and enjoying access exceeds his utility when forgoing all trips
4 A possible alternative interpretation of the question is addressed in
Appendix I.
5 These data do not allow accurate imputation of the opportunity costs of
travel time. Rather than invoking a completely arbitrary guess about time
•.osts, we opt to ignore this component while acknowledging that the empirical
.esults will certainly reflect this decision. To the extent that time costs
are important, the social values of access implied by the travel cost portion
of the model will be underestimated.
-------
and thereby avoiding both the tax and the travel costs associated with each
trip:
(1) AU(Y.M.T) - max, U(Y-M,.T.,) - U 0, or
AV(Y,M,T) - V(Y-T.M) • V(Y) > 0,
where U signifies the direct utility function and V the corresponding indirect
utility. Crucially, as pointed out by McConnell (1988), the optimal quantity
demanded in the first term of the direct utility formulation in (1) would be
endogenously determined and is presently unobserved.
The TCM question, however, concerns the respondent's optimal quantity
demanded under existing conditions. If the utility surface implied by the
discrete-choice CVM response truly describes the configuration of individuals'
preferences, then it should also be consistent with the current observed
behavior, namely demand for access days in an environment where per-day
specific access prices (beyond M) are currently zero.6 The Marshallian demand
function, q(Y,M), corresponding to the same utility function will be given by
the maximization of the Lagrangian:
(2) maxq U(Y-Mq,q) s. t. Y - z + Mq.
Theoretically, the utility maximizing decisions of economic agents,
whether real or hypothetical, should reflect the same underlying structure of
preferences. Conditional on the extent to which the functional form chosen
6 Except for the hypothetical nature of the discrete choice question in the
contingent valuation context, the models used in this paper have much in
common with the strategies employed in King (1980) and in Venti and Wise
(1984) , where consumer choices are modeled explicitly as the result of utility
maximization. In contrast, earlier empirical discrete choice/demand models
accommodated the choice process in a "reduced form" manner similar to the
approaches used in the literature on switching regressions or sample
selection.
-------
8
for U(z,q) is an adequate representation of the preferences of individuals in
this sample, this supposition will be used to impose parameter constraints
across the two parts of the model. Requiring that respondents' professed
behavior in a hypothetical context be consistent with their observed behavior
in real markets should attenuate the degree of bias due to the hypothetical
nature of the CVM question. In turn, the CVM information allows the
researcher to "fill in" some information about demand that is not captured by
the range of the currently observable demand data and it can temper biases in
the travel cost information due to underestimation of the true opportunity
costs of access.
One key question to be addressed in this study is whether CVM and TCM
data do indeed elicit the same preferences. When parameter constraints are
imposed across two models, it is also possible to allow the corresponding
parameters to differ, taking on any values the data suggest. This option
allows for a rigorous statistical comparison of the different utility
configurations implied by the CVM and the TCM data. Contingent on the
validity of the assumption of quadratic utility, one can test statistically
the hypothesis that the corresponding parameters in the two models are the
same. This is implicitly a test of whether professed behavior in the
hypothetical market is consistent with observed behavior in a real market. If
utility parameter equivalence is rejected, then one might suspect that the
contingent valuation technique and/or the travel cost method might be
unreliable in this specific application.
Travel cost models seem to enjoy broader acceptance than CVM models,
although rudimentary travel cost models like the one employed here can also
have serious deficiencies. Fortunately, if the researcher harbors prior
opinions regarding the relative or absolute reliability of these two types of
-------
9
information, these priors can be readily incorporated into the estimation
process. Consequently, even if parameter equivalence is rejected initially,
there will be some recourse.
In addition to these basic issues, this paper describes a number of
extensions which demonstrate the flexibility of this model as a prototype for
subsequent work in non-market resource valuation.
II. AN ILLUSTRATIVE EXAMPLE
Between May and November of 1987, the Coastal Fisheries Branch of the
Texas Department of Parks and Wildlife conducted a major in-person survey of
recreational fishermen from the Mexico border to the Louisiana state line.
The "socioeconomic" portion of the survey is most pertinent here. The
specific CVM question asked of respondents was: "If the total cost of all
your saltwater fishing last year was more, would you have quit fishing
completely?" At the start of each survey day, interviewers randomly chose a
starting value from the list $50, $100, $200, $400, $600, $800, $1000, $1500,
$2000, $5000, and $20,000. On each subsequent interview, the next value in
the sequence was used. Therefore, offered values can be presumed to have no
correlation whatsoever with the characteristics of any respondent. In
addition to this question, respondents were asked "How much will you spend on
this fishing trip from when you left home until you get home?" The survey
also established how many trips the respondent made over the last year to all
saltwater sites in Texas.7 Five digit zip codes were collected, which allows
establishment of residency in Texas.
7 Unfortunately, the duration of each trip is unknown, so it must be assumed
that the majority are one-day trips, which may or may not be entirely
plausible. Here, the term "trip" is used synonymously with "fishing day."
-------
10
Income data were not collected from each respondent, but the five-digit
zip codes allow merging of the data with 1980 Census median household incomes
for each zip code. Zip codes cover relatively homogeneous "neighborhoods," at
least when compared to income data on the county level, for example.
Individuals' consumption patterns tend to conform somewhat to those of their
neighbors, so median zip code income may be a better proxy for "permanent"
disposable income than actual current self-reported income. There is high
variance in median incomes across zip codes, so the Census income variable may
actually make a substantial and accurate contribution to controlling for
income heterogeneity among the survey respondents.8
In other work utilizing the entire dataset (Cameron, Clark, and Stoll,
1988) it has been determined that subsets of individuals in the sample exhibit
extreme behavior. The full sample has therefore been filtered somewhat for
use in this demonstration study. Since the initial models presume identical
underlying utility functions for all individuals, those who report more than
sixty fishing trips per year are discarded from the sample. It is relatively
likely that these individuals are atypical, since 90% of usable sample reports
fewer than this number of days. The median number of trips reported is
between eleven and twelve. This research is therefore clearly directed at
"typical" anglers.
It is also the case in the full usable sample from the survey that some
individuals respond that they would keep fishing if the cost had been $20,000
higher when $20,000 exceeds the median household income of their zip code.
8 While the use of group averages instead of individual income information
undeniably involves errors - in-variables complications in the estimation
process, the distortions may in fact be not much greater than they would be
with the use of self-reported income data in an unofficial context. It is
well known that many individuals have strong incentives to misrepresent their
incomes if they do not perceive a legal requirement to state them correctly.
-------
11
Since the assignment of value thresholds was completely exogenous, the
estimating sample includes only those respondents who were posed values up to
and including the $2000 offer. Everyone offered values greater than this was
excluded, regardless of their answer to the CVM question.
The final criterion for inclusion in the sample for this study was that
a respondent should not report spending more than $100 on this fishing trip.
Again, a very large proportion of the sample passes this criterion. When
market expenditures are reported to be much larger than this, it seems
reasonable to suspect that capital items have been included, so that it would
be invalid to treat these costs as "typical" for a single fishing trip.
Current expenditures over $2000 were reported by several respondents.
Descriptive statistics for the variables used in this paper are
contained in Table I.
III. THE STOCHASTIC SPECIFICATION
It may be helpful to think of the model developed in the following
sections as a nonlinear analog to a more familiar econometric model. The
conceptual framework is similar to a system of two equations with one right-
hand side endogenous variable, cross-equation parameter restrictions, and a
non-diagonal error covariance matrix. However, one of the dependent variables
is continuous and one is discrete, both equations are highly nonlinear in
parameters, and the simultaneity in the model involves an endogenous variable
which is not observed directly, but must be counterfactually simulated.
In order to have the option of constraining the coefficients of the
utility function (and hence the indirect utility function) as well as those of
the corresponding Marshallian demand function to be identical, the discrete
:hoice model and the demand equation must be estimated simultaneously. To fix
-------
Table I
Descriptive Statistics for the Variables
(n - 3366)
Acronym
Description
Mean
Std. dev.
median household income for respondent's
5-digit zip code (in $10,000)* (1980 Census
scaled to reflect 1987 income; factor-1.699)
3.1725
0.6712
M current trip market expenditures, assumed 0.002915 0.002573
to be average for all trips (in $10,000)
T annual lump sum tax proposed in CVM scenario 0.05602 0.04579
(in $10,000)
q reported total number of salt water fishing 17.40 16.12
trips to sites in Texas over the last year
I indicator variable indicating that respondent 0.8066 0.3950
would choose to keep fishing, despite tax T
PVIET proportion of population in respondent's 0.002497 0.006217
5-digit zip code claiming Vietnamese ancestry
a Dollar-denominated quantities are expressed in $10,000 units throughout
the study, so that squared income and squared net income do not become
too large, resulting in extremely small probit coefficient estimates
which thwart the optimization algorithm.
-------
12
ideas, it is helpful to begin by considering the two components of the joint
model completely separately, ignoring any potential error correlation.
A. A Separate CVM Choice Model
The decision to work within the framework of direct, rather than
indirect, utility functions buys easy characterization of the shapes of
consumer indifference curves. Under the hypothetical CVM scenario, the
respondent is asked to choose between ceasing to use the resource and paying
no lump-sum tax, or continuing to consume a revised optimal quantity of access
q(Y-T,M) at a new lower net income. Unless one can assume that there is no
income effect, q(Y-T,M) will probably be less than the current optimal
quantity, q(Y,M). But if, for the initial exposition, it is temporarily
assumed that the income elasticity of demand for access is zero, one can begin
by considering how the CVM component of the joint model should be estimated.
It will be convenient to model the discrete choice elicited by the CVM
question using conventional maximum likelihood probit (rather than logit)
techniques, where the underlying distribution of the implicit dependent
variable, the true utility difference, is presumed to be Normal. Since
AU(Y,M,T) in equation (1) can at best be only an approximation, assume that
for the ifch observation, AUi - AUj* + e , where is a random error term
distributed N(0, a2). AUt*, the systematic portion of the utility difference
on the right hand side of equation (1) will be represented in what follows as
f(xi,^).
In conventional probit models, AUa is unobserved, but if AUt is "large"
(i.e. AU£ > 0), one observes an indicator variable, It (the "yes/no"
response), taking on a value of one. Otherwise, this indicator takes the
value zero. In constructing the likelihood function for this discrete
response variable, the following algebra is required:
-------
13
(3) Pr( IA - 1 ) - Pr ( AU. > 0 ) - Pr ( ^ > - fCx^/9) ).
Since eL has standard error a, dividing through by a will create a standard
normal random variable, Z, with cumulative density function
(4) Pr( et > - Xi'£ ) - Pr ( Z > - f(x.lt0)/o )
- Pr ( Z < f(xi,^)/a )
- 9 (f(xi,^)/a),
by the symmetry of the standard normal distribution.
At best, in cases where f(x ,0) is linear-in-parameters, the vector 0
can only be identified up to a scale factor, since it only ever appears in
ratio to a. (However, this is quite acceptable, because the solutions to the
consumer's utility maximization problem are invariant to monotonic
transformations of the utility function.) The probability of observing It - 0
is just the complement of Pr^ - 1), namely 1-4 (f (xA ,$)/^)/a)] + (1 - It) log { 1 -[* (f(xL,0)/o)] }
If f(xit0) was linear in and if q(Y-T,M) could be observed or assumed
to be equal to q(Y,M), this separate discrete choice model could readily be
estimated by any number of maximum likelihood routines in packaged statistical
programs (such as SAS or SHAZAM). For compatibility with what follows,
however, when q(Y-T,M) is made endogenous, this application requires a general
MLE algorithm. (In this paper, the GQOPT nonlinear function optimization
package is used). The endogenous demands, q(Y-T,M) will be functions of the
same parameters appearing in (5). When the formulas for these demands are
substituted into f(x. ,fi), these functions will usually no longer be linear
functions of the £ parameters.
-------
14
B. A Separate Demand Model
The systematic portion of the TCM Marshallian demand function resulting
from the optimization problem in (2) will be denoted by gCx^/9) . In
estimating this model separately, one might assume that q1 - gCx^) + r^,
where r) N(0, vz) . This suggests that nonlinear least squares (by maximum
likelihood) is an appropriate estimation method.
The log-likelihood function associated with the demand model is
therefore:
(6) log L - -(n/2)log(2ir) - n log v - (1/2) Zt{ [q4 - g(x1(0)]/u}2
Again, there exist packaged computational routines to estimate such
nonlinear models, but this application requires a general function
optimization program to allow for subsequent constrained joint estimation of
this model and the utility difference model.
C. Constrained Joint Estimates, Independent Errors
To impose the requirement that the two decisions (one real and one
hypothetical) reflect the identical underlying utility function, the CVM and
TCM models must be estimated simultaneously. With independent errors, it is
simple to combine the two specifications by summing the two separate log-
likelihood functions and constraining the corresponding Pi coefficients in
each component to be the same:
(7) log L - -(n/2)log(2w) • n log u - (1/2) ^ { [qt - g(x1,^)]/v}2
+ S, { I, log [* (f(x1,/9)/a)] + (1 - I4) log ( 1 -[* (f(xlf0)/a)] ) }.
D. Constrained Joint Estimates, Correlated Errors
Realistically, unobservable factors which affect respondents' answers to
the CVM discrete choice question are simultaneously likely to affect their
-------
15
actual number of fishing days demanded. To accommodate the influence of
unmeasured variables, one can allow for a correlation, p, between the ei error
terms in the discrete choice model and the »; error terms in the demand
model.9 Assume that these errors have a bivariate normal distribution,
BVN(0, 0, a2, v2, p).
In empirical discrete/continuous choice models, it is frequently more
convenient not to work directly with the joint distribution of the errors.
Instead, one can take advantage of the fact that the joint density can be
represented equivalently as the product of a conditional density and a
marginal density. In order to derive the model with nonzero p, one can
exploit the fact that for a pair of standardized normal random variables, say
Wj and W2, the conditional distribution of W2, given W " w , is univariate
Normal with mean (p wt) and variance (1 - p2) .
When allowing for nonzero values of p, then, the term #(f(x ,/9)/a) in
the discrete-choice portion of equation (7) will be replaced by:
(8) * { [(f(xlf0)/a) + p ZJ / (1 - p2)1/2 }
where Zi - [q± - g(xlt)9)]/u, the standardized fitted error in the demand
function, evaluated at the current parameter values. Clearly, if p - 0, this
model collapses to the model with independent errors described in the previous
section.
IV. AN EXPLICIT FUNCTIONAL FORM AND CLASSES OF RESULTS
The basic model proposed in this paper (and its variants) uses a
quadratic direct utility specification for U(z,q). Other discrete/continuous
If the estimated value of the error correlation, p, is substantial and
statistically significant, one probably ought to generalize the specification,
if possible, to accommodate systematic heterogeneity across respondents.
Section V will address this issue.
-------
16
modeling exercises have begun with an indirect utility function, since
commodity prices (rather than quantities) are more plausibly assumed to be
exogenous for the typical consumer. In the present context, however, we
desire to maintain the geometric intuition behind direct utility functions and
their associated indifference curves.10 We have selected the quadratic form
for the direct utility function because of its simplicity and because a number
of other familiar specifications are unsuitable for the derivation of
associated Marshallian demand functions (also discussed in Appendix II).
For identical consumers, the simplest quadratic direct utility
specification is:
(9) U(z,q) — f}^ z + f)2 q + z2/2 + zq + q2/2
Under the current scenario for the respondent, consumption of the Hicksian
composite good z is (Y - Mq) and q will be non-zero for anyone being
interviewed, so the utility function in (9) is really a function of Y and q.11
(9') U(Y, q) - 0l (Y-Mq) + 02 q + (Y-Mq)2/2 + (Y-Mq)q + 05 q2/2.
The specific form of the utility difference which dictates a respondent's
answer to the CVM question will be linear in the same parameters as U:
(10) AU(Y,M,T) - f(xt,0) - ^ {[Y-Mq-T] - Y} + fi2 q
+ 03 {[Y-Mq-T]2 - Y2)/2 + ^ [Y-Mq-T] q + 05 (q)2/2.
10 A quadratic indirect utility version of the model is discussed in Appendix
II. Unfortunately, the calibrated model does not satisfy the regularity
conditions for valid indirect utility functions.
11 In-person CVM surveys typically sample only current users of the resource.
When access price increases ( or simply positive access prices) are being
contemplated, this does not pose much of a problem. However, when projected
scenarios involved improved resource attributes, one must really survey
potential users as well as current users to elicit an accurate measure of
aggregate demand responsiveness.
-------
17
The first order conditions for the Lagrangian in equation (2) yield a
corresponding Marshallian demand for q of:
(11) q(Y,M) - g(xt ,0) - [ 02 + Y - 0l M - 03 Y (M) ] /
[ 20k (M) - M2 - 05 ].
Since every additive term in both the numerator and denominator of this
expression contains a multiplicative 0 coefficient, the demand function is of
course invariant to the scale of the 0 vector. Consequently, it is necessary
to adopt some normalization of the demand function parameters (for example,
02 - 1, an entirely arbitrary and inconsequential choice). Thus the form of
the demand function actually estimated will be:
(12) q(Y,M) - [ 1 + (0*) Y - (y91*)(M) - (0*) Y (M) ] /
[ 2(0*)(H) - (03*) (M)2 - 0* ].
where 0* - 0^/02. This demand function is highly non-linear in M.
Crucially, when we endogenize the q in equation (10) by substituting the
formulas for q(Y-T,M) based on the calibrated demand models in (11) or (12),
we are effectively converting the direct utility specification into an
indirect utility specification! But if the indirect utility function V(Y-T,M)
- U(Y-T,q(Y-T,M)) were to be written out in full, it would be a complex and
unappealing formula. Instead, we will describe our results in terms of the
implied direct utility function U(z,q).
The central empirical results in this study are the estimates of the 0
parameters of the assumed underlying quadratic direct utility function. All
of the economically interesting empirical measurements in this paper are
derived from this calibrated utility function. Throughout, the empirical
-------
18
utility function should exhibit properties which are consistent with economic
intuition about plausible shapes for these functions.
First, the derivatives of the underlying direct utility function are:
(13) au/az - + £3z + 04q a2u/az2 - p3
d\J/dq - p2 + /3,z + 05q a2U/3q2 - 05
d2U/dzdq -
The marginal utilities of the composite good z and of access days q will
depend on the local values of z and q. Whether or not each marginal utility
is increasing or decreasing will be revealed by the signs of fi3 and 05.
If both 03 and are negative, the fitted utility function will be
globally concave, and a globally optimal combination of z and q will be
implied. The budget constraint will be binding unless the implied global
optimum is attainable inside the budget set. The formulas for the global
optimum will be strictly in terms of the estimated coefficients:
(14) qa"u - [-fi2 + (^ V*3>] / ^5 " <0*2/03>l
" - (-^ . 0kq*)/03
Admissible fitted quadratic utility functions are not necessarily
strictly concave, however. The bundle at which both marginal utilities go to
zero may correspond to a saddle point of the complete fitted utility function.
But only quasi-convexity in the positive orthant is required. To assess
compliance with this regularity condition, one can easily examine the
configuration of the fitted utility function's indifference curves.
An indifference curve through any arbitrarily chosen bundle (z',q') can
be identified by first determining the level of utility this bundle
represents:
-------
(15) U' - 01 z' + 02 q' + ^ z'2/2 + z'q' + 05 q'2/2.
To find all other bundles (z,q) which provide utility U', one merely sets up
the quadratic formula for z:
(16) (Pz/2)z2 + + 04q)z + [/32q + ($,/2)q2 - U'] - 0
Plots of empirical indifference curves are highly intuitive and relatively
novel and will be used throughout the discussion to highlight the differences
in estimated preference structures.
Once the corresponding Marshallian demand function has been calibrated
by joint estimation of the utility parameters, we are usually curious about
the implied price and income derivatives:
(17) 3q/3M — ( -a^M-^M^K^+^Y) - 2(^-^M) ] /
[2^M-/93M2-05]2
3q/3Y - [/V03M] / [2/3aM-/33M2-/95]2 .
From the demand curves, policy makers are also sometimes interested in
estimates of the reservation price. One simply sets q - 0 in equation (11)
and solves the resulting quadratic formula for (M). Given the current level
of M, the reservation level of any additional potential per-day access charge
can readily be determined.
One of the ultimate empirical objectives of this research concerns
estimation of the total social value of recreational access to this fishery.
One measure of value is the equivalent variation, E, which can be viewed as
the fixed tax which would make these anglers just indifferent between paying
the tax and continuing to fish, or not paying the tax and forgoing their
-------
20
fishing opportunities. Algebraically, E is given by the equation maxq U(Y-Mq-
E,q) - U(Y,0).
But completely depriving everyone of access to the resource is an
extremely drastic proposition. So we also consider the equivalent variation
formulas that give the social costs of limiting access to a proportion a of
current (fitted) access levels, where 0 < a < 1 . The equivalent variation
for such partial restrictions is given by maxq U(Y-Mq-E,q) - U(Y-aMq,aq).
Letting D - (2/9.M - ^M2 - , R - <02+/84Y-01M-03MY)/D and S -
-------
21
A general formula for partial loss of access could easily be devised, but this
paper will focus on the equivalent variations.
V. SPECIFIC EMPIRICAL ESTIMATES
A. The Basic Model
The "basic model" constrains the quadratic direct utility parameters and
the corresponding parameters in the Marshallian demand function for fishing
days to be identical. The model initially assumes equal reliability of the
two types of information (CVM and actual market demand), and allows the post-
tax quantity demanded in the discrete choice model to be determined
endogenously according to the same demand function. The model also allows for
correlated errors in the two decisions. The first pair of columns in Table II
give these results (the second pair of columns will be discussed later). Both
the estimated quadratic direct utility function parameters and the
corresponding implied (normalized) Marshallian demand parameters are provided.
The utility function Implied by these parameter estimates is globally
concave, with a slightly positively sloped principal axes for the ellipses
that form its level curves. (The relevant lower left portions of these curves
are interpreted as indifference curves). Of course, the quadratic form is
merely a local approximation to the true utility function. Nevertheless, if
the entire surface of the true utility function was quadratic, the apparent
global optimum of that function would be located at 28.4 fishing days and
$289,823 in median zip code income (compared to sample means of 17.4 fishing
days and $31,725 in income). Thus the utility function is well-behaved in the
relevant region. At the means of the data, the two marginal utilities are
positive. The implied price elasticity of demand at the means of the data is
-0.074 and the income elasticity is 0.078, although these elasticities change
substantially with deviations away from the sample mean values. To establish
-------
Table II
Fitted Quadratic Direct Utility Parameters
(with and without parameters constrained to be identical
for CVM and TCM portions of model)
Parameter
Constrained 0s
Point Est.
(Asymp. t-ratio)
Implied
**- P/P2
Unconstrained $s
Point Est.
(Asymp. t-ratio)
Implied
0*- P/P,
(z)
h
P3 (z2/2)
(zq)
(q2/2)
*1 *-^2
3.309
(8.237)a
0.1192
(19.55)
-0.1167
(-1.836)
0.002579
(2.006)
-0.006837
(-22.80)
16.01
(81.98)
0.2315
(9.086)
27.76
1.0
-0.9790
0.02164
-0.05736
1.276
(0.7457)
28.17
(2.573)
1.498
(2.834)
2.263
(2.147)
-502.3
(-1.311)
75.89
(5.756)
1.0
-10.89
(-2.428)
-0.01749
(-0.9029)
-0.04739
(-14.97)
15.97
(82.04)
0.2505
(9.749)
0.04530
1.0
0.05318
0.08033
-17.83
max Log L -15708.17 -15640.61°
a Asymptotic t-ratios in parentheses.
b CVM utility parameters do not satisfy regularity conditions.
0 Likelihood ratio test statistic for four parameter restrictions - 115.12.
Equivalence of utility parameters is soundly rejected.
-------
22
a visual benchmark for this basic model, for art individual with mean income
and travel costs, an indifference curve for the empirical quadratic utility
function, the budget constraint through (my.O). and the fitted maximum
attainable indifference curve are shown in Figure 1.
Using the basic constrained model that assumes one common utility
function for all respondents, it is possible to use equation (18) to compute
fitted values for the equivalent variation (either for each respondent, or at
the means of the data). Across the 3366 respondents in this sample, the
fitted values of E for a complete loss of access appear in the first row of
Table III (a - 0).12 Over the estimating sample, the average point estimate
for the equivalent variation for a complete loss of access is $3451 (or,
alternatively, at the means of the data, it is $3423). Minimum and maximum
values in the sample are also provided.
Table III also gives the model's estimates for the equivalent variation
associated with successively smaller restrictions on days of access (a denotes
the proportion of current consumption to which each individual's access days
are restricted).13 For an across-the-board 10% reduction in fishing days, for
example, the average calculated utility loss by these respondents would be
only $35, although values as high as $52 and as low as $19 can obtain, due
solely to different incomes and travel costs faced by different respondents.
The main policy interest in equivalent variations for partial
restrictions on access stems from the need to make optimal allocations of
finite fish stocks between recreational anglers and commercial harvesters. If
12 For the single individual with average characteristics in Figure 1, this
quantity would be determined by taking the parallel downward shift in the
budget constraint which would leave the new constraint just tangent to the
lower indifference curve.
13 The computed equivalent variation, plotted as a function of a, is convex
when viewed from below.
-------
other
goods
($'0000)
3.9
EMPIRICAL PREFERENCES
3.6
\ . maxU(Y.M)
3.0'
2.7"1-
0.8
\
V
\
U(Y,0)
budgec
constraint
^q(Y,M)
6.0
12.0
13.0
24.0
30.0
36.0
fishing
access days
Figure 1 - Indifference curves at optimum and at zero access
days, for respondent with mean income and travel costs.
-------
Table III
Fitted Individual Equivalent and
Compensating Variation Estimates* for
the Basic (Constrained) Model (Table II)
Valuation mean max min
Measure:
Equivalent
Variation
a - 0.0b
$ 3451
$ 5132
$ 1857
a - 0.1
2799
4166
1505
CM
O
1
a
2214
3298
1190
a - 0.3
1697
2529
912
a — 0.4
1248
1861
670
a - 0.5
867
1294
465
a - 0.6
555
829
298
0
1
0
313
467
168
a - 0.8
139
207
75
a - 0.9
35
52
19
Compensating
Variation
a - 0.0 $ 3560 $ 5361 $ 1899
* Since the sane utility function is presumed for
all respondents, individual variations in
these quantities stem solely from differences in
income and travel costs.
k For access days restricted to the fraction a of
fitted current access days.
-------
23
faced with a proposal to cut back on recreational access, it would be
necessary to quantify the social losses to recreational anglers, compare these
losses to the anticipated gains accruing to commercial harvesters, and then to
argue that such a redistribution of the catch would result in a potential
Pareto improvement.1*
The final row of Table III provides, for comparison, the corresponding
compensating variation for a complete loss of access (i.e. for a - 0 only).
As is typical, the compensating variation for the loss is larger than the
equivalent variation for the same loss. Here, however, the difference is
largely an artifact of the quadratic form chosen for the utility function.
The concentric ellipses which form the level curves of a globally concave
utility function can be expected to have this relationship.
B. Different Preferences Implied by Real versus Contingent Data
We require both a constrained and an unconstrained specification if we
plan to use a formal likelihood ratio test statistic to determine whether the
utility parameters implied by the CVM data alone are consistent with those
estimated jointly using both CVM and TCM data. The constrained specification
(the basic model just described) appears in the first pair of columns in
Table II.
For the unconstrained model, the demand information necessary to compute
the endogenous quantity in the CVM discrete choice model is calculated using
only the utility function parameters for the CVM portion of the model. We
therefore allow the discrete choice CVM model exclusively to imply values for
14 In a richer specification, with enough shift variables to more closely
capture the variations in quantity demanded, it would be an interesting
exercise to assess total aggregate losses due to restrictions of access to
specific numbers of days. The present data are not appropriate for simulating
these policy changes.
-------
0X, P2, 03, and 05. The observed TCM demand decisions will imply separate
values for and fi5*.
The second pair of columns in Table II displays results for an
unconstrained model corresponding to the first pair of columns in the same
table. The point estimates do not bode well for the consistency of the
preferences elicited by the two types of responses. First of all, it is
especially unsettling to note that the quadratic direct utility function
implied by the CVM data alone does not even conform to the regularity
conditions expected of a valid utility function. At the means of the data,
the implied marginal utility from an additional access day is negative; there
is also increasing marginal utility with respect to the composite good. The
TCM quadratic direct utility parameters, however, are thoroughly acceptable.
(The only link between the two submodels is the estimated error correlation,
P¦)
Nevertheless, there must still be some information about preferences in
the CVM data, and the recorded responses on these surveys dictate these
particular parameter values. We can certainly still compare the maximized
value of the log-likelihood in the constrained and unconstrained models in
order to assess whether the imposition of cross-equation parameter
restrictions is tenable. A likelihood ratio test for the set of four
parameter restrictions embodied in the "basic" model soundly rejects these
restrictions.13 For this quadratic specification, the CVM- and TCM-elicited
preference functions are different.
15 It may be suspected that the TCM estimates systematically understate the
true value of access (due to underestimates of the actual opportunity costs of
access) and that the CVM estimates systematically overstate the true value of
access (due to the incentives embodied in the way the question was posed). If
data deficiencies make it too implausible to force compatibility of these
responses with a common underlying set of preferences, the researcher would of
course be free to report the two types of value estimates separately.
-------
25
For a respondent with mean characteristics, Figure 2 shows the empirical
indifference curves passing through the bundle (0,Y) for (i.) the "basic"
constrained model and (ii.) the demand portion of the unconstrained model.
The greater curvature of the indifference curve for the restricted parameters
implies that E (the equivalent variation) based on the joint model, will be
substantially larger than E based on observed TCM market demand behavior
alone. For the unrestricted TCM demand parameters, the fitted equivalent
variation at the means of the data is only $1686 (versus about $3451 for the
constrained model).
The implied inverse demand functions corresponding to the different sets
of preferences implied by the joint model and by the unconstrained TCM model
are shown in Figure 3. When the CVM responses and observed TCM demand
behavior are constrained to reflect the same set of quadratic preferences, the
reservation price is about $409. The unrestricted TCM demand behavior implies
a much lower reservation price. Thus the CVM (i.e. hypothetical market)
scenario does seem to invite respondents to overstate the strength of their
demand for resource access, as one might suspect (and/or the TCM indirect
market data understates the strength of demand).
C. Differing Reliability for Real versus Contingent Data
The basic model (with or without the utility parameters constrained
across the two sub-models) reflects the presumption that the decisions which
respondents claim they would make under the hypothetical scenario proposed in
the CVM question deserve to be treated as equally credible when compared to
their actual market behavior regarding number of fishing days demanded. This
need not be the case.
In other research on CVM (Cameron and Huppert, 1988), Monte Carlo
techniques were used to demonstrate the wide range of referendum CVM value
-------
EMPIRICAL PREFERENCES
budget
constraint
TCM
preferences
2.91
joint model
preferences
0.0
4.0
9.0
12.0
20.0
24.0
q
Figure 2 - U(Y,0) for respondent with mean travel costs,
according to constrainted joint model preference parameters
and according to TCM portion of model with separate sets of
preference parameters (CVM parameters fail to satisfy
regularity conditions and are not shown).
-------
fishing 20.0]T
access
days
(q)
ft
EMPIRICAL INVERSE DEMAND CURVES
i\
15. fl] \\
19.0
5.0
TCM \
preferences
joint model
preferences
\
0.8
0.0
125.0 251.0
375.0
i i r'
500.0 625.0 750.0
total price of access (M)
Figure 3 - Inverse demand curves corresponding to
constrained joint model preference parameters, and according
to TCM parameters from unconstrained model, for respondent
with mean income and travel costs. (CVM parameters do not
satisfy regularity conditions and are not shown.)
-------
26
estimates which can result simply as an artifact of the arbitrary assignment
of the threshold values on the questionnaires. One conclusion in that study
was that researchers should probably insist on vastly larger samples for
referendum CVM data, in order to offset the inefficiencies in estimation which
result from the highly diffuse information in referendum responses. By
itself, this property of referendum data might be sufficient to warrant a
discounting of its credibility when it is combined with "point" information
from the same sized sample.
Fortunately, researchers are free to use their own prior opinions to
adjust the relative credibility of each type of information. This can be done
in an ad hoc fashion, by employing non-unitary weights on the respective terms
in the log-likelihood function (see Appendix IV). Alternately, it can be done
more rigorously, by making assumptions about the variances of the
distributions of the estimated /9 parameters around the "true" mean of the £
vector.16
In the discussion that follows, we assume that CVM data are presumed to
be less reliable than travel cost data, since this has been a typical
sentiment among researchers in this area. However, the demand information
inferred from the travel cost data is also likely to be unreliable, especially
since TCM applications often assume that the opportunity cost of access is
constant as access days increase. If opportunity costs rise, as they most
likely do, TCM will underestimate the implicit value of access, perhaps
severely.17 Also recall that we do not impute an arbitrary value of travel
16 We owe this helpful suggestion to Ed Learner.
17 If increasing opportunity costs of access can be captured in the data,
there exist econometric strategies for dealing with non-linear budgets sets
which could undoubtedly be adapted to this type of problem. (See Hausman,
1985.)
-------
27
time in this study. Depending upon the relative qualities of the two types of
data, then, appropriate discounting of each type of information can be decided
ex ante.
Utilizing Explicit Priors on the Distributions of 0 and 0*
Let 0 continue to denote the utility parameter estimates derived from
the CVM data, and let 0* be the utility parameter estimates from the TCM data.
Let 0r signify the true but unknown utility parameter vector. (Without loss
of generality, we can normalize the second element, 02, to unity in all three
cases.) Now assume that conditional on the true 0T, 0 and 0* are
statistically independent and that the elements of 0/0T are distributed
N(l,a2) and the elements of 0*/0r are distributed N(l,
-------
28
What are the consequences for our ultimate estimates of the equivalent
variation for a complete loss of access? In Table IV, the first column,
reproduced from Table II, reflects an implicit assumption that a - a - 0.
(The implied Marshallian demand parameters corresponding to the CVM portion of
the model are given in the second column.) Nothing is "tying together" the
two sets of estimates for the utility parameters, so they are very different
indeed.
In contrast, for arbitrarily selected standard errors a - 1.0 and
a - 1.0, the third column of Table IV displays the revised estimates of 0 and
"ft t
$ , along with the additional, separate, estimates of the true & . (The
fourth column again shows the Marshallian demand parameters implied by the CVM
P estimates.) Ultimately, of course, we are interested in the value
implications of the estimates. At the means of the data, these "true" /9T
parameters imply an equivalent variation for a complete loss of access of
$3378 (which is very little different from the $3423 at the means of the data
for the basic model).
To illustrate a more-extreme case, we also include another pair of
columns in Table IV. In this case, the assumed standard error of /9//3T (for
the CVM parameters) is increased to 3.0. A standard error this large would
seem to discredit the CVM data substantially. The assumption of poorer-
quality information has the anticipated effect upon the precision of the three
sets of utility parameters in the model. The asymptotic t-ratios for all of
the different fi parameters drop substantially, with the coefficients on z2
and zq becoming insignificant in all three cases. However, the resulting
equivalent variation according to /31 shrinks only to $3124.
To assess the sensitivity of the parameter estimates and the welfare
implications to different assumptions about the distributions of and $*
-------
Table IV
Joint Models with Separate CVM and TCM Parameters
(CVM and TCM discounted by disproportionate variances)
no a, a*, <7 -1.0 - 3.0
a2 - 1.0 a2 - 1.0
Parameter Point Implied Point Implied Point Implied
Est. 0* Est. 0* Est. 0*
0, (z)
02 (q)
03 (zV2)
0„ (zq)
0* (q /2)
e2*-e2/f>2
P3*'03/02
e*-P
-------
(relative to £T), one can perform a grid search across different values of a
and a* to produce a range of values for the "true" f) coefficients and for the
implied equivalent variations. These are summarized in Table V. (Since these
functions are extremely expensive to optimize, we provide results only for
combinations of a and a* where a > a*. It seems likely, a priori, that the
CVM data are at least as noisy as the TCM data, although both may be
questionable.) The implied equivalent variations, EV, for each set of error
assumptions, appear in bold print, implying a surprising robustness of the
value estimates to differing reliabilities of the two types of data.
What conclusion is implied? A very wide range of different assumptions
can be made about the relative reliability of CVM and TCM data, without
producing too much difference in the ultimate welfare implications of the
fitted preference functions. This result should be greatly reassuring,
although it is conditional upon the maintained hypotheses of quadratic direct
utility and has been demonstrated for this one sample only.
D. Accommodating Respondent and/or Resource Heterogeneity
The models described above have presumed that these respondents are
homogeneous on all dimensions other than income, Y, proposed tax, T, number of
fishing days, q, and typical market expenditures, M. It is a simple matter,
however, to relax this assumption.
For example, one can explore the effects of allowing the utility
parameters to vary continuously with the level of a sociodemographic variable.
In the ad hoc valuation models explored in Cameron, Clark, and Stoll (1988),
it was found that the Census proportion of people in the respondent's zip code
who report themselves as being of Vietnamese origin, PVIET, seemed to be
-------
Table V
Results of Grid Search across Different Error Assumptions
For the Distribution of the CVM and the TCM Parameter Vectors
Travel Cost
Contingent Information:
Valuation
Information: a* -0.5 1.0 1.5 2.0 2.5 3.0
0.5
Hi
hi
*5T
EV at means:
1.0
hi
^1
^5
EV at means:
1.5
Pul
*5T
EV at means:
2.0
fill
hi
fiul
fis
EV at means:
2.5
fill
fi,
*T
3.0
EV at means:
ft T
fizl
fiul
fibT
EV at means:
27.90
-1.021
0.02139
-0.05742
$3412
28.15
-1.070
0.02108
28.30
-1.134
0.02070
-0.05735
-0.05763
$3395
$3378
28.64
28.75
29.01
-1.177
-1.224
-1.335
0.02043
0.02013
0.01944
-0.05720
-0.05750
-0.05796
$3364
$3348
$3320
29.39
29.53
29.74
-1.331
-1.391
-1.482
0.01947
-0.05698
$3317
30.53
-1.566
0.01802
-0.05665
$3245
32.17
-1.887
0.01600
-0.05617
$3141
0.01910
-0.05725
$3300
30.64
-1.614
0.01770
-0.05692
$3229
32.32
-1.945
0.01561
-0.05642
$3125
0.01852
-0.05773
$3272
30.84
-1.702
0.01712
-0.05738
$3202
32.51
-2.025
0.01506
-0.05686
$3099
30.10
-1.636
0.01852
-0.05773
$3233
31.10
-1.820
0.01633
-0.05805
$3165
32.77
-2.142
0.01427
-0.05749
$3062
31.51
-1.998
0.01516
-0.05892
$3116
32.96
-2.247
0.01350
-0.05840
$3019
33.08
-2.347
0.01270
-0.05963
$2970
3
The values for EV may or may not be statistically significantly different.
They are the solutions of the elaborate quadratic formulas given in
equation (18) in the body of the paper.
-------
30
influential in a wide range of models.19 Allowing this variable to shift the
parameters of the quadratic utility function, one can replace the constant 0
by the varying parameter (0^ + 7JPVIET1) for j - 1,...,5. Table VI
demonstrates that the PVIET variable does indeed make a statistically
significant difference to the overall fit of the model and to the parameters
of the utility function.20 Individually, only 75, reflecting the additional
curvature of the utility function with respect to fishing access days, is
statistically significantly different from zero. However, the whole set of
shift terms is jointly significant according to the likelihood ratio test
statistic value of 28.40 (where x* os(5) - 11.07).
A visual display of the effect on preferences of allowing for
heterogeneity with respect to the PVIET variable is displayed in Figure 4. As
benchmark levels, PVIET-0 and PVIET-.02 are selected. (Maximum PVIET in the
sample is 0.0649). Other than this distinction, the indifference curves
pertain to individuals both having the overall sample's mean income and travel
costs.
The higher the proportion of individuals of Vietnamese ancestry in the
respondent's zip code, the greater the curvature of the indifference curves,
and the larger the implied equivalent variation for a loss of access to the
fishery. Current optimal numbers of days are similar for the two
representative angl«rs, so the large discrepancy between the vertical
intercepts of the two empirical indifference curves suggests that while the
two socioeconomic groups exhibit similar current behavior, they respond
19 This is consistent with anecdotal evidence which suggests than many people
in this socioeconomic group supplement their diets with "recreationally-
caught" fish.
20 Both the income and PVIET variables are certainly measured with a degree of
error due to reliance on Census zip code means. With specific data at the
individual level, the following results would certainly be somewhat different.
-------
Table VI
Jointly Estimated Model;
Heterogeneous Utility Function
(varies with proportion Vietnamese)
Coefficient
and Variable
Estimate
(asy. t-ratio)
Pi (z)
02 (q)
03 (z2/i
(zq)
P5 (q2/2)
7j (zPVIET)
72 (qPVIET)
73 (z2PVIET/2)
7, (zqPVIET)
7, (q2PVIET/2)
2.897
(2.761)
0.1195
(14.87)
0.1210
(0.3711)
0.003829
(1.800)
-0.007125
(-21.84)
96.64
(0.7534)
-0.08279
(-0.09106)
-58.89
(-1.467)
-0.3573
(-1.395)
0.08352
(6.583)
15.95
(81.93)
0.2302
(8.971)
Max. logL
-15693.97a
a Compare to basic model in Table II.
-------
4.5
other
goods
($'0000)
ALLOWING FOR SOCIODEMOGRAPHIC HETEROGENEITY
4.0' \
joint model
preferences when
PVIET - 0.02
joint model
preferences when
PVIET - 0.00
/
budget constraint
s
2.5
9.8
i
6.0 12.0 18.0 24.0 30.8 36.0
q (fishing access days)
Figure 4 - Systematic variation in preferences when utility
parameters are allowed to vary linearly with the zip code
proportion of census respondents of Vietnamese origin.
Plotted for respondent with mean income and travel costs.
-------
fishing 23.0
access
days
EMPIRICAL INVERSE DEMAND CURVES
(q)
10.3
for joint model
preferences
when FVIET - 0.02
for joint model
preferences
when PVIET - 0.00
300. a
123.3
373.0
623.0
733.3
price of access (M)
Figure 5 - Differences in empirical demand curves according
to proportion Vietnamese for two respondents with otherwise
identical income and travel costs.
-------
31
systematically differently to the hypothetical CVM question. Respondents from
zip codes with higher proportions of population with Vietnamese ancestry are
more inclined to claim that they would continue to fish despite substantial
annual access fees. Figure 5 shows how these different preferences translate
into systematically different inverse demand curves. The demand curve for the
PVIET - 0.02 group is situated considerably further out than that for the
PVIET - 0 group.
What is the policy significance of the finding that preferences for
fishing access can vary across sociodemographic groups? Different preferences
imply that any policy measure the government might contemplate will have
distributional consequences. This will be true whether the policy affects
real incomes or the relative price of access or if it consists of access
restrictions. Distributional effects can be of critical importance in policy-
making.
Ethnic differences are just one of a variety of sources of heterogeneity
which could be recognized explicitly in resource valuation models of this
type. For models intended to allow simulation of specific policy measures, it
will also be important to incorporate dimensions of heterogeneity which can be
affected by these policy actions. For example, individual values for access
to a recreational fishery are affected not only by angler characteristics, but
also by attributes of the resource in question. In one illustration, for a
subsample of this dataset, we have addressed the effects on social value of
respondent's perceptions about pollution levels (Cameron, 1988b). Not
surprisingly, deteriorating environmental quality reduces the demand for
access and diminishes the social value of the resource. Likewise,
improvements increase social value. This type of model can be used to
-------
32
simulate anticipated social benefits accruing to recreational anglers if
government or private expenditures are devoted to cleanup efforts.
We have also supplemented a subset of the survey data used here with
independently gathered data on the abundance of the primary gamefishing target
species (Cameron, 1988c). The experiment reveals that garaefish abundance
makes intuitively plausible and statistically significant differences in
preferences and therefore in the social value of the resource. This type of
model can be used to simulate the social benefits to recreational anglers as a
consequence of fish stock depletions or enhancement programs.21
VI. CONCLUSIONS AND CAVEATS
A fully utility-theoretic specification distinguishes this analysis from
much earlier empirical work on the valuation of non-market resources. By
concentrating on identifying the underlying preference structure for access
days versus all other goods and services, theoretically sound measures of
access values (equivalent and compensating variations) can readily be
produced.
Several features of the "basic" model should be emphasized. First, it
starts from an assumption of quadratic direct utility, presumed to explain the
hypothetical contingent valuation responses. Second, the associated non-
linear Marshallian demand functions are employed to explain the observed
demand decisions by the respondents (a "travel cost" type of model). Third,
the corresponding parameters in the utility and the demand functions are
21
For our three examples of how respondent and resource heterogeneity can be
accommodated in this prototype model, we have assumed that these sources of
heterogeneity are mutually orthogonal, so that they may be entered
individually and separately. For sufficiently large surveys, the complexity
of these heterogeneous models is limited only by the variables upon which data
have been collected and by computing capacity. Very elaborate models can
potentially be accommodated.
-------
33
constrained to be identical. Fourth, the quantity demanded under the CVM
scenario is fully endogenized. And finally, unobservable attributes of
respondents are allowed to affect both types of responses simultaneously
through a non-zero (estimated) error correlation.
The "basic model" forms a minimal prototype for models in a wide range
of applications in resource valuation. However, this paper has also described
a variety of important extensions --potentially very relevant to subsequent
researchers. "Prior" assumptions about the relative qualities of the
hypothetical CVM questions and the "real" travel cost data can be used to
modify the influence of each of these responses during joint estimation the
utility parameters. Examples have also demonstrated that it is
straightforward to allow the parameters of the quadratic preference structure
to vary systematically with the levels of (exogenous) respondent or resource
attributes.
To review the central empirical findings (for these data, in combination
with the assumption of quadratic preferences), the "basic model" yields a
sample average fitted equivalent variation of $3451 for a complete loss of
access to the fishery. In contrast, if access days for each individual were
restricted by only 10%, the average equivalent variation would be only $35.
The implications of the model for small local variations are probably more
reliable, although in this case, the complete loss is explicitly "within the
range of the data" because of the information extracted from the CVM
responses.
Some caveats should be emphasized. The sample for this application was
consciously trimmed along a number of dimensions. Most notably, anyone who
reported fishing more than 60 days per year was dropped from the sample. When
attempting to fit a single utility function to an entire sample, the
-------
34
assumption of identical preferences must be at least roughly tenable. People
who fish more than 60 days per year probably have fundamentally different
preferences. With enough detailed information about the exogenous
sociodemographic attributes of these individuals that might account for these
differences, one could accommodate broad heterogeneity. This survey, however,
provides little such information. In order to highlight the capabilities of
the. model (without obscuring the relationships due to unrecognized
heterogeneity), it is necessary to disenfranchise some extremely avid anglers.
Consequently, if these average values are scaled up to the population of
anglers, the total will underestimate the true value of the fishery.
Fortunately, with more detailed surveys (and future generations of computing
hardware and software), more comprehensive models will certainly be
practicable.
From a policy standpoint, it is also critical to emphasize that in many
applications, the benefits computed for the group of resource users
represented by the survey sample will comprise only a portion of the total
social benefits generated by the resource. Non-consumptive use of the
resource will often be substantial; option and existence value can sometimes
be larger by orders of magnitude than the user values implied by surveys such
as the one analyzed in this study. The dollar measures of benefits produced
here, for example, are only a lower bound on the total social benefits enjoyed
by residents of Texas, the rest of the United States, the continent, or the
entire world.
Methodologically, this research has demonstrated that it is indeed
feasible, and probably highly desirable, to employ referendum contingent
valuation data in the context of a fully utility-theoretic model whenever the
quality of the data justify such an effort. These results also demonstrate
-------
35
that forcing contingent valuation utility parameter estimates to be consistent
with observed demand behavior can have a substantial effect on the estimated
preference structure, the implied demand functions, and ultimately on the
apparent social value of the resource or public good.
It has also been demonstrated that jointly estimating the
discrete/continuous choices of respondents without parameter constraints
allows a rigorous statistical check of the consistency of the hypothetical CVM
responses with demonstrated real market decisions (conditional on the
functional form chosen for utility). The implications of this dimension of
the problem are being explored in greater depth in some follow-up research.
Previous validation studies have typically relied on entirely separate models
for CVM data and other types of data, such as travel cost information or
market experiments. This earlier strategy allows comparisons of point
estimates of value, but precludes any statistical assessments of the degree of
similarity between the results. In contrast, the joint models presented here
permit standard likelihood ratio tests. For this sample, the hypothetical CVM
data and the observed TCM data appear to imply sharply different sets of
preferences if completely independent sets of utility parameters are
estimated. In other applications, however, consistent responses under the
real and hypothetical scenarios may be readily accepted. Such a finding would
reinforce the credibility of contingent valuation procedures in those
contexts.
When CVM and TCM data are combined in the estimation process, in order
to exploit all of the information available, it has been demonstrated that the
researcher can systematically accommodate into the estimation process any
"ior opinion regarding the relative reliability of the two types of data. It
-------
36
is possible to like the two source of preference information without forcing
the implied utility function to be exactly identical.
In sum, this research demonstrates the value of combining both
contingent valuation and travel data whenever possible. Pooling of these two
types of valuation information allows the advantages of each technique to
temper the disadvantages of the other. Making the underlying preference
structure of consumers the core of the analysis facilitates joint modeling of
the two decisions. It also allows a rigorous assessment of the probable
responses of individual consumers under a wide range of simulated
counterfactual scenarios, and permits welfare estimates which are consistent
with neoclassical microeconomic theory.
-------
37
REFERENCES
Agnello, R.J. (1988): "The Economic Value of Fishing Success: An Application
of Socio-Economic Survey Data," manuscript, Department of Economics,
University of Delaware.
Anderson, L.G. (1980): "An Economic Model or Recreational Fishing,"
unpublished manuscript, University of Delaware, December.
Bishop, R.C., and T.A. Heberlein (1979): "Measuring Values of Extramarket
Goods: Are Indirect Measures Biased?" American Journal of
Agricultural Economics 61, 926-930.
Bishop, R.C., T.A. Heberlein, and M. J. Kealy (1983): "Contingent Valuation
of Environmental Assets: Comparisons With a Simulated Market,"
Natural Resources Journal 23, 619-633.
Brookshire, D.S. and D.L. Coursey: "Measuring the Value of a Public Good: An
Empricial Comparison of Elicitation Procedures," American Economic
Review 77, 554-566.
Brookshire, D.S., M.A. Thayer, W.D. Schulze, and R.C. D'Arge (1982): "Valuing
Public Goods: A Comparison of Survey and Hedonic Approaches,"
American Economic Review 72, 165-177.
Cameron, T.A. (1988a): "A New Paradigm for Valuing Non-market Goods Using
Referendum Data: Maximum Likelihood Estimation by Censored Logistic
Regression," forthcoming, Journal of Environmental Economics and
Management.
Cameron, T.A. (1988b): "The Effects of Gamefish Abundance on Texas
Recreational Fishing Demand: Welfare Estimates," unpublished mimeo,
Department of Economics, University of California at Los Angeles.
Cameron, T.A. (1988c): "Using the Basic 'Auto-validation' Model to Assess the
Effect of Environmental Quality on Texas Recreational Fishing Demand:
Welfare Estimates," Department of Economics, University of California
at Los Angeles, Working Paper #522, September.
Cameron, T.A., J. Clark, and J.R. Stoll (1988): "The Determinants of Value
for a Marine Estuarine Sportfishery: The Effects of Water Quality in
Texas Bays," Department of Economics, University of California at
Los Angeles, mimeo.
Cameron, T.A., and D.D. Huppert (1988): "'Referendum' Contingent Valuation
Estimates: Sensitivity to the Assignment of Offered Values,"
Department of Economics, University of California at Los Angeles,
Working Paper #519, September.
Cameron, T.A. and M.D. James (1986): "The Determinants of Value for a
Recreational Fishing Day: Estimates from a Contingent Valuation
Survey," Canadian Technical Report of Fisheries and Aquatic Sciences,
No. 1503, Fisheries and Oceans, Canada.
-------
38
Cameron, T.A., and M.D. James (1987): "Efficient Estimation Methods for
'Closed-Ended' Contingent Valuation Surveys," Review of Economics and
Statistics 69, 269-275.
Clawson, M., and J.L. Knetsch (1966) Economics of Outdoor Recreation,
Washington, DC, Resources for the Future, 1966.
Cummings, R.G., D.S. Brookshire, and W.D. Schulze, eds. (1986) Valuing
Environmental Goods: An Assessment of the Contingent Valuation
Method, Rowman and Allanheld, Totowa, New Jersey.
CRC (1981): CRC Standard Mathematical Tables (26th edition) W.H. Beyer (ed),
Boca Raton: CRC Press, Inc.
Donnelly, D.M., Loomis, J.B., Sorg, C.F., Nelson, L.J. (1985): "Net Economic
Value of Recreational Steelhead Fishing in Idaho," Resource Bulletin,
United States Department of Agriculture, Forest Service, Fort
Collins, Colorado 80526.
Dubin, J.A., and D. McFadden (1984): "An Econometric Analysis of Residential
Electric Appliance Holdings and Consumption," Econometrica 52, 345-
362.
Hanemann, W.M. (1984a): "Discrete/Continuous Models of Consumer Demand,"
Econometrica 52, 541-561.
Hanemann, W.M. (1984b): "Welfare Evaluations in Contingent Valuation
Experiments with Discrete Responses," American Journal of
Agricultural Economics, 66, 322-341.
Hausman, J.A. (1985) "The Econometrics of Non-linear Budget Set,"
Econometrica (November) 1255-1282.
Huppert, D.D. (1988): "An Examination of Nonresponse Bias and Divergence
Among Value Concepts: An Application to Central California
Anadromous Fish Runs," Draft report, National Marine Fisheries
Service, Southwest Fisheries Center, La Jolla, CA 92037 (May 26,
1988) .
King, M. (1980) "An Econometric Model of Tenure Choice and the Demand for
Housing," Journal of Public Economics, 14, 137-159.
Maddala, G.S. (1983): Limited-dependent and Qualitative Variables in
Econometrics, Cambridge University Press, Cambridge.
McConnell, K.E. (1988): "Models for Referendum Data," unpublished
mimeograph, Department of Agricultural and Resource Economics,
University of Maryland.
McConnell, K.E. (1979): "Values of Marine Recreational Fishing: Measurement
and Impact of Measurement," American Journal of Agricultural
Economics 61, 921-925.
-------
39
McConnell, K.E. and V.J. Norton, (undated) "An Economic Evaluation of Marine
Recreational Fishing: A Review," Department of Resource Economics,
University of Rhode Island, Kingston, Rhode Island 02881.
McConnell, K.E. and I.E. Strand (1981): "Some Economic Aspects of Managing
Marine Recreational Fishing," in Economic Analysis of Fishery
Management Plans, L.G. Anderson (ed.), Ann Arbor Science Publishers,
Ann Arbor, Mi, 245-66.
Mitchell, R.C., and R.T. Carson, (1989) Using Surveys to Value Public Goods:
The Contingent Valuation Method, Resources for the Future,
Washington, D.C.
Morey, E.R. and Rowe, R.D. (1985): "The Logit Model and Exact Expected
Consumer's Surplus Measures: Valuing Marine Recreational Fishing,"
unpublished manuscript, Department of Economics, University of
Colorado.
Morey, E.R., and W.D. Shaw (1986): "The Impact of Acid Rain: A
Characteristics Approach to Estimating the Demand for the Benefits
from Recreational Fishing," Department of Economics, University of
Colorado, Boulder, CO 80903.
Rowe, R.D., E.R. Morey, A.D. Ross, and W.D. Shaw (1985): "Valuing Marine
Recreational Fishing on the Pacific Coast," Report prepared for the
National Marine Fisheries Service, National Oceanic and Atmospheric
Administration, La Jolla, California.
Samples, K.C., and R.C. Bishop (undated): "Estimating Social Values of Sport
Caught Fish: A Suggested Approach," unpublished manuscript,
Department of Agricultural and Resource Economics, University of
Hawaii-Manoa, Honolulu, HI 96822.
Samples, K.C., and R.C. Bishop (1985): "Estimating the Value of Variations in
Anglers' Success Rates: An Application of the Multiple-Site Travel
Cost Method." Marine Resource Economics, 55-74.
Schulze, W.D, R. D'Arge, and D.S. Brookshire (1981): "Valuing Environmental
Commodities: Some Recent Experiments," Land Economics 57, 151-172.
Sellar, C., J.R. Stoll and J.P. Chavas (1985): "Validation of Empirical
Measures of Welfare Change: a Comparison of Norunarket Techniques,"
Land Economics 61, 156-175.
Smith, V.K. (1988): "Selection and Recreation Demand," American Journal of
Agricultural Economics 70, 29-36.
Thomson, C.J. and D.D. Huppert (1987): "Results of the Bay Area Sportfish
Economic Study (BASES)," U.S. Department of Commerce, NOAA Technical
Memorandum, National Marine Fisheries Service.
Vaughn, W.J., and C.S. Russell (1982): "Valuing a Fishing Day: An
Application of a Systematic Varying Parameter Model," Land Economics
58, 450-463.
-------
40
Venti, S., and D. Wise (1984), "Moving and Housing Expenditure," Journal of
Public Economics 16, 207-243.
-------
40
APPENDIX I
An Alternative Interpretation of the Contingent Valuation Question
In this study, an alternative interpretation of the CVM question is
conceivably possible. Perhaps respondents think of the access fee T as
implicitly reflecting a price change at their current consumption level,
q(Y,M), rather than a lump sum tax. They may interpret the question as asking
whether or not they would choose non-zero access days if the price per day
went from M to M+(T/q(Y,M)). In this case, the the CVM question would seem to
be asking respondents whether their post-price change optimal consumption of
access days would be positive. (I.e. if their optimal number of access days
was negative, their highest utility would correspond to zero access days,
providing that preferences are well-behaved.) The results reported in this
paper have emphasized the "lump sum tax" interpretation, but some results for
the alternative "price change" interpretation are provided here for
comparison, since the interpretation does affect the resulting estimates of
resource value.
Rather than the utility-difference underlying the discrete response in
equation (5), this projected optimal consumption level would "drive" the
discrete choice portion of the model. A "yes" response implies that the
respondent's optimal consumption of access days under the hypothesized
scenario is positive. A "no" would mean that optimal consumption would
actually be negative, but zero days are the fewest which can be consumed. The
"yes/no" response thus provides censored information regarding the magnitude
of optimal quantity demanded. Unlike conventional probit models, where the
location of the distribution is unknown (and therefore set arbitrarily to
zero), the "threshold" in this case is exactly zero days. As above, g(x.,/9)
will be adopted as the generic representation for the Marshallian demand
-------
41
function corresponding to the quadratic utility model, where the variables xt
include income and the "price" of a day of access. As in Section III, i> can
be used as the same (constant) standard error of the conditional distribution
of quantities demanded. The magnitude of u can be inferred from observed
consumption under current prices, so the conditional dispersion of the
unobservable dependent variable in the CVM model is "known" (in contrast to
the conventional probit situation).
Providing, then, that it is reasonable to assume that real and
hypothetical behavior are derived from the identical set of underlying
preferences, the discrete responses to the CVM question can be used to
supplement the estimation of the underlying demand parameters. Specifically,
the expression (f(x. ,fi)/o) in equations (5) and (7) will be replaced by
g(x1*,^)/u, where xt* includes current actual income, but price M is replaced
by the hypothesized (M+T/q(Y,M)).
One difference under this interpretation of the CVM question is that
this specification no longer allows identification of the individual utility
parameters (01 through 05, up to the scale factor, a, of the unobservable
dispersion in the latent variable driving the CVM response). Only the demand
parameters, 0*, 0^*, and ps* and u can be identified. Fortunately, the
utility function is invariant to the scale of the parameters and arbitrarily
setting 02 - 1 will result in exactly the same implications in terms of
optimizing behavior.
The demand parameter estimates for the utility function under this
fundamentally different interpretation of the CVM question appear in
Table 1.1. It is not surprising that the point estimates differ
systematically from their counterparts in the body of the paper.
-------
42
For this version of the joint model, the marginal utilities at the means
of the data are positive; the price elasticity of demand for access days is
about -0.035; the income elasticity is 0.11. The implied global optimum is
20.2 access days and $78212 in median household income.
While the fitted utility function under this interpretation is
completely plausible from a theoretical standpoint, the implications of this
model are quite a bit different from the "lump-sum tax" interpretation. The
sample mean of the fitted equivalent variations for a complete loss of
resource access, according to these preferences, is markedly higher, at $7386
(with standard deviation $2244). Clearly, subsequent surveys will have to be
very careful in conveying to respondents exactly what type of scenario is
intended, since the interpretation of the question can make almost an order of
magnitude difference in the results.
-------
Table 1.1
Model with CVM Question Interpreted as Price Change
Parameter Point Estimate
(asymp. t-ratio)
0-,* (z) 19.80
(5.366)
/92* (q) 1.000
/93* (z2/2) -2.613
(-2.573)
/94* (zq) 0.03155
(1.726)
05* (q2/2) -0.06163
(-18.23)
16.18
(86.75)
0.08754
(3.080)
Max. LogL
-15708.12
-------
44
APPENDIX II
Alternative Direct and Indirect Utility Specifications
Other linear-in-parameters functions that have been widely used
empirically include the translog and the generalized Leontief specifications.
The translog is quadratic in the logarithms of the arguments, but it is
critical for the basic model in this paper that direct utility levels be
defined and non-zero when consumption of one commodity (namely, recreation
days) goes to zero. This disqualifies the ordinary translog model, since this
function is only defined over strictly positive quantities of each good.22
The generalized Leontief specification satisfies the boundary
requirements, and is generally considered to be a more "flexible" functional
form than the quadratic. However, while a generalized Leontief indirect
utility function can readily be differentiated to yield Marshallian demands,
this similar functional form for the direct utility function yields
Marshallian demands which are prohibitively complex.
Empirical research on consumer decisions has sometimes employed the
Stone-Geary utility function and its corresponding "linear expenditure system"
demand equations. This specification may at first seem attractive, but it too
is only appropriate when one is considering interior consumer optima. In this
case, the utility function would be:
ft ft
(II.1) U (z,q) - (z - pj 2 (q - £3)
The corresponding demand for fishing days will be given by:
22 One could, of course, shift the utility surface one unit towards the origin
along the dimension of each good by adding one to each quantity within the
functional form for the translog direct utility. However, when the direct
utility function, rather than the indirect utility function, takes on a
translog functional form, the associated Marshallian demand functions are
awkward to derive; they are even more awkward if the function is additively
shifted.
-------
45
(II.2)
q - 03 + (04/p) [Y - 0X - 03 p]
where the price of the composite good, z, has again been normalized to unity.
This utility function is not linear in parameters, so initial estimates
cannot be obtained via a conventional maximum likelihood probit package. But
there is a bigger problem, stemming from the necessity of considering utility
levels for zero days of access. In particular, the systematic portion of the
utility difference function, which would form the non-linear "index" function
for the discrete choice portion of the model, would take the following form:
The problem for estimation stems from the last term. The coefficient 04 is
often fractional. Attempting to take the 04-root of a negative number can be
expected to create difficulties. Furthermore, the usual interpretation of 03
is that is represents "subsistence" consumption levels of commodity q, so
negative values of the parameter itself are unlikely to result, or to be
defensible intuitively, if they do. As expected, in attempts to estimate this
model using the data employed in the rest of this study, the algorithm
persistently failed.
The quadratic form is a useful local approximation to any arbitrary
surface. Why not then expand to third-order terms? Several of the quantities
of interest which are derived from the calibrated model necessitate solving
the fitted utility function for the value of one of its arguments. The
standard formula for computing quadratic roots is straightforward to use. The
formulas for the roots of cubic equations are considerably less easy. (See
CRC, 1981, p.9.) However, continuing empirical research explores such forms,
@2
(II.3) AU - [(Y-M-T) - 0J [q - 03]
[ Y - ^ ] [ - 03 ]
-------
46
since the results for quadratic utility specifications suggest that a higher
degree of parameterization might be supported.23
Contemporaneous work by Huppert (1988) employs an alternative strategy
in the context of a standard simultaneous equations model. He begins with a
simple functional form (log-linear) for the Marshallian demand specification
and accepts the corresponding (unnamed) functional form for the underlying
utility function. Huppert's payment card contingent valuation responses are
treated as a continuous variable, so that the joint estimation of the utility
and demand parameters can be accomplished via standard packaged simultaneous
non-linear least squares algorithms.
It is interesting to compare the results derived using a quadratic
direct utility function (and implicitly its associated indirect utility
function) with those derived for a model that begins with an indirect utility
function which is quadratic in prices and income. This will imply a very
different function form for the direct utility function.
If indirect utility, V, is quadratic in the price of z, the price of q
(i.e. M), and income Y, the terms in the unitary price of z will be absorbed
into a constant and into the coefficients on M and Y. The effective
functional form will be:
(II. 4) V(M, Y) - qx M + a2 Y + a3 M2/2 + a4 MY + a5 Yz/2.
The corresponding Marshallian demand for q is given by application of Roy's
Identity:
23 The data appear to support cubed terms in z and q, but the optimization
algorithm cannot seem to settle upon coefficients for the second-order
interaction terms, z2q and zq2. The two cubed terms do make a statistically
significant improvement in the log-likelihood function for the model.
-------
47
(II.5) q(Y,M) - - (3V/3M)/OV/3Y)
-(-«!" «3M - a4Y)/(a2 + a4M + a5Y),
or, normalizing <*2 to unity:
(II. 6) q(Y,M) - (- a* - q3*M - a4*Y)/(l + a4*M + a* Y) .
The respondent will decide to pay lump sum tax T and continue fishing if
V(M.Y-T) > V(Y), i.e. , if
(II.7) AV(Y,M,T) - £(xl,j3) - ^ M + a2 (-T)
+ a3 M2/2 + a4 M(Y - T) + a, [(Y-T)2 - Yz]/2 > 0.
The equivalent variation, E, which would leave the respondent
indifferent between fishing and not fishing is given by the quadratic root E
of:
(II. 8) a5/2 E2 - [ az + c^M + a5Y ] E + [c^M + a3M2/2 + a4MY ] - 0.
The joint model can be set up as in the text of the paper, except now we
have f(xi,)3) - AV(Y,M,T) and g(xit0) is replaced by the Marshallian demand
formula derived in this section.
The indirect utility approach has the distinct advantage that it does
not require endogenous determination of post-tax quantity demanded, q(Y-T,M).
However, the direct utility specification corresponding to this representation
of preferences is prohibitively awkward to derive, so the intuitive advantages
of standard indifference curve diagrams are beyond our reach.
Nevertheless, it is straightforward to estimate the joint model of
indirect utility differences and the corresponding Marshallian demands. We
have done so. The parameter estimates appear in Table II.1.
-------
48
Unfortunately, while the direct utility approach used in the body of the
paper easily satisfies the regularity conditions for a valid utility function,
this is not the case for the quadratic indirect utility specification used
here. V(M,Y) should be nonincreasing in M and nondecreasing in Y. At the
means of the data, however, the parameters given in Table II.1 produce a value
of 97.87 for 3V/5M and a value of -5.653 for 3V/3Y. As a consequence of these
irregularities, the values we compute for the equivalent variation associated
with a loss of access are nonsensical. In other applications, however, the
indirect utility approach (possibly using alternative functional forms) may
prove to be satisfactory, or even preferable, to the direct utility model,
especially if it is deemed unnecessary to provide empirical indifference
curves as a visual aid.
*
-------
Table II.1
Quadatic Indirect Utility Specification
Parameter
0X* (M)
02*
03* (M2/2)
01* (MY)
05* (Y2/2)
Point Estimate
(asymp. t-ratio)
75.50
(6.642)
-4.123
(-6.667)
-4936.81
(-8.237)
11.59
(3.374)
-0.4929
(-2.624)
15.97
(82.04)
0.2043
(8.506)
Max. LogL
-15957.66
-------
50
APPENDIX III
Estimates in the absence of travel cost data
In some applications, M may be measured accurately and may be relatively
constant across fishing days, but in other cases, it may not. Sometimes, the
researcher may be better off ignoring the questionable information on M, and
using a simpler "Engel curve" model as opposed to a "demand function" (where
equation numbers indicate revisions of the original specification):
(1') AU - U( Y - T, q1 ) - U( Y, 0 ) > 0.
If the data on M are excluded, z will be identically Y.
(10') AU(Y,T) - 0l { [Y-T] - Y) + P2 q1
+ 03 {[Y-T]2 - Y2}/2 + [Y-TJq1 + 0, (qx)2/2.
(11') q(Y) - [ 1 + (0*) Y ] / [ - p* ].
(17') dq/dp - [ ^(^-^Y) - 2^(02+^Y) ] / lfl3}2
3q/3Y -
In order to appreciate the benefits of joint estimation with income data
and numbers of trips but in the absence of travel costs as proxy data for
prices, one can consider the estimates of the utility function parameters when
the data on M in this sample are ignored. Table III.l displays these results.
At the means of the data, these fitted parameters imply a utility function
with positive marginal utility from other goods, but very slightly negative
marginal utility from access days. This implies that the utility function in
this case is not globally concave. The saddle point of the utility function
is located at 12.25 access days and $-47348. Nevertheless, the level curves
are still convex to the origin. At the means of the data, the price
-------
elasticity of demand for access days is -0.125 and the income elasticity is
0.0682.
Figure III.l shows the effects on the fitted preference function of
ignoring travel costs in the estimation phase. As benchmarks, this figure
includes the "basic" indifference curve for a typical respondent (curve E) as
well as the indifference curve based on the CVM portion (curve A) and the
demand portion (curve D) of the unrestricted model. Here, however, attention
should be focused on the indifference curve for a model similar to the basic
model except that the available data on travel costs are ignored (curve A).
Even this very "thin" information about market demand pulls the parameter
estimates a long way away from the unrestricted CVM estimates depicted by
curve A. Still, it is not clear in this application that the resulting (much
smaller) equivalent variation estimates will be superior to those generated by
the CVM portion of the unrestricted model.
-------
Table III.l
Jointly Estimated Model Ignoring
Travel Costs (i.e. M - 0; Only Engel
Curves from Observed Demand Employed)
^ (z) 3.586
(1.342)
0. (q) 0.1259
(13.19)
03 (z2/2) 0.7711
(0.9538)
(zq) 0.005329
(2.058)
05 (q2/2) -0.008213
(-22.46)
u 16.12
(81.85)
P 0.2343
(9.076)
log L
-15679.17
-------
FigureH.I- For respondent with mean income and travel costs,
effects of ignoring travel costs during estimation
of utility parameters by modified basic model:
actual budget constraint (C), indifference curve
from basic model (E), indifference curve from the CV
portion of the unrestricted model (A), indifference
curve from demand portion of unrestricted model (D),
and indifference curve from model estimated without
travel cost (using only Engel curve information) (B).
-------
53
APPENDIX IV
An Ad Hoc Reweighting Scheme
Researchers who work with maximum likelihood estimation of models using
sample data are by now very familiar with reweighting procedures for scaling
the influence of different observations to allow the sample to more nearly
reflect the proportions of each types of person in the entire population.
Each observation in the sample is represented by one additive term in the log-
likelihood function, each bearing an implicit unit weight. Non-unit weights,
based on cross-tabulations performed on the population and on the sample, are
computed by calculating the ration of population proportions to sample
proportions in each cell of the cross-tabulation. Respondents who represent
undersampled groups in the population then have their contribution to
parameter estimation scaled up; oversampled respondents are given weights of
less than unity to decrease their influence on the final parameter estimates.
If CVM and TCM responses are treated as equally credible, the two terms
in the log-likelihood function in (7) corresponding to each type of
information each receive an implicit unit weight. Fortunately, the
dismantling of the joint normal error distribution into a conditional times a
marginal error distribution leaves the error correlation, p, determined
entirely within the discrete choice CVM portion of the likelihood function.
It seems feasible, therefore, to "undo" the CVM and TCM terms in the
likelihood function and to scale the influence of each type of information in
determining the final parameter estimates.
If, for example, intuition suggests that the available CVM information
is only half as reliable as the "real" travel cost information, one might
change the weights on the CVM terms in the log-likelihood function to 2/3 and
those on the TCM demand terms to 4/3 (so that the weights still sum to two).
-------
54
This ratio of the weights will be designated as a "reliability" factor of .5
for the CVM information.
Given the maintained hypothesis of a quadratic utility function, one can
ask just how small the weight on the CVM information would have to become
before LR tests could just fail to reject the null hypothesis of parameter
equivalence for the two models. For equal unit weights (relative weight -
1.0) the results for the constrained and unconstrained models from Table II
are reproduced in Table IV.1. The second pair of columns in that table show
the consequences of decreasing the relative weight on the CVM information.
The relative reliability of the CVM information has been decreased to 0.1 and
it is still possible to reject the hypothesis of common utility parameters.
It would therefore be quite a "stretch" to bring the utility implications of
the hypothetical CVM responses into line with observed demand behavior in this
particular application.
Still, the observed demand behavior might itself be misleading if the
true opportunity costs of access are poorly proxied by travel costs. It may
be inappropriate to expect the preferences implied by the two types of value
information to be identical. Likewise, the simple quadratic utility function
and homogeneous preferences may be too restrictive. Therefore, this finding
does not necessarily refute the equivalence of the true preferences underlying
these two types of responses.24
24 We have extended the specification of the direct utility function to
include cubic terms in z and q. The data are not rich enough to support
separate parameters for the terms z2q or zq2. For the new "basic" model with
seven utility parameters, the maximized value of the log-likelihood function
is -15699.41. For the corresponding "unrestricted" model with separate CVM
and TCM parameters, convergence has not been attained after several hundred
iterations, but the log-likelihood function has been driven as high as
-15631.95, which is more than adequate to reject the restrictions.
-------
Table IV.1
Joint Models with Separate CVM and TCM Parameters
(CVM and TCM equally credible; CVM discounted by weighting;
CVM discounted by disproportionate variances)
Parameter
Rel.wt.
- 1.0.a
Rel.wt.
1
o
Basic
Unconstr.
Basic
Unconstr.
Model
Model
Model
Model
P, (z)
3.909
1.276
7.840
1.290
(8.237)
(0.7457)
(6.385)
(0.2952)
02 (q)
0.1192
28.17
0.1399
39.43
(19.55)
(2.573)
(12.64)
(0.9207)
(z2/2)
-0.1167
1.498
-1.036
1.494
(-1.836)
(2.834)
(-2.986)
(1.111)
(zq)
0.002579
2.263
-0.001093
3.157
(2.006)
(2.147)
(-0.6008)
(0.8039)
05 (q2/2)
-0.006837
-502.3
-0.007060
-983.3
(-22.80)
(-1.311)
(-13.47)
(-0.4689)
-
75.89
_
76.03
(5.756)
(7.703)
P2*-02/P2
1.0
1.0
V-Vi
.
-10.89
-11.88
(-2.428)
(-3.567)
-
-0.01749
-
-0.02129
(-0.9029)
(-1.495)
-
-0.04739
-
-0.04721
(-14.97)
(-20.09)
V
16.01
15.97
15.98
15.97
(81.98)
(82.04)
(110.5)
(110.6)
p
0.2315
0.2505
0.2324
0.2495
(9.086)
(9.749)
(4.030)
(4.166)
max Log L
-15708.17
-15640.61b
-25938.13
-25920.04°
a "Rel. wt." is the size of the weight on the hypothetical CVM
information relative to the weight on the observed demand behavior.
b LR test for hypothesis of same fi parameters for CVM and TCM utility
functions is 115.12 (when the 5% critical value of the *2 test
statistic is 9.49 and the 1% critical value is 13.28).
c LR test for same fi parameters is 36.1; still rejects hypothesis.
-------
55
APPENDIX V
Implementing These Prototype Models in Other Applications
The illustration in this paper pertains to the valuation of a particular
recreational fishery. However, the joint model developed here is potentially
applicable to the valuation of any non-market good where consumers would have
to incur varying travel costs in order to engage in the process of
consumption. Individually, the travel cost method and the contingent
valuation methods each have shortcomings. Implications drawn from their
combined evidence are likely to be much more robust.
While relatively good, the data used in this paper are still less than
ideal. The specific implications of the fitted models described here must be
judged accordingly. But this research has provided vital groundwork for
future studies.
First, the sampling procedures used in the gathering of the data
employed in this study were not ideal. In particular, rotating sites for the
survey were chosen, and virtually everyone who passed during the 10 a.m. to 5
p.m. period was interviewed. This precludes "outgoing" surveys for avid
anglers who may be out well before 10 a.m., although many of these anglers
would be intercepted upon their return. A more serious problem is that we
cannot identify respondents who have been interviewed more than once. At
best, we have a reasonable sample of fishing trips, not anglers, so the
estimated preferences may be biased towards those of frequent anglers. This
problem cannot be remedied with this data set.
It would be highly desirable to have individual-specific measures of
income (and other sociodemographic variables). Census zip code means are
helpful, but much information is lost in using group averages as proxies for
-------
56
the true variables. If at all possible, the survey instrument should elicit
these data for each respondent.
The contingent valuation question should be phrased so as to make it
clear whether the hypothesized change is intended to be a lump-sum change in
income (as modeled in the body of this paper), or a change in relative prices
(as explored in Appendix I). This information is vital to the utility-
theoretic formulation of the estimating model, and great care must be taken to
ensure that the CVM question is completely unambiguous.
The present survey asks about travel costs for the current fishing day.
What the model requires is typical costs for a typical fishing trip, or better
yet, enough information to construct the actual schedule of opportunity costs
as they increase with number of access days. This would make the travel cost
portion of the model more reliable. The current model also must presume that
individuals fish most of the time at the same location. Much more
sophisticated analyses will be required in order to introduce site choice
modeling into this framework.25
Respondents could be asked specifically about how sure they are
concerning their hypothetical responses to the CVM and travel cost questions.
This information could be incorporated into the weighting scheme for the auto-
validation of the CVM data.
Option and existence values cannot be captured with the current data
set. Selection problems in the assessment of recreation demand have received
considerable attention recently (e.g. Smith, 1988). A random sample of
households in the target population could be contacted by telephone. If they
do not currently consume access days, quantity demanded will simply be zero.
25 At present, site choice modeling has been pursued in a largely atheoretic
multiple discrete choice framework. Blending the two approaches might have to
wait for further computer software and hardware innovations.
-------
57
Travel costs to relevant sites could still be elicited and appropriate CVM
questions could be formulated to allow extension of this modeling framework to
non-use demands.
-------
1
Subject to Revision
October 23, 1988
(rev'd: June 9, 1989)
The Effects of Variations in Gamefish Abundance
on Texas Recreational Fishing Demand: Welfare Estimates
by
Trudy Ann Cameron
Department of Economics
University of California, Los Angeles 90024-1477
ABSTRACT
In an extensive earlier paper (Cameron, 1988a) we developed a fully
utility-theoretic model for the demand for recreational fishing access days,
applied to a sample of 3366 Texas Gulf Coast anglers. The model employs
"contingent valuation" and "travel cost" data, jointly, in the process of
calibrating a single utility function defined over fishing days versus all
other goods and services. The theoretical specification (quadratic direct
utility) and the econometric implementation will not be reproduced here. In
this application, we supplement the original data set with information from
the ongoing Resource Monitoring Program of the Texas Department of Parks and
Wildlife. The RMP concerns all species, but we focus on the abundance of the
primary game fish (red drum) across the eight major bay systems and over time.
This improves upon earlier studies which utilize endogenous actual catch
information. We allow the parameters of the underlying utility function to
vary systematically with exogenously measured abundance to assess the impact
of this important resource attribute upon the demand for access days. We use
empirical estimates (and counterfactual simulations) of equivalent variation
as measures of the social value of the fishery under current conditions and
under alternative fish stock scenarios.
* This research was supported in part by EPA cooperative agreement
#CR-814656-01-0. The raw data were provided by Jerry Clark of the Texas
Department of Parks and Wildlife and by ICSPR (the Inter-University Consortium
for Social and Political Research).
-------
The Effects of Variations in Gamefish Abundance
on Texas Recreational Fishing Demand: Welfare Estimates
2
1- Introduction
In Cameron (1988a), we derived and estimated the parameters of a
quadratic utility function for a trimmed sample of Texas Gulf Coast
recreational fishermen. The utility function, in its simplest form, is
defined over fishing access days and all other goods and services (income).
The novelty of that paper is primarily its utilization of a fully utility-
theoretic framework for analyzing both "contingent valuation" (CV) data
(respondents anticipated behavior under hypothetical scenarios) and "travel
cost" data (respondents' actual behavior in the consumption of access days).
The latter form of data gives us a feel for the consequences of small local
variations in access prices; the former provides additional information,
however hypothetical, regarding more drastic changes in the consumption
environment.
The earlier paper develops the basic specification and goes on to
consider several extensions to that basic model: discounting the influence of
the CV data in the estimation process; estimation without travel cost data
(only income and consumption); and the accommodation of heterogeneous
preferences. In the last category, we demonstrated that it is straightforward
to adapt these models to allow for systematic variation in the preference
function according to geographical or sociodemographic factors.
In this paper, we will again employ heterogeneous utility functions, but
we will only be able to exploit a subset of the data. We wish to concentrate
upon the potential effects of respondents' perceptions about resource quality
on their demand (valuation) of access to the recreational fishery.
-------
3
Readers are referred to Cameron (1988a) for a vital preface to this
research. We avoid extensive duplication in this paper by presuming readers
are familiar with the findings of the earlier paper.
2• Outline of the Specification
As before, we will adopt the quadratic family of utility functions, for
the same variety of reasons explained in the earlier paper. We will let U
denote direct utility, Y will be income, and M will be current fishing day
expenditures ("travel costs", roughly). Also, q will be the number of fishing
days consumed and z (- Y - Mq) will denote consumption of other goods and
services. We will let A denote the abundance of red drum, the primary
gamefish species. The quadratic direct utility function will thus take the
form:
(1) U - z + q + 03 zz/2 + zq + 05 qZ/2,
where the f} are no longer constants, but will be allowed to vary linearly
with the level of A: 0* - 0 + 7^ A, j-l,...,5.
3. Data
The data used for this model consist of a 3318 observation subset of the
3366 observations used in the earlier paper. The data come from an in-person
survey conducted by the Texas Department of Parks and Wildlife primarily
between May and November of 1987 .(although there are a few observations for
the first days of December). The primary purpose of the survey is to count
numbers and species of fish making up the recreational catch, but during this
particular period, additional economic valuation questions were posed to
respondents.
In particular, the contingent valuation question took the form: "If the
total cost of all your saltwater fishing last year was more, would you
have quit fishing completely?" At the start of each day, interviewers
-------
randomly chose a starting value from the list $50, $100, $200, $400, $600,
$800, $1000, $1500, $5000, and $20,000. In addition, respondents were queried
regarding actual market expenditures during the current trip: "How much will
you spend on this fishing trip from when you left home until you get home?"
This is as close as we can get to a measure of "travel cost."
The same basic criteria for deleting particular observations are applied
in this paper as are described in Cameron (1988a). The same caveats regarding
the sample also apply in this case. The sample employed in this study is
slightly smaller only because our gamefish abundance data are drawn from a
separate source: the Resource Monitoring Program of Texas' Department of
Parks and Wildlife. We have their data only for April through the end of
November, so the few December interviews in the survey sample were simply
dropped.
The Resource Monitoring Program uses several types of fishing gear: gill
nets, bag seines, beach seines, trawls, and oyster dredges. The Program
involves vast numbers of samples being drawn across the entire Gulf Coast.
For 1983-1986, we had over 23,000 samples, with complete records of the
numbers of individuals of each species collected in the sample. Since low
temperatures in 1984 resulted in a substantial fish kill along the Texas Gulf
Coast, we utilize only those samples drawn in 1985 and 1986 to construct our
abundance measures. Also, only gill nets capture the types of fish that
recreational anglers would be seeking, so we use only the catch using this
gear type. Still, we have roughly 5400 samples to work with.
One problem, however, is that gill nets were apparently not used during
the months of July and August. So we must fill in for missing data for these
two months. Fortunately, for each month and each of the eight major bay
systems along the coast, we typically have between 40 and 80 samples in each
of the two years. Once we have computed mean "catch per unit effort" for each
month and each bay, the time series for the April-November data is fairly
-------
5
smooth for the seven most usual species of game fish (red drum, black drum,
spotted seatrout, croakers, sand seatrout, sheepshead, and founder). We have
used quadratic approximations for the May-October range of the data to fill in
abundance estimates for the two missing months.
Preliminary atheoretic logit models based upon the contingent valuation
data suggest that among the top three recreational target species--red drum,
spotted seatrout, and flounder--only variations in the number of red drum have
a statistically significant effect upon the implied value of a recreational
fishing day. Consequently, we elect to employ only the abundance of red drum
as a control for resource quality in this study.
The means and standard deviations for both the full sample of 3366 and
the subset of 3318 responses are given in Table 1. As can be seen, the subset
is still representative of the larger sample.
4. Utility Parameter Estimates
To assess whether or not the preference function differs systematically
with the level of gamefish abundance, we estimate two models. First, we re-
estimate the "basic" joint model from the earlier paper using just the subset
of 3318 observations. This specification constrains the /? coefficients to be
identical across all levels of gamefish abundance. Then we generalize the
model by allowing each fi to be a linear function of A, which involves the
introduction of five new a parameters. Since the "basic" specification is a
special case of the model incorporating heterogeneity, a likelihood ratio test
is the appropriate measure of whether A "matters." Results for the two models
are presented in Table 2. The LR test statistic is 8.18. The 5% critical
value for a *2(5) distribution is 11.07, and 10% critical value is 9.24. Thus
the LR test just fails to reject independence of the utility function from the
abundance of gamefish. (However, if one were to generalize the utility
function to include only the interaction term zA and its coefficient 7 , and
-------
Table 1
Descriptive Statistics for Full Sample arid "Gamefish Abundance" Subset
Variable
Description
Full Sample Subset
(n - 3366) (n - 3318)
Y median household income for respondent's 3.1725 3.2772
5-digit zip code (in $10,000) (1980 Census (0.6712) (0.6705)
scaled to reflect 1987 income; factor-1.699)
M current trip market expenditures, assumed 0.002915 0.002927
to be average for all trips (in $10,000) (0.002573) (0.002576)
annual lump sum "tax" proposed in CV
scenario (in $10,000)
0.
(0.
05602
04579)
0.05608
(0.04576)
reported total number of salt water fishing 17.40 17.37
trips to sites in Texas over the last year (16.12) (16.14)
indicator variable indicating that respondent 0.8066 0.8071
would choose to keep fishing, despite tax T (0.3950) (0.3946)
Resource Monitoring Program, catch per unit
effort of red drum (gill nets) by month and
by major bay system
0.1487
(0.06161)
-------
Table 2
Parameter Estimates for "Basic"
and "Gamefish Abundance" (A) Models
Parameter
Basic Model
Abundance
Model
(n - 3318)
(n - 3318)
Pl (z)
3.192
5.039
(7.968)
(6.266)
P2
0.1191
0.1133
(19.18)
(10.87)
£3 (z2/2)
-0.08953
-0.2622
(-1.056)
(-1.322)
^4 (zq)
0.002661
0.004570
(1.967)
(1.164)
(q2/2)
-0.006862
-0.006920
(-22.16)
(10.31)
(zA)
-
-12.85
(-2.390)
72 CqA)
-
0.03166
(0.5281)
73 (z2A/2)
-
1.191
(0.6256)
74 (zqA)
-
-0.01112
(-0.4287)
75 (q2A/2)
-
0.0004552
(0.1137)
va
16.03
16.03
(81.46)
(81.38)
P
0.2354
0.2343
(9.187)
(9.033)
Log L
-15485.96
-15481. 87b
® See Cameron (1988a) for discussion of the v and p parameters.
X2 test statistic is 8.18; at 10% level, *2(5) - 9.24.
-------
6
none of the other variables or 7 coefficients, the incremental improvement in
the fit of the model would be statistically significant. The 0.5 percent
critical value of a *2(1) distribution is only 3.84.)
5. Implications of Fitted Parameter Estimates
In the earlier paper, several properties of the estimated models were
recommended for attention. Here, the properties of the fitted utility
function vary across levels of gamefish abundance, A. Consequently, we will
examine the fitted utility function at the subsample mean of A ( ) as
well as at several other benchmark levels. It is entirely possible to compute
values for several interesting quantities for each individual in the sample.
Here, however, we will focus initially on the "mean" consumer.
Table 3 summarizes several properties of the fitted utility function for
the several levels of gamefish abundance. As expected, changes in gamefish
abundance substantially affect the value respondents place on access to this
fishery. Value in this case is measured several ways. Compensating variation
(CV) is the amount of additional income a respondent would require, if denied
access to the resource, to make their utility level the same as that which
could be achieved with the optimal level of access. Equivalent variation (EV)
is the loss of income which would leave the respondent just as much worse off
as would a denial of access. We also compute the equivalent variation for
partial reductions in the level of access.
A visual depiction of the effect of gamefish abundance on the
preferences of anglers (defined over fishing days and all other goods) is
provided in Figure 1 for A - 0.1 and for A - 0.2. As anticipated,
indifference curves for A - 0.2 have considerably greater curvature, implying
that anglers are less willing to trade off fishing days for other goods when
gamefish abundance is higher. In contrast, with lower abundance, the
curvature is considerably less, implying that under these circumstances,
-------
4.1
0 0
Y
o.o
o.l
12.1
II.•
14.8
actos day4
Figure ( - Effects of change! In the abundance of the
prlaary gaaeflah on preferences for fishing access days.
Eaplrlcal Indifference curves for eean consuaer with
abundance at 0.2, 0.1, and 0.0. (Actual aean - 0.149,
standard deviation — 0.062, usable saaple size n - 3318.)
28.8
5.8
oo
0.1
8.8
pr.it t {
t Ll «?t>ci
Figure X ¦ Eaplrlcal Inverse deaand curves for fishing
access days for aean consuaer at prlaary ganeflsh abundance
levela of 0.2, 0.1 and 0.0. (Actual aean - 0.149, standard
deviation - 0.062, usable saaple alza n - 3318.)
-------
anglers consider other goods to be relatively better substitutes for fishing
days. For example, when A - 0.1, the same change in the relative price of a
fishing day will lead to a larger decrease in the optimal number of days
consumed than when A - 0.2.
In addition to the properties of the utility function and its
corresponding Marshallian demand functions, we might be interested in
calculating the derivatives of these Marshallian demand functions with respect
to the level of the A variable. The Marshallian demand function for the model
with heterogeneity is:
(2) q - [ (02+72A) + (W)Y - - (/33+73A)MY ] /
[ 2(/?4+74A)M - (£3+73A) M2 - (05+75A) ]
Figure 2 plots the inverses of these fitted Marshallian demand functions
(with access days q on the vertical axis, and the price of access on the
horizontal axis). These demand curves are drawn for an individual with mean
income Y and mean travel costs M.
As A varies from 0.0 to 0.1 to 0.2 (compared to the actual mean value of
0.1487), these demand curves shift out further and further. Observe that,
although the demand function can be highly non-linear in M, the fitted values
of the parameters (for these data and in combination with the sample mean
angler characteristics) happen to yield demand functions which are almost
linear.
Notice that variations in A, in the fitted model, have rather dramatic
effects upon the implied "choke price" (reservation price) for access to the
resource: the greater the gamefish abundance, the higher the choke price.
This can be interpreted as implying that with greater levels of preferred
gamefish abundance, higher and higher prices for access would be willingly
paid before individuals will cease entirely to go fishing.
-------
8
Table 3 also gives the utility maximizing number of fishing days
demanded, q, at the sample mean values of M and Y, as a function of the
changing levels of gamefish abundance, A. Note that this optimal number of
days is not very sensitive to A. This is a consequence of the fact that
changes in A seem to have a substantial effect upon the curvature of
indifference curves; they have less of an effect on their location.
The variation in the configuration of preferences, and the obvious
shifts in the demand curves as a function of A imply that the social value of
access to the fishery will depend upon the level of gamefish abundance at
fishing sites. To illustrate this sensitivity, we can concentrate upon the
equivalent variation for a complete loss of access to the resource, as a
function of A, for a representative consumer with sample mean levels of Y and
M. These variations can be detected by scanning across the columns in Table
3. Table 3 suggests that for a typical angler, improving gamefish abundance
(red drum only) by a factor of 1.5 times its current level of A - .1487 would
increase the annual value of access to the fishery by about 36% and improving
abundance by 1.2 would increase access values by about 12%. In contrast,
decreasing abundance to 0.8 of its current level would decrease the annual
value of access by about 10%; decreasing abundance to 0.5 of its current level
would decrease access values by 22%. If it is safe to extrapolate these
estimates (based on functionally "local" variations in actual abundance
levels) to a scenario where red drum are completely eliminated, the loss in
access values would be about 37%. (Remaining value would derive from the
catch of other species, and from the non-catch utility derived from fishing
days. )
6• Discussion and Conclusions
As mentioned above, a full explanation of the empirical innovations
embodied in the use of a joint contingent valuation/travel cost model for
-------
Table 3
Properties of che Fitted Utility Function (for "Mean" Consumer)
(n - 3318; valid sample with available abundance data)
Property
at 1.5(mean A) at 1.2(mean A)
at mean A at 0.8(mean A) at 0.5(mean A)
at A
Utility Function
Parameters:
0\*
"X
Pi*
Pc*
2.173
0.1204
0.03545
0.002089
-0.006818
2.746
0.1190
-0.04961
0.002586
-0.006838
3.129
0.1180
-0.08504
0.002916
-0.006852
3.511
0.1171
-0.1205
0.003247
-0.006865
4.084
0.1157
-0.1736
0.003743
-0.006886
5.039
0.1133
-0.2622
0.004570
-0.006920
Function Maximum:
z*
q*
-528.08
-144.18
57.40
39.10
37.93
33.37
29.98
31.23
24.16
29.93
19. 73
29.40
Demand Elasticity wrt
price
Income
-0.05569
0.05568
-0.06598
0.07288
-0.07278
0.08428
-0.07915
0.09529
-0.08919
0.1121
-0.1063
0.1405
Optimal number of
Access days (q)
17.65
17.45
17.31
17.17
16.97
16.62
Compensating Variation
for Complete Loss of
Access
$4873
$4046
$3620
$3266
$2835
$2299
Equivalent Variation
for Complete Loss of
Access
$4796
$3943
$3515
$3164
$2741
$2221
EV for Access Restricted
to a of Current Fitted Level,
for a -
0.1
$3885
0.2
3069
0.3
2350
0.4
1726
0.5
1199
0.6
767
0.7
431
0.8
192
0.9
48
$3196
2527
1936
1423
988
633
356
158
40
$2850
2254
1727
1270
882
565
318
141
35
$2566
2029
1555
1143
795
509
286
127
32
$2223
1758
1348
991
689
441
248
110
28
$1801
1425
1092
803
558
357
201
89
22
-------
9
valuing a recreational fishery is given in Cameron (1989). This paper
represents a specific generalization of the model which allows the parameters
of the direct quadratic utility function to vary systematically with the level
of just one species of gamefish. We have selected the most popular gamefish
species (red drum). A more elaborate model, of course, could let the utility
parameters vary systematically with any number of characteristics of the
resource, not just the abundance of a single species of gamefish.
Since we concentrate only upon red drum abundance, even the reduction to
zero of red drum stocks (in the most extreme simulation described in the last
section) will not lead everyone to cease fishing entirely. Other species of
gamefish will remain. In this specification, variations across location and
month in red drum abundance may be correlated with the abundance of other
species. If this is the case, our red drum abundance measure will be
capturing variations in the abundance of more than one species. Nevertheless,
we do not capture the distinct effects of any seasonal or location variation
in species abundance that is uncorrelated with red drum abundance.
The simulated variations in red drum abundance used as illustrations in
this paper are by far the coarsest simulations that could be generated by a
model such as this. We have concentrated solely on variations in abundance as
they would affect a representative consumer with mean income and travel costs.
However, since each individual's estimated preference function depends on the
abundance of red drum during the month and in the bay system in which they are
fishing, the model is perfectly able to simulate the impact upon the value of
fishery access to individuals of forecasted changes in red drum abundance
either by month or by geographical area. As the configurations of
individuals' indifference curves change, so will their optimal number of
ishmg days and the equivalent variation associated with partial or complete
loss of access.
-------
10
The intent of this paper, therefore, is to illustrate the versatility of
the constrained, jointly estimated contingent valuation/travel cost model for
recreational fisheries valuation. It is satisfying to find thoroughly
plausible changes in economic quantities as a consequence of exogenous
variations in resource characteristics. This generalization of the "common
utility function" model to a "systematically varying utility function" model
should serve as a very useful prototype for subsequent research.
-------
11
REFERENCES
Cameron, Trudy Ann, (1989) "Combining Contingent Valuation and Travel Cost
Data for the Valuation of Non-market Goods," a revision of "Empirical
Discrete/Continuous Choice Modeling for the Valuation of Non-market
Resources or Public Goods," Working Paper #503 (1988), Department of
Economics, University of California at Los Angeles, September.
Cameron, Trudy Ann, (1988b) "The Determinants of Value for a Marine Estuarine
Sportfishery: The Effects of Water Quality in Texas Bays," Discussion
Paper #523, Department of Economics, University of California at Los
Angeles, September.
Cameron, Trudy Ann (1988c) "Using the Basic 'Auto-Validation' Model to Assess
the Effect of Environmental Quality on Texas Recreational Fishing
Demand: Welfare Estimates," Discussion Paper #522, Department of
Economics, University of California at Los Angeles, September.
-------
Using the Basic "Auto-validation" Model
to Assess the Effect of Environmental Quality
on Texas Recreational Fishing Demand: Welfare Estimates
by
Trudy Ann Cameron
Department of Economics
University of California, Los Angeles, CA 90024-1477
UCLA Working Paper No. 522
September 1988
-------
Subject to Revision
September 23, 1988
Using the Basic "Auto-validation" Model
to Assess the Effect of Environmental Quality
on Texas Recreational Fishing Demand: Welfare Estimates
by
Trudy Ann Cameron
Department of Economics
University of California, Los Angeles 90024-1477
ABSTRACT
In an extensive earlier paper (Cameron, 1988a) we developed a fully
utility-theoretic model for the demand for recreational fishing access days,
applied to a sample of 3366 Texas Gulf coast anglers. The model employs
"contingent valuation" and "travel cost" data, jointly, in the process of
calibrating a single utility function defined over fishing days versus all
other goods and services. The theoretical specification (quadratic direct
utility) and the econometric implementation will not be reproduced here.
Instead, we focus specifically on the implications of an extension to this
model. We employ a subset of 506 observations from the same survey for which
respondents were asked to indicate their ex post subjective assessment of the
environmental quality at the fishing site. We allow the parameters of the
underlying utility function to vary systematically with the perceived level of
environmental quality to assess the impact of environmental factors on the
demand for access days. Treating the 10-point response scale for
environmental quality (E) as a continuous variable, we find (among other
results) that for the average angler improving E from one standard deviation
below the mean to one standard deviation above increases the value of the
fishery (measured by equivalent variation) by about $1400 (about 50%).
* This research was supported in part by EPA cooperative agreement
#CR-814656-01-0.
-------
2
Using the Basic "Auto-validation" Model
to Assess the Effect of Environmental Quality
on Texas Recreational Fishing Demand
1. Introduction
In Cameron (1988a), we derived and estimated the parameters of a
quadratic utility function for a trimmed sample of Texas Gulf Coast
recreational fishermen. The utility function, in its simplest form, is
defined over fishing access days and all other goods and services (income).
The novelty of that paper is primarily its utilization of a fully utility-
theoretic framework for analyzing both "contingent valuation" (CV) data
(respondents anticipated behavior under hypothetical scenarios) and "travel
cost" data (respondents' actual behavior in the consumption of access days).
The latter form of data gives us a feel for the consequences of small local
variations in access prices; the former provides additional information,
however hypothetical, regarding more drastic changes in the consumption
environment.
The earlier paper develops the basic specification and goes on to
consider several extensions to that basic model: discounting the influence of
the CV data in the estimation process; estimation without travel cost data
(only income and consumption); and the accommodation of heterogeneous
preferences. In the last category, we demonstrated that it is straightforward
to adapt these models to allow for systematic variation in the preference
function according to geographical or sociodemographic factors.
In this paper, we will again employ heterogeneous utility functions, but
we will only be able to exploit a subset of the data. We wish to concentrate
upon the potential effects of respondents' perceptions about environmental
quality on their demand (valuation) of access to the recreational fishery.
-------
3
Readers are referred to Cameron (1988a) for a vital preface to this
research. We avoid extensive duplication in this paper by presuming readers
are familiar with the findings of the earlier paper.
2. Outline of the Specification
As before, we will adopt the quadratic family of utility functions, for
the same variety of reasons explained in the earlier paper. We will let U
denote direct utility, Y will be income, and F will be current fishing day
expenditures ("travel costs", roughly). Also, q will be the number of fishing
days consumed and z (- Y - Fq) will denote consumption of other goods and
services. We will let E denote subjective environmental quality. The
quadratic direct utility function will thus take the form:
(1) U - ^ z + 02 q + 03 z2/2 + 0h zq + ps qz/2,
where the 0^ are no longer constants, but will be allowed to vary linearly
with the level of E: f)* - ^ E, j-1 5.
3. Data
The data used for this model consist of a 506 observation subset of the
3366 observations used in the earlier paper. The data come from an in-person
survey conducted by the Texas Department of Parks and Wildlife between May and
November of 1987. The primary purpose of the survey is to count numbers and
species of fish making up the recreational catch, but during this particular
period, additional economic valuation questions were posed to respondents.
In particular, the contingent valuation question took the form: "If the
total cost of all your saltwater fishing last year was more, would you
have quit fishing completely?" At the start of each day, interviewers
randomly chose a starting value from the list $50, $100, $200, $400, $600,
-------
4
$800, $1000, $1500, $5000, and $20,000. In addition, respondents were queried
regarding actual market expenditures during the current trip: "How much will
you spend on this fishing trip from when you left home until you get home?"
This is as close as we can get to a measure of "travel cost."
The same basic criteria for deleting particular observations are applied
in this paper as are described in Cameron (1988a). The same caveats regarding
the sample also apply in this case. The sample employed in this study is
smaller only because the ex post subjective environmental quality questions
were asked of only approximately one-eighth of the full sample. This question
was just one of eight rotating questions on special issues.
The precise wording of the environmental quality question was "To what
extent were you able to enjoy unpolluted natural surroundings [during this
fishing trip]?" Responses were given on a Likert-type scale of 1 to 10, with
10 being highest. The means and standard deviations for both the full sample
of 3366 and the subset of 506 responses are given in Table 1. As can be seen,
the subset is fairly representative of the larger sample.
4. Utility Parameter Estimates
To assess whether or not the preference function differs systematically
with the level of environmental quality, we estimate two models. First, we
re-estimate the "basic" joint model from the earlier paper using Just the
subset of 506 observations. This specification constrains the (3 coefficients
to be identical across all levels of environmental quality. Then we
generalize the model by allowing each /9 to be a linear function of E, which
involves the introduction of five new a parameters. Since the "basic"
specification is a special case of the model incorporating heterogeneity, a
likelihood ratio test is the appropriate measure of whether E "matters."
Results for the two models are presented in Table 2. The LR test statistic is
-------
Table 1
Descriptive Statistics for Full Sample and "Environmental" Subset
Variable
Description
Full Sample Subset
(n - 3366) (n - 506)
median household income for respondent's 3.1725
5-digit zip code (in $10,000) (1980 Census (0.9995)
scaled to reflect 1987 income; factor-1.699)
current trip market expenditures, assumed 0.002915
to be average for all trips (in §10,000) (0.002573)
annual lump sum "tax" proposed in CV 0.05602
scenario (in $10,000) (0.04579)
reported total number of salt water fishing 17.40
trips to sites in Texas over the last year (16.12)
indicator variable indicating that respondent 0.8066
would choose to keep fishing, despite tax T (0.3950)
3.1681
(1.0134)
0.003255
(0.002767)
0.05661
(0.04770)
15.78
(15.32)
0.7905
(0.4073)
E Likert-scale subjective ex post assessment
of current environmental quality at site
8.073
(2.177)
-------
Table 2
Parameter Estimates for "Basic"
and "Environmental" Models
Parameter
Basic Model
Environmental
Model
01 (z)
1.381
1.218
(1.080)
(0.6385)
02 (3)
0.1109
0.04825
(6.635)
(1.051)
0Z (z2/2)
0.6173
1.081
(1.526)
(1.106)
£4 (zq)
0.008387
0.006219
(1.990)
(0.4773)
(q2/2)
-0.008041
-0.003755
(-8.611)
(-1.383)
7], (zE)
-
0.07805
(0.4148)
72 (q£)
-
0.007991
(1.389)
73 (z2E/2)
-
-0.07346
(-0.6631)
74 (zqE)
-
0.0003104
(0.1882)
75 (q2E/2)
-
-0.0005533
(-1.664)
15.13
15.15
(31.79)
(31.76)
P
0.2929
0.2975
(4.631)
(4.637)
Log L
-2339.80
-2334.69
a See Cameron (1988a) for discussion of additional parameters.
-------
5
10.22. The 5% critical value for a *2(5) distribution is 11.07 and the 10%
critical value is 9.24. Thus, the improvement in the log-likelihood just
misses being statistically significant at the 5% level for this small sample.
Nevertheless, this difference seems large enough to warrant pursuing the
implications of the fitted model. In any case, we can be confident that the
statistical significance would improve with larger samples.
5- Implications of Fitted Parameter Estimates
In the earlier paper, several properties of the estimated models were
recommended for attention. Here, the properties of the fitted utility
function vary across levels of environmental quality, E. Consequently, we
will evaluate the function at the subsample mean of E (8.0731) as well as at
the maximum value of E (10) and at a lower benchmark value (6), which
represents approximately one standard deviation below the mean. It is
entirely possible to compute values for several interesting quantities for
each individual in the sample. Here, however, we will focus on the "mean"
consumer. Note that we have elected to use the mean values for income and
fishing day expenses computed for the entire sample of 3366, on the
presumption that the means in this sample are more typical of the mean for the
population as a whole. (This is arbitrary; the results will be similar for
the "mean" consume in the smaller subset.)
Table 3 summarizes several properties of the fitted utility function for
the three benchmark levels of environmental quality. As expected, decreases
in environmental quality substantially affect the value respondents place on
access to this fishery. Value in this case is measured several ways.
Compensating variation is the amount of additional income a respondent would
require, if denied access to the resource, to make their utility level the
same as that which could be achieved with the optimal level of access.
-------
Table 3
Properties of the Fitted Utility Function
Property
E - 10
E - 8.0731
E - 6
Utility Function
Parameters:
01*
02*
02*
0i*
05*
Function Saddle
Point:
1.998
0.1282
0.3467
0.009324
-0.009288
1.848
0.1128
0.4883
0.008726
-0.008222
1.686
0.09619
0.6406
0.008082
•0.007075
z*
q*
•5.973
7.802
-3.954
9.518
-2.764
10.44
Demand Elasticity wrt
price
income
-0.06034
0.1623
-0.07351
0.1610
¦0.09211
0.1593
Compensating Variation
for Complete Loss of
Access
$3742
$2970
$2283
Equivalent Variation
for Complete Loss of
Access
$3741
$2997
$2314
EV for Access Restricted
to a of Current Fitted Level,
for a -
0.1
$3018
$2418
$1867
0.2
2376
1903
1470
0.3
1814
1453
1122
0.4
1329
1064
823
0.5
921
737
570
0.6
588
471
364
0.7
330
265
205
0.8
147
117
91
0.9
37
29
23
-------
6
Equivalent variation is the loss of income which would leave the respondent
just as much worse off as would a denial of access. We also compute the
equivalent variation for incomplete reductions in the level of access.
A visual depiction of the effect of environmental quality on the
preferences of anglers (defined over fishing days and all other goods) is
provided in Figure 1 for E - 10 (which can be considered "good" environmental
quality) and for E - 6 ("relatively poor" environmental quality). As
anticipated, indifference curves for E - 10 have considerably greater
curvature, implying that anglers are less willing to trade off fishing days
for other goods when the environmental quality is high. In contrast, with
poorer environmental quality, the curvature is considerably less, implying
that under these circumstances, anglers consider other goods to be relatively
better substitutes for fishing days. For example, when E - 6, the same change
in the relative price of a fishing day will lead to a larger decrease in the
optimal number of days consumed than when E - 10.
In addition to the properties of the utility function and its
corresponding Marshallian demand functions, we might be interested in
calculating the derivatives of these Marshallian demand functions with respect
to the level of the E variable. The Marshallian demand function for the model
with heterogeneity is:
(2) q - [ (02+72E) + (V*E>X * <^i+^1E)F * 1 /
[ 2<^+t4E)F - (03+73E) F2 - (/35+7sE) ]
Table 4 gives the utility maximizing number of fishing days demanded at the
sample mean values of F and Y, as a function of the subjective level of
environmental quality, E. Locally, there are only very slight differences in
these fitted demands as a consequence of environmental changes.
-------
£«/
-------
E
1
2
3
4
5
6
7
8
9
10
Table 4
Optimal Demand, Derivatives and Elasticities
wrt Environmental Quality
(evaluated at mean Y and F, n - 3366)
q* 3q/3E (dq/3E)(E/q*) EV for complete
loss of access
14.72
0.2876
0.01953
$ 1046
14.97
0.2260
0.03018
1264
15.18
0.1822
0.03601
1499
15.34
0.1501
0.03912
1751
15.48
0.1257
0.04060
2022
15.60
0.1068
0.04110
2314
15.70
0.09193
0.04100
2630
15.78
0.07993
0.04052
2971
15.86
0.07014
0.03981
3340
15.92
0.06204
0.03896
3741
-------
7
We may be especially interested in the derivative of this fitted demand
function with respect to E. It will depend not only on F and Y, but also on
the level of E itself:
(3) dq/dE - {[2(^+74E)F - (03+j3E) F2 - (05+75E) ] [iz + 7J - 7^ - 73FY]
- K02+72E) + (VltE>Y " (^+7^)F - (^3+73E)FY]
[2 7J - 73F2 - 75]} / [ 2(^4+74E)F - (/J3+73E) F2 - (^5+75E) ]2.
This formula is untidy, but can be readily computed. Table h gives the values
of this derivative as well as the corresponding elasticity, (3q/3E)(E/q), for
the full range of integer values of E which are possible in the data.
A visual display of the effects of changes in E upon the configuration
of the fitted inverse demand curve for an individual with mean Y and F is
presented in Figure 2. Observe that, although the demand function can be
highly non-linear in F, the fitted values of the parameters (for these data
and in combination with the sample mean angler characteristics) yield demand
functions which are almost linear. Each fitted demand curve passes through
the value of F and the corresponding particular fitted value of q* (for each
E) for this representative consumer. Notice that variations in E, in the
fitted model, have rather dramatic effects upon the implied choke price for
access to the resource: the better the environmental quality, the higher the
choke price.
The variation in the configuration of preferences, and the obvious
shifts in the demand curves as a function of E imply that the social value of
access to the fishery will depend upon the subjective level of environmental
quality at fishing sites. To illustrate this sensitivity, we have computed
the equivalent variation for a complete loss of access to the resource, as a
function of E, for a representative consumer with sample mean levels of Y and
-------
6*/
\ X \
0.8
8.9
82.e
162. e
24C.8
328.8
<2o.
453. e
$
Figura 1. Effaces of incraaalng aubjactiva anvironnantal
quality on lnvaraa damand curva for an anglar vlch
aaapla aaan charactarlatlca.
-------
8
F. These equivalent variations are also given in Table 4. Bear in mind that
the range of E from 6 to 10 accounts for approximately one standard deviation
on either side of the mean value reported in the sample. The EV estimates in
Table 4 suggest that for a typical angler, improving environmental quality
from the "6" level to the "10" level would add approximately $1400 to the
annual value of access to the fishery (an increase of over 50%).
This value must be considered in relation to the actual distribution of
E values in the sample. Tables 5 and 6 give the details of these responses.
Almost 40% of the sample is completely satisfied with current environmental
quality. This suggests an alternative "simulation" based on the fitted model.
Instead of simply considering the mean angler, it is also possible to simulate
changes in E for each individual angler in the sample. Under current
conditions, the equivalent variation for a complete loss of access varies over
the sample from $648 to $4235, with a mean of $3037 and a standard deviation
of $778. If we take every respondent who reported a subjective environmental
quality level of less than 10 and increase their value of E by one unit, the
distribution of these fitted equivalent variation values can be expected to
change. In fact, the new fitted values vary from $839 to $4238, with a mean
of $3253 and a standard deviation of $715. Thus the increase in the mean of
the equivalent variations, when we improve by one unit the experiences of
those who were less than completely satisfied experience currently, Is
approximately $216. If we could scale this up to the entire population, this
represents an increase in the social value of the fishery of approximately
6.6%.
6. Subjective Environmental Qualities as a Function of Physical Measures
The subjective environmental quality question on the Texas Parks and
Wildlife Survey elicits information about overall environmental quality. We
-------
Table 5
Descriptive Statistics for E Variable
MOMENTS
N 506
MEAN 8.07312
STD DEV 2.17742
SKEVNESS -1.216
SUM 4085
VARIANCE 4.74118
KURTOSIS 0.897612
QUANTILES(DEF-4)
100%
MAX
10
99%
10
75%
Q3
10
95%
10
50%
MED
9
90%
10
25%
Q1
7
10%
5
0%
MIN
1
5%
4
It
1
RANGE
Q3-Q1
MODE
9
3
10
-------
Table 6
Frequency Distribution of E Values
FREQ
CUM.
PERCENT
CUM
FREQ
PERCENT
1
]*
7
7
1.38
1.38
2
]*
7
14
1.38
2.77
3
] **
10
24
1.98
4.74
4
] **
11
35
2.17
6.92
5
J*********
46
81
9.09
16.01
6
J*****
25
106
4.94
20.95
7
]********
41
147
8.10
29.05
8
J *******************
93
240
18.38
47.43
9
J ****************
81
321
16.01
63 .44
10
*************************************
185
506
36.56
100.00
+ + — + — +— + — +— + — +— + .
20 40 60 80 100 120 140 160 180
FREQUENCY
-------
9
do not presently have access to typical or specific air quality measurements
for different areas along the Texas Gulf Coast, but in the course of related
research (Cameron, 1988b), we have attempted to determine how a variety of
water quality measures are related to respondents' subjective assessments of
environmental quality.
From a variety of auxiliary sources reported in Cameron (1988b),
including the Texas Department of Water Resources, and the Resource Monitoring
division of Texas Parks and Wildlife, we have obtained data on the
characteristics of tens of thousands of water samples over the few years up to
and including the time period of the valuation survey. Most of the water
quality "parameters" have been averaged by month and by each of the eight
major bay systems along the Texas Gulf Coast. A few are available only by bay
system. (See the original document for details.)
Table 7 reproduces the results for E regressed on a variety of water
quality parameters in an ad hoc specification. Not surprisingly, the
relationship between the subjective environmental quality measure and
"typical" water quality is quite weak. For this reason, we do not devote
space in this paper to a discussion of the explanatory variables. The reader
is referred to Cameron (1988b) for this information. Certainly, many more
physical factors will affect perceptions than simply the few for which we have
measurements. Attributes of the respondent can also be expected to have some
impact upon the subjective assessments of environmental quality. Other
regressions reported in the appendices of Cameron (1988b) examine the
influence of socioeconomic variables on these responses. They also establish
the presence of some seasonal and geographical variation.
-------
Table 7
OLS Regression of "Ability to Enjoy Unpolluted
Natural Surroundings: on Measured Water Quality Variables
F-TEST
4.247
OBS
695
PARAMETER
STANDARD
T FOR HO:
VARIABLE
ESTIMATE
ERROR
PARAMETER-0
INTERCEP
8.334
1.860
4.481
MTURB
0.001600
0.01016
0.158
MSAL
0.01851
0.01795
1.031
MDO
-0.2415
0.1387
-1.742
TRANSP
0.02034
0.01311
1.551
DISO
0.2204
0.1077
2.047
RESU
0.005304
0.006889
0.770
NH4
6.053
3.659
1.654
NITR
-2.236
1.155
-1.936
PHOS
2.357
1.700
1.386
CHLORA
-0.002728
0.02576
-0.106
LOSSIGN
-0.009637
0.02440
-0.395
OILGRS
-0.003734
0.001145
-3.261
CHROMB
0.02663
0.02361
1.128
-------
10
8. Conclusions
Clearly, there is good evidence that angler's value of the fishing
experience is affected by their subjective assessment of environmental
quality. For this small sample from the Texas survey, allowing for
heterogeneous preferences which vary with environmental quality makes a
statistically significant improvement in the econometric model at almost the
5% level. Despite the fact that we have lumped all other goods in the
consumption bundle into a single composite, the fundamental regularity
conditions for a utility-theoretic model are satisfied. Of course, all of the
caveats mentioned in Cameron (1988a) and Cameron (1988b) also apply to this
analysis, so the results must be interpreted with some caution.
Unambiguously, if anglers' perceptions of environmental quality can be
improved, our model indicates that the social value of the resource will be
increased (and vice versa, of course). What is clear, however, is that a
better link must be forged between perceptions and actual physical quantities
of pollutants (both air and water). We need to know just what it takes to
raise someone's response from an 8 to a 9 on this type of Likert-scale
question. This will require cooperation between physical and social
scientists.
-------
11
REFERENCES
Cameron, Trudy Ann, (1988a) "Empirical Discrete/Continuous Choice Modeling for
the Valuation of Non-market Resources or Public Goods," Working Paper
#503, Department of Economics, University of California at Los Angeles,
September.
Cameron, Trudy Ann, (1988b) "The Determinants of Value for a Marine Estuarine
Sportfishery: The Effects of Water Quality in Texas Bays," Discussion
Paper # , Department of Economics, University of California at Los
Angeles, September.
------- |