LA-9699-MS
Los Alamos National Laboratory is operated by the University of California for the United States Department of Energy under contract W-7405-ENG-36.
A Regional Recreation Demand
and Benefits Model
Los Alamos National Laboratory
Los Alamos.New Mexico 87545
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An Affirmative Action/Equal Opportunity Employer
This work was supported by the US Environmental Protection Agency,
Freshwater Division, Environmental Research Laboratory.
Edited by Lidia G. Morales, S Division
This report has been reviewed by the Corvallis Environmental Research
Laboratory, US Environmental Protection Agency, and approved for publica-
tion. Mention of trade names or commercial products does not constitute
endorsement or recommendation for use.
DISCLAIMER
This report was prepared as an account of work sponsored by an agency of the United States Government.
Neither the United States Government nor any agency thereof, nor any of their employees, makes any
warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness,
or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would
not infringe privately owned rights. Reference herein to any specific commercial product, process, or
service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its
endorsement, recommendation, or favoring by the United States Government or any agency thereof. The
views and opinions of authors expressed herein do not necessarily state or reflect those of the United
States Government or any agency thereof.
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EPA ERL-Corvallis Library
00004341
LA-9699-MS
UC-11
Issued: March 1983
A Regional Recreation Demand
and Benefits Model
Ronald J. Sutherland
L
Los Alamos National Laboratory
Los Alamos, New Mexico 87545
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CONTENTS
ABSTRACT 1
EXECUTIVE SUMMARY 2
CHAPTER I. INTRODUCTION 5
CHAPTER II. RECREATION BENEFITS AND DISPLACED FACILITIES 11
1. Introduction 11
2. An Overview of Benefits in the Recreation Literature. ... 13
A. Knetsch 13
B. Mi shan 16
C. Freeman 18
D. Support for the Conventional Measure of Benefits ... 20
3. The Theoretical Underpinning for the Conventional
Measure of Recreation Benefits 22
4. Consumer Surplus with Multiple-Price Changes, 26
5. Conclusions 30
CHAPTER III. ESTIMATING RECREATION TRIPS WITH A GRAVITY MODEL 31
1. Gravity Model Overview 35
2. Gravity Model Input Variables 39
A. Fraction Factors (F-0 39
B. Trip Production Model (P.) 43
C. Attractions Model (A.) -1 51
3. Calibrating the Gravity Model 54
CHAPTER IV. Estimating an Outdoor Recreation Demand Curve 61
1. Estimating a Travel-Cost Demand Curve and Consumer
Surplus: An Overview 61
2. Travel-Cost Demand and Valuation Estimates: Some
Illustrations 67
A. Aggregating Recreation Activities 67
B. Substitute Sites 68
C. Some Empirical Estimates for Swimming 70
CHAPTER V. Survey Estimates of the Willingness to Pay to Recreate and
the Value of Travel Time 74
1. Introduction 74
2. Direct Willingness to Pay Estimates 74
3. The Value of Recreation Travel Time 75
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CONTENTS (cont)
CHAPTER VI. THE SENSITIVITY OF TRAVEL-COST ESTIMATES OF RECREATION DEMAND
AND VALUATION TO VARIOUS COMPUTATION AND SPECIFICATION ISSUES. . 80
1. The Three Issues 81
2. The Sensitivity of Travel-Cost Estimates to Various
Assumptions 83
A. Functional Form of the First-Stage Demand Curve. ... 84
B. Size of Origin Zone 91
3. Conclusions and Implications 96
CHAPTER VII. EMPIRICAL ESTIMATES OF RECREATION BENEFITS OF IMPROVED WATER
QUALITY IN THE PACIFIC NORTHWEST 101
1. Determinants of Recreation Value and Use 101
2. Demand and Valuation Estimates for Selected Lakes 106
3. Benefits of Improving Water Quality in Streams 109
4. Conclusions 116
APPENDIX A. DATA TABLES
Table A.I. Population Centroids, Population, and Counties . . .119
Table A.2. Recreation Centroids by Name, County, and
Centroid Number 123
Table A.3. Recreation Activity Days Produced by Centroid. . . .128
Table A.4. Recreation Facility Variables, Existing and
Potential, from Improved Water Quality by
Recreation Centroid 132
Table A.5. Annual (1979) Recreation Value by Activity and by
County for Washington, Idaho, and Oregon 137
APPENDIX B. HOUSEHOLD SURVEY QUESTIONNAIRE 140
Table B.I. Frequency Distribution of Recreation Trips Using
1980 Household Survey Data 143
ACKNOWLEDGEMENTS 144
REFERENCES ,145
VI
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TABLES
Number Page
1 Regression Estimates of Gamma Specification of the Decay Curve. ... 42
2 Regression Estimates of Exogenous and Endogenous Attractions (in
Natural Logs) 53
3 Trip Interchange Matrix 55
4 Demand and Valuation Estimates for Swimming in Selected
Washington Centroids 72
5 Direct Willingness to Pay Estimates per Recreation Day 76
6 Direct Estimates of the Value of Recreation Travel Time 78
7 Annual Valuation Estimates for Boating in Selected Washington
Centroids Using a Semilog and Double-Log Functional Form 86
8 Demand and Valuation Estimates Using a Semilog and Double-Form
and Endogenous Quantity Demanded 88
9 Travel-Cost Valuation Estimates Using a Semilog and Double-Log
Form and a $0.25 Price Increment 90
10 Semilog and Valuation Estimates Using 10-Mile and 20-Mile Origin
Zones 92
11 Estimates of Quantity Demanded by Centroid Using Semilog and
Double-Log Forms and Various Definitions of Origin Zones (in
Thousands of Visitor Days) 94
12 Double-Log Valuation Estimates Using 10-Mile and 20-Mile Origin
Zones 96
13 Annual Recreation Demand and Value of Selected Lakes in the
Pacific Northwest (1979 Dollars) 107
14 Annual Recreation Benefits of Improved Water Quality in Streams
by Activity and by County for Washington, Oregon, and Idaho 113
VI 1
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FIGURES
Number Page
1 Recreation Demand and Benefits: The Knetsch Analysis 14
2 Consumers' Surplus: The Case of Perfect Substitutes 18
3 Demand for Two Recreation Sites 19
4 Consumer's Surplus Using Ordinary and Compensated Demand Curves ... 23
5 Measuring Benefits with Multiple-Price Changes 28
6 Decay Curves for Camping, Fishing, Boating, and Swimming 42
7 Estimating Consumers' Surplus Using Bode's Rule 66
8 Price-Quantity Observations for a Recreation-Site Demand Curve. ... 83
9 The Effect of Substitute Sites on Demand and Value 103
vm
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A REGIONAL RECREATION DEMAND AND BENEFITS MODEL
by
Ronald J. Sutherland
ABSTRACT
This report describes a regional recreation demand and benefits model that
is used to estimate recreation demand and value (consumers' surplus) of four
activities at each of 195 sites in Washington, Oregon, Idaho, and western
Montana. The recreation activities considered are camping, fishing, swimming,
and boating. The model is a generalization of the single-site travel-cost
method of estimating a recreation demand curve to virtually an unlimited number
of sites. The major components of the analysis include the theory of recreation
benefits, a travel-cost recreation demand curve, and a gravity model of regional
recreation travel flows. Existing recreation benefits are estimated for each
site in the region and for each activity. Recreation benefits of improved water
quality in degraded rivers and streams in the Pacific Northwest are estimated on
a county basis for Washington, Oregon, and Idaho. Although water quality is
emphasized, the model has the capability of estimating demand and value for new
or improved recreation sites at lakes, streams, or reservoirs.
This research documented in this report was started in June 1978 and
completed in September 1982.
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EXECUTIVE SUMMARY
A regional recreation demand and benefits model is described and used to
estimate recreation demand and value (consumers' surplus) of four activities at
each of 195 sites in the Pacific Northwest. The recreation activities
considered are camping, fishing, swimming, and boating. The essence of the
model is that it generalizes the single-site travel-cost method of estimating a
recreation demand curve to virtually an unlimited number of sites. The major
components of the analysis include the theory of recreation benefits, a
travel-cost recreation demand curve, and a gravity model of regional recreation
travel flows. Recreation benefits of improved water quality in degraded rivers
and streams in the Pacific Northwest are estimated on a county basis for
Washington, Oregon, and Idaho. The model is also illustrated by estimates of
existing recreation benefits of selected lakes where water quality is good.
Potential and existing recreation benefits are high for sites located near large
urban areas and relatively low for rural sites. The model provides quantitative
estimates of these benefits. Although water quality is emphasized, the model
has the capability of estimating demand and value for new or improved recreation
sites at lakes, streams, or reservoirs.
Recreation benefits are defined as willingness to pay, or alternatively as
consumers' surplus, and measured as the area under the recreation site demand
curve. An improvement in water quality at one site implies an outward shift in
the demand curve for that site and a redistribution of demand from substitute
sites. The issue of the proper measurement of benefits at an improved site when
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there are displaced facilities is analyzed with the conventional utility
maximization model for consumer behavior. The analysis shows that benefits
measured under a single demand curve are net benefits and automatically account
for any displaced facilities.
Two major limitations of the travel-cost method of estimating recreation
demand are its failure to consider substitute sites and the expense of applying
it on a site-by-site basis. A gravity model is used here to overcome each
limitation. This model distributes recreation trips to every site in the region
on the basis of relative travel costs and relative attractiveness of each site.
The output of the gravity model is a trip interchange matrix that is the main
input for travel-cost demand curves for each site in the region.
The conventional gravity model is a distribution model, which means that it
only estimates the distribution of trips between productions and attractions,
which are assumed exogeneous. Because the model does not estimate total demand
at each destination, its applicability is limited for most recreation purposes.
The gravity model is extended here by estimating it iteratively with an
attractions model. As a result, the desirable properties of the gravity model
that determine the distribution of trips also influence total demand at each
s i te.
After a demand curve and consumers' surplus are estimated for each of 195
sites in the region, a simulation analysis is used to determine the sensitivity
of the results to three computational and specification choices that must be
made in the analysis. A semilog specification of a recreation site demand curve
is shown to be preferable to a double-log specification. Recreation trip
origins may be defined as a system of concentric zones, or as each population
centroid. Demand and valuation results are shown to be sensitive to the
definition of an origin, although the best definition is not determined.
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Quantity demanded at several sites was estimated using travel-cost demand curves
and compared to independent estimates of quantity demanded. Errors in these
quantity estimates are particularly large when a double-log specification is
used, and the errors also depend on the definition of the origin zone.
The regional model is used to estimate recreation demand and consumers'
surplus for the four activities at each of 195 sites in the region. Demand and
valuation are again estimated assuming that each officially degraded river
becomes "fishable and swimmable," which is the goal of the 1977 Clean Water Act.
Recreation benefits of improved water quality are estimated quantitatively on a
county basis and for each of the four activities.
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CHAPTER I
INTRODUCTION
The Clean Water Act of 1977 (U.S. Congress 1977) reaffirms the national
goal of eliminating the discharge of pollutants into navigable waters by 1985.
This Act defines an interim 1983 goal of protecting fish, shellfish, and
wildlife and providing for recreation. These goals—expensive, perhaps
impossible to attain in an absolute sense—are becoming less feasible because of
the increasing political importance of competing goals. The desire to expand
energy supplies and to reduce inflation may conflict with regulations that
attempt to achieve a high level of water quality. Furthermore, the benefits to
be gained by achieving the Federal goals may not be sufficient in some cases to
justify their costs.
The Environmental Protection Agency has begun to incorporate economic
factors into its evaluation of water (and air) quality improvement programs.
Although the Agency has not completed its approach to defining economic
efficiency and to performing marginal analyses, there is a clear movement toward
including costs and benefits in the decisionmaking process. However, a major
difficulty in attempting to use quantitative cost-benefit estimates is that the
Agency has no well-developed and tested procedures for making these estimates.
Specifically, the marginal costs of making incremental improvements in water
quality in streams and lakes are difficult to estimate. Similarly, the Agency
does not have well-developed and tested procedures for obtaining dollar
estimates of the benefits of improvements in water quality.
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Although several uses of water may be enhanced by quality improvements,
recreation benefits appear to be the most extensive.1 Therefore, this effort
will focus on the development of a model to estimate recreation benefits of
improved water quality on a regional basis. The model should possess the
conventionally desirable properties of reliability and theoretical soundness,
but it is also important that the model be operational. Specifically, the model
should be able to estimate dollar benefits with a consistent methodology over a
large number of sites, quickly and with reasonable cost. One function of the
EPA, both at their headquarters in Washington, D.C., and at the regional
offices, is to select from a large number of potential sites water-quality
improvement projects that are to be funded. Single-site analyses are time
consuming and expensive and therefore of limited value. The model presented
here combines the gravity model with a travel-cost analysis of recreation
behavior to estimate benefits at any site in the Pacific Northwest, which
corresponds to EPA Region X, excluding Alaska.
Although the EPA is the intended user of this work, other Federal agencies
may find the model appropriate for their recreation planning needs. The Water
Resources Council (1979), through its procedures for evaluating costs and
benefits, defines the evaluation procedures for water-oriented construction
projects that Federal agencies are legally obliged to follow. The Water
Resources Council emphasizes three points: (1) recreation benefits should be
defined as consumers' surplus; (2) demand should be measured with the travel-
cost method or direct willingness-to-pay approach; and if possible, (3) a
regional estimator model should be employed. At present, fewer than a handful
According to Freeman (1979a), recreation benefits are more than half of the
total potential water quality benefits and more than three times larger than the
next most significant benefit.
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of models meeting these criteria have been constructed and none has received
widespread acceptance. The model presented here uses the travel-cost approach
on a regional basis and measures benefits in terms of consumers' surplus.
Because the model meets the criteria of the Water Resources Council, it is
appropriate for use by those Federal agencies concerned with water-based
recreation.
The construction of new reservoirs and the upgrading of existing reservoirs
may encourage additional recreation use, particularly if the appropriate
facilities are provided. The model is designed to estimate the change in
recreation demand and value resulting from an increment in recreation oppor-
tunities. The water-based recreation activities analyzed here include camping,
fishing, boating, and swimming. Because these activities are treated
separately, in effect four models are constructed. The uniqueness of the model
is that demand and benefits can be estimated for any site in the region, which
in this study consists of Washington, Oregon, Idaho, and western Montana.
Demand and value are estimated separately for 195 recreation centroids and for
each of four activities. Because origin and destination centroids can be added
or deleted, the model is capable of analyzing demand and value for any site in
the Pacific Northwest region.
Chapter II provides the conceptual basis for estimating value and benefits.
Recreation benefits are defined as net willingness to pay and measured as
consumers' surplus. An improvement in water quality produces an outward shift
in the recreation-site demand curve. The increase in benefits is measured as
the area between the new and initial demand curves and above the market price,
which is typically zero.
A critical step in estimating recreation benefits for a specific site is
estimating the recreation demand curve for that site. Chapter IV is a review of
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the travel-cost method for developing these estimates. The travel-cost method
has been used extensively with a good measure of theoretical and empirical
support. However, there are several limitations of this approach, for example,
the time bias, but the most serious problem for agencies requiring analysis of
several sites is the expense and level of effort required to analyze a single
site. Vis it-rate data by origin are required for each site, and the data from
one site usually cannot be applied to other sites. These data are obtained from
either household surveys or site attendance estimates, and in either case are
not readily available. When identifying projects to be funded, the Agency must
select from a large number of candidates. The time and survey expense required
to estimate a travel-cost demand curve limits its applicability when it is
necessary to select a few sites from among a large number of alternatives. In
this study, the travel-cost demand curve approach is generalized to include a
large number of sites within a region and can be applied with minimum time and
expense. The development and use of regional estimator models is recommended by
the Water Resources Council (1979) and is also recommended by Dwyer, Kelly, and
Bowes (1977). In addition to economizing on information, such a model can more
accurately reflect the influence of substitute sites.
The input data required in a travel-cost demand analysis include travel
(mileage) costs and visit rates for each population center that sends visitors
to the site being analyzed. Obtaining the visit-rate data is the main time and
financial constraint to applying the travel-cost approach over a large number of
sites. A regional household recreation survey was undertaken in 1980 covering
each of the three Northwestern states. The survey results are used to estimate
the number of recreation trips by activity emanating from each population
centroid in the region. A gravity model is used to allocate recreation trips
from each origin in the region and from external zones to each recreation
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destination. The model includes 155 population centroids (origins) and has 195
recreation centroids (recreation destinations). The purpose of Chapter III is
to develop a regional recreation gravity model. The inputs of the gravity model
are also developed and these include a trip production model, an attractiveness
model, trip-length frequency distributions and a travel distance or impedance
matrix. The output of the gravity model is a trip interchange matrix that, for
each destination in the region, is the number of trips from each origin in the
region. When those trips are divided by their corresponding population, visit
rates are obtained, and they are the critical input in a travel-cost demand
curve. By combining household recreation survey results with a gravity model, a
model is constructed that has the capability of producing travel-cost demand and
valuation estimates for any site in the region.
The main components of the recreation model include the conceptual measure
of benefits and value (Chapter II), the gravity model (Chapter III), and the
travel-cost demand curve (Chapter IV). Chapter V is an examination of some
computation and specification issues involved in calculating a travel-cost
demand curve. The functional form of the demand curve and the size of the
origin zone are analyzed as possible determinants of travel-cost estimates. In
Chapter VI, the operation of the model is discussed and some applications of the
model are presented for both lakes and streams. The first application of the
model is an estimate of recreation benefits at five selected lakes in the
Northwest. The lakes are selected as representative of both urban and rural
lakes. Other things being equal, benefits are estimated to be significantly
larger in urban than in rural lakes. Recreation benefits which would accrue if
the degraded rivers and streams in the Northwest were made fishable and
swimmable are estimated on a county basis. The model is also used to estimate
demand and benefits resulting from improving water-based recreation areas and
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from constructing new facilities. Agencies that may have an interest in this
work include the Soil Conservation Service, Water and Power Resources Service
(formerly the Bureau of Reclamation), Army Corps of Engineers, and others that
need to estimate recreation benefits resulting from water-related projects. In
a study in progress (Sutherland 1982d), the model is being used to estimate
recreation demand and value of the Flathead Lake and existing river system in
western Montana.
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CHAPTER II
RECREATION BENEFITS AND DISPLACED FACILITIES
1. Introduction
The proper measure of the monetary value of a recreation site has long been
of interest to academic researchers and to recreation planners in state and
federal agencies. The economic concept of net willingness to pay (or consumer
surplus) is now widely accepted as the appropriate measure of benefits.
However, a complexity arises when the net willingness to pay for a new or
improved site comes at the expense of an existing substitute site. If measured
benefits of the new site contain a large component of benefits which have been
redistributed from other sites, then these estimated benefits overstate true
social benefits.
The issue of how to treat benefits which are redistributed from displaced
facilities can be resolved with basic economic principles. The resolution has
practical importance to recreation researchers and planners. If benefits can be
measured correctly by estimating net willingness to pay for the new or improved
site and excluding benefits foregone, then estimating recreation site benefits
is feasible. If, however, foregone benefits must explicitly be subtracted from
the benefits of a new site, then all relevant substitutes must be identified and
their demand curves estimated. Such a task is empirically difficult. The
importance of being able to value a recreation site, or more appropriately, the
recreation use of a site, requires that we have a concise definition of these
benefits.
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Some recreation literature is reviewed in Section 2, where it is shown that
some researchers are not sure how to treat displaced benefits. Other
researchers have constructed elaborate econometric models which explicitly
subtract benefits redistributed from substitute sites. The most commonly held
view is that benefits can be measured correctly by estimating willingness to pay
at the new or improved site and ignoring shifts in the demand for substitutes.
A main objective in reviewing these studies is to show the absence of the neces-
sary justification for this position. Indeed, researchers who argue that
benefits from displaced facilities can be ignored often derive their support by
quoting each other.
One objective of this chapter is to determine the proper measure of
benefits of a new or improved recreation site when demand for this site comes at
the expense of existing sites. This chapter will serve as the theoretical
foundation for the benefit measure used in the regional recreation demand model.
In Section 3, benefits are demonstrated to be measured correctly as net
willingness to pay for a new or improved site and any displaced benefits can be
ignored. The main objective here is to provide theoretical support for this
view. The appropriate measure of benefits can be derived from basic economics
principles, and it depends on the assumption of whether the prices of other
goods, such as substitute sites, remain constant. In Section 4, the development
of a new recreation site is assumed to affect the price of other goods. The
proper measure of recreation benefits now must include the change in benefits in
those markets where prices have changed. This case is clearly the exception,
because the price of a recreation site is either zero or fixed, and is therefore
insensitive to changes in other prices.
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2. An Overview of Benefits in the Recreation Literature
A brief overview of benefits measurement in the recreation literature is
presented focusing on two questions: (1) What is the appropriate measure of
benefits of a new or improved site when demand for that site comes at the
expense of substitute sites? and (2) What is the explicit theoretical just-
ification for the commonly accepted definition of benefits?
All recreation benefit analyses contain some definition of benefits, but
the issue of measuring benefits when there exist close substitutes has only
recently been considered. For instance, in the exchange by Stevens (1966, 1967)
and Burt (1967) on the fishing benefits of water pollution control, no
consideration was given to demand shifts for fishing at substitute sites.
Reiling, Gibbs, and Stoevener (1973, p. 3) reveal a clear preference for
avoiding this issue by explicity assuming that expanded use of one site does not
come at the expense of substitute sites. Some of the more recent literature by
Knetsch (1977), Mishan (1976), Freeman (1979a) and Cesario and Knetsch (1976) is
reviewed, which explicitly considers measuring benefits at one site when there
exist substitute sites. The focus is on how benefits are measured and
particularly on how this benefit measure is justified.
A. Knetsch
Knetsch (1977) is concerned with the evaluation of benefits at a proposed
site when there is an identical displaced facility requiring a greater
travel-cost. To review Knetsch's position, the demand curve for an existing
site is depicted in Figure 1. Quantity demanded is 1,000 recreation days and
consumers' surplus is $2,500. Assume that a second and identical site is
constructed that reduces travel costs by $1 for each population centroid. The
demand curve for the proposed site appears on the right hand side of Figure 1.
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FIGURE 1
RECREATION DEMAND AND BENEFITS: THE KNETSCH ANALYSIS
Existing Site
Proposed Site
-co-
o>
o
1000
Quantity
( Recreation Days)
1000 1500
Quantity
(Recreation Days)
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The area above $1 and under this demand curve is equal to the area under the
demand curve for the existing site. According to Knetsch, the demand curve for
the new site slopes downward and to the right from a price less than $1 to P =
0. The demand curve but becomes horizontal at $1 because at a fee of $1 or more
all recreationists return to the initial site. The increase in total benefits
is $1,250, which is the area under the new (kinked) demand curve. Knetsch
concludes that the demand curve for the new facility must reflect existing
facilities, but the loss in value of the existing facility can and should be
ignored in calculating the net gain of the new facility.
Unfortunately, in Knetsch1s analysis measured benefits at the new site do
not include a redistribution of willingness to pay from a substitute site
because no redistribution occurs. The willingness to pay for the first site is
$2,500 before the new site is constructed and, at a price of $1 or more at the
new site, it is $2,500 after the new site is constructed. As the price of the
new site rises above $1, the willingness to pay for the existing site remains
unchanged. Knetsch1s analysis is based on a special case where the demand curve
for the substitute site doesn't shift. Because there is no decrease in
willingness to pay for the substitute site, his analysis provides no support for
the position that the decrease in willingness to pay for substitute sites can be
neglected when measuring net benefits of a new or improved site.
However, a particularly important econometric implication of Knetsch1s
analysis is the need to include some measure of substitutes when estimating the
site demand function. If the specification of the proposed site excludes the
existing site, the continuous demand curve from Q = 1,500 to P = $6 would be
estimated. Benefits would be overestimated by $2,500. By correctly specifying
the demand for the proposed site, the kinked demand curve would presumably be
15
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estimated. Benefits of the proposed site would be correctly estimated at
$1,250.
B. Mis nan
Mishan (1976), in his authoritative treatise on cost-benefit analysis,
addresses the issue of measuring consumers' surplus when increased purchases of
one good are at the expense of other goods. Mishan states that if a new good is
introduced or the price of a good falls, consumers' surplus should be measured
by neglecting changes in consumers' surplus of alternative goods. He says:
... I append a note to this chapter containing a simple
example in order to reassure the reader that in
measuring the consumers' surplus of a new good, or a
good the price of which has changed, he should neglect
the induced shifts of demand of related goods, (p. 32)
The reduction in the demand for the substitute good shifts the demand schedule
to the left producing a decrease in consumers' surplus. According to Mishan,
this loss "... is not to be regarded as a loss of consumers' surplus...";
instead, "This reduction in area is simply the consequence of consumers
bettering themselves by switching from good y to the new lower priced good x."
(p. 34).
When Mishan considers relatively close substitutes he uses a demand
schedule for each good, and asserts that the area under the demand schedule for
the substitute good can be ignored. He defends his position by example and
illustration, but changes the case so that the two goods are perfect substi-
tutes. Because what was two goods is now only one good, an aggregate demand
schedule replaces two separate schedules. Specifically, Mishan considers the
demand for transportation across a certain water body where a ferry service is
being replaced by a bridge. With the ferry service the price is P0 and
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consumers' surplus is area P0ab in Figure 2. After the bridge is constructed,
the ferry is discontinued and the price of transportation falls to Px.
According to Mishan, the appropriate measure of the benefits of constructing the
bridge is the area under the demand curve and between the new and initial price
(PiPobc).
When measuring the increment to benefits, it is possible to think of
consumers' surplus foregone as being subtracted from the gross increase. With
the ferry service, consumers' surplus was area P0ab. After the ferry is
discontinued, consumers' surplus resulting from the bridge is P^c. The
increment in consumers' surplus is total surplus after the ferry service (P^c)
minus consumers' surplus foregone from the bridge (P0ab); this increment is
PaP0bc. The reason for subtracting consumers' surplus foregone is that the
ferry service is discontinued, and the bridge demand schedule assumes that the
ferry is not in operation.
Assuming that the ferry could operate if the price were P0, the demand
schedule for the bridge is deb as before, but it becomes perfectly elastic at
price P0. The amount of consumers' surplus is the same as above, but it is the
area above price P^ and below the bridge demand schedule. No consumers' surplus
is subtracted because no consumers' surplus is foregone.
Mishan1 s position is that benefits of a new site (in this case a bridge)
can be measured by neglecting shifts in the demand for substitutes. However,
his justification is an illustration that, in principle, is identical to
Knetsch's. By considering the case of perfect substitutes and a single demand
curve, Mishan provides no support for the position that the markets for
substitutes can be ignored when measuring benefits at a new or improved site.
In Mishan's case, like Knetsch's, there is no redistribution in consumers'
surplus.
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FIGURE 2
CONSUMERS' SURPLUS: THE CASE OF PERFECT SUBSTITUTES
Quantity
C. Freeman
The analysis of Mishan and Knetsch are special cases and not useful in
analyzing the general case where the site demand curve shifts to the right and
the demand for substitutes shifts to the left. Freeman (1979b) has explicitly
addressed the issue of measuring recreation benefits when the demand curve for
substitute sites shifts, so his analysis is reviewed. In Figure 3, the initial
demand curves for site A and B are denoted as DAI and DR2. An improvement in
water quality at site A shifts the demand curve outward to D.3 and the demand
for the substitute shifts inward to DBI. Benefits of the improvement are
measured as the area between the new and initial demand curves for site A and
above the market price (area BDGE). According to Freeman, no consideration
should be given to the decrease in willingness to pay for the substitute site,
area RSVU. He states:
In utilizing this measure of benefits, there is no need
to take into account changes in recreation use at other
sites or savings in travel cost (Knetsch 1977). These
are captured by the BECD [BDGE in Figure 3] benefit
measure, (p. 199)
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FIGURE 3
DEMAND FOR TWO RECREATION SITES
Site A
Site B
b T
DAI DA2 DA3
DBI DB2 DB3
Qi
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Freeman's conclusion is that benefits can be measured by demand curve shifts at
the improved site and demand shifts at substitute sites do not explicitly enter
into the benefit calculation. Freeman provides no justification for neglecting
the decrease in consumers' surplus at substitute sites, except for his reference
to Knetsch. My review of Knetsch's position revealed it to be a special case
where there is no decrease in willingness to pay for the substitute site.
D. Support for the Conventional Measure of Benefits
The validity of Freeman's position is not an issue at this point. Rather,
the contention here is that the recreation benefits literature (as exemplified
by Knetsch, Mishan, and Freeman) does not contain persuasive theoretical
justification for the position that displaced benefits should be ignored when
calculating net benefits of a new or improved site. Although Mishan, Knetsch,
and Freeman reach the same conclusion, they offer no evidence that shifts in the
demand for substitutes should be ignored when calculating benefits of a new or
improved site. Yet their position seems to be the accepted view of recreation
researchers. For instance, Cesario and Knetsch (1976, p. 101) state:
That is, the value measurement for a new site is
measured independently of any diminutive effects on the
use of existing sites. Any losses in consumer surplus
at existing sites are irrelevant to the calculation
(even though it may be informative for planning purposes
to calculate the magnitude of these quantities). Such
losses merely reflect changed demand characteristics and
losses in the value of some fixed assets, and should
have no bearing on the benefit calculation for the
proposed site which would be judged on its merits alone
(McKean 1958; Mishan 1971; Knetsch 1974).
Cesario and Knetsch provide no rigorous justification for this position, relying
instead on references such as Mishan and Knetsch. The above review of Knetsch
20
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and Mishan argues that they do not support the view that any losses of consumer
surplus at existing sites are irrelevant.
Although the sample of recreation benefits literature reviewed here is
small, the work is probably the most important in this area. On the basis of
this review, two general conclusions are suggested. First, the prevailing view
is that benefits of a new or improved site can be measured as the area between
the new and initial demand curve and above the market price and, furthermore,
that demand shifts for substitute sites need not be considered. Second, the
theoretical support for this position has not been made explicit in this
1iterature.
In an analysis of the potential benefits of a new ski site at Mineral King,
Cicchetti, Fisher, and Smith (1976) challenge the commonly held view that
benefits can be measured by considering only the impacted site.1 Cicchetti et
al. specify a simultaneous demand equation model in which the price of each ski
site is an argument in each demand curve. They assert that specifying a
multisite model allows them to estimate the effects of a change in the price at
one site on demand and consumers' surplus at the substitute sites. In an edited
version of the Mineral King study, Krutilla and Fisher (1975, p. 198) state that
the new Mineral King site would result in a reduction in demand for substitute
sites and these effects are captured by measuring the change in consumers'
surplus over multiple sites. Bishop and Cicchetti (1973) further explain the
benefit measure used in the Mineral King paper:
1Burt and Brewer (1971) used a multiequation model very similar to that of
Cicchetti et al. (1976).
21
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In a recent paper Cicchetti, Fisher, and Smith (1972)
simultaneously estimate the demand for various skiing
sites in California. The location of other sites and
therefore their relative prices are taken into account
explicitly by using a generalized least squares
regression approach. The benefits of new sites at
various locations can be determined by simultaneously
estimating the change in consumer surplus for the
alternative sites, (p. Ill)
The estimate of consumers' surplus in the Mineral King study explicitly reflects
the reduction in willingness to pay for substitutes. This position is in marked
contrast to that taken in the studies discussed above and implies the need to
define the theoretical underpinnings of the prevailing view.
3. The Theoretical Underpinning for the Conventional Measure of Recreation
Benefits
The above review of the definition of recreation benefits suggests some
ambiguity on the issue and the absence of agreement on theoretical support for
any particular definition. Benefits are now demonstrated to be properly
measured by considering only the demand curve for the affected site. Further-
more, this demonstration follows from an application of economic principles.
The following analysis may assume an environmental improvement at a
recreation site (hence a demand curve shift), a decrease in the price of a site,
or the introduction of a new site. On grounds of expositional convenience,
consider the net benefits of introducing a new recreation site. Panel B in
Figure 4 depicts an ordinary demand curve (ODC) and a Hicks compensated demand
curve (HCDC), where OD depicts the quantity of the new good demanded at price
?i.2 Net benefits of the new good can be measured as the area under the
2A decrease in the price of a good increases the quantity demanded because
people substitute this good for other goods and because the lower price effec-
tively increases real income. The ordinary demand curve reflects both this
substitution and income effect. The compensated demand curve reflects only the
substitution effect and presumes that real income is unchanged.
22
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FIGURE 4
CONSUMERS' SURPLUS USING ORDINARY AND COMPENSATED DEMAND CURVES
Panel A
a>
u
Quantity of X (Recreation Days at New Site)
Panel B
Ordinary
.Demand Curve
±
i
1 Compensated
I Demand Curve
C D
Quantity of X( Recreation Days at New Site)
23
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compensated demand curve and above the market price, area PxPoF. This area
reflects the change in consumers' surplus caused by introducing the new good and
is defined as the willingness to pay for the new good over the above actual
payment. On grounds of empirical necessity and the work by Willig (1976),
consumers' surplus, as measured under the ordinary demand curve, is generally
considered an acceptable approximation to the area under the compensated demand
curve. According to Knetsch, Freeman, Mishan, and Cesario and Knetsch, benefits
of a new site are measured as the area under the compensated demand curve, or
approximately as the area under the ordinary demand curve. At issue is whether
this area correctly measures the benefits of a new site and what consideration
if any should be given to benefit from displaced facilities.
This question is answered by deriving a demand curve for a new recreation
site using indifference curves and price lines. Assume that a utility-
maximizing consumer allocates all his income between good X (the new recreation
opportunity) and a composite of all other goods, which is termed Hicksian money.
Before the recreation opportunity was provided, the consumer purchased only the
composite good and did not consume good X. As depicted in Panel A of Figure 4,3
this initial allocation is defined by point A, which is the point of tangency
between price line P0 and indifference curve I0. After the recreation
opportunity is provided, Pt becomes the price of recreating relative to the
price index of the composite good and the consumer maximizes utility by moving
from point A to point G. The change in welfare, as measured by the compensating
variation, is AB after it has been converted to dollar terms by multiplying by
the price index of the composite good. A well-known proposition in welfare
economics, and critical point here, is that this measure of consumer surplus in
3The diagram in Figure 4 was presented by Currie, Murphy, and Schmitz (1971).
24
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Panel A corresponds to consumer surplus as measured under the compensated demand
curve in Panel B. We can now focus on the welfare gain AB in Panel A.
Recreation use at the new site (good X) comes partially at the expense of
substitutes, which in this case is the composite good. As a result of the new
recreation opportunity, use at the site becomes OD (Panel A) and demand for the
substitute decreases by AJ. Hence the improvement in welfare, which is measured
by the movement from indifference curve I0 to 11, clearly reflects a reduction
in demand for the substitute composite good. The demand curve and consumer
surplus in Panel B do not imply how foregone benefits should be treated.
However, the derivation of this demand curve and the corresponding measure of
consumer surplus (AB in Panel A) show clearly that measured consumer surplus is
a net increment to benefits.
The above analysis supports the conventional measurement of benefits,
subject, however, to a stringent assumption. As seen in Figure 4, Panel A, the
composite good is an aggregation or weighted sum of all other goods, where the
weights are the prices of these goods. As stated originally by Hicks (1939, p.
33), if the relative prices of a group of commodities are given and unchanged,
these commodities can be lumped together and treated as a composite good.
Hicks' theorem of group commodities is being used to justify defining the
decrease in relative price of good X. Specifically, the above conclusion
assumes that lowering the price of a new good does not affect the relative
25
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prices of other goods.4 If the introduction of a new site affects relative
prices of other goods, the composite good theorem is not applicable. At issue,
then, is determining the proper measure of consumer surplus under conditions of
multiple-price changes.
4. Consumer Surplus with Multiple-Price Changes
The view that recreation benefits can be measured by considering only the
market for the single affected site is correct if we assume an ordinary
Marshallian partial equilibrium demand curve.5 In the Marshallian demand curve,
prices of all other goods are fixed, and therefore Hicks' theorem of composite
goods is applicable.6 In this section we consider the measure of recreation
benefits when a new or improved site affects prices in more than one market.
Although the recreation literature gives little attention to this issue, it
has been treated at length in the welfare theory literature by Harberger (1971)
and Mohring (1971) among others. Borrowing an illustration from Mohring, assume
two goods, margarine and butter, whose demand functions can be written as
4According to the Cicchetti et a]_. analysis, for each individual, relative
prices of existing sites are invariant to the construction of a new site.
However, the price of the new site relative to that of existing sites differs
according to the origin of the individual. The latter point does not nullify
the use of the composite good theorem, which seems appropriate in the Cicchetti
et al. study and in the Burt and Brewer study. In these studies, there was a
decrease in the price of the new site that produced a shift in the demand for
substitute sites, but relative prices of these substitute sites remains
constant. Burt and Brewer and Cicchetti et al. used a quadratic benefit
estimation equation that is a generalized approach for integrating a system of
equations, in this case, when prices change at one or more sites. Because only
one price changes (the new site), the simpler technique of integrating that
demand equation would have been appropriate.
5The Marshallian demand curve is a sufficient but not necessary condition to
consider only the affected site. If all other prices change proportionately,
the composite good theorem still holds.
6Freeman (1979b, p. 35) and Mishan (1976, p. 32) recognize the necessity of
invoking Hicks' composite good theorem when analyzing benefits in a single
market.
26
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Qm = fi
% = ^V V Y) '
where the price of margarine (P ) and the price of butter (P.) enter into each
demand equation along with income (Y). Initial equilibrium in the margarine and
butter markets is defined in Figure 5 by points A and C, respectively. The
margarine market is analogous to our proposed site, except that Mohring's
initial change is a reduction in price. The price of margarine falls from P' to
P" which produces a decrease in the demand for butter from D. to D' If the
price of butter remains constant at P' consumer surplus is measured as the area
under the margarine demand schedule between the new and initial price.
Mohring emphasizes that even though the butter demand schedule shifts, this
fact need not be considered when measuring the increase in benefits resulting
f
from lower priced margarine. This point corresponds to our conclusion in the
previous section that benefits are correctly measured under the demand curve for
the affected recreation site, and displaced facilities can be ignored.
Suppose the illustration is changed so that a decrease in the price of
margarine decreases the demand for butter as before, but now the price of butter
falls from P! to PV. This price decrease in butter increases the net willing-
ness to pay for butter and the increment in consumer surplus must be added to
the increase in consumer surplus for margarine to obtain the appropriate measure
of welfare change. This point is well recognized in the welfare economics
literature and can be generalized to state that the change in consumer surplus
resulting from price changes in several markets is the sum of the increment of
consumer surplus in each market (Harberger 1971).
Mohring emphasizes the ambiguity of measuring the change in consumer
surplus in the butter market, and he notes that three measures have been
proposed. Using the initial butter demand curve, consumer surplus is P"P'CD,
27
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FIGURE 5
MEASURING BENEFITS WITH MULTIPLE-PRICE CHANGES
Demand for Margarine
Demand for Butter
but this measure is PVP/FE if the new demand schedule is used. If we move from
b b
the initial to new demand schedule, the change in consumers' surplus is P/CEPo-
Because a rationale can be presented for each of these definitions, the measure-
ment of consumer surplus is, in general, sensitive to the definition chosen.
This point is recognized in the welfare theory literature and has led Silberberg
(1972) to conclude that the appropriate change in utility or welfare cannot be
defined unambiguously. Hotel!ing (1938) noted this indeterminancy in the
measure of benefits and also the condition under which consumer surplus could be
measured unambiguously. This condition is known as the integrability condition,
and means that the demand curves have identical cross partial derivatives with
respect to prices. The integrability condition for the margarine and butter
demand curves is
8Q, 9Q
x x
9Pm 9Pb
28
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which says that the change in the quantity of butter (Q. ) demanded resulting
from a change in the price of margarine equals the change in the quantity of
margarine (Q ) demanded resulting from a change in the price of butter As
noted by Mohring (p. 356), this condition holds if the demand curves are Hicks
income-compensated or if the income elasticity of demand for both goods is zero.
Burt and Brewer (1971) and Cicchetti et al. (1976) recognized this requirement,
and therefore specified their demand equations as linear and symmetrical.
These conclusions can be restated in terms of our main concern of valuing a
recreation site that has a substitute site. Let the price of recreating be
defined as the entrance fee or as travel costs. If a decrease in the price of a
recreation site (or the construction of a new site) affects the demand for
substitutes or complements, but leaves their prices (entrance fees or travel
costs) unchanged, benefits are estimated properly as the area under the site
demand curve and between the initial and new price. No explicit consideration
should be given to the decrease in willingness to pay for the substitute site.
Alternatively, if the decrease in the price of a site causes a change in
relative prices of other goods, such as a substitute site, the increment
(decrement) in consumer surplus in the substitute site resulting from the price
change must be added (subtracted) to that of the first site to obtain the total
change in consumer surplus.
A peculiar feature of outdoor recreation is that the price of recreating,
as measured by entrance fees, is generally zero. Where entrance fees are
charged, for example campgrounds, these prices are insensitive to the intro-
duction or improvement in substitute sites. Where travel costs are used as a
proxy for price, the travel cost to substitute sites is invariant to a demand
shift at the site being analyzed. Therefore, for most all practical applica-
tions in recreation, including the travel-cost approach that is used here,
29
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benefits of a new or improved site can be measured correctly as consumer surplus
at the new or improved site.
5. Conclusions
This chapter addresses the issue of the proper measure of benefits at a new
recreation site when demand for that site comes partially at the expense of
substitute sites. The literature reviewed indicates that some researchers have
avoided the issue; others have explicitly subtracted benefits foregone. The
prevalent view is that benefits can be measured by considering only the new site
demand curve. The limitation with this view is the absence of any theoretical
justification. As shown here, benefits are measured correctly by considering
only the demand curve for the new site, but this demand curve must be correctly
specified to consider existing sites. Use of the conventional microeconomic
model of consumer behavior shows that recreation benefits, measured as
willingness to pay for the new site, automatically net out benefits foregone
from substitute sites. In the special case where the introduction of a new site
causes prices of other sites or goods to change, the increment in benefits is
the net sum of consumers' surplus in these affected markets.
30
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CHAPTER III
ESTIMATING RECREATION TRIPS WITH A GRAVITY MODEL
In Chapter II it was established that recreation benefits can be defined as
the area under the recreation demand curve above the market price. Chapter IV
contains a discussion of the travel-cost approach to estimating a recreation
demand curve. This chapter presents the methodology used to obtain the input
data of the travel-cost demand curves. A 1980 regional household recreation
survey is used to estimate the number of recreation trips by activity from each
origin in the region. An attractiveness model is used to obtain preliminary
estimates of the attractions of each site in the region. The distribution of
trips between each origin and destination is estimated by using a gravity model.
The gravity model and attractiveness model are then integrated, and quantity
demanded at each site is estimated with the revised attractiveness model. The
output of the gravity model is the number of visitor days received by each site
in the region by activity and emanating from each origin in the region. These
outputs are the basic input required to calculate a travel-cost demand schedule
for each recreation site in the region.
This analysis of recreation behavior differs from existing studies by
virtue of magnitude, with 195 recreation centroids defined over three and
one-half states. This scale is considerably larger than those in the regional
models of Burt and Brewer (1971), Cichetti, Fisher, and Smith (1976), Cesario
and Knetsch (1976) and Knetsch, Brown, and Hansen (1976). The primary advantage
of this size model is that any site within the region can be analyzed. Also,
31
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the influence of all potential substitute sites is most likely to be reflected
in a larger model. The ability to analyze a large number of sites results from
the use of household surveys to estimate recreation trips by origin and a
gravity model to estimate the distribution of these trips.
Most recreation analyses focus on one activity or treat recreation as a
composite homogeneous good, for example, Stevens' (1966) estimate of the fishing
benefits resulting from improved water quality. In contrast, this analysis
considers four activities: camping, fishing, boating, and swimming. A focus on
one activity may be inadequate when several activities respond to water-quality
improvement. These four activities are not homogeneous; they differ in their
response to site characteristics such as water quality, average travel distance
and length of stay, and value per activity day. Furthermore, the relative
composition of these activities varies widely across recreation sites. For
these reasons, the above four activities are analyzed separately.
A fundamental difference between this study and other regional travel-cost
studies is the method of obtaining input data. In the regional models of
Cesario (1973, 1974, 1975), Cesario and Knetsch (1976), Cheung (1972), and
Knetsch, Brown, and Hansen (1976), origin-destination data were obtained from
site attendance records or on-site surveys. In this study, origin-destination
allocations are estimated from a gravity model that uses origin data from
household recreation surveys. The costs and benefits of this approach relative
to that of using site-specific attendance data merit brief comment.
The initial cost of a regional household recreation survey and regional
model is of course substantial, but once the survey is taken and model con-
structed, the marginal cost of analyzing additional sites is less than that of
most single-site analyses. The cost of using existing attendance records is
low, but in the Northwest, these data are deficient in both quantity and
32
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quality. Several agencies, such as the Corps of Engineers, Water and Power
Resources Service, U.S. Forest Service, and state parks departments have total
attendance data, but not by origin. Agencies may define attendance in terms of
visits, visitor days, recreation days or activity days, and the definitions of
these terms tend to vary between agencies. The on-site survey approach is less
expensive when the number of sites is small, but more expensive when the number
of sites is large. The number of sites at which the costs of the household
survey and site survey approach are equal cannot be defined a priori.
The household survey approach coupled with the model presented here offers
significant advantages over the on-site survey approach. The present model can
estimate demand and consumers' surplus for a proposed site at any location in
the region. The on-site survey approach obviously cannot obtain attendance data
for a proposed site; so the demand function for the proposed site must be
estimated by assuming that the site is similar to an existing site. The demand
for a site depends on site characteristics, distance to population centers, size
of the population centers, and alternative sites available to each population
origin. A model based on these variables can be used to estimate input data for
the demand curve of a proposed site; but the model would, at best, produce
reliable estimates of total quantity demanded. However, the distribution of
these trips by origin would be estimated with large errors unless substitute
recreation opportunities were accurately modeled for each origin. Existing
regional models do not have this capability, and consequently are limited in
terms of estimating demand curves for proposed sites. The model presented here
can estimate total quantity demanded for a proposed site and the distribution of
this demand by origin. In addition to being able to estimate demand and
benefits for any site in the region, the estimates should be more reliable than
those based on "similar sites" and site-attendance data.
33
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The travel-cost approach is not applicable when most users come from one
origin because travel distances and, hence travel costs, will not possess
significant statistical variability. The average distance traveled for fishing,
swimming, and boating is about 40 miles, and a large number of recreation sites
are located near urban areas. If the site survey defines origin as county or
city, the data will be inadequate for a large number of sites. The methodology
used here permits dividing urban areas into several population centroids. In
this way, the travel cost is measured accurately for a large number of
recreators, and travel costs will vary over these users.
As a brief overview, the model consists of four integrated components: a
trip production model, an attractiveness model, a trip distribution (gravity)
model, and a demand and valuation model. The trip production model is used to
estimate the number of recreation days by activity that emanate from each
population centroid in Washington, Oregon, Idaho, and western Montana. The
attractiveness model is used to estimate the attractiveness, or total quantity
demanded, of each recreation centroid in the region. Recreation days produced
and attracted enter a gravity model where they affect the distribution of
recreational travel. A gravity model estimates a trip interchange matrix that,
for each recreation centroid, is the number of activity days received from each
origin. These outputs are used to estimate a travel-cost demand curve for each
recreation destination and for each of the four activities considered.
Recreation value is measured as the area under the demand curve and above the
market price, which in this study is presumed to be zero. An improvement in
water quality coupled with an increase in facilities produces an outward shift
in the demand curve, and the area between the initial and new curve represents
the benefits of improved water quality.
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1. Gravity Model Overview
The gravity model as applied to travel behavior is a trip distribution
model that is used to estimate trip interchanges between all pairs of origins
and destinations. Normally, the number of trips produced and received by each
zone are exogenous variables. The endogenous variable is the allocation of
these productions. The basic premise of the model is that the number of trips
produced by origin i and attracted to destination j is directly proportional to
(1) the total number of trips produced in i, (2) attracted to j, and (3)
inversely proportional to a function of spatial separation between the zones.
The gravity model is ideally suited to estimate the distribution of
recreation travel. However, the most stringent limitation of the model, for
purposes of recreation analysis, is the requirement that attractions are
exogenous. According to this assumption, the quantity of recreation use
demanded at each site is known, and the gravity model solves for the allocation
of this demand by origin. Previous versions of this study, including Sutherland
(1982c), are subject to this limitation. The gravity model is developed in this
chapter first, along traditional lines, and using exogenous attractions. In the
latter part of this chapter, the gravity model is extended to simultaneously
estimate attractions. This extension is shown to result in a substantial
improvement, both theoretically and empirically, in the regional recreation
demand model.
The gravity model has a long history of successful applications in
economics and in transportation analysis, but has also been used to analyze
recreation travel. The primary use of the gravity model in economics has been
to analyze regional trade flows. Anderson (1979, p. 106) conjectures that this
model is the most successful empirical trade device to evolve in the last 25
years. Regional economics books, such as Isard's (1960), typically contain a
35
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discussion of this model. However, the most frequent application of the gravity
model is to estimate both interurban and intraurban travel flows. The gravity
model appears to have had a long and successful history as a tool for analyzing
travel flows. The prominent position of this model is confirmed by the
attention given it in the transportion engineering texts, such as those by
Hutchinson (1974), Dickey (1975), and Stopher and Meyburg (1975).
The gravity model owes its theoretical foundation to Newton's Law of
Gravitational Force, which stated loosely, is that the gravitational force
between two bodies is directly proportional to the product of their masses and
inversely proportional to the square of the distance between them. A frequent
criticism of the model as applied in economics is that the theoretical founda-
tions are in physics and not in the principles of social behavior. This
criticism has been answered by some recent work that establishes a theoretical
foundation for the gravity model. For example, Anderson (1979) provides a
theoretical explanation of the model as applied to commodities. Niedercorn and
Bechdolt (1969) derive a gravity model from consumer theory by using a loga-
rithmic and power utility function.
Despite theoretical support and extensive empirical success in predicting
urban travel, the gravity model has been used infrequently in analyzing recre-
ation travel and with limited success. Ellis and Van Doren (1966) found the
gravity model predictions of camping in Michigan to be less reliable than those
from a systems theory model. Freund and Wilson (1974) obtained some rather
large discrepancies between gravity model predictions of recreation behavior in
Texas and observed behavior.
Several specifications of the model have been put forth; the specification
used here is one which is used widely in transportation analysis and was
developed by the Bureau of Public Roads (1965). The equation is
36
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A. F.
(III.l) T,, = P, =-f-^
and the constraints are
(III. 2) IT.. = P. and
j
(III.3) IT.. = A.
,- iJ J
where i refers to origin and j to destination. The symbols in (III.l) are
defined as
T-- = number of activity days produced at i and attracted to j,
P. = number of activity days produced at i,
A. = number of activity days attracted to the jth recreation centroid, and
J
F-- = a calibration term for interchange ij, which reflects the effect of
J distance.
Equation (III.2) states that the estimated trip interchange matrix (T. .)
must imply that the total number of trips from origin i (IT..) is equal to the
j 1J
exogenous number of trips produced. In the calibration procedure used here and
elsewhere, this constraint is satisfied automatically. According to Eq.
(III.3), the estimated trip distribution matrix, which estimates the number of
trips terminating at each site, must also be consistent with exogenously
estimated attractions.
The gravity model, as generally used, is a distribution model; it takes a
given number of recreation activity days emanating from population centroids and
distributes these days according to the relative attractiveness and spatial
impedance between centroids. In the special case where site-attendance data and
trip-production data are available, the gravity model is well suited to estimate
37
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allocation of these trips. If site-attendance data are unavailable, they must
be estimated by a demand model. Ideally, a demand model would include travel
costs to all substitute sites and the relative attractiveness of all substitute
sites. Such a demand model would be quite similar to the gravity model. In
this study, the gravity model is extended to include endogenous attractions;
hence, it becomes a demand and distribution model.
As noted by Ewing (1980), Eq. (III.l) has two important properties. Adding
destinations to the system or increasing the attractiveness of the existing
destinations will increase the number of trips to that destination, but at the
expense of alternative destinations. That is, the total number of trips is
exogenous. Second, the model allocates trips by considering the substitut-
ability between recreation centroids, a property particularly important for
recreation analysis. The proportion of trips emanating from i with destination
j is a function of the attractiveness and spatial impedance of destination j
relative to that of alternative recreation centroids in the system. As
reflected in the denominator of Eq. (III.l), all sites in the region are
considered as potential substitutes being analyzed. This property, plus the
definition of substitutes in terms of both travel distance and attractiveness,
make the gravity model appealing for a regional recreation analysis. Because
the quantity of recreation demanded at each site depends on the same variables
that are in the gravity model, it is important to incorporate this inter-
dependence in the overall model.
When applied to transportation problems, the dependent variable is trips;
however, the variable of interest in recreation studies is recreation days or
activity days. In this study, the terms will be used synonymously, and a
distinction will be made only for trips of more than one day. Origins and
destinations are often defined as zones or centroids. The term population
38
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centroid is used to define the origin zone, and recreation centroid to define
recreation zone. In each case, a centroid is a point but is used to represent
origins and destinations of the neighboring area.
The rationale for using a gravity model is that the estimated trip inter-
change matrix (T-.) serves as an input in estimating a large number of
travel-cost demand schedules. Each column vector in T. . estimates the number of
recreation activity occasions produced at origin i with a specific recreation
destination. In this study j = 1,2, ..., 195 so 195 demand curves can be esti-
mated for each of the four activities considered. Because destinations can be
added to the analysis, the model potentially can estimate a demand curve and
recreation value for each activity and for any site in the region. The
construction of the gravity model input data is explained in Section 2.
2. Gravity Model Input Variables
The three gravity model input variables are developed in this section. The
spatial impedance variable (F..) is discussed first, followed by the trip
production model (P.) and the attractiveness model (A.).
A. Fraction Factors (F..)
A necessary input to construct the F. . terms is the impedance matrix (I..),
which contains the minimum driving distance from each population centroid
(internal and external to the region) to each recreation centroid in the three
and one-half state region. This matrix was estimated by first defining the
population and recreation centroids of each county, and where appropriate,
multirecreation or multipopulation centroids were used per county. There are a
total of 129 counties in Washington, Oregon, Idaho, and western Montana, but
there are 141 internal population centroids and 195 recreation centroids. In
39
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this model the remainder of the United States and Canada is divided into 14
external zones, so there are a total of 155 population (origin) centroids.
Table A.I in Appendix A lists the population centroids by name and county and
gives the corresponding population. Table A.2 lists the recreation centroids by
name and the corresponding county. After each centroid was defined and located
on a highway map, a network was constructed to show the distance between inter-
sections along major roads. Possible routes from each population centroid to
each recreation centroid were thereby identified. A computer program was used
to solve for the minimum driving distance between each population and recreation
centroid. The resulting travel distances constitute a 155-by-195 impedance
matrix. Each column vector in this matrix denotes the minimum one-way mileage
from each population centroid to a specific recreation centroid. The impedance
matrix is an input in the gravity model, and the column vectors in the matrix
will also be used as inputs in the travel-cost demand curves.
The F. . variable in (III.l) reflects the influence of travel distance (or
time) on the propensity to travel. This variable is estimated as the dependent
variable in a trip-length, relative frequency distribution, which is also termed
a decay curve.
Our 1980 regional household survey included a question on the one-way
travel distance in miles for each recreation trip. Because the sample size
exceeds 3,000 and several persons in each household may have taken numerous
trips, only a subsample of the sample results is used to estimate the decay
curves. We sampled every fifteenth questionnaire and recorded the number of
activity days by type and the corresponding one-way miles traveled.
The widespread use of gravity models has resulted in serious study of the
shape of decay curves and ways to estimate them. One approach is to use the
power function F.. = Po0,-,- where F.. is the proportion of trips from i to j
' J ' J J
40
-------
and D.. is the corresponding distance. Another option is the exponential
function F. . = p0e ^1 ij. Either of these functions may be adequate, but quite
often decay curves are humped and highly skewed to the right. For instance,
people are more likely to travel 40 to 50 miles to camp than to travel 5 to 10
miles, particularly if they live near city center in a large city.
The preferred decay curve model of most researchers is a gamma distribu-
tion, which is a combination of the exponential and power functions:
(III.4) F... = P0D?J.e"p2Dij .
The px coefficient may be positive and thereby allow for a peak in the decay
curve. This specification is used to estimate a decay curve for each of the
four activities being considered. The results are presented in Table 1.
The coefficients for the exponent are not negative as expected, nor are
they statistically significant. The R2 values indicate that each of the
equations has rather low explanatory power. These apparently discouraging
results are easy to explain. The raw data do not depict the above relationship
for three of the four activities. Consequently, one of the reasons for using
the gamma distribution is not applicable to those data. Also, respondents
tended to round off their distance traveled on long trips to the nearest 50
miles. For example, respondents indicated a total of 522 recreation days at 300
miles and no recreation days at 310 or 290 miles. The tendency for long trips
to consist of "spikes" (and zeros) means that the regression estimate is too
high in the tails. The consequence of using the gamma estimates in Table 1 in
the gravity model would be to allocate far too many people on long trips.
The data error caused by respondents' rounding distances to the nearest 50
miles implies that any specification estimated with ordinary least squares would
not yield a good fit. Consequently, the decay curves are estimated here using
41
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TABLE 1
REGRESSION ESTIMATES OF A GAMMA SPECIFICATION OF THE DECAY CURVE
Activity
Swimming
Camping
Fishing
Boating
Intercept
6.73
(8.22)
5.76
(7.46)
6.77
(7.85)
5.98
(6.78)
Power
-1.30
(-2.58)
-0.051
(-1.05)
-1.18
(-2.20)
-1.09
(-2.03)
Exponent
0.03
(0.99)
0.01
(0.28)
0.02
(0.49)
0.03
(0.71)
R2
0.34
0.10
0.34
0.25
Note: The numbers in parentheses are t values. R2 is the coefficient of deter-
mination.
FIGURE 6
ESTIMATED DECAY CURVES USING EXPONENTIAL SMOOTHING
SWIMMING
CAMPING
FISHING
BOATING
0
0
50 100 150 200 250 300 350 400 450 500
MILES
42
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exponential smoothing. In this procedure, the estimated proportion of people
traveling any distance is equal to the sum of the proportion of people traveling
the previous x distances divided by x. After experimenting with x = 5, 10, and
15, it was decided to smooth over the previous 10 distance groups, where
distance is also measured in 10-mile increments. The estimated decay curves
using exponential smoothing are depicted in Figure 6. The trip-length frequency
distributions in Figure 6 show that recreationists who swim, fish, and boat
strongly prefer to travel short distances. In contrast, the camping decay curve
is peaked, with most camping trips occurring between 50 and 100 miles.
The main use of these decay curves is to transform impedance values into
the F.. matrices. By substituting each impedance value into the four decay
curves, an F.. matrix is constructed for each activity. This matrix is one
input in the gravity model, Eq. (III.l). The estimates in an F.. matrix can be
interpreted as the probability that a recreator residing in origin i will travel
the distance from i to destination j.
B. Trip Production Model (P..)
A household recreation survey was conducted in the fall of 1980 to obtain
data to estimate recreation trips produced by origin by type of trip. A
telephone survey was undertaken by the Survey Research Center at Oregon State
University, specifically for use in this model. Appendix B contains a copy of
the questionnaire. A statistical methodology used to construct trip-production
estimates was developed by Carter (1981) as part of her dissertation. In the
methodology she developed, the sampling unit is the county, not the individual
or household, as is typical in most studies. Forty counties (out of 119
counties in Washington, Oregon, and Idaho) were sampled, with the average size
of 75 households per county. A recreation trip production model, based on the
43
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40 sampled counties, was then used to extrapolate to the remaining counties.
Because trip productions are estimated to be negative for few counties, the
overall reliability of the estimates cannot be confirmed. An alternative trip
production model is developed here, estimated with the Oregon State survey data.
In most recreation participation analyses, the sampling unit is the
individual, and a specific activity is being considered. Because a high propor-
tion of individuals generally do not participate in the specific activity, there
is a corresponding large number of zeroes. The assumption of normality is
therefore likely to be violated. Most resarchers have employed a two-step
procedure. First, a dichotomous dependent variable is used to denote whether
the person participated and, for those persons who participated, the number of
days participating is the dependent variable in the second model. The
independent variables in these models are demographic, such as age, sex, and
income, and some measure of the supply of recreation opportunities.
A common and serious problem shared by these models is their very low
overall explanatory power. For instance, Davidson, Adams, and Seneca (1966)
obtained R2 values of 0.28, 0.11, and 0.11 for the probability of participating
in swimming, fishing, and boating, respectively. Hay and McConnell (1979)
obtain R2 of 0.02 and 0.03 for participating in nonconsumptive recreation such
as wildlife photography. Cicchetti (1973) reports the goodness of fit for
several recreation participation equations (p. 69, 73, 75), and each is below
0.18, and several are less than 0.10. In previous versions of this model, I
used the conventional two-step procedure and obtained unsatisfactory results.
In addition to the statistical difficulty of a large number of zero
responses, there may be conceptual difficulties with focusing on individuals and
single activities. Where the family unit recreates together, individuals do not
act independently. Also, household members may participate in several activ-
44
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ities during one recreation trip; hence activities, like household members, may
not be separate and independent.
An implicit assumption in previous participation analyses is that
participation per capita varies across regions. However, this assumption has
apparently been untested in the literature. One estimator of per capita
participation is the sample mean number of recreation days per person.
Considering the low explanatory power of most recreation participation models,
this estimator may be quite reasonable. As a minimum, one should test
statistically whether mean participation varies across geographical boundaries
within the sample region before estimating a regression model. If the
hypothesis of equal means cannot be rejected, the regression approach will be
futile and the sample mean becomes the appropriate and certainly most convenient
estimator.
The recreation participation model developed here differs from those in the
literature first by using the household as the sample unit and by focusing on
recreation trips as a composite variable and then explaining the composition of
a trip by activity. The conceptual rationale for focusing on the household is
that recreation decisions may often be joint decisions where the entire family
participates. The probable interdependent decisionmaking within the family
suggests that the household is a more appropriate unit for analysis than the
individual. The statistical benefit of focusing on households is the increased
probability that at least one member of the household participates in recrea-
tion.
By considering a composite of recreation activities, the probability that
someone in the household participates is again increased. A zero response is
obtained only when no one in the household participates in any of the four
45
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activities. The number of zero responses in most studies and the conventional
two-step estimation procedure is no longer necessary.
More than one recreation activity is often undertaken during one recreation
trip. For example, during a weekend camping trip, some family members may fish
and boat while others swim, and some family members may enjoy each activity.
The demand curve for recreating by a single activity may be different from one
for the same activity where other activities also occur. The interdependence of
recreation activities will be considered by analyzing recreation trips as a
composite and then explaining the activity composition of these trips.
Consider first the possibility that the most appropriate recreation
participation estimator is the sample mean of trips per household. The
hypothesis that populations have the same participation rate can be tested by a
one-way analysis of variance. The formal statistical hypothesis is that the
mean number of trips per household is constant across subregions within the
total region. The first test is whether the mean number of trips per household
is constant across the three states. The sample means equal 5.5, 5.5, and 8.6
for Oregon, Idaho, and Washington, respectively, for summer trips and 1.6, 1.3,
and 2.9 trips per household for winter trips. The observed F statistics are
20.23 (summer) and 17.55 (winter), which reject the hypothesis of equal means
across the three stages.
The second test is whether the mean number of trips per household is
constant across counties for the 40 counties sampled. The observed F statistics
are 3.67 (summer) and 2.90 (winter), which are larger than expected at the 95
percent level if the means were constant. The third hypothesis is that means
are equal across counties where counties are grouped by state. Reporting the
summer F values first and the winter values second, the F statistics are 2.42
and 2.90 for Oregon, 5.11 and 1.85 for Idaho, and 1.93 and 1.18 for Washington.
46
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Each of these F values suggests rejecting the hypothesis of equal means at the
95 percent level. However, some of the F values are close to their theoretical
value, which is not true of the above two tests.1
The implication of these tests is that recreation participation (in
camping, fishing, boating, and swimming) differs across the three states in the
region and between counties within each state. The main source of this
variation comes from Washington residents who recreate more on the average than
Oregon and Idaho residents.
Because mean trips per household are apparently not constant across
counties in the region, the nonrandom variation in household trips should be
explained. The number of trips per household (summer plus winter) is postulated
to be a linear function of demographic and recreation supply variables. The
only demographic variables included in the model are household size and
household income, because these are the only demographic data for which data
were collected.
The relevant supply measure of recreation opportunities includes the
necessary recreation facilities and the distance of these facilities from the
population centroid. The recreation facilities used here are: number of
camping units, boat ramps, linear designated beach feet, and river-plus-
shoreline miles for camping, boating, swimming, and fishing, respectively. The
recreation supply variables, defined as recreation accessibility, are estimated
as a function of the availability of facilities, and the willingness to travel
the necessary distance to these facilities. Let F.. denote the probability of
J
xAn examination of the raw data indicated that six households reported taking
more than 150 trips during either the summer or winter. These observations were
treated as outliers and the analysis of variance tests were rerun. Even after
omitting these six observations, all the above hypotheses were rejected at the
95 percent level.
47
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driving the distances from population centroid i to the jth recreation centroid.
The recreation accessibility of each population centroid (RA.) for one activity
is estimated by summing recreation facilities (Fac.) over all recreation
J
centroids in the region weighted by the probability of driving the corresponding
distances. That is,
195
(III. 5) RA.. - I F^. FaCj
J
where i = 1, 2, ..., 155 and where RA. measures the accessibility of recreation
opportunities to the ith population centroid. Equation (III. 5) must be
estimated separately for each of the four activities because the friction
factors (F. .) and facilities are unique to each activity. Using Eq. (III. 5),
recreation accessibility was estimated for each activity and for each population
centroid in the region.
As a measure of the supply of recreation opportunities, recreation
accessibility has some commendable properties. First, every recreation
destination in the region is considered in this measure. Second, these
opportunities are summed, but weighted by the probability of driving the
necessary distance. Limitations of this measure are the data requirements to
estimate it and that congestion is ignored.
From the above-defined variables, the trip production model is expressed as
(HI. 6) TJ = f (HS.j, Y-, RAc, RAf) RAb, RAg , Dl5 D2)
where the variables are defined as:
T. = number of trips produced by household i,
HS. = number of people in household i,
RA , . = recreation accessibility for camping, fishing, boating, and
' ' ' swimming,
48
-------
D! = dummy variable = 1 if Oregon, and 0 otherwise, and
D2 = dummy variable = 1 if Idaho, and 0 otherwise.
The state dummy variables are included because the analysis of variance tests
revealed recreation participation rates vary across states.
The number of households surveyed exceeded 3,000, which yielded more data
than is necessary for regression analysis. Those respondents who failed to
answer a question, particularly on family income, were deleted as were one-half
of the remaining responses. Using a sample size of 1545 households, a trip-
production model is estimated to be:
(III.7) T. = 5.71 + 0.983 HS. + 0.879 Y. + 0.0001 RA - 0.014 RA + 0.0008 RA
1 (4.35) 1 (3.84) "* (0.14) S (-2.55) C (0.14)
+ 0.346 RA - 1.695 Di - 3.345 D2
(2.01) (-1-25) (-2.83)
where t values are in parentheses and R2 = 0.053. The encouraging results from
Eq. (III.7) are that household size and income have positive coefficients that
are highly significant. Unfortunately, only one recreation accessibility
variable (boating) is significant and of proper sign.
The main purpose of Eq. (III. 7) is to estimate the number of trips per
household for each population centroid in the region. Because the model will be
used for estimating purposes, it should not contain insignificant coefficients.
After eliminating the insignificant variables, the model becomes
(III.8) T. = 5.005 + 0.993 HS. + 0.876 Y. - 4.084 Da - 3.053 D2
1 (4.399) 1 (3.846) "" (-4.709) (-3.865)
where R2 = 0.049, and where household size and income remain highly significant.
The negative coefficients for the dummy variables are consistent with the
49
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analysis of variance result that participation rates differ across the three
states.
The recreation accessibility variables do not appear in Eq. (III.8) because
they are not significant. Recreation facility variables are subject to serious
measurement errors, which at least partially explains their estimated insignif-
icance. An implication of the insignificance of the accessibility variables is
that increasing recreation facilities will not cause people to increase their
participation, although they may redistribute their demand for recreation sites.
Equation (III.8) is used to estimate the expected number of recreation
trips produced by household for each county in the three-and-one-half state
region and western Montana. Census data for 1980 on household size by county
and 1979 Department of Commerce county income data were substituted into Eq.
(III.8) to estimate trips per household by county. The number of households by
county—obtained from the 1980 census—was multiplied by trips per household to
estimate total trips per county.2
The Oregon State University survey data were also used to allocate total
recreation days by county to the four activities: camping, fishing, boating,
and swimming. Treating each state separately, frequency distributions were
constructed showing the proportion of days of participation in each activity
(see Table B.I in Appendix B). These proportions were then multiplied by total
2Total county trip data were transformed into total recreation days by first
multiplying trips by the average length of stay. For Oregon, Idaho, and
Washington, the sample survey estimates are: 2.439, 2.194, and 2.453 days per
trip, respectively. The average size of a recreation party is estimated to be
the mean household size, which is 2.60, 2.85, and 2.61 for Oregon, Idaho, and
Washington according to the 1980 census. Total recreation days per county are
estimated as the product of total trips, average length of stay, and number of
persons per trip. For the three-state region, households average about 8.6
trips per year and, considering household size and length of stay, about 55.4
recreation activity days per year.
50
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recreation days by county to estimate number of days by activity for each
county.
Estimates of activity days were also constructed for ten counties in
western Montana. Regional mean sample data were used to produce these
estimates. The estimates of recreation trips produced by activity and by
population centroid appear in Appendix A, Table A.3.
C. Attractions Model (A.)
J
The gravity model also requires an estimate of the attractions (quantity
demanded) of each recreation centroid. Attractions are postulated to be an
exponential function of recreation facilities and the accessibility of the
recreation centroid, which measures the likely demand on that centroid. Demand
for recreation sites tend to vary inversely with the distance to population
centers. The responsiveness of attractions to changes in facilities should
therefore be positively related to the nearness of these facilities to popula-
tion centers. Furthermore, attractions should respond to increments in
facilities at a diminishing rate, because demand cannot increase indefinitely in
proportion to facilities. The attractiveness model is specified in exponential
form to allow for the diminishing returns effect and the interaction between
facilities and accessibility.
Accessibility of recreation centroids, called population accessibility, is
a function of the number of trips produced by each population centroid and the
likelihood that these trips will terminate at that recreation centroid. The
accessibility of each recreation centroid is estimated by summing trips produced
(P.) by all population centroids weighted by the probability of driving the
distance to the recreation centroid. That is, population accessibility for the
jth centroid is
51
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155
(HI.9) PA.. = I F..P.
where the F-- values are obtained from the decay curves. Estimates from Eq.
(III.9) were constructed for each recreation centroid in the region and for each
of the four activities being analyzed. Population accessibility estimates are
one input in the recreation attractiveness model.
The attractiveness model also assumes that demand at a site is a positive
function of the site characteristic. The facility variables used are camping
units, river and shoreline miles, boat ramps, and linear designated beach feet
for camping, fishing, boating, and swimming, respectively. U.S. Forest Service
data on visitor days and facilities by ranger district were used with the
accessibility data obtained from Eq. (III.9) to estimate the attractiveness
model. As seen in the first four rows in Table 2, the accessibility coeffi-
cients are significant in only two of the four equations. This insignificance
is due partially to poor quality data because similar estimates based on older
survey data showed this variable to be significant. The positive accessibility
coefficients indicate that use for each activity is greatest for those sites
located near large production centroids. The facility variables are overall
significant and have positive signs as expected. As the equations are in multi-
plicative form, a positive accessibility exponent implies that the responsive-
ness of use to facilities is positively related to the accessibility of a site.
That is, for a given increment in facilities, use will be greatest for those
sites that are most accessible. Facility and accessiblity data for each
recreation centroid were substituted into Eq. (III.10)-(III.13) to estimate
relative attractiveness of each centroid in the region. The sum of attractions
to all sites estimated by the attractions model will not likely equal total
52
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TABLE 2
REGRESSION ESTIMATES OF EXOGENOUS AND ENDOGENOUS ATTRACTIONS (in natural logs)
Equation
Number
(III. 10)
(III. 11)
(III. 12)
(III. 13)
(III. 10' )
(III. 11' )
(III. 12' )
(III. 13')
Activity
Swimming
Camping
Fishing
Boating
Swimming
Camping
Fishing
Boating
Intercept
1.060
(0.943)
-0.396
(0.372)
-5.637
(-2.408)
1.242
(0.698)
-4.052
(-2.309
-2.763
(-2.315)
12.020
(2.419)
-9.716
(3.730)
Recreation
Facil ity
0.194
(2.902)
0.631
(5.460)
0.533
(15.862)
0.586
(3.363)
0.163
(2.585)
0.509
(4.781)
0.545
(16.199)
0.621
(4.287)
Recreation
Access.
-0.216
(-0.721)
0.466
(2.123)
0.354
(1.956)
0.691
(1.394)
0.576
(2.487)
0.591
(3.955)
0.248
(2.636)
1.408
(4.210)
Coef. of Det.
Sample Size
R2 -
n =
R2 =
n =
R2 =
n =
R = 0
n =
R2 =
n =
R2 =
n =
R2 =
n =
R2 =
n =
0.18
42
0.41
49
0.78
74
.25
36
0.29
42
0.52
49
0.79
74
0.47
36
Note: the numbers in parentheses are t values. The dependent variables
are activity days for swimming, camping, fishing, and boating, respectively.
The first independent variable is the facility variable, which is linear desig-
nated beach feet (BF.), camp sites (CS.), acceptable river miles (RM-), and boat
ramps (BR.)- The second independent' variable is accessiblity for swimming,
camping, fishing, and boating, respectively.
trips produced in the region. An accounting identity and condition of the
gravity model is that total trips produced equals total trips received. The
attractions model therefore estimates relative attractiveness, and these
attractions are scaled to sum to total trips produced.
The three inputs in the gravity model, P., A., and F-- have been estimated
with a trip production model, a trip attractions model, Eq. (III.10)-(III.13),
and by transforming the impedance matrix with the decay curves. The output of
53
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the gravity model is a trip interchange matrix (T. .) that gives the number of
trips emanating from population centroid i with recreation centroid j as the
destination.
The statistical estimates of the attractiveness model are unimpressive in
terms of overall explanatory power and in the failure of the accessibility
variable to be positive and significant. Recreation data are typically of low
quality and the data used in the attractiveness model are no exception. In
addition, there may be a specification problem with the attractiveness model.
The gravity model has the desirable property of distributing trips according to
the attractiveness of a recreation site relative to all substitute sites in the
region, and according to effect of distance to the site (R^-,-). relative to all
sites in the region. The gravity model includes the effect of substitute sites
in terms of relative travel distance (or travel time) and relative attractions.
Incorporating this property into the attractiveness model would be highly
desirable. Because one input for this extension results from calibrating the
gravity model, a discussion of this calibration procedure is provided first.
3. Calibrating the Gravity Model
A trip interchange (T. •) matrix is illustrated in Table 3. A row depicts
the number of trips received by each destination centroid emanating from a given
origin. Similarly, the columns depict the number of trips emanating from each
population centroid with a given destination. Because the region is defined to
be closed, the total number of trips produced must equal the total number of
trips received, which in turn equals the total sum of trips in the trip inter-
change matrix.
Unfortunately, the best estimates of T.. are not obtained simply by substi-
tuting the input data into the gravity model [Eq. (III.l)] and solving. First,
54
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TABLE 3
TRIP INTERCHANGE MATRIX
j
i
1
2
Trip Interchange Matrix (T..)
"i J
1 2 ...
TH T12
j j
21 22
m
Tlm
T
'2m
Trip
Productions
pi
ITlj = Pl
VT D
II 2j P2
Tnl Tn2 ' ' Tnm ZTnj Pm
J
Attractions i i J
A- = Ax = A2 =IITii
j i j J
the estimated trip-length (miles one way) frequency distribution obtained from
using the estimated T.. values and the impedance matrix typically would not
correspond with the assumed known distributions, that is, the decay curves.
Second, the estimated number of trips received at each recreation centroid would
not correspond with the attractiveness input data, which means that the sum of
the column vectors in Table 3 would not equal A,.
J
The gravity model is therefore calibrated with an iterative technique where
a new trip interchange matrix (T-.) is estimated by each iteration. The
elements of the new T. . matrix are used to estimate a trip-length frequency
distribution and are summed vertically to estimate A.. These estimates are
J
compared with the assumed known decay curves and A. values, and if a significant
J
55
-------
discrepancy exists, the iterative process continues. The gravity model is
calibrated to produce a T.. matrix that yields a decay curve corresponding to
the exogenous decay curve and estimated attractions that correspond to exogenous
attractions. When the estimated and observed A. values and decay curves are
J
satisfactorily close, as judged by some predefined criteria, the iterations
conclude.
To define this calibration technique more precisely, recall that the
conventional gravity model includes the constraint, Eq. (III. 2), which in terms
of Table 3 is
M
(III. 14) IT,. = A. , for each j.
n J J
Each iteration of the gravity model necessarily satisfies the production
constraint, Eq. (III. 2), because the ratio component of Eq. (III.l) sums to one.
However, Eq. (III. 14) is not generally satisfied by the first or even second
iteration. The calibration technique brings the estimated and observed trip
length distributions together and also satisfies Eq. (III. 14). In each
iteration, attractions are multiplied by the coefficient bc, which reflects the
discrepancy between A. and IT., estimated in the previous iteration. This
J i \J
adjustment coefficient is obtained from
(III. 15) bc = b0'1 ZT c-1
i 1"J
where c designates the number of the iteration. The attractions for each
iteration after the first iteration are estimated by multiplying the previous
56
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attractions by the adjustment coefficient obtained from Eq. (III.11). This
procedure results in Eq. (III.10) being approximately satisfied.
According to this conventional calibration technique, the number of trips
received by each recreation centroid is exogenous, and the gravity model solves
for the distribution of recreation travel. The number of trips received by each
recreation centroid is estimated by the attractiveness model, Eq. (III.10)-
(III. 13), on the basis of facilities at the site and accessibility of the site.
The attractiveness model, as defined thus far, does not consider the effect of
substitute sites as does the gravity model.
A procedure similar to Eq. (III.15) is used to adjust the friction factors
F... The travel distance factors used in the cth iteration (F..c) are equal to
the product of the factors used in the previous iteration (F-. ) and the ratio
of observed to calibrated trips which occur from i to j. That is,
(HI.16) F..C = F0:1^
ij ij GM
where the numerator is the percent of trips implied by the decay curves and GM
is the percent of trips for the same distance that is predicted from the gravity
model. The gravity model is calibrated using an iterative approach as defined
by Eq. (III.15) and (III.16). Three iterations are generally required for the
trip interchange matrix (T..) to approximately satisfy the attractions
constraint, Eq. (III.3), and to produce a decay curve that closely corresponds
with the observed decay curve.
The empirical estimates of the attractiveness model in Table 2 are
disappointing, particularly because two of the accessibility coefficients failed
to be significantly positive as expected. Recall that accessibility is
estimated as the sum of trips produced weighted by the F. . values, which are
probabilities of driving various distances. The F. . values are estimated from
57
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decay curves, which in turn are estimated with regionwide trip-length data. The
decay curves are probably an accurate representation of recreation travel
overall, but they are not necessarily accurate for any individual site. If a
recreation site is close to a large urban area, most trips will have short
travel distances, and the tail of the decay curve will terminate close to the
origin. Alternatively, if all origins to a site are several miles away, the
appropriate decay curve must reflect a large area under these corresponding
distances.
The attractiveness model estimated above presumed that a decay curve
estimated with regionwide data would be applicable to each site. A preferred
alternative is to estimate a decay curve for each site which reflects the
influence of substitute sites.
The gravity model produces a T.. matrix (Table 3), but it also estimates an
F.. matrix via the iterative procedure. An F-. matrix is a gravity model input
variable and it is based on a single regional decay curve. The algorithm for
computing T. . is iterative, and it continues to adjust the F.. values until
estimated attractions balance with A- and the decay curve implicit in the T..
J J
matrix balances with the regional decay curve. The iterative calibration
process [Eq. (III.16)] results in a new F-. matrix in each iteration. Implicit
in this matrix is a decay curve that is unique to each site. The final
iteration produces an F.. matrix where each column vector implicitly contains a
decay curve unique to the corresponding destination. As these F.. values are
computed by the gravity model, they reflect the influence of the independent
variables in the gravity model.
The gravity model was estimated using the input variables defined above,
including the attractiveness variables predicted from Eq. (III. 10)-(III-13) in
Table 2. From this version of the gravity model, the estimated F.. values were
58
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obtained. These values were then used to reestimate the recreation access-
ibility measure and then to reestimate the attractiveness model.
Empirical estimates of the second version of the attractiveness model
appear as Eq. (III.10')-(III.13') in Table 2. The explanatory power of the
model, as measured by R2, shows an improvement in each of the four equations
over the previous estimates. Each of the accessibility coefficients is positive
and is significant at the 1 percent level. Overall, on empirical grounds, this
two-stage procedure for estimating the attractiveness model results in a
dramatic improvement in the model.3 On theoretical grounds, the model is also
improved because the same varibles that determine the distribution of recreation
travel also influence total demand at each site. In addition to being a
distribution model, the gravity model, along with the attractiveness model,
becomes a trip demand model.
The gravity model as estimated in this study produces two outputs necessary
to estimate demand and benefits for recreation sites. First, quantity demanded
is estimated for each centroid and for each of the four activities. By changing
the level of facilities at a centroid, the attractiveness of the centroid
changes [Eq. (III.10')-(III.13')] and, through the gravity model, so does the
total number of trips received. For each recreation centroid, the gravity model
also estimates the number of trips received from each origin. These data are
transformed into visit rates and are a critical output in estimating travel-cost
demand curves. Estimating a gravity model requires constructing an impedance
3Three of the four equations in Table 2 use data from only 49 ranger districts,
whereas the fishing equation is based on 74 observations. Destinations on the
original highway network conformed to only 49 ranger districts. When this
network was expanded to include all ranger districts, and a larger impedance
matrix was constructed, the new attractiveness equation (except for fishing)
failed to show a statistical improvement. For this reason, only the new fishing
equation is used.
59
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matrix, which reflects the minimum travel distance from each origin (population
centroid) to each destination (recreation centroid) in the region. These
minimum travel distances, when multiplied by travel cost per mile, yield
travel-cost estimates that are necessary to estimate recreation demand curves.
60
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CHAPTER IV
ESTIMATING AN OUTDOOR RECREATION DEMAND CURVE
In Chapter II recreation benefits are defined as net willingness to pay, or
alternatively as consumers' surplus, and measured as the area under a recreation
demand curve and above the market price. A detailed explanation of the travel-
cost method of estimating a recreation demand curve is presented in Section 1 in
this chapter. Recreation demand curves and net willingness to pay are estimated
for each of 195 recreation centroids and for each of the four activities being
studied. A gravity model of recreation travel was developed in Chapter III.
The purpose of this model is to estimate recreation trips by origin to each site
in the region, and thereby to provide an input in estimating travel-cost demand
curves. A sample of these demand estimates is presented in Section 2 of this
chapter. Section 2 also includes a discussion of the significance of substitute
sites as well as disaggregating recreation into four specific activities.
1. Estimating a Travel-Cost Demand Curve and Consumer Surplus: An Overview
Willingness to pay for a recreation site can be estimated directly or
indirectly. In the direct approach an interviewer confronts the recreationist,
and using an appropriate survey instrument, asks the recreationists their
willingness to pay. There are some numerous and impressive case studies of the
direct approach, but for purposes here, it has two serious limitations. An
expensive and time-consuming survey must be undertaken for each site analyzed.
Also, it is particularly difficult to estimate potential benefits of a site
61
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which doesn't exist or to estimate increased benefits from the potential
improvement of a site. The critical need to assess potential benefits over a
large number of sites precludes the use of direct estimates of willingness to
Pay.
In the travel-cost method (TCM), willingness to pay is estimated indirectly
on the basis of observed travel patterns, and not, as in the direct approach,
from what people say they would do in response to hypothetical situations. For
this reason, most analysts have preferred the travel-cost approach to the direct
approach. Although the TCM has numerous limitations, some of which will be
dealt with here, it will serve as the basis for estimating recreation demand and
value. The rationale for using the TCM is first its credibility, which results
from its widespread use and official sanction by the Water Resources Council
(1979). The objective of this study is to develop, test, and apply a model that
can estimate recreation demand and value at any site in a large region. There
are no viable alternatives to the TCM in terms of models that are theoretically
sound and operational on a regional basis.
In this study, travel-cost demand curves are estimated for each of four
activities (fishing, swimming, camping, and boating) and for a large number of
sites, which are termed recreation centroids. A travel-cost demand schedule is
now developed, but the notation is simplified by assuming one activity and one
recreation centroid. Let T. be the annual number of visitor days emanating from
the ith population centroid and recreating at the site being analyzed, and let
N.. be the population of the ith population centroid. Using C. for the travel
cost per person per visitor-day from the ith zone, the equation
(IV.1) T1/N1 - f(C.)
62
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relates visit rates to travel costs. Equation (IV.1) is the general form of
what Clawson (1959) termed the demand curve for the recreation experience, and
it is often referred to as a per capita demand curve or visit-rate schedule.
The regression estimate of this equation is used to generate a site demand curve
by first multiplying the equation by the population of the ith zone (N.) to
obtain
n. - f(C.)N. ,
then summing all origins to obtain
(IV.2) ZTn. = If(Ci)N1 ,
which yields an estimate of total visitor-days as a function of total travel
costs.
The essence of the TCM is that a site demand curve is inferred from the
empirical relationship of visit rates by origin to corresponding travel costs
[Eq. (IV.1)]. Although travel costs are a transaction cost, not a market price,
they are treated as an implicit market price. The response of total recreation
days to hypothetical prices is obtained by assuming that recreationists would
respond to prices (entrance fees) just as they respond to the same change in
travel costs. To estimate total visitor-days as a function of increased travel
costs or market prices, AP is inserted in Eq. (IV.2) to obtain
(IV.3) IT = Zf(C. + AP)Ni .
i i
The prices for a site demand curve may be selected somewhat arbitrarily,1 but
*The issue of the sensitivity of consumer surplus estimates to the size of
price increment is considered in Chapter V.
63
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should begin at zero and cover the full range of the demand curve. The quantity
of visitor days demanded at each price is obtained from Eq. (IV. 3) by letting
each price equal AP and solving for the corresponding quantity (IT.). A
recreation site demand curve can then be estimated from these price-quantity
observations. The site demand curve is usually estimated as a regression
equation obtained from the price-quantity points. The final step is to estimate
consumers' surplus, which is typically the integral of the estimated demand
equation.
The focus of this study is on total quantity demanded at a zero price and
on consumers' surplus, but not on the site demand curve per se. Furthermore,
using regression analysis to estimate a site demand curve raises the issue of
the proper functional form. Also, a regression estimate may be highly sensitive
to the choice of hypothetical prices substituted in Eq. (IV.3). Because a site
demand curve is unnecessary and regression analysis introduces some potential
problems, an alternative procedure is developed.
The following chapter will demonstrate that a semilog form of the visit-
rate demand schedule is reasonably good and superior to that of the double-log
form. Using this form, Eq. (IV.1) becomes
(IV.4) In (Tj/N^ = a + $C. + e. .
Taking antilogs of the regression estimate of Eq. (IV.4), multiplying by N., and
summing yields
(IV.5) ZT. =ea + P(Ci+ AP)
which corresponds to Eq. (IV.3). The price increments used here are $1 from $0
to $4, $2 from $4 to $12, $4 from $12 to $76, or until a successive price incre-
64
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merit increases consumers' surplus by less than one percent. Initially,
one-dollar price increments were used from $0 to $76, but experimentation showed
that most of the consumers' surplus occurs at relatively low prices. Also,
extensive computer time is required to perform the large number of calculations
required for 780 (195 x 4), first-stage demand curves. For these two reasons,
larger price increments were used as higher prices.
The hypothetical prices and the quantities generated from Eq. (IV. 5) can be
used to estimate recreation demand and value.2 In lieu of estimating the
site-demand curve, consumers' surplus is estimated directly by applying Bode's
Rule to the price-quantity data. Bode's Rule is an algorithm for integrating a
fourth degree polynomial that fits five points equally spaced on the horizontal
axis. Suppose that we are given five such points x., where i = 0, ..., 4.
Bode's rule approximates
X4
J f(x) dx
by fitting a fourth degree polynomial through the five points (x.. f(x.)).
Bode's Rule is3
X4 Ok
S f(x) dx = ^ (7f0 + 32fj + 12f2 + 32f3 + 7f4)
Of6 f- h7
where E = , x0 < £ < x.
2The approach here follows Clawson's original two-step method of estimating a
visit-rate schedule and using it to generate a site-demand schedule, except that
the integral of the site-demand schedule is estimated without actually estimat-
ing that schedule. An alternative and simpler approach would be to integrate
the first-state curve directly.
3Bode's Rule is given in Davis and Robinowitz (1967, p. 30) and in Abramowitz
and Stegun (1964, p. 886).
65
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but the remainder E is set equal to zero. The h term is the interval, which in
our case is the price increment used in Eq. (IV.5).
The use of Bode's Rule is illustrated by Figure 7. The first series of
five equally spaced points is the prices from $0 to $4 in increments of $1. The
corresponding quantities are obtained from Eq. (IV.5). A fourth degree
polynomial is connected to these five points, and Bode's Rule is used to measure
the area under this segment of the demand curve. The next series of five
equally spaced points includes the price-quantity observations where prices
ranged from $4 to $12 in $2 increments. Bode's Rule is again applied to
estimate the consumer surplus corresponding to this segment of the demand curve.
The process continues until the last application of the algorithm increases
consumer surplus by less than one percent of the total.
FIGURE 7
ESTIMATING CONSUMERS'SURPLUS USING BODE'S RULE
O
Q
UJ
O
LU
O
<
O
6 8
PRICE $
10
12
66
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2. Travel-Cost Demand and Valuation Estimates: Some Illustrations
This study departs from the recreation literature not only in the number of
sites considered, but in the number of separate recreation activities. Also,
the gravity model permits each site in the region to be considered as a possible
substitute for every other site in the region. This section first presents a
brief discussion on aggregating recreation activities and then discusses the
issues of substitute sites. The model is illustrated by presenting some demand
and value estimates of swimming.
A. Aggregating Recreation Activities
In most recreation analyses, recreation is construed as a single homogen-
eous good. Such an assumption may be appropriate when estimating the demand for
a national park, but it is inappropriate when analyzing the demand for water-
based recreation. In this study, recreation is disaggregated into four
activities: swimming, fishing, boating, and camping. The first three activ-
ities are water dependent and camping is water related. In the Northwest, most
camping occurs near water, and camping is therefore a potential benefit of
improving water quality or of constructing water recreation areas.
The optimal degree of disaggregation is a matter of judgment because
increased reliability and realism must be weighed against costs, complexity, and
lack of data. It is important to consider the above activities individually
because they often occur separately; they have different trip-length frequency
distributions and they respond to different water-quality parameters. For
instance, an increase in water temperature may be lethal to cold-water fish, but
may enhance water quality for swimming.
None of the four activities is homogeneous, implying that even further
disaggregation could be useful. For instance, kayaking is a specialized type of
67
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boating requiring rapidly flowing water, and this activity is quite different
from speed boating or sail boating. Similarly, fishermen may have quite
different preferences for salmon, trout, and catfish. Data requirements
preclude disaggregating activities beyond the four being considered, and
therefore a qualification is required. If a change in water quality affects one
type of activity that is not representative of the general category, the model
will not produce reliable results. For instance, if an exogenous change affects
kayaking, where willingness to pay exceeds that for boating in general, the
model will produce valuation estimates with a downward bias.
B. Substitute Sites
According to the economic theory of consumer behavior, the quantity of a
good demanded depends on the price of the good, the budget constraint and the
price of substitute goods. The conventional travel-cost analysis excludes the
price of substitutes and this omission is one of the more serious limitations of
the analysis. At least three issues are associated with the availability of
substitute sites: (1) the correct measure of the increment in consumers'
surplus given that consumers' surplus may be redistributed from a substitute
site; (2) the statistical bias in the travel-cost demand curve; and (3) esti-
mating the response of use to a quality or facility change given the attract-
iveness of alternative sites. The first issue is discussed in Chapter II, where
it is argued on the basis of conventional theory that benefits are measured
correctly by not subtracting benefits foregone from substitute sites.
The omission of the price of substitutes may introduce a statistical bias
into the price coefficient estimate. For those recreationists located rela-
tively near a site, there are likely to be few substitute sites, hence their
demand schedule may be relatively inelastic. As we consider travel zones
68
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farther from the recreation site, the number of substitute sites increases and
the price elasticity correspondingly diminishes. The relationship between visit
rates and travel costs may therefore produce a biased estimate of price
elasticity.
This bias is one reason for the recent interest in regional models. Dwyer,
Kelly, and Bowes (1977), in their review of the recreation demand literature,
conclude .that regional models are an improvement over single-site analyses.
Regional simultaneous equation models have been constructed by Burt and Brewer
(1971) and by Krutilla and Fisher (1975) where six sites were considered in each
study. Neither of these models is easily transferable to other regions or
activities, nor is it clear that all relevant substitute sites were considered.
The substitute sites considered in most demand analyses are those near the
site being analyzed, but this consideration is insufficient. For example,
suppose that people travel up to 100 miles to camp and that we are interested in
the benefits of a new campground. The market area for the new campground would
be within a circle with 100-mile radius with the proposed site in the center.
Any existing site within this area is a potential substitute for the proposed
site. However, the area encompassing substitute sites that must be considered
is significantly larger than the market area for the proposed site. Visitors
who would travel up to 100 miles to the new or improved site would travel 100
miles in any direction to an identical site. Consequently, a site 200 miles
from the proposed could be a substitute for that site because it would attract
visitors who reside half-way between the two sites. If visitors would travel up
to x miles to recreate at a new or improved site, the area of potential
substitute sites is a circle with radius 2x miles. The number of potential
substitute sites is therefore much larger than is commonly recognized. Price
69
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elasticity estimates in this study, as in previous studies, may be biased
because the influence of substitute sites is not adequately considered.
Recreation analyses are as much concerned with estimating the quantity of
recreation demanded as with estimating a price elasticity. The increment in
quantity demand at an improved site depends upon the attractiveness of substi-
tute sites and the relative travel distances to these sites. A virtue of the
gravity model [Eq. (III.l)] is that recreation trips are distributed simul-
taneously to all sites on the basis of attractions to each site and the relative
effect of spatial impedance. The gravity model permits each site in the region
to be a substitute for every other site and the model also considers substitutes
in terms of travel distances and attractions.
C. Some Empirical Estimates for Swimming
The data necessary to estimate a travel-cost demand schedule include visits
or visit rates by origin and the corresponding travel cost. Visit data by
origin are estimated for each site by the gravity model, which is discussed in
the previous chapter. The travel-cost data include the travel distance from
each population centroid to each recreation centroid and the round trip cost per
person per vehicle mile. One-way travel distances are obtained from the
impedance matrix, which is explained in Chapter III. According to the U.S.
Federal Highway Administration, the total cost per mile for an intermediate size
car in 1981 is 23.8 cents per mile. However, the variable cost is 6.6 cents per
mile for gas and oil plus 5.6 cents for maintenance, accessories, parts, and
tires, for a total of 12.2 cents per mile. This estimate of 12.2 cents was
doubled to adjust for round-trip costs and then divided by the average number of
70
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persons per vehicle (3.47) to obtain 7.753 cents.4 The average length of stay
is one day for swimming, boating, and fishing, but two days for camping; so
7.753 cents is divided by two to obtain mileage costs for camping activities.
A recreation experience demand function is estimated in semilog form for
each of four activities and for each of 195 centroids in the origin (these
centroids are defined in Appendix A). Total quantity demanded, consumers'
surplus and surplus per trip were also estimated for these activities and
centroids. A sample of the demand and valuation estimates for swimming is
presented in Table 4. The first three columns in this table identify the
recreation centoid by number, county, and name. Linear designated beach feet
and recreation accessibility (RA..) are inputs in the attractiveness model, and
A. are estimated attractions from this model. The gravity model estimates total
J
quantity demanded with Eq. (III.3), and these estimates are presented in column
7 of Table 4. As indicated by column 8, most recreation centroids receive trips
from over 100 origin zones. An inspection of the trip interchange matrix (T. .)
indicated that the large majority of trips emanate from relatively few origin
zones. Columns 9-12 are the first-stage demand statistics and overall show a
high level of significance. Consumers' surplus is estimated with Bode's Rule,
and surplus per trip is simply total surplus divided by quantity demanded
(column 7).
The demand and valuation estimate presented in Table 4 reflect one activity
(swimming) out of four being considered, and 20 recreation sites out of 195 in
the region. However, the demand and valuation estimates based on this sample
are representative of the other activities and of the entire region. The
4The number of persons per vehicle is estimated as the sample mean of the
household regional recreation survey. This number is larger than the mean
household size in each of the four states in the region.
71
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(V)
TABLE 4
DEMAND AND VALUATION ESTIMATES FOR SWIMMING IN SELECTED WASHINGTON CENTROIDS
Recreation
Centroid
Number
(1)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Notes:
form. RA .
County
(2)
Adams
Asotin
Benton
Chelan
Chelan
Clallum
Cl all urn
Clall urn
Clark
Columbia
Cowlitz
Cowlitz
Douglas
Oerrt
Franklin
Garfield
Grant
Grant
Grant
Recreation Centroid
(3)
Northeast Corner
Fields Spring St. Park
Crow Butte State Park
Lake Wenatchee
Lake Chelan State Park
Bogachiel State Park
Neah Bay State Park
Dungeness State Park
Battleground State Park
Lewis and Clark St. Park
Merwin Reservoir
Seaquest State Park
Chief Joseph
Twin Lakes
Lyons Ferry State Park
Pataha Creek
Potholes State Park
Sun Lakes State Park
Steamboat State Park
Gray's Harbor Bay City
Quantity
measures
demanded was estimated from
Linear
Beach
Feet
(4)
1
2000
1850
200
870
1200
1100
1100
1085
1
1
1
100
400
1000
1
1000
2930
1000
1
RA .
(5)SJ
413
116
211
641
145
129
79
722
912
219
522
881
111
201
220
167
238
210
219
576
A,
(6)J
119,815
199,415
277,589
366,156
198,291
194,775
145,165
517,662
590,879
83,203
137,210
185,382
119,167
210,193
257,529
71,319
269,245
298,494
256,888
145,131
the gravity model. NOZ
the swimming accessibility of a recreation
centroid
Quantity
Demanded
(7)
109,926
82,308
215,045
391,439
111,302
49,393
24,431
534,887
806,747
80,600
109,345
229,694
65,854
99,762
220,907
44,194
224,317
194,961
153,903
118,689
is the number
divided by 1,
Experience Demand
Curve Statistics C
NOZ In a
(8) (9)
126 7.67
134 8.34
135 8.85
125 9.06
116 8.55
107 8. 18
94 8. 14
124 9.34
135 9.29
136 7.29
121 7.83
127 8.12
108 8.09
122 8.64
139 8.64
131 7.34
133 8.89
130 8.86
127 8.73
120 7.90
B
(10)
-0.225
-0.225
-0.243
-0.239
-0.242
-0.230
-0.238
-0.234
-0.228
-0.220
-0.231
-0.229
-0.242
-0.244
-0.230
-0.229
-0.244
-0.237
-0.238
-0.233
origin zones. The
000. These
t R2
(11) (12)
-32.3 0.877
-31.5 0.872
-31.6 0.873
-39.2 0.914
-37.6 0.907
-31.8 0.876
-35.3 0.899
-35.7 0.898
-38.8 0.912
-29.0 0.852
-36.2 0.900
-36.7 0.903
-36.3 0.901
-33.3 0.885
-31.7 0.873
-31.8 0.874
-33.7 0.887
-35.2 0.895
-34.3 0.890
-32.4 0.878
demand curve is
lonsumers'
Surplus
$
(13)
436,053
324,576
674,364
1,661,722
645,566
260,539
131,485
2,515,514
5,435,151
196,873
797,108
1,345,905
454,320
595,718
631,644
151,382
687,471
777,465
606,162
613,219
specified
estimates were obtained from Eq.
Surplus
per Trip
$
(14)
3.96
3.94
3.13
4.24
5.80
5.27
5.38
4.70
6.73
2.44
7.28
5.85
6.90
5.97
2.85
3.42
3.06
3.98
3.93
5.16
in semi log
(III. 13).
-------
consumers' surplus estimate of $4.31 per swimming day is comparable in magnitude
to the other activities and of the other recreation centroids.
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CHAPTER V
SURVEY ESTIMATES OF THE WILLINGNESS TO PAY
TO RECREATE AND THE VALUE OF TRAVEL TIME
1. Introduction
The willingness to pay to recreate can be estimated directly using sample
surveys or indirectly by estimating a recreation demand curve and measuring the
area under this curve. The indirect demand curve approach is used in this
study. Taking a regional household recreation survey in the summer of 1980
afforded the opportunity to include a question on willingness to pay. The
objective of obtaining direct estimates of consumer surplus is to compare them
to the direct estimates when all other factors are equal.
Recreation travel patterns are influenced by travel cost, which is measured
at least partially by vehicle operating expenses. An opportunity cost of travel
is foregone time, and recreationists may consider travel time as an additional
travel cost, or as a benefit. Empirical evidence from the current household
survey on the value of recreation travel time is also presented in this chapter.
The objective in presenting these results is to provide empirical evidence on
the travel time bias in recreation studies.
2. Direct Willingness-to-Pay Estimates
Obtaining credible estimates of willingness to pay using sample survey is a
challenging endeavor. Even at best, the estimates may not inspire much confi-
dence. Obtaining these estimates sometimes involves lengthy and expensive
74
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personal interviews using a "bidding game" approach. The approach taken here is
much less ambitious. The resources available permitted one question to be
included on the questionnaire.
Most recreation benefit studies use either the indirect or the direct
approach, but not both. The observed differences between results from these
approaches owe partially to the different approaches and to other differences,
such as sites analyzed, activities included, and date of study. The objective
here is to compare direct willingness-to-pay estimates with indirect estimates
of the same activities, region, and time period.
Although the complete household survey is included in Appendix B, the
direct willingness-to-pay question is provided here. The question is
What is the maximum daily use fee you would be willing
to pay for this recreation facility rather than forego
using it?
We explicitly asked for the daily fee to obtain a consumers' surplus estimate
per visitor-day.
The frequency distribution of responses is presented in Table 5. Virtually
all the respondents indicated a willingness to pay between $2 and $10 per trip
to recreate. The mean value per trip is $5.62, and the mode and median are each
$5. The indirect estimates of willingness to pay obtained in this study are in
the $3 to $6 range with an average of about $4.20.
3. The Value of Recreation Travel Time
The essence of the travel-cost approach to estimating a recreation demand
curve is that the cost of traveling is an empirical proxy for price and the
relationship between travel costs and visit rates is used to impute a site-
demand curve. If travel costs are estimated as vehicle operating costs and the
75
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TABLE 5
DIRECT WILLINGNESS-TO-PAY ESTIMATES PER RECREATION DAY
Monetary1
Value
($)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15+
Frequency
1
7
27
58
38
0
33
26
21
8
39
3
3
2
0
8
Relative
Frequency
0.0027
0.0192
0.0741
0.1594
0.1044
0.2472
0.0906
0.0714
0.0577
0.0219
0.1071
0.0081
0.0081
0.0054
0.0000
0.0220
Total 364 1.00
Other statistics are: Mean = $5.619, Median = $5.00, Mode = $5.00, Standard
Deviation = $2.93
1The monetary values are less than or equal to these numbers. For example, all
estimates above $1 and less than or equal to $2 are recorded as $2.
correct measure of travel costs includes some value of travel time, then the
estimated demand curve is a biased representation of the true demand curve.
The above point is well recognized in the recreation literature. The
concensus in this literature is that travel time is a positive cost of travel
and therefore must be included in empirical estimates of travel-cost demand
curves. In one of the more widely quoted studies, Cesario (1976) concludes that
the recreation value of travel time is approximately 1/3 the average national
wage rate. This study has received the official endorsement of the Water
76
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Resources Council in that the Council recommends use of this value in the
travel-cost analyses.
In the infinitely flexible and continuously adjustable world of neoclass-
ical economics, the cost of travel time may be defined in terms of foregone
earnings. At the conceptual level, the cost of traveling is its opportunity
cost, which is what one gives up in order to travel. The neoclassical view is
questionable on empirical grounds, because generally people do not have the
flexibility to trade work time for travel time. However, a more fundamental
objection to using the wage rate as an opportunity cost can be raised on
conceptual grounds. The real cost of foregone work time is not wages, but the
utility of income minus the disutility of work. Gross wages are not likely to
be a good proxy to the net benefits of employment.
In addition to the conceptual objections to valuing travel time in terms of
foregone earnings, there is room for skepticism about the reliability of
Cesario's empirical estimate. Cesario's estimate was derived from a literature
review of several studies of how commuters value their journey-to-work travel
time. Recreation is a leisure time, discretionary activity, which is quite
different from the daily required journey-to-work trip. The recreationist has
the option of choosing a destination so as to have a positive value of travel
time. The commuter is generally rigidly constrained to arrive at a destination
not of his own choosing and to do so during peak traffic hours.
The above reservations about the accepted view on the travel time bias led
to the inclusion of two questions on the household recreation survey. These
questions are:
Ql. Some people feel that time spent traveling to a
recreation site is an inconvenience while others
enjoy it. How about you?
77
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1. Enjoyed travel time
2. Prefer to shorten travel time
3. Refused
4. Don't know, no answer
Q2. About how much would you be willing to pay to
shorten the total travel time for this last trip by
one half?
The total sample size is 2,249, of which 107 respondents refused to answer or
did not know. Of the remaining respondents, 1,865 enjoyed their travel time,
whereas only 276 would prefer to shorten their travel time. These results
suggest that travel time is a net benefit, not a cost. Vehicle operating costs
probably overstate recreation travel costs, not understate them.
The objective in question one is to determine whether travel time is a net
cost or a benefit. The objective of the second question is to obtain a
quantitative estimate of what is presumed to be a cost. The frequency distri-
bution of survey results is presented in Table 6.
TABLE 6
DIRECT ESTIMATES OF THE VALUE OF RECREATION TRAVEL TIME
Boundaries
0.0 -
2.0 -
4.0 -
6.0 -
8.0 -
10.0 -
12.0 -
14.0 -
16.0 -
18.0 -
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
Frequency
1178
23
46
4
2
33
0
12
0
29
Relative
Frequency
0.888
0.017
0.035
0.003
0.002
0.025
0.000
0.009
0.000
0.022
Total 1327 1.00
Other statistics are: Mean = $1.069, Median = 0.0, Mode = 0.0, Standard
Deviation = 3.65
78
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The most impressive result in Table 6 is that 88 percent of the respondents
are not willing to pay anything to shorten their travel time by 50 percent.
Fewer than 3% of the total respondents are willing to pay more than $5 to
shorten their travel time by 50 percent. The results in Table 6 cast doubt that
recreationists, at least in the Northwest, perceive their travel time as a cost.
The question that now arises is whether recreationists deliberately incur
vehicle operating costs in order to spend more time traveling. Unfortunately,
the survey evidence is insufficient to answer this question. The main result is
that the cost of recreation travel time, at least in the Pacific Northwest, and
for the four activities considered, is not positive. On this basis, travel cost
will be measured as vehicle operating costs. Of course, these results should
not be applied to value travel time by commuters in large urban areas.
79
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CHAPTER VI
THE SENSITIVITY OF TRAVEL-COST ESTIMATES OF RECREATION DEMAND AND
VALUATION TO VARIOUS COMPUTATIONAL AND SPECIFICATION ISSUES
The travel-cost demand curves developed and estimated in Chapter IV are
based on a semilog form of the first-stage demand curve, origins defined as
recreation centroids, and total quantity demanded estimated from a gravity model
with endogenous attractions. This chapter uses a Monte Carlo simulation
analysis to test the robustness and correctness of some of the input assumptions
in the model. Specifically, the focus of this chapter is on three specification
and computational choices required by the TCM which may influence estimates of
the demand curve and consumers' surplus. The three issues investigated here are
(1) the functional form of the first-stage demand curve; (2) the width of the
concentric zones; and (3) the estimate of total quantity demanded. The
objective is to determine the sensitivity of travel-cost demand and valuation
estimates to various assumptions concerning these four points. The method of
analysis is to apply the TCM to several sites under various assumptions and to
contrast the results.
Applying the TCM and estimating consumers' surplus requires that some
assumption be made on each of these points. Choices are often made inadvert-
ently; at least there is little analysis of the sensitivity of the results to
variations in the computational procedure. The first section of this chapter
contains a brief discussion of the possible significance of the three points.
Section 2 contains the empirical estimates of travel-cost demand and valuation
80
-------
estimates under these various assumptions. The conclusions and implications are
discussed in Section 3.
1. The Three Issues
Many empirical demand curves in the economics literature are specified in
double-log form, perhaps because the coefficients may be interpreted as elas-
ticities.1 In the recreation literature, the semi log specification is most
prevalent, although linear functions have been used.2 An issue considered here
is the relative merit of the semi log and double-log specification of the
first-stage demand curve and the sensitivity of the valuation estimates to the
choice of these two functional forms.
In the TCM, visit rates from various origins are regressed against corre-
sponding travel costs. Since the pioneering work of Clawson and Knetsch (1966),
origins have been defined by a series of concentric rings around the recreation
site. For instance, if recreationists travel a maximum of 200 miles and rings
are defined every 20 miles, then there are 10 origin zones and 10 observations
for the experience-demand schedule. Similarly, if a ring is defined every 10
miles, there will be 20 travel zones and 20 observations for estimating the
visit-rate schedule. Alternatively, each population centroid may be construed
as a separate origin, and the number of observations is therefore determined by
the number of such centroids. A second issue is the sensitivity of the demand
and valuation estimates to the definition of the origin zone.
xln their literature surveys on the demand for money, Laidler (1977) and
Goldfeld (1973) present empirical estimates in favor of a log-log specification.
2Linear demand curves have been used by Burt and Brewer (1971) and by
Cicchetti, Fisher, and Smith (1976) because this specification is required by
some properties of their models.
81
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There are at least two ways to estimate total quantity of recreation
demanded at a zero price. An estimate can be generated endogenously by
substituting a zero price increment in the experience demand curve. Cesario and
Knetsch (1976, p. 100) apply this method and it is generally used when
site-attendance data are unavailable. In most travel-cost analyses, quantity
demanded is estimated exogeneously by site-attendance data. Clawson (1959)
estimated quantity demanded in this manner and Knetsch (1974, p. 83) and others
have followed his lead. Estimates of consumers' surplus, and particularly
consumers' surplus per trip, may be sensitive to the choice between these
quantity-demanded estimates.
If the demand curve is constrained to intersect the observed quantity
demanded, then the magnitude of the hypothetical price increments in the
first-stage demand curve may affect consumers' surplus. Figure 8 depicts a
hypothetical demand curve generated from price-quantity observations using $1
price increments in the first-stage demand curve. In Panel A, quantity a is
estimated from the first-stage demand curve by letting AP = 0, and quantity c is
assumed to be the correct estimate. Consumers' surplus estimated as the area
under cbd will be less than the surplus estimated as the area under abd. Panel
B depicts an estimate of consumers' surplus when price increments of $0.25 are
used from 0 to $1, and $1 price increments are used thereafter. If the demand
curve is constrained to include the correct quantity demanded, consumers'
surplus in Panel B (Oced) exceeds that in Panel A (Ocbd) by an amount equal to
ceb. If quantity demanded is estimated incorrectly, the magnitude of the
hypothetical price increment could affect the results.
The discussion to this point offers some a priori possibilities that
specification and computational choices in estimating a travel-cost demand curve
may affect the results. Empirical evidence on the sensitivity of the results to
82
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FIGURE 8
PRICE-QUANTITY OBSERVATIONS FOR A RECREATION SITE DEMAND CURVE
PANEL A
DEMAND CURVE
SI PRICE INCREMENT
PANELS
DEMAND CURVE
$0.25 PRICE INCREMENT
O
Q
UJ
Q
D
>
<
O
O
D
UJ
O
<
UJ
O
<
o
PRICE S
PRICE S
these choices is presented in Section 3 by estimating several travel-cost demand
curves under alternative conditions using the model described below.
2. Sensitivity of Travel-Cost Estimates to Various Assumptions
Because the 195 recreation centroids and four activities included in the
regional model are more than sufficient for this analysis, we quite arbitrarily
consider the demand for boating at 20 Washington recreation centroids, numbered
17.0 to 26.0 (column 1 in the accompanying tables). These centroids include
those in King County, which contains Seattle and is heavily populated, as well
as sparsely populated counties east of the Cascade Mountains. By including both
urban and rural counties in the sample, the travel-cost estimates reflect a
diversity of realistic conditions. The rationale for sampling a relatively
large number of centroids (20) is that certain adverse consequences may be
observed only occasionally, and a large sample increases the likelihood of such
a result. Also, results based on a single site may reflect a special case, and
be inconsistent with results obtained over a wide range of experience.
83
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The sensitivity of travel-cost estimates to each of the computational
issues being considered depends upon the assumption made on the other three
issues. The interdependence of these issues precludes analyzing them indi-
vidually. We consider first the functional form of the first-stage demand
curve, focusing on the semi log form and the double-log form. Results will be
presented by generating quantity estimates endogenously and by assuming that
quantity demanded is exogenous. Travel-cost estimates will then be presented
using various size origin zones. We will show that the results are sensitive to
the definition of origin zone and this sensitivity in turn depends on the choice
of quantity demanded and on the functional form.
A. Functional Form of the First-Stage Demand Curve
The issue of proper form of a recreation demand curve has been studied by
Zeimer et al. (1980) and by Smith (1975). The studies are similar in that only
one site was considered and a statistical analysis, namely a Box-Cox transforma-
tion, was used to statistically estimate the most appropriate functional form.
Smith rejected the linear form because it provided a poorer fit of the data than
the double-log and semilog form. However, Smith also concluded that even though
the latter two forms fit the data and provided reasonable results, each form
must be considered inappropriate. Zeimer et a_[. used the Box-Cox transformation
procedure and concluded that a semilog form is appropriate and a linear form is
inappropriate, and further that consumers' surplus estimates are highly
sensitive to the choice of functional form.
In considering the various functional forms, double-log and semilog
(logarithm of the dependent variable) are candidates, but the linear form need
not be considered. Ziemer et al. and Smith provide evidence against the linear
form, and scatter plots of several sites indicate a distinct curvilinear
84
-------
relationship. The evidence against the appropriateness of the linear form is
persuasive, and in this study, we consider the double-log and semilog functional
form.
The objective of analyzing these two forms is first to determine if the
results are sensitive to the choice of functional form and if so, to determine
that of the two forms seems most appropriate. Four criteria are suggested that
may be useful in identifying the most appropriate form. First, the coefficients
of determination are a relevant but not decisive indicator, particularly if
estimated over several sites. Second, estimates of consumers' surplus per trip
should be somewhat stable across sites and should be similar to those reported
elsewhere in the literature. Third, the first-stage demand curve should
estimate closely the known quantity demanded at a zero price when AP = 0 is used
in Eq. (IV.5). Finally, goodness of fit and consumers' surplus estimates should
be insensitive to other computational decisions, particularly if the decisions
are made arbitrarily. These properties are not espoused as rigorous statistical
criteria that will necessarily determine the unambiguous superiority of one
functional form. Because previous studies have not been able to resolve this
issue on statistical or theoretical grounds, it is appropriate to employ a Monte
Carlo analysis, where a demand curve for several sites is estimated with each
functional form and the results are compared.
First-stage demand curves for boating [Eq. (IV.4)] are estimated for 20
centroids using both double-log and semilog forms, where the logarithm is taken
of the dependent variable. These estimates are based on population centroids as
origin zones, a $1 price increment in Eq. (IV.5), and quantity demanded
estimated exogeneously. The results are presented in Table 7. The coefficients
of determination, columns 2 and 5, indicate that each form fits the data
reasonably well, but the semilog model has more explanatory power in 19 of the
85
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TABLE 7
ANNUAL VALUATION ESTIMATES FOR BOATING
SEMI LOG AND DOUBLE-LOG FUNCTIONAL FORM
IN SELECTED WASHINGTON CENTROIDS USING A
Semilog Results*
Double-Log Results
Recreation
Centroid
Number
(1)
17.0
17.1
17.2
18.0
19.0
19.1
20.0
21.0
22.0
22.1
22.2
23.0
23.1
23.2
24.0
24.1
24.2
24.3
25.0
26.0
R2
(2)
0.851
0.863
0.873
0.885
0.740
0.829
0.727
0.888
0.766
0.751
0.673
0.884
0.884
0.874
0.841
0.810
0.805
0.812
0.874
0.785
Consumers '
Surplus
(in $1000)
(3)
2,163
5,239
5,596
283
141
536
548
1,008
15
27
34
228
231
1,253
19
31
39
67
205
52
Surplus
per Day
$
(4)
6.22
5.48
5.12
4.50
4.28
6.15
5.20
5.83
2.57
2.56
2.32
5.44
5.08
5.78
2.67
2.55
2.72
2.87
4.89
2.42
R2
(5)
0.645
0.605
0.666
0.724
0.660
0.686
0.582
0.702
0.744
0.729
0.699
0.695
0.691
0.636
0.781
0.740
0.747
0.747
0.732
0.724
Consumers'
Surplus
(in $1000)
(6)
2,757
5,577
11,564
334
142
620
526
886
18
58
69
220
331
1,975
35
136
60
1,606
168
109
Surplus
per Day
$
(7)
7.94
5.83
10.58
5.31
4.78
7.11
5.00
5.13
3.18
5.57
4.79
5.24
7.26
9.12
4.97
11.05
4.11
68.95
4.00
5.17
column mean 0.820
886
4.24
0.696
1,360
9.23
* In the semilog form the logarithm is taken of the dependent variable.
20 cases. The semilog surplus-per-day estimates are more stable than the
corresponding double-log estimates. Dwyer, Kelley, and Bowes (1977) review
several empirical studies of recreation behavior, but only a few of these
studies deal specifically with boating. If we presume that other water-based
activities have a value comparable to boating or that boating is typical of
outdoor recreation in general, we may conjecture on the basis of Dwyer et aJL
that value-per-day estimates below $1 or above $10 are outside the range of many
86
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existing studies. The double-log estimate of surplus per day of $68.95 for
centroid 24.3 is clearly untenable, and the double-log surplus-per-day estimates
of $10.85 and $11.05 appear suspiciously high.
A few of the surplus-per-day estimates, such as those for centroids 18.0
and 20.0, are insensitive to the choice of functional form, but some estimates
are highly sensitive to this choice. This result indicates the inadequacy of
analyzing the issue of functional form by considering only one site. The
results in Table 7 do not establish that either form is correct or incorrect,
but the consistently lower explanatory power of the double-log form and the wide
variation in surplus-per-day estimates cast some doubt about the appropriateness
of this form.
The sensitivity of the above results to the choice of quantity demanded is
observed by reestimating the above equations where quantity demanded is obtained
from the visit-rate schedule using a zero price increment. Table 8 compares the
results of demand and valuation estimates obtained with a semilog and a
double-log form where quantity demanded is estimated endogeneously. The assumed
known quantity demanded is in column 2 and the semilog and double-log quantity
estimates are in columns 3 and 6 respectively. Several of the double-log form
estimates of total quantity demanded contain very large errors. For instance,
the double-log form produces an estimate of 111 million boating days at Lake
Washington (centroid 17.2), which errs by approximately 110 million days. The
quantity estimates from a semilog form are much closer aproximations to total
use, but the discrepancies are notable.
Comparing the consumers' surplus and surplus-per-day estimates of the
semilog and double-log form (Table 6) indicates dramatic differences in results.
Total surplus estimates with a double-log form average about four times those of
a semilog form, but the surplus-per-day estimates are considerably smaller for
87
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oo
oo
TABLE 8
DEMAND AND VALUATION ESTIMATES USING A SEMI LOG AND DOUBLE-LOG FORM AND ENDOGENOUS QUANTITY DEMANDED
Recreation
Centroid
Number
(1)
17.0
17.1
17.2
18.0
19.0
19.1
20.0
21.0
22.0
22.1
22.2
23.0
23.1
23.2
24.0
24.1
24.2
24.3
25.0
26.0
Mean
Exogeneous
Quantity
Demanded
(in 1000)
(2)
347
956
1,092
63
33
87
105
113
6
10
15
42
45
217
7
12
14
23
42
21
166
Semi log Results
Quantity
Demanded
(in 1000)
(3)
534
1,270
1,354
70
36
134
135
244
4
8
9
57
59
303
5
9
10
19
49
17
216
Consumers'
Surplus
(in $1000)
(4)
2,221
4,337
5,677
285
142
551
557
1,030
14
26
32
233
235
1,280
18
30
38
66
207
50
902
Surplus
per Day
$
(5)
4.16
4.20
4.19
4.10
3.96
4.11
4.12
4.22
3.52
3.33
3.73
4.06
4.02
4.22
3.60
3.49
3.67
3.40
4.25
2.96
3.87
Double-Log Results
Quantity
Demanded
(in 1000)
(6)
3,751
17,657
111,807
572
122
475
882
800
15
130
102
389
1,279
10,549
52
1,223
84
7,081
91
1,015
8,234
Consumers'
Surplus
(in $1000)
(7)
3,817
10,774
45,793
492
169
741
767
1,081
21
95
97
328
715
7,003
50
512
81
3,988
181
418
3,856
Surplus
per Day
$
(8)
1.02
0.61
0.41
0.86
1.38
1.56
0.87
1.35
1.37
0.74
0.95
0.84
0.56
0.42
0.94
0.42
0.97
0.52
1.99
0.41
0.91
-------
the double-log form. Without a benchmark for comparison, we cannot be certain
which estimates are most accurate. Because the double-log form yields gross
errors in the quantity estimates, it is possible that similar errors character-
ize the surplus estimates. Comparing total surplus semilog estimates in Table 7
with those in Table 8 indicates a very close correspondence. The result that
total surplus estimates are insensitive to the choice of quantity demanded
(given a semilog form) is significant. In contrast, the total surplus and
surplus-per-day estimates using a double-log form are highly sensitive to the
choice of quantity estimate.
The sensitivity of the valuation results to the size of the hypothetical
price increment is analyzed by using a price increment of $0.25 from zero to $1
in the first-stage demand curve and a $1 price increment thereafter. The choice
of price increment does not affect the (experience) demand statistics, but it
may affect the area under the site demand curve. Table 9 depicts double-log and
semilog estimates of total consumers' surplus and surplus per visitor-day for
each of the 20 centroids considered, using a $0.25 price increment up to $1. We
again observe significant discrepancies between the double-log and semilog
results. The double-log surplus-per-day estimate of $133.61 for centroid 24.3
is beyond any tenable limit, and several other double-log results appear
unreasonably high. In contrast, the surplus-per-day estimates using a semilog
form are between $2 and $6, which is in the area of other studies.
Tables 7, 8, and 9 present a comparison of semilog and double-log results
under alternative computational assumptions. A comparison of the average
results across the three tables provides one measure of the appropriateness of
these two forms. Using a semilog form, consumers' surplus averaged $886, $902,
and $897 thousand per site and $4.24, $3.87, and $4.25 per visitor day in Tables
7, 8, and 9 respectively. Using a double-log form, consumers' surplus estimates
89
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TABLE 9
TRAVEL-COST VALUATION ESTIMATES USING A SEMILOG AND DOUBLE-LOG FORM AND A $0.25
PRICE INCREMENT
Semi log Results
Recreation
Centroid
Number
(1)
17.0
17.1
17.2
18.0
19.0
19.1
20.0
21.0
22.0
22.1
22.2
23.0
23.1
23.2
24.0
24.1
24.2
24.3
25.0
26.0
Mean
Consumers'
Surplus
(in $1000)
(2)
2,205
5,307
5,651
285
142
547
554
1,024
14
26
32
232
234
1,272
19
31
38
66
206
50
897
Surplus
per Day
$
(3)
6.34
5.55
5.17
4.52
4.30
6.27
5.27
5.93
2.50
2.51
2.23
5.53
5.14
5.88
2.60
2.49
2.66
2.83
4.93
2.38
4.25
Double-Log Results
Consumers'
Surplus
(in $1000)
(4)
3,503
8,284
24,974
437
159
710
627
1,023
20
82
89
284
536
3,919
45
303
74
3,111
177
245
2,430
Surplus
per Day
$
(5)
10.08
8.66
22.85
6.95
4.81
8.14
5.96
5.92
3.56
7.83
6.12
6.76
11.76
18.09
6.34
24.66
5.12
133.61
4.23
11.57
15.66
Note:
demanded.
These results are
based on an exogenous
estimate of
total quantity
per site are $1,360, $902, and $2,430 thousand per site and $9.23, $0.91, and
$15.66 per visitor-day. Double-log results are highly sensitive to the choice
of hypothetical price increment in Eq. (IV.5) and to the choice of quantity
demanded at a zero price. Double-log results also show wide differences across
sites, even when computational assumptions are identical. In contrast, the
semilog results are relatively stable across sites and much less sensitive to
the choice of price increment in Eq. (IV.5) and to the choice of quantity
90
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demanded. These results do not support the use of the double-log form and
suggest that a semi log form is to be preferred.
B. Size of Origin Zone
When the travel-cost method was presented by Clawson (1959) and by Clawson
and Knetsch (1966), origins were aggregated into zones defined by a series of
concentric circles. There does not appear to have been any serious analysis of
the appropriate size of these origin zones, nor of the sensitivity of the
results to various size zones.8 The above results use each population centroid
in the region as a potential origin zone. Evidence on the sensitivity of
travel-cost demand and valuation to the definition of the origin zone is
obtained by comparing the above results to those obtained using 10-mile and
20-mile origin zones. Consider two systems of concentric circles, one at
10-mile and one at 20-mile intervals from the recreation centroid. Origin zones
are now defined as the area between each ring and visit rates are defined as
total trips from each zone per 1,000 population of the zone. The travel cost
from each zone is the weighted average travel cost of all centroids within the
zone where the weights are the number of trips per centroid.
Travel-cost demand and valuation estimates using 10- and 20-mile origin
zones are presented in Table 10. Comparing the results using a 10-mile zone
with those of a 20-mile origin shows similar estimates for several sites, but
quite dissimilar estimates for others. The estimates in Table 10 are comparable
to the semi log results in Table 7 because they are based on a semi log specifica-
tion, a $1 price increment in Eq. (IV.5), and quantity demanded estimated
8Brown and Nawas (1973) have argued that observations should be based on
individuals, rather than aggregations of people. As they use site-attendance
data, visit rates reflect the frequency of participation of and not the
aggregate participation rate of the population.
91
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TABLE 10
SEMILOG VALUATION ESTIMATES USING 10-MILE AND 20-MILE ORIGIN ZONES*
10 Mile Origin Zones
20 Mile Origin Zones
Recreation
Centroid
Number
(1)
17.0
17.1
17.2
18.0
19.0
19.1
20.0
21.0
22.0
22.1
22.2
23.0
23.1
23.2
24.0
24.1
24.2
24.2
25.0
26.0
R2
(2)
0.675
0.764
0.768
0.935
0.631
0.547
0.619
0.824
0.258
0.620
0.170
0.882
0.895
0.815
0.916
0.903
0.835
0.830
0.840
0.699
Consumers'
Surplus'
(in $1000)
(3)
$1,394
3,463
3,775
111
82
444
394
767
117
60
361
118
120
890
9
53
29
139
98
102
Surplus
Per Trip
(4)
$4.01
3.62
3.45
1.77
2.47
5.10
3.75
4.44
20.52
5.70
24.87
2.82
2.62
4.11
1.36
4.31
2.02
5.97
2.35
4.80
R2
(5)
0.787
0.749
0.868
0.977
0.668
0.470
0.751
0.827
0.216
0.716
0.474
0.948
0.928
0.913
0.919
0.903
0.877
0.806
0.915
0.698
Consumers'
Surplus
(in $1000)
(6)
$1,415
3,606
2,830
91
81
587
337
882
217
44
313
114
109
868
7
44
23
106
75
80
Surplus
Per Trip
(7)
$4.07
3.77
2.59
1.44
2.45
6.73
3.21
5.11
38.12
4.21
21.58
2.73
2.39
4.01
0.97
3.56
1.61
4.56
1.79
3.76
Mean
0.720
$626
$5.50
0.771
$591
$5.93
*These estimates are based on a $1 price increment in Eq.
demanded estimated exogeneously.
(IV.5), and quantity
exogenously. Comparing the results on these two tables indicates that
aggregating population centroids into concentric zones increases consumers'
surplus by an average of over $1 per trip. Furthermore, consumers' surplus
estimates on Table 7 appear uncorrelated with those on Table 10. Estimates of
total surplus for centroids 17.1 and 17.2 are over $1 million lower when
population centroids are aggregated into zones. However, the aggregation
process increases the surplus estimates per trip for centroids 22.0 and 22.2 by
92
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over 300 percent. The surplus-per-trip estimates for these two recreation
centroids exceed $20, and the coefficients of determination are relatively lower
for these two centroids. The results for these two centroids may be regarded as
outliers and therefore dismissed, but it is significant that aggregating
population centroids into zones produced outliers whereas use of population
centroids as origins did not.
The conclusion that travel-cost valuation estimates are sensitive to the
definition of the origin zone raises the question of which definition is most
appropriate. The average of the coefficients of determination favor the use of
population centroids as origin zones; but the differences in R2 values between
models do not provide sufficient evidence to resolve this issue. The two
extreme estimates (centroid 22.0 and 22.2) obtained from the 10- and 20-mile
origin zone equations raise a question about aggregating, but are also not
compelling evidence against it. A third potential indicator of the proper model
is the ability of the statistical estimate of the first-stage demand curve to
estimate known quantity demanded at a zero price.
Table 11 depicts the assumed known quantities and endogenous estimates of
this variable using 10- and 20-mile origin zones and using recreation centroids
as origin zones. The main result is that aggregating population centroids into
either 10- or 20-mile zones substantially improves the ability of the model to
predict total use at a zero price. Although aggregating populations improves
the predictive ability of the model in this sense, the quantity estimates for
several centroids still contain substantial errors.
The result that aggregating population centroids into concentric zones does
not improve the R2 values, but does improve the estimates of total quantity
demanded, is easily explained. Visit rates diminish with distance from the
site, but the number of population centroids increases with distance from the
93
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TABLE 11
ESTIMATES OF QUANTITY DEMANDED BY CENTROID USING SEMILOG AND DOUBLE-LOG FORMS
AND VARIOUS DEFINITIONS OF ORIGIN ZONES (IN THOUSANDS OF VISITOR-DAYS)
Semi log Results
Double-Log Results
Recreation
Centroid
Number
(1)
17.0
17.1
17.2
18.0
19.0
19.1
20.0
21.0
22.0
22.1
22.2
23.0
23.1
23.2
24.0
24.1
24.2
24.3
25.0
26.0
Exogeneous
Quantity
Demanded
(2)
347
956
1,092
63
33
87
105
113
6
10
15
42
45
217
7
12
14
23
42
21
Recreation
Centroids
(3)
534
1,270
1,354
70
36
134
135
244
4
8
9
57
59
303
5
9
10
19
49
17
Ten -
Mile
Origin
Zone
(4)
352
912
1,009
47
32
97
114
148
18
18
43
37
39
206
7
26
16
61
30
32
Twenty -
Mile
Origin
Zone
(5)
313
829
833
34
27
87
98
145
24
14
40
31
33
185
4
21
13
43
24
26
Recreation
Centroids
(6)
3,751
17,657
111,807
572
122
475
882
800
15
130
102
389
1,279
10,549
52
1,223
84
7,081
91
1,015
Ten-
Mi le
Origin
Zone
(7)
492
1,357
1,656
56
45
134
261
243
34
39
101
48
55
345
6
20
15
68
37
106
Twenty
Mile
Origin
Zone
(8)
540
1,381
1,333
44
59
155
240
337
51
48
113
51
50
325
4
18
12
43
34
116
Mean
166
216
171
141
8,234
256
248
Note: The quantity estimates in columns 3 through 8 are obtained by
letting AP = 0 in the appropriate least squares estimate of Eq. (IV.4).
site. When population centroids are used as origins, there is a large number
of observations of low visit rates that are close to the regression line.
The very few origin zones that have high visit rates and account for most of
the total visits have relatively little influence on the regression line. The
visit rates of the close origin zones are often estimated with large
residuals. Aggregation results in a large number of good-fitting observations
94
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being combined into a few observations and, hence, reduces their influence on
R2.
Aggregation decreases the total number of observations and thereby
increases the relative weight of the close origins in determining the regres-
sion line. The error in estimating these visit rates thereby decreases, and
hence, so does the error in estimating total visits. The "solution" to the
visit estimation problem is not increased aggregation; because aggregating
from a 10-mile origin zone to a 20-mile origin zone actually decreases the
reliability of predicting total visits (see Table 11, columns 4 and 5).
Indeed, total visits could be predicted exactly if populations were of
constant size across origins.9
Simulation estimates of each of these cases were again made using a
double-log form. The results using a $1 price increment and exogenous
quantity demanded are presented in Table 12. The coefficients of determina-
tion in columns 2 and 5 are lower for a double-log model than for a semilog
model when population centroids are aggregated into 10- or 20-miles zones.
Furthermore, most of the surplus-per-day estimates are higher than one could
reasonably expect. Overall, the aggregation process provides no credibility
to the double-log form. This result also follows when we consider the
double-log estimates of total use at a zero price. As seen in Table 11,
aggregating population centroids into 10- or 20- mile origin zones improved
the predictability of the model in terms of total use. However, the double-
log model predicts total use with a larger error than a semilog model,
regardless of the choice of origin zone.
9The estimated residuals in predicting visit rates necessarily sum to zero,
that is, I(V. - V.) = I(T./N. - T./N.) - 0. If the population of each origin is
identical, NI(T. - T.) = 0, visits (T.) are also predicted exactly.
95
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TABLE 12
DOUBLE-LOG VALUATION ESTIMATES USING 10-MILE AND 20-MILE ORIGIN ZONES
10-Mile Origin Zones
20-Mile Origin Zones
Recreation
Centroid
Number
(1)
17.0
17.1
17.2
18.0
19.0
19.1
20.0
21.0
22.0
22.1
22.2
23.0
23.1
23.2
24.0
24.1
24.2
24.3
25.0
26.0
R2
(2)
0.556
0.599
0.608
0.803
0.493
0.536
0.535
0.723
0.366
0.491
0.175
0.775
0.844
0.736
0.797
0.813
0.782
0.711
0.764
0.461
Consumers'
Surplus
(in $1000)
(3)
8,810
34,694
36,984
405
500
2,312
8,386
7,171
1,050
906
4,326
902
926
9,984
15
180
62
238
505
3,242
Surplus
per Day
$
(4)
25.36
36.29
33.84
6.44
15.10
26.54
79.72
41.52
184.24
87.75
298.29
21.52
20.31
46.10
2.04
14.69
4.26
10.23
12.05
153.28
R2
(5)
0.596
0.588
0.673
0.804
0.454
0.434
0.555
0.668
0.283
0.469
0.399
0.878
0.903
0.855
0.776
0.792
0.822
0.670
0.772
0.459
Consumers'
Surpl us
(in $1000)
(6)
18,546
38,203
19,616
770"
1,631
5,044
7,732
15,291
2,114
1,658
5,345
1,445
1,150
9,324
15
227
60
230
561
4,083
Surpl us
per Day
$
(7)
53.39
39.96
17.95
12.25
49.38
57.90
73.51
88.54
371.10
158.72
368.54
34.46
25.25
43.06
2.15
18.49
4.15
9.92
13.39
193.05
0.627
6,080
55.93
0.643
6,653
.81.76
3. Conclusions and Implications
This chapter presents travel-cost demand and value estimates for boating in
20 recreation centroids in Washington. The objective of the analysis is to
determine the sensitivity of the results to three specification and computa-
tional assumptions, and thus to determine which assumptions are most appro-
priate.
A Monte Carlo analysis is used to examine questions that have not been
resolved theoretically or empirically. We can find plausible results for at
least one centroid in each of the tables; but by observing results for several
96
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sites, the deficiencies in various assumptions becomes apparent. The recreation
literature has given only cursory attention to the issues considered here and
many existing studies have been based on a single site.
The preference of most recreation analysts for a semilog specification of
the first-stage demand function over a double log is confirmed by these results.
In terms of goodness of fit, stability of results across sites, accuracy of
predicting quantity demanded at a zero price, and a priori reasonableness of
results, this specification is clearly superior to the double log.
Some recreation analysts, such as Common (1973), have used a double-log
specification with satisfactory results. However, Common and others have tried
alternative specifications for only one site. For some centroids, consumers'
surplus estimates are insensitive to the specification, but this result is a
special case that may be observed in a sample of one site. A particularly
serious problem with the double-log specification is that on occasion it can
produce totally unrealistic results. The source of this problem is unclear and
cannot be determined from the regression estimates of the experience demand
schedule. The cause of these occasional drastic results may, to a lesser
extent, affect the apparently tenable results, hence these estimates should also
be considered suspect.
This analysis of boating at 20 recreation centroids reflects a small sample
of the 195 centroids and four recreation activities considered in the regional
model. Recreation experience demand curves were estimated for each centroid and
for each activity using both a double-log and semilog specification. The
results are simliar to those reported here, with some estimates of consumers'
surplus varying in sensitivity to the choice of functional form. About five
percent of the results using a double-log specification are unreasonable.
97
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The price-quantity observations depend upon the price increment used in Eq.
(IV.5) and hence the area under these price-quantity observations, which is
consumers' surplus, could also be affected by the size of the price increment.
As seen by comparing Table 7 with Table 9, when a double-log form is used, total
surplus and surplus per trip are sensitive to the size of this price increment.
With a semilog specification, the results using a $0.25 price increment up to $1
and a $1 increment thereafter are virtually identical to those obtained using a
$1 increment. The robustness of the semilog also suggests its superiority to
the double-log form.
Quantity demanded at a zero price is usually estimated exogenously from
site data, but it can also be estimated by setting AP = 0 in Eq. (IV.5). The
first estimate is based on observed (visit-rate) data and the second estimate is
based on visit rates estimated from a regression equation. The two estimates
are not identical, but one would hope that differences would be small and have a
mean of zero. When origin zones are defined as population centroids, we observe
wide differences between exogenous quantity estimates and quantity estimates
obtained from Eq. (IV. 5). One implication of this result is that if empirical
estimates of Eq. (IV.5) were used to predict visits at a similar proposed site,
a substantial error would be expected. Second, visit-rate schedules would yield
inaccurate estimates of the effect of initiating an entrance fee on total use.
As seen in Panel B of Figure 1, imposing a fee may lead to an increase in
predicted visits.
When a semilog model is used, discrepancies in quantity estimates do not
produce discrepancies in total consumers' surplus estimates (compare Table 7,
column 3, with Table 8, column 4). This result implies that it may be feasible
to estimate surplus at a proposed site, even when use cannot be estimated with
reliability. Errors in estimating quantity demanded have a negligible effect on
98
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total surplus because surplus is estimated with Bode's Rule and not as the area
under a regression equation. A regression estimate of a site-demand equation
would be affected by the choice of quantity demanded. However, by using Bode's
Rule to measure area under several points, the choice of one price-quantity
point affects the area only in the neighborhood of that point. A second
compelling reason for using Bode's Rule is to avoid the issue of the appropriate
functional form of the site-demand curve.
The most disconcerting result of this chapter is that valuation estimates
are sensitive to the definition of the origin zone. When each population
centroid is construed as a separate zone, the explanatory power of the model is
higher on the average than when centroids are aggregated into 10- or 20-mile
zones. Furthermore, aggregating centroids results in a substantial loss of
degrees of freedom, which with other things being equal, is undesirable, and in
this case causes the results to become unstable. However, aggregating popula-
tion centroids into origin zones improves the accuracy by which total use is
predicted at a zero price.
Most travel-cost studies have been based on an aggregation of population
centroids into concentric zones. The choice of a 10-mile versus 20-mile system
of concentric circles affects the results, but there is a greater disparity
between using zones and using population centroids as origins. A consequence of
using each centroid as an origin is that a large proportion of the centroids
account for a small proportion of the trips. In rough numbers, about 95 percent
of the centroids account for only 10 to 15 percent of the trips. The experience
demand curve is therefore influenced disproportionately by centroids that
account for very few trips. There is some justification for using each
population centroid as an origin zone and for aggregating centroids into
concentric zones. The best choice is unclear. Because travel-cost valuation
99
-------
estimates are sensitive to the definition of the origin zone, this is an
important topic for future work.
100
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CHAPTER VII
EMPIRICAL ESTIMATES OF RECREATION BENEFITS OF IMPROVED
WATER QUALITY IN THE PACIFIC NORTHWEST
This chapter presents empirical estimates of recreation benefits to be
gained through improving water quality of degraded rivers and preserving water
quality in selected lakes in the Pacific Northwest. The first section of this
chapter presents a brief overview of the main determinants of recreation demand
and valuation. The objective is to provide an intuitive explanation of the
model and of the subsequent empirical estimates. The second section presents
estimates of existing recreation benefits of eight selected lakes. The sample
permits a contrast in benefits between urban and rural locations. Section 3
estimates recreation benefits on a county basis of improving water quality in
all the degraded rivers in the Pacific Northwest.
1. Determinants of Recreation Value and Use
Travel-cost analyses have documented that recreation behavior can be
explained quite well by four independent variables: population size, travel
cost to the site, site characteristics, and the availability of substitute
sites. The population centers that send recreators to a specific site are
obviously a critical determinant of potential demand. The actual number of lake
users is influenced more by the potential number of users than perhaps by any
other variable. However, populations of equal size do not necessarily produce
the same number of recreation trips. Demographic characteristics such as
101
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household size and income influence participation rates. In the Northwest,
these variables influence the number of trips per household [Eq. (III.8)], but
population size is the main determinant of days spent recreating.
The number of users of a lake is influenced significantly by the distances
to the population origins. Recreators typically are adverse to travel and
therefore, other things being equal, the greater the required travel distance,
the fewer will be the users of a lake. The increase in travel costs, particu-
larly gasoline, in the last several years could increase the demand for lakes
closer to population centers at the expense of more distant sites. In addition
to the aversion to travel, distance also tends to diminish use because the
greater the distance from origins to the recreation site, the greater the
probability of preferred substitutes closer to the population origins.
The use and value of a recreation site depends on the existence of compe-
titive or substitute recreation sites. If a site has one or more close
substitutes, the value-per-unit day will be less than if the site has no close
substitutes. A site preferred over its competitors will have a high use even
though a low value per use day. A site that is generally less preferred than
its competitors will have low use and low value per day. Furthermore, substi-
tute sites may be located in the same proximity, but this is certainly not
necessary. Figure 9 depicts two population centers that, for illustrative
purposes, are assumed to be located on the same straight road. In this illu-
stration, there are four recreation sites that are assumed to be identical
except for location. Most, if not all, recreators from population center 1 will
visit site A. Site B is not a close substitute for site A because of greater
travel costs. Recreators from population center 2 will recreate at sites C and
D, which are close substitutes because of their identical travel distances, even
102
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FIGURE 9
THE EFFECT OF SUBSTITUTE SITES ON DEMAND AND VALUE
Distance
(in miles) <- 5 ^ <- 25 -»• •*- 10 -» <- 30 -* <- 30 ->
Center Site A Pop. 1 Site B Site C Pop. 2 Site D
(Population,
Recreation)
Trips from 100
Origin
Trips to 95 10 48
Destination
Value per $5 $0.50 $1
Day
100
47
$1
though they are 60 miles apart. In contrast, sites B and C are not close
substitutes even though they are only 10 miles apart.
In this illustration, site A receives the greatest use and has the greatest
value-per-user day. Demand is relatively price inelastic because the site has
no close substitute. Sites C and D receive significant use but have low values
per user day; the demand for each of these sites is very price elastic because
each site is a close substitute for the other. Site B is closer to a population
center than is either site C or site D, however B is dominated by other sites
preferred by both population centers. Thus, site B receives only minimal use
and has a low value per day. By implication it may not be cost-effective to
improve recreation opportunities at site B, because the presence of a preferred
substitute discourages use at B.
This example illustrates the importance of considering substitute sites
when selecting lakes for restoration. To emphasize this point, consider the
conditions in Figure 9, and assume that water quality is uniformly poor at all
sites. Now, which lakes would be cost-effective to restore? The highest
103
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priority in items of recreation benefits is likely to be site A. This site has
the greatest potential demand because it is located near a population center and
has no close substitutes. Sites C or D are also a high priority, but it would
probably be cost-effective to restore only one of these sites. If one of these
two lakes were restored, use and value per day would be high at that site. If
both were restored, use would be divided between the lakes and value per day
would be low. If site A and either C or D were restored, restoring lake B would
probably not be cost-effective because of the availability of preferred
substitutes.
The fourth major determinant of recreation demand and value is the site
characteristics including lake size, aesthetics, recreation facilities, and
water quality. These characteristics, in combination, determine the ability of
a site to attract recreators from various origins. Defining, weighing, and
measuring these characteristics has proven a major challenge to researchers
analyzing recreation demand and value. Recreation facility data serve as a
proxy for these characteristics because these data are available on a county
basis across the entire region.
If a lake is to be used for public recreation, it must have public access.
Also, there must be facilities appropriate to the various recreation activities.
For instance, a swimming beach is important for swimming, boat ramps are
necessary for boating, and camping facilities are required for camping. No
particular facilities are required for fishing, but the appropriate site
characteristic is probably the anticipated catch.
Water quality is one characteristic of a site and like other aesthetic
qualities, it is subjective and difficult to define and to measure. Estimating
the response of recreation use and value to changes in water quality is also
difficult because this response varies widely across sites and depends on the
104
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initial value of the other determinants of recreation demand. To illustrate,
assume that water quality of each site in Figure 9 is identical and can be
described as moderate to good. Under these assumptions, water quality
improvement would encourage additional demand at site C or site B, but not both,
because these sites are close substitutes. Improving water quality at site A
will not encourage additional use because site A is already heavily utilized and
cannot attract recreationists from substitute sites.
Water-quality improvement efforts may be directed toward maintaining
existing good water as well as improving the quality of degraded water.
Maintaining existing value and use may be the goal of preventive water-quality
programs if in the absence of such action, water would become degraded and use
would decline. Referring again to Figure 9, water-quality protection would not
appear to be justified at site B, because of negligible demand. This result
depends critically on two assumptions: (1) that water quality is uniformly good
at other sites; and (2) there exists a site that is preferred to site B.
However, if water quality were uniformly poor, improving site B would encourage
a significant increase in use from both population centers 1 and 2. Preventive
actions may not be justified at C or D because if either site became unusable,
demand would merely shift to the other site, which is a close substitute.
However, if both sites were threatened, maintaining quality at both sites or at
least at one site would induce large benefits. The site with the greatest
potential preservation value is clearly site A. The uniqueness of site A is its
high existing value and use, which are determined by its nearness to a popula-
tion center and the absence of close substitutes. This point can be general-
ized. The greater the current use of a site and the fewer its substitutes, the
stronger is the justification for preserving water quality at that site. Even
with the stringent assumption that water quality is uniformly good to moderate,
105
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the basic conclusion is that those sites that offer the greatest potential
increase in use and value are not necessarily the sites where preserving the
existing level of water quality is cost-effective.
2. Demand and Valuation Estimates for Selected Lakes
A sample of eight lakes was selected to indicate the recreation value of
preserving good water quality at urban versus rural locations. The demand and
valuation estimates of these lakes are explained in terms of the determinants of
demand, as described in the previous section. Although three of the lakes
considered here are affected by the EPA's Clean Lakes Program (Liberty, Medical
and Fernridge Reservoir), demand and benefits are estimated under the assumption
that existing water quality does not discourage use.
A summary of the demand and valuation estimates is presented in Table 13.
Column 3 contains data on facilities for the corresponding activity. This
variable is a proxy for the characteristics of a recreation site and should be
positively correlated with demand and value of the site. The accessibility of a
recreation site is measured as the weighted sum of recreation activity days
emanating from each population center, as defined by Eq. (III.5). The weights
are the probability that a person will travel the distance from the respective
origin to the corresponding recreation site. Accessibility reflects the joint
influence of population size and distance. The closer a site to population
centers and the greater the number of recreation trips produced by these
centers, the larger the accessibility number. The level of facilities and
accessibility of a site jointly determine total visitor-days by activity for the
site.
The first two lakes shown in Table 13, Lake Washington and Lake Sammamish,
are large urban lakes with numerous recreation facilities. These lakes are
106
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TABLE 13
ANNUAL RECREATION DEMAND AND VALUE OF SELECTED LAKES IN THE PACIFIC NORTHWEST (1979 DOLLARS)
Recreation
Centroid
Number
(1)
17.1
17.2
10.0
24.0
48.1
32.0
32.2
103.2
Lake and County
(2)
Lake Sammamish
King County
Lake Washington
King County
Twin Lakes
Ferry County
Perrygin Lake
Okanogan County
Priest Lake
King County
Medical Lake
Spokane County
Liberty Lake
Spokane County
Fernridge Reservoir
Lane County
Activity
(3)
Swimming
Campi ng
Fishing
Boati ng
Total
Swimming
Camping
Fishing
Boati ng
Total
Swimming
Camping
Fishing
Boating
Total
Swimming
Camping
Fishing
Boating
Total
Swimming
Camping
Fishing
Boating
Total
Swimming
Camping
Fishing
Boating
Total
Swimming
Camping
Fishing
Boating
Total
Swimming
Camping
Fishing
Boating
Total
Facility*
(4)
3,000
150
220
12
7,000
1
100
39
400
117
525
4
275
120
800
4
6,750
1,265
310
26
150
4
61
5
100
25
50
1
6,608
200
75
33
Access.**
(5)
2,755,403
2,633,395
2,003,932
1,596,838
2,883,916
2,511,231
2,199,562
1,656,586
201,214
507,609
117,229
223,566
90,521
333,922
45,169
139,078
218,585
550,561
143,338
240,518
989,653
1,357,021
650,469
705,431
1,232,264
1,637,891
851,309
880,733
309,616
777,142
335,729
254,786
Annual
Visitor
Days
(in 1000)
(6)
4,069
2,123
1,745
4,424
12,361
4,837
153
1,791
9,616
16,397
100
170
95
41
406
46
93
47
18
204
157
640
112
137
1,046
747
134
509
563
1,953
844
441
639
303
2,218
383
446
311
193
1,333
Recreation
Value
(in $1000)
(7)
18,446
8,038
5,085
30,968
62,557
21,880
603
4,589
66,773
93,845
596
905
535
342
2,378
393
729
402
194
1,718
818
2,743
485
1,005
5,051
3,114
551
1,806
3,594
9,065
3,970
1,829
2,387
2,114
10,300
2,236
2,147
1,117
1,741
7,241
Value
per
Trip
S
(8)
4.54
3.79
2.91
7.00
5.06
4.52
3.94
2.56
6.94
5.72
5.97
5.33
5.64
8.33
5.86
8.58
7.87
8.54
10.76
8.42
5.22
4.29
4.31
7.35
4.83
4.17
4.10
3.55
6.38
4.64
4.70
4.15
3.79
6.97
4.64
5.83
4.81
3.59
9.01
5.43
*The facilities for the activities are: linear beach feet, camping units, acceptable river and shore-
line miles, and number of boat ramps.
**Access. means accessibility and is a positive function of the nearness to population centers and the
size of these centers. See Eq. (III.13), p. 52.
107
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located in the Seattle Standard Metropolitan Statistical Area (SMSA), the
largest concentration of people in the Northwest. The annual value of the
water-based recreation activity on these lakes is estimated to be $93.8 and
$62.6 million, respectively, making them the most valuable recreation lakes in
the region.1 These high annual values reflect the combination of short travel
distance, large population centers, and numerous recreation facilities, particu-
larly for swimming and boating.
Of the other six lakes in Table 13, three are urban and three are rural.
Twin Lakes, Perrygin Lake, and Priest Lake are each more than 50 miles from a
major population center. In contrast, Medical Lake and Liberty Lake are within
20 miles of Spokane, Washington (SMSA population is 304,058), and Fernridge
Reservoir is about 12 miles from Eugene-Springfield, Oregon (SMSA population,
271,130). Fernridge Reservoir is used more extensively than the other lakes and
has a corresponding higher value. The use and value of the other five lakes is
similar.
The significance of an urban versus rural location is easily appreciated by
comparing swimming estimates of two urban lakes, Medical and Liberty, with those
of the two rural lakes, Perrygin and Twin Lakes. Medical and Liberty have only
150 and 100 linear beach feet, respectively, whereas Perrygin and Twin Lakes
have 275 and 400 linear swimming beach feet. The urban lakes are very
accessible (see column 5, Table 13), and the two rural lakes relatively
inaccesible. Thus, even though the two urban lakes offer fewer swimming
opportunities (measured by linear beach feet), they receive more use and have a
corresponding higher value than the rural lakes.
1Crater Lake, in Oregon, attracts visitors nationwide and even from abroad, but
not for recreation reasons, because fishing, boating, and swimming are
prohibited. Crater Lake certainly has a high value, but it is not included in
this study.
108
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Although benefit estimates are presented here for only eight lakes in the
Northwest, some general conclusions are suggested. First, those lakes that
offer extensive recreation opportunities and are located near large population
centers will receive extensive recreation use, and this use will have a high
total value. The demand and valuation estimates for Lake Washington and Lake
Sammamish reflect their proximity to large population centers and their abundant
recreation facilities. The estimate of annual recreation value of $7.2 million
for Fernridge Reservoir is significantly less than the estimates of the above
two lakes. However, this reservoir is smaller, located further from a popula-
tion center, and the population center has fewer people. The counterpart to the
principle stated above is that lakes without recreation facilities that are
located a significant distance from major population centers will not be heavily
used and will have corresponding low recreation values. The two lakes farthest
from population centers, Twin Lakes and Perrygin Lake, have the lowest total
recreation value. Two of the lakes (Newman and Liberty) are not particularly
attractive in terms of their recreation facilities, but are located near
Spokane, Washington, which is a large urban center. The other three lakes are
located in rural areas but offer appealing site characteristics that attract
recreators from several miles.
3. Benefits of Improving Water Quality in Streams
This section presents estimates of recreation benefits that would accrue if
the degraded rivers and streams in the Pacific Northwest were made fishable and
swimmable.
In the Northwest, camping, fishing, swimming, and boating generally occur
where water quality is high and appropriate facilities are available. In those
areas where water is degraded, recreation facilities have not been provided and
109
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recreation does not occur. Water quality and recreation facilities are
complements and for purposes of this study are assumed to be perfect comple-
ments. Improved water quality will not stimulate recreational use unless there
is a corresponding improvement of related facilities such as swimming beaches,
boat ramps, or campsites. Recreation facilities are not viewed as a true causal
variable, but as a statistical proxy for a large number of nonquantifiable
variables that in combination determine the attractiveness of a recreation
site.2 Fishing is the exception as no facilities are required for fishing. The
quality variable that is assumed comparable to recreation facilities is the
number of fishable river miles and lake shoreline miles. The exogenous
variables that drive the model are: linear swimming beach feet, number of boat
ramps, camping units, and fishable river and shoreline miles. An increase in
any of these variables will increase demand and consumers' surplus, where it is
implicit that water quality is "acceptable" for recreational purposes.
Similarly, an improvement in water quality must be accompanied by an increase in
one or more of the above variables if use and benefits are to be affected.
The Region X (Seattle) office of the U.S. Environmental Protection Agency
(EPA) has published a series of water-quality assessment reports covering each
major river basin in the Pacific Northwest. Water quality was assessed for each
major stream and for various reaches on these streams using both recreational
and biological criteria. Water quality is indicated for recreation in general
2A report by the Institute of Transportation and Traffic Engineering (1971, ch.
7) includes an effort to construct a recreation attractiveness index for camping
by defining 28 characteristics of campgrounds and applying factor analysis to
select the most important factors. The factors that were selected accounted for
41.5% of the variance in the observed data. It is not feasible to apply a
similar approach in this study because much of the required data do not exist,
and the data that are available are of poor quality. The large scale effort
that would be required to complete the analysis is not justified by the
improvement in the results.
110
-------
and is not estimated for each of the four activities analyzed in this paper.
Water quality was not measured on a continuous scale, rather it was judged to be
acceptable, objectionable, or not acceptable. An acceptable stream is one
meeting the 1983 Federal water-quality goals of fishable and swimmable streams.
Although standard water quality parameters, for example, turbidity, were used in
assessing water quality, professional judgment was also a factor. The objec-
tionable and not acceptable river stretches were noted on U.S. Geological Survey
base maps for each of the three states. A planimeter was then used to tabulate
degraded and acceptable river miles on a county basis. The resulting estimates
of acceptable and degraded river miles serve as the basic water-quality
inventory data for this study.
Given the assumption that water quality and facilities are perfect comple-
ments, it is feasible to estimate water-quality benefits by estimating the
benefits of increasing facilities on degraded rivers. The number and type of
facilities that could be constructed if water quality were improved was
estimated by state recreation planners. The assistance of these planners was
sought because of their first-hand knowledge of the recreational potential of
the various areas in their respective states. The recreation planners were
shown a U.S. Geological Survey base map (scale 1:500,000) of their state with
the degraded rivers marked and asked the following question for each degraded
river segment. "If water quality were improved, would this area be conducive to
any of the four activities being considered here?" When the answers were
affirmative, the next question asked was, "How many facilities by type could
reasonably be constructed along the degraded river?" Although this method of
estimating the potential increment in facilities certainly lacks scientific
rigor, all recreation facilities data were obtained from the state recreation
111
-------
officials, whose responsibility is to recommend the development of state recre-
ation areas.
Based on these interviews with the state recreation planners, estimates
were made of the potential increment in recreation facilities (boat ramps,
swimming beach feet, and campsites) that could be constructed at each recreation
centroid if the degraded water were improved. Estimates of observed and
potential facilities by activity and recreation centroid are presented in
Appendix A, Table A. 5. The incremental variable that enters the model for
fishing is degraded river miles by centroid. This variable was estimated with
EPA data and did not require the assistance of the recreation planners. The
estimated increment in facilities should be interpreted as the maximum potential
change and not as an estimate of what would occur if water quality were
improved. Recreation benefit estimates therefore represent an upper bound that
can be attained only by cooperation with those responsible for planning and
developing recreation sites.
Recreation demand and value was estimated for each of four activities and
for each of the 195 selected recreation centroids in the Northwest on the basis
of existing water quality and level of facilities (see Table A.4). Demand and
value were again estimated assuming that all degraded water was made fishable
and swimmable and the assumed facilities were constructed. The increments in
benefits for each activity are presented on a county basis in Table 14. The 16
recreation centroids in western Montana are not included in this analysis.
The main result from Table 14 is that substantial incremental benefits,
(for example, over one million dollars) are concentrated in a few counties and
that most counties show much lower benefits. As expected, the counties with the
largest potential benefits are those accessible to the largest populations. The
Washington counties with the largest populations in order are King, Pierce, and
112
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TABLE 14
ANNUAL RECREATION BENEFITS OF IMPROVED WATER QUALITY IN STREAMS BY ACTIVITY AND
BY COUNTY FOR WASHINGTON, OREGON, AND IDAHO
County
Adams
Asotin
Benton
Chell an
Cl all urn
Clark
Columbia
Cowl i tz
Douglas
Ferry
Franklin
Garfield
Grant
Grays Harbor
Island
Jefferson
King
Kitsap
Kittitas
Klickitat
Lewi s
Lincoln
Mason
Okanogan
Pacific
Pend Oreille
Pierce
San Juan
Skagit
Skamania
Snohomish
Spokane
Stevens
Thurston
Wahkiakum
Walla Walla
Whatcom
Whitman
Yakima
Total Incre-
mental
Benefits
Swimming
$
0
0
20,471
0
0
0
0
0
65,794
0
0
0
26,692
0
0
0
0
0
0
0
0
0
0
0
0
0
0
467,354
0
0
637,896
0
251,302
0
0
0
-0
0
1,469,509
Camping
$
0
222,016
0
0
0
0
0
0
414,745
138,208
0
0
194,394
0
0
0
2,358,906
0
204,163
0
0
0
0
127,453
0
0
1,347,167
0
0
0
0
1,051,884
0
0
0
0
0
0
453,419
6,512,335
Washington
Fishing
$
0
2,598
14,071
0
0
0
0
0
7,207
8,101
0
0
1,830
0
0
0
14,373
0
0
0
0
0
0
0
0
0
165,450
0
0
0
0
0
36,335
26,445
0
7,960
0
0
11,993
296,363
Boating
$
0
30,327
0
0
0
0
0
25,015
24,616
0
0
0
0
0
0
0
693,112
0
0
0
154,300
0
0
136,550
0
0
1,050,138
0
0
0
0
870,667
0
5,360,468
0
0
0
0
1,013,475
9,360,668
Total
Recreation
Benefits
$
0
254,941
34,542
0
0
0
0
27,015
512,362
146,309
0
0
196,224
26,692
0
0
3,066,391
0
204,163
0
154,300
0
0
264,003
0
0
2,562,755
0
467,354
0
0
2,560,447
36,335
5,638,215
0
7,960
0
0
1,478,887
17,638,895
113
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TABLE 14 (continued)
County
Ada
Adams
Bannock
Bear Lake
Benewah
Bingham
Blaine
Boise
Bonner
Bonnevil le
Boundary
Butte
Camas
Canyon
Caribou
Cassia
Clark
Clearwater
Custer
Elmore
Franklin
Fremont
Gem
Gooding
Idaho
Jefferson
Jerome
Kootenai
Latah
Lemhi
Lewi s
Lincoln
Madison
Minidoka
Nez Perce
Oneida
Owyhee
Payette
Power
Shoshone
Teton
Twin Falls
Valley
Washington
Total Incre-
mental
Benefits
Swimming
$
0
0
131,356
0
0
0
3,808
0
0
7,705
0
34,910
0
29,048
21,400
139,965
22,589
12,091
2,988
0
2,662
20,775
0
129,722
0
22,572
0
0
0
618
0
52,829
18,864
0
0
64,168
0
0
0
185,954
40,826
86,172
0
5,647
$1,036,669
Camping
$
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
73,216
17,311
0
0
0
0
0
0
0
0
0
0
1,300
0
0
0
0
0
0
0
0
0
67,601
0
0
0
0
$159,428
Idaho
Fishing
$
0
0
0
0
0
37,707
88,530
0
0
15,237
0
34,481
0
12,798
0
19,925
2,390
0
106,986
0
4,184
5,506
0
0
0
164,082
0
0
0
0
0
40,659
57,764
0
0
21,117
10,828
0
0
0
13,092
43,814
0
149
$679,249
Boating
$
0
652
0
925
0
5,993
0
0
0
0
0
0
0
37,532
0
8,706
0
17,922
5,267
0
2,435
697
0
4,583
0
0
0
0
0
653
0
0
0
0
0
2,956
0
0
0
45,743
2,107
3,740
11,954
0
$151,865
Total
Recreation
Benefits
$
0
652
131,356
925
0
43,700
92,338
0
0
22,942
0
69,391
0
79,378
21,400
168,596
24,979
103,229
132,552
- 0
9,281
26,978
0
134,305
0
186,654
0
0
0
2,571
0
93,488
76,628
0
0
88,241
10,828
0
0
299,298
56,025
133,726
11,954
5,796
$2,027,211
114
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TABLE 14 (continued)
County
Baker
Benton
Clackamas
Clatsop
Columbia
Coos
Crook
Curry
Deschutes
Douglas
Gilliam
Grant
Harney
Hood River
Jackson
Jefferson
Josephine
Klamath
Lake
Lane
Lincoln
Linn
Malheur
Marion
Morrow
Multnomah
Polk
Sherman
Tillamook
Umati 1 1 a
Union
Wai Iowa
Wasco
Washington
Wheeler
Yamhill
Total Incre-
mental
Benefits
Total Regional
Incre-
mental
Benefits
Swimming
$
0
1,597,504
0
0
0
0
2,858
0
157,796
65,229
0
0
0
0
0
0
0
0
0
0
0
875
0
0
0
0
112,649
0
0
0
0
0
0
56,586
0
1,353,222
$3,346,719
$5,852,897
Oregon
Camping Fishing Boating
$
0
0
0
0
0
0
179,842
0
83,710
485,883
0
0
6,877
0
0
0
0
1,099
0
711,274
62,287
0
0
0
0
0
0
0
0
0
0
0
0
62,669
0
766,698
$2,360,339
$9,032,122
$
0
42,056
0
0
0
21,716
0
0
11,016
110,447
0
0
1,734
47,798
0
0
0
0
0
87,815
64,894
0
0
0
0
0
30,448
0
0
0
0
0
0
4,515
0
26,336
$448,775
$1,424,387
$
0
0
97,130
0
0
0
12,601
0
4,506
40,153
0
0
0
0
0
0
0
0
0
0
0
10,720
0
0
0
0
192,895
0
0
0
8,325
0
0
358,683
0
181,793
$906,806
$10,419,339
Total
Recreation
Benefits
$
0
1,639,560
97,130
0
0
21,716
195,301
0
257,028
701,712
0
0
8,611
47,798
0
0
0
1,099
0
799,089
127,181
11,595
0
0
0
0
335,992
0
0
0
8,325
0
0
482,453
0
2,328,049
$7,062,639
$26,728,745
115
-------
Spokane, and these counties show corresponding large recreation benefits. The
most populated counties in Idaho and Oregon are Ada and Multnomah. Each county
has no water-quality benefits, but neither county has a water-quality problem.
Fifty-eight of the total 119 counties indicate zero total potential recrea-
tion benefits and several more show no benefits for certain activities. Of
these 58 counties, 33 have no officially degraded water and therefore have no
potential benefits. An additional 16 counties that have a water-quality
problem were judged to be not conducive to recreation even if water quality
were improved. These counties are typically rural where agriculture is the
economic base.
Zero or low benefits also occur for those counties that are significant
distances from population centers. Even if water quality were improved and
facilities added, demand would not increase significantly in those areas that
are inaccessible. Preservation values are significantly larger than potential
incremental benefits for each activity and for each state. This result owes to
the abundance of existing accessible recreation opportunities. The attractions
model, Eq. (III-61)-(III-9') (Table 2), provides empirical evidence that the
response of attractions to facilities diminishes as the level of facilities
increases. The results in Table 14 cannot be extrapolated to other regions that
may have different population densities, existing recreation opportunities, and
water-quality problems.
4. Conclusions
A model has been presented that can be used to estimate recreation benefits
for four water-based activities within a three and one-half state region. Bene-
fits can be estimated for any single site or for several sites simultaneously.
Benefits also can be estimated for preserving existing water quality as well as
116
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improving degraded water. The main conclusion is that, with respect to the
three Northwestern states, the largest potential recreation benefits exist near
the population centers. In contrast, improving water quality in sparsely
populated agricultural areas will probably not stimulate a substantial increase
in recreation demand.
The benefit estimates in Table 14 may appear discouraging in terms of the
economic viability of meeting the national goal of "fishable and swimmable"
water. Indeed, improving water quality in some agricultural areas may not be
cost-effective. However, potential recreation benefits at several sites exceeds
$1 million per year. Also, certain nonrecreation benefits such as property
values, aesthetic values, option demand, and perhaps drinking water and health
benefits are likely to display the same geographic pattern as recreation
benefits. That is, these potential benefits may also correlate with population
densities. A more comprehensive analysis of benefits, focusing particularly on
those listed above could conclude that total water-quality benefits are
substantially larger than those presented in Table 14. For example, in a
valuation study of the Flathead Lake and River system in western Montana using
this model, recreation values are estimated to be $6.3 million per year
(Sutherland 1982d). However, in the same study, nonuser values (option,
existence, and bequest) are estimated to be $97.3 million per year for the same
region.
117
-------
APPENDIX A
DATA TABLES
118
-------
TABLE A.I
POPULATION CENTROIDS, POPULATION, AND COUNTIES
Population
Centroid
Number
1.0
2.0
3.0
3.1
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
17.1
17.2
17.3
17.4
18.0
19.0
20.0
21.0
22.0
23.0
24.0
25.0
26.0
27.0
28.0
29.0
30.0
31.0
31.1
32.0
33.0
34.0
35.0
36.0
37.0
38.0
39.0
County
Adams
Asotin
Benton
Benton
Chellan
Clallum
Clark
Columbia
Cowl itz
Douglas
Ferry
Frank! i n
Garfield
Grant
Grays Harbor
Island
Jefferson
King
King
King
King
King
Kitsap
Kittitas
Klickitat
Lewi s
Lincoln
Mason
Okanogan
Pacific
Pend Oreille
Pierce
San Juan
Skagit
Skamania
Snohomish
Snohomish
Spokane
Stevens
Thurston
Wahkiakum
Walla Walla
Whatcom
Whitman
Yakima
Washington
Population Centroid
Othello
Clarkston
Kennewick
Richland
Wenatchee
Port Angeles
Vancouver
Dayton
Kelso
Watervi 1 le
Republ ic
Pasco
Pomeroy
Moses Lake
Aberdeen
Oak Harbor
Port Townsend
Seattle
Auburn
Kent
Renton
Bellevue
Port Orchard
Elensburg
Goldendale
Chahal is
Davenport
Shelton
Omak
Raymond
Newport
Tacoma
Friday Harbor
Mt. Vernon
Stevenson
Everett
Edmonds
Spokane
Col vi lie
Olympia
Cathlamet
Walla Walla
Bel 1 ingham
Pul Iman
Yakima
Population
13,322
16,822
42,383
66,291
44,980
51,224
192,060
4,098
79,489
22,156
5,748
34,613
2,483
48,040
66,356
44,016
15,903
998,909
50,568
37,925
38,397
139,061
145,990
24,866
15,879
55,450
9,597
30,896
30,654
17,234
8,561
482,692
7,793
63,184
7,914
221,739
114,214
341,058
29,008
124,249
3,824
47,267
105,198
40,321
170,767
(continued)
119
-------
TABLE A.I (continued)
Population
Centroid
Number
40.0
41.0
42.0
43.0
44.0
45.0
46.0
47.0
48.0
49.0
50.0
51.0
52.0
53.0
54.0
55.0
56.0
57.0
58.0
59.0
60.0
61.0
62.0
63.0
64.0
65.0
66.0
67.0
68.0
69.0
70.0
71.0
72.0
73.0
74.0
75.0
76.0
77.0
78.0
79.0
80.0
81.0
82.0
83.0
County
Ada
Adams
Bannock
Bear Lake
Benewah
Bingham
Blaine
Boise
Bonner
Bonnevil le
Boundary
Butte
Camas
Canyon
Caribou
Cassia
Clark
Clearwater
Custer
Elmore
Frankl in
Fremont
Gem
Gooding
Idaho
Jefferson
Jerome
Kootenai
Latah
Lemhi
Lewi s
Lincoln
Madison
Minidoka
Nez Perce
Oneida
Owyhee
Payette
Power
Shoshone
Teton
Twin Falls
Valley
Washington
Idaho
Population Centroid
Boise
Council
Pocatel lo
Montpel ier
St. Maries
Blackfoot
Ketchum
Horseshoe Bend
Sandpoint
Idaho Fall
Bonners Ferry
Arco
Fairf ield
Namp
Soda Springs
Burley
Dubois
Orof ino
Chalis
Mountain Home
Preston
St. Anthony
Emmet
Gooding
Grangevil le
Rigby
Jerome
Couer d'Alene
Moscow
Salmon
Kami ah
Shoshone
Rexburg
Rupert
Lewiston
Mai ad City
Homedale
Payette
American Falls
Kel logg
Driggs
Twin Falls
McCall
Weiser
Population
172,843
3,347
65,448
6,946
8,295
36,473
9,825
2,998
24,155
65,971
7,302
3,351
809
83,601
8,689
19,476
798
10,383
3,392
21,502
8,892
10,806
11,967
11,845
14,724
15,316
14,804
59,914
28,667
7,444
4,084
3,439
19,502
19,693
33,232
3,233
8,239
15,827
6,879
19,234
2,907
52,869
5,633
8,815
(continued)
120
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TABLE A.I (continued)
Population
Centroid
Number
84.0
85.0
86.0
86.1
87.0
88.0
89.0
89.1
90.0
91.0
91.1
92.0
93.0
94.0
95.0
96.0
97.0
98.0
98.1
99.0
100.0
101.0
102.0
103.0
104.0
104.1
105.0
106.0
106.1
107.0
107.1
108.0
109.0
110.0
111.0
112.0
113.0
114.0
115.0
116.0
117.0
118.0
119.0
County
Baker
Benton
Clackamas
Clackamas
Clatsop
Columbia
Coos
Coos
Crook
Curry
Curry
Deschutes
Douglas
Gil 1 iam
Grant
Harney
Hood River
Jackson
Jackson
Jefferson
Josephine
Klamath
Lake
Lane
Lincoln
Lincoln
Linn
Malheur
Malheur
Marion
Marion
Morrow
Multnomah
Polk
Sherman
Tillamook
Umati 1 la
Union
Wai Iowa
Wasco
Washington
Wheeler
Yamhill
Oregon
Population Centroid
Baker
Corval 1 is
Lake Oswego
Oregon City
Astoria
St. Helens
Coqui 1 le
Coos Bay
Prinevi 1 le
Gold Beach
Brookings
Bend
Roseburg
Condon
Canyon
Burns
Hood River
Medford
Ashland
Madras
Grants Pass
Klamath Falls
Lakeview
Eugene
Newport
Lincoln City
Albany
Vale
Ontario
Salem
Woodburn
Heppner
Portland
Dallas
Moro
Til lamook
Pendleton
La Grande
Enterprise
The Dalles
Hillsboro
Fossil
McMinnvi 1 le
Population
16,127
68,078
193,085
44,120
32,467
35,709
15,453
48,477
13,097
13,186
3,749
62,117
93,100
2,061
8,216
8,306
15,810
115,279
16,156
11,556
52,937
59,048
7,523
271,130
15,185
20,129
87,743
18,727
8,164
181,964
22,490
7,525
559,058
45,201
2,177
21,170
58,816
23,935
7,269
21,711
245,684
1,511
55,230
(continued)
121
-------
TABLE A.I (continued)
Population
Centroid
Number
120.0
121.0
122.0
123.0
124.0
125.0
126.0
127.0
128.0
County
Cascade
Flathead
Gal latin
Flathead
Lake
Lewis and Clark
Lincoln
Missoula
Silver Bow
Western Montana
Population Centroid
Great Falls
Kali spell
Bozeman
Whitefish
Poison
Helena
Libby
Missoula
Butte
Population
89,367
41,462
67,414
10,000
19,098
49,992
17,731
79,091
95,067
External Zones
129.0
130.0
131.0
132.0
133.0
134.0
135.0
136.0
137.0
138.0
139.0
140.0
141.0
143.0
Eastern Montana
British Columbia
British Columbia
Alberta
Wyomi ng
Utah
Nevada
Cal i form' a
Alaska
Eastern Canada
North Central
Northeast
Southeast
South Central
Bil 1 ings
Vancouver
Cranbrook
Calgary
—
—
—
—
—
—
—
—
—
— - —
159,117
2,206,608
200,000
1,838,037
470,816
1,461,037
799,184
23,668,562
330,000
18,687,959
50,571,000
61,880,000
41,487,000
31,440,000
Notes: The population estimates for western Montana counties include
neighboring counties, for
Missoula includes Mineral
and Powell; and Jefferson
estimates for all United
from the 1980 census, U.S.
of Population and Housing
which no population
and Granite; Butte
includes Beaverhead
States counties and
Department of Commerce,
(by state), 1981.
centroid is used. For instance,
includes Silver Bow, Deer Lodge,
and Ravalli counties. Population
states are preliminary estimates
Bureau of Census, 1980 Census
122
-------
TABLE A. 2
RECREATION CENTROIDS BY NAME, COUNTY, AND CENTROID NUMBER
Recreation
Centre id
Number
1.0
2.0
3.0
4.0
4.1
5.0
5.1
5.2
6.0
7.0
8.0
8.1
9.0
10.0
11.0
12.0
13.0
13.1
13.2
14.0
14.1
14.2
15.0
15.1
16.0
16.1
16.2
17.0
17.1
17.2
18.0
19.0
19.1
20.0
21.0
22.0
22.1
22.2
23.0
23.1
23.2
24.0
24.1
County
Adams
Asotin
Benton
Chelan
Chelan
Clal Turn
Clallum
Cl all urn
Clark
Col umbia
Cowlitz
Cowl i tz
Douglas
Ferry
Frankl in
Garfield
Grant
Grant
Grant
Grays Harbor
Grays Harbor
Grays Harbor
Island
Island
Jefferson
Jefferson
Jefferson
King
King
King
Kitsap
Kittitas
Kittitas
Klickitat
Lewi s
Lincoln
Lincoln
Lincol n
Mason
Mason
Mason
Okanogan
Okanogan
Recreation Centroid
Northwest corner
Field Springs State Park
Crow Butte State Park
Lake Wenatchee State Park
Lake Chelan State Park
Bogachiel State Park
Neah Bay State Park
Dungeness State Park
Battleground State Park
Lewis and Clark State Park
Merwin Reservoir
Seaquest State Park
Chief Joseph
Twin Lakes
Lyons Ferry State Park
Pataha Creek
Potholes State Park
Sun Lakes State Park
Steamboat State Park
Bay City
Ocean City State Park
Lake Quinalt
Camano Island State Park
Deception Pass State Park
Kalaloch
Olympic National Park
Dosewallips State Park
Snoqualm
Lake Sammamish
Lake Washington
Horshoe Lake
Wawapum State Park
Lake Kachess
Horsethief Lake State Park
Ike Kinswa State Park
Grand Coulee Dam
Fort Spokane
Sprague Lake
Lake Cushman
Bel fair
Dash Point State Park
Pearrygin Lake State Park
Conconolly State Park
(continued)
123
-------
TABLE A. 2 (continued)
Recreation
Centroid
Number
24.2
24.3
25.0
26.0
26.1
27.0
27.1
27.2
28.0
29.0
29.1
30.0
30.0
31.0
31.1
32.0
32.1
32.2
32.3
32.4
33.0
33.1
33.2
34.0
35.0
36.0
37.0
37.1
37.2
37.3
38.0
39.0
40.0
41.0
42.0
43.0
44.0
45.0
46.0
46.1
47.0
48.0
48.1
49.0
50.0
County
Okanogan
Okanogan
Pacific
Pend Oreille
Pend Oreille
Pierce
Pierce
Pierce
San Juan
Skagit
Skagit
Skamania
Skamania
Snohomish
Snohomish
Spokane
Spokane
Spokane
Spokane
Spokane
Stevens
Stevens
Stevens
Thurston
Wahkiakum
Walla Walla
Whatcom
Whatcom
Whatcom
Whatcom
Whitman
Yakima
Ada
Adams
Bannock
Bear Lake
Benewah
Bingham
Blaine
Blaine
Boise
Bonner
Bonner
Bonnevil le
Boundary
Recreation Centroid
Alta Lake State Park
Osoyoos Lake State Park
Fort Canby
Skookum Lakes
Crawfield
Alder Lake
Mount Ranier National Park
Tolomerie State Park
Morgan State Park
Bayview State Park
Rockport State Park
Spirit Lake
Beacon Rock State Park
Wenberg State Park
Skyomish Park
Four Lakes
Newman Lake
Liberty Lake
Lake Williams
Long Lake
Wains Lake
Loon Lakes
Kettle Falls Recreation
Miller State Park
Cathlamet
Columbia State Park
Birch Bay State Park
Mount Baker
Colonial Bay
Ross Lake
Ross Lake
Rimrock Lake
Lucky Peak Reservoir
Oxbow Dam
Lava Hot Springs
Area
Bear Lake Recreation Area
Heyburn State Park
Blackfoot River
Sun Valley
Alturas Lake
Lowman
Lake Pend Oreille
Priest Lake
Palisades Reservoir
Copeland
(continued)
124
-------
TABLE A.2 (continued)
Recreation
Centroid
Number
51.0
52.0
53.0
54.0
55.0
55.1
56.0
57.0
58.0
58.1
59.0
59.1
60.0
61.0
62.0
63.0
64.0
64.1
64.2
64.3
65.0
66.0
67.0
68.0
69.0
70.0
71.0
72.0
73.0
74.0
75.0
76.0
76.1
77.0
78.0
79.0
80.0
81.0
81.1
82.0
82.1
83.0
84.0
85.0
86.0
County
Butte
Camas
Canyon
Caribou
Cassia
Cassia
Clark
Clearwater
Custer
Custer
Elmore
Elmore
Frankl in
Fremont
Gem
Gooding
Idaho
Idaho
Idaho
Idaho
Jefferson
Jerome
Kootenai
Latah
Lemhi
Lewi s
Lincol n
Madison
Minidoka
Nez Perce
Oneida
Owyhee
Owyhee
Payette
Power
Shoshone
Teton
Twin Falls
Twin Falls
Valley
Valley
Washington
Baker
Benton
Clackamas
Recreation Centroid
Craters Moon
Magic Reservoir
Lake Lowell
Blackfoot Reservoir
Lake Cleveland
Snake River
Sheridan Reservoir
Dworshak Reservoir
Mackay Reservoir
Stanley Basin Recreation Area
Anderson Ranch
Atlanta
Devil Creek Reservoir
Island Park Reservoir
Black Canyon Dam
Hagerman Valley
Corn Creek
Pittsburg Landing
Selway Falls
Powell Recreation Area
Snake River
Snake River
Fernan Lake
Deary Helmer Area
Yellow J. Lake
Winchester Lake
Richfield Area
Snake River
Snake River
Hells Gate
Daniels Reservoir
Mountain View Reservoir
Bruneau State Park
Payette
American Falls Reservoir
St. Joe River
Victor Area
Cedar Creek Reservoir
Snake River
Dagger Falls
McCall Lake
Brownlee Reservoir
Phillips Reservoir
River Park
Milo McLeur State Park
(continued)
125
-------
TABLE A.2 (continued)
Recreation
Centroid
Number
86.1
87.0
87.1
88.0
89.0
90.0
91.0
91.1
92.0
92.1
93.0
93.1
93.2
93.3
94.0
95.0
96.0
97.0
98.0
98.1
99.0
100.0
101.0
101.1
102.0
103.0
103.1
103.2
104.0
104.1
105.0
106.0
107.0
108.0
109.0
110.0
111.0
112.0
113.0
114.0
115.0
116.0
117.0
118.0
119.0
County
Clackamas
Clatsop
Clatsop
Columbia
Coos
Crook
Curry
Curry
Deschutes
Deschutes
Douglas
Douglas
Douglas
Douglas
Gil liam
Grant
Harney
Hood River
Jackson
Jackson
Jefferson
Josephine
Klamath
Klamath
Lake
Lane
Lane
Lane
Lincoln
Lincoln
Linn
Malheur
Marion
Morrow
Multnomah
Polk
Sherman
Til lamook
Umatil la
Union
Wai Iowa
Wasco
Washington
Wheeler
Yamhill
Recreation Centroid
Mount Hood Area
Ecola State Park
Fort Stevens State Park
Scaponia
Sunset Bay State Park
Prineville Res. State Park
Boardman State Park
Humbug Mountain State Park
Wickiup Reservoir
Tumalo
Winchester Bay
Diamond Lake
Wildlife Safari
Sutherlin
J. S. Burres State Park
Clyde Holiday State Park
Malheur Lake
Bonneville Dam
Howard Prairie
Lost Creek Area
Cove Palisades State Park
Indian Mary C. Park
Klamath Lake
Crater Lake
Goose Lake
Honeymoon State Park
MacKenzie Bridge
Fern Ridge Reservoir
Otter Crest
Devils Lake State Park
Foster Lake
Lake Owyhee State Park
Detroit Lake
Boardman Park
Rooster Rock
Independence
Deschutes River State Park
Tillamook Bay
Weston Area
Hilgard Junction State Park
Wai Iowa Lake
Memaloose State Park
Scoggins Reservoir
She! ton Wayside
Stewert Grenfeld State Park
(continued)
126
-------
TABLE A. 2 (continued)
Recreation
Centroid
Number
120.0
120.1
121.0
121.1
121.2
121.3
121.4
125.0
126.0
127.0
127.1
126.1
129.0
130.0
131.0
132.0
County
Lake
Lake
Flathead
Flathead
Flathead
Flathead
Flathead
Lincol n
Missoula
Canada1
Canada1
Missoula
Deer Lodge
Meagher
Cascade
Park
Recreation Centroid
Flathead Lake (1)
Flathead Lake (2)
Flathead River (1)
Flathead River (2)
Hungry Horse Dam
Whitefish Lake
McGregor Lake
Lake Koocanusa
Lake Alva
Calgary Rec.2
Cranbrook Rec.
Missoula Rec.
Butte Rec.
Helena Rec.
Great Falls Rec.
Bozeman Rec.
1These two recreation centroids are in Canada.
2The recreation centroids defined by Rec. reflect a proxy for the composite
recreation sites close to a particular population center.
127
-------
TABLE A.3
RECREATION ACTIVITY DAYS PRODUCED BY CENTROID
Recreation
Centroid
Number
1.0
2.0
3.0
3.1
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
17.1
17.2
17.3
17.4
18.0
19.0
20.0
21.0
22.0
23.0
24.0
25.0
26.0
27.0
28.0
29.0
30.0
31.0
31.1
32.0
33.0
34.0
35.0
36.0
37.0
38.0
39.0
County
Adams
Asotin
Benton
Benton
Chellan
Clallem
Clark
Columbia
Cowlitz
Douglas
Ferry
Frank! in
Garfield
Grant
Grays Harbor
Island
Jefferson
King
King
King
King
King
Kitsap
Kittitas
Klickitat
Lewi s
Lincoln
Mason
Okanogan
Pacific
Pend Oreille
Pierce
San Juan
Skagit
Skamania
Snohomish
Snohomish
Spokane
Stevens
Thurston
Wahkiakum
Walla Walla
Whatcom
Whitman
Yakima
Total
Washington Activity
Swimming
987
1,299
3,399
5,316
3,710
4,134
14,721
341
6,460
1,666
391
2,678
290
3,560
5,293
3,247
1,266
95,739
4,352
3,264
4,352
1,088
11,242
1,816
1,204
4,289
820
2,409
2,358
1,413
593
36,682
658
4,698
554
17,027
8,771
26,374
2,079
9,884
289
3,524
8,205
2,595
13,006
327,962
Occasions
Camping
1,128
1,484
3,884
6,076
4,240
4,724
16,824
389
7,383
447
447
3,061
239
4,069
6,050
3,711
1,447
109,415
4,973
3,730
4,973
1,243
12,848
2,075
1,376
4,902
937
2,753
2,695
1,615
678
41,922
752
5,369
633
19,459
10,025
30,142
2,376
11,296
330
4,028
9,377
2,966
14,864
374,812
(in 100)
Fishing
671
882
2,309
3,611
2,521
2,808
10,001
231
4,389
266
266
1,819
142
2,419
3,596
2,206
860
65,042
2,956
2,217
2,956
739
7,637
1,233
818
2,914
557
1,636
1,602
960
493
24,920
447
3,992
376
11,567
9,959
17,917
1,412
6,715
196
2,394
5,574
1,763
8,836
222,801
Boating
661
870
2,276
3,561
2,485
2,769
9,861
228
4,327
262
262
1,794
140
2,385
3,546
2,175
848
64,129
2,915
2,186
2,915
729
7,530
1,216
807
2,873
549
1,613
1,580
947
397
24,571
441
3,147
371
11,412
5,879
17,666
1,393
6,621
193
2,361
5,496
1,738
8,712
219,691
128
(continued)
-------
TABLE A.3 (continued)
Recreation
Number
40.0
41.0
42.0
43.0
44.0
45.0
46.0
47.0
48.0
49.0
50.0
51.0
52.0
53.0
54.0
55.0
56.0
57.0
58.0
59.0
60.0
61.0
62.0
63.0
64.0
65.0
66.0
67.0
68.0
69.0
70.0
71.0
72.0
73.0
74.0
75.0
76.0
77.0
78.0
79.0
80.0
81.0
82.0
83.0
County
Ada
Adams
Bannock
Bear Lake
Benewah
Bingham
Elaine
Boise
Bonner
Bonnevi 1 le
Boundary
Butte
Camas
Canyon
Caribou
Cassia
Clark
Clearwater
Custer
Elmore
Franklin
Fremont
Gem
Gooding
Idaho
Jefferson
Jerome
Kootenai
Latah
Lemhi
Lewis
Lincoln
Madison
Minidoka
Nez Perce
Oneida
Owyhee
Payette
Power
Shoshone
Teton
Twin Falls
Valley
Washington
Total
Idaho Activity
Swimming
4,143
73
1,412
141
181
714
232
64
500
1,434
152
69
2
1,771
185
423
19
225
72
417
169
206
247
239
313
287
311
1,313
571
162
91
73
330
391
793
66
147
336
144
436
58
1,194
130
186
20,422
Occasions
Camping
11,287
199
3,846
383
493
1,944
632
174
1,363
3,907
413
188
6
4,824
504
1,151
52
614
19
1,136
460
561
673
652
852
782
846
3,576
1,555
440
247
199
900
1,066
2,160
180
400
915
393
1,187
157
3,253
353
508
55,627
(in 100)
Fishing
9,972
176
3,398
339
436
1,717
558
154
1,204
3,452
365
166
5
4,262
445
1,017
46
543
173
1,003
406
496
594
576
753
691
747
3,159
1,374
489
218
176
795
942
1,908
159
354
809
347
1,048
139
2,874
312
449
49,146
Boating
3,172
56
1,081
108
139
546
178
49
383
1,098
116
53
2
1,356
142
323
15
173
55
319
129
158
189
183
239
220
238
1,006
437
124
69
56
253
300
607
51
112
257
110
333
44
914
99
143
15,634
(continued)
129
-------
TABLE A.3 (continued)
Recreation
Centroid
Number
84.0
85.0
86.0
86.1
87.0
88.0
89.0
89.1
90.0
91.0
91.1
92.0
93.0
94.0
95.0
96.0
97.0
98.0
98.1
99.0
100.0
101.0
102.0
103.0
104.0
104.1
105.0
106.0
106.1
107.0
107.1
108.0
109.0
110.0
111.0
112.0
113.0
114.0
115.0
116.0
117.0
118.0
119.0
County
Baker
Benton
Clackamas
Clackamas
Clatsop
Col umbia
Coos
Coos
Crook
Curry
Curry
Deschutes
Douglas
Gil 1 iam
Grant
Harney
Hood River
Jackson
Jackson
Jefferson
Josephine
Klamath
Lake
Lane
Lincoln
Lincoln
Linn
Malheur
Malheur
Marion
Marion
Morrow
Multnomah
Polk
Sherman
Til lamook
Umatil la
Union
Wai Iowa
Wasco
Washington
Wheeler
Yamhill
Total
Oregon Activity
Swimming
466
1,779
181
1,450
983
1,097
482
1,447
395
398
112
1,918
2,741
60
243
253
498
3,371
460
323
1,651
1,724
222
8,229
618
466
2,605
494
243
5,428
671
259
19,768
1,283
68
668
1,703
681
216
696
8,175
47
1,653
82,228
Occasions
Camping
948
3,618
12,571
2,949
2,000
2,232
981
2,943
804
810
229
3,991
5,575
122
494
515
1,012
6,857
935
547
3,359
3,507
451
16,738
1,257
948
5,299
1,005
495
11,040
1,365
527
40,207
2,609
139
1,359
3,465
1,384
440
1,416
16,628
96
3,361
167,248
(in 100)
Fishing
554
2,115
7,351
1,724
1,169
1,305
574
1,721
470
474
134
2,281
3,260
71
289
301
592
4,010
547
384
1,964
2,050
264
9,787
735
554
3,098
588
289
6,455
798
308
23,510
1,526
81
794
2,026
809
257
828
9,723
56
1,966
97,792
Boating
294
1,122
3,900
915
620
692
304
913
249
251
71
1,210
1,730
38
153
160
314
2,128
290
204
1,042
1,088
140
5,193
390
294
1,644
312
154
3,425
423
163
12,475
809
43
422
1,075
430
136
439
5,159
30
1,043
51,887
(continued)
130
-------
TABLE A.3 (continued)
Recreation
Number
120.0
121.0
122.0
123.0
124.0
125.0
126/0
127.0
128.0
Western
County
Cascade
Flathead
Gal latin
Jefferson
Lake
Lewis and Clark
Lincol n
Missoula
Silver Bow
Total
Montana
Swimming
3,591
2,317
1,729
261
761
2,020
731
3,702
3,876
17,181
Activity Occasions
Camping
4,948
3,192
2,382
359
1,047
2,780
1,008
5,101
5,341
23,656
(in 100)
Fishing
3,798
2,450
1,829
276
804
2,130
774
3,916
4,100
18,160
Boating
2,439
1,574
1,175
177
516
1,370
497
2,515
2,633
11,663
External Zones
129.0
130.0
131.0
132.0
133.0
134.0
135.0
136.0
137.0
138.0
139.0
140.0
141.0
142.0
Eastern Montana
Vancouver, B.C.
Cranbrook, B.C.
Calgary
Wyoming
Utah
Nevada
Cal i form' a
Alaska
Eastern Canada
North Central
Northeast
Southeast
South Central
4,400
2,481
275
1,300
120
2,106
220
15,603
64
1,456
1,298
595
323
1,132
5,200
1,684
187
900
198
3,465
479
24,736
105
971
2,137
980
531
1,864
4,500
1,172
130
650
68
1,183
164
8,436
36
652
729
335
181
637
2,700
3,432
381
1,906
96
1,699
236
12,156
52
1,906
1,045
479
260
914
Note: Missoula county includes Mineral and Granite counties. Silver Bow
county includes: Deer Lodge, Powell, Beaverhead, and Ravalli counties.
131
-------
TABLE A.4
RECREATION FACILITY VARIABLES, EXISTING AND POTENTIAL, FROM IMPROVED WATER
QUALITY BY RECREATION CENTROID
Recreation
Centroid
Number
1.0
2.0
3.0
4.0
4.1
5.0
5.1
5.2
6.0
7.0
8.0
8.1
9.0
10.0
11.0
12.0
13.0
13.1
13.2
14.0
14.1
14.2
15.0
15.1
16.0
16.1
16.2
17.0
17.1
17.2
18.0
19.0
19.1
20.0
21.0
22.0
22.1
22.2
23.0
23.1
23.2
Campsites
County Exist.
Adams
Asotin
Benton
Chelan
Chelan
ClaTlum
Cl all urn
Clallum
Clark
Columbia
Cowl itz
Cowl itz
Douglas
Ferry
Franklin
Garfield
Grant
Grant
Grant
Grays Harbor
Grays Harbor
Grays Harbor
Island
Island
Jefferson
Jefferson
Jefferson
King
King
King
Kitsap
Kittitas
Kittitas
Klickitat
Lewis
Lincoln
Lincoln
Lincoln
Mason
Mason
Mason
0
0
108
340
359
92
125
75
147
40
75
138
33
117
67
0
263
296
173
191
177
100
348
254
125
125
150
138
150
0
198
25
415
104
350
80
80
67
140
250
156
Pot.
0
35
108
340
359
102
125
75
147
40
75
138
130
167
67
0
292
425
173
191
177
113
348
254
155
125
150
179
241
0
198
66
415
104
350
80
80
67
140
250
156
Linear
Beach Feet
Exist.
0
2000
1850
200
870
1200
1100
1100
1085
0
0
0
100
400
1000
0
1000
2930
1000
0
450
270
0
600
2360
2000
3350
1925
3000
7000
1400
7000
4500
1325
1995
1300
1300
1400
240
400
240
Pot.
0
2231
2850
200
870
1200
1100
1100
1085
0
0
0
294
400
1000
0
1140
3124
1000
0
723
358
0
600
2658
2000
3350
2198
3601
7000
1400
7000
4500
1325
2383
1300
1300
1400
240
400
240
Boat Ramps
Exist.
3
7
17
4
4
4
5
4
14
3
14
4
3
4
9
0
15
2
5
8
10
8
10
14
8
2
6
11
12
39
16
4
9
12
14
2
1
1
5
5
5
Pot.
3
10
17
4
4
4
5
4
14
4
14
4
4
4
9
0
16
1
5
8
12
9
10
14
8
2
6
13
16
39
16
4
9
12
16
2
1
1
5
5
5
River Miles
Exist.
381
148
300
362
362
200
56
250
291
241
250
140
314
525
246
210
308
58
276
150
235
244
0
0
122
281
450
483
220
100
41
142
489
622
514
198
180
220
120
120
110
Pot.
381
198
503
370
370
200
87
250
291
365
250
140
452
745
246
215
350
100
276
150
300
263
0
0
180
281
450
542
350
100
41
200
489
706
598
198
180
220
120
120
110
(continued)
132
-------
TABLE A.4 (continued)
Recreation
P a nt* vn "i r4
L»tr 1 1 L, I U I U
Number
24.0
24.1
24.2
24.3
25.0
26.0 "
26.1
27.0
27.1
27.2
28.0
29.0
29.1
30.0
31.0
31.1
32.0
32.1
32.2
32.3
32.4
33.0
33.1
33.2
34.0
35.0
36.0
37.0
37.1
37.2
37.3
38.0
39.0
40.0
41.0
42.0
43.0
44.0
45.0
46.0
46.1
47.0
48.0
48.1
Campsites
County
Okanogan
Okanogan
Okanogan
Okanogan
Pacific
Pend Oreil le
Pend Oreille
Pierce
Pierce
Pierce
San Juan
Skagit
Skagit
Skamania
Snohomish
Snohomish
Spokane
Spokane
Spokane
Spokane
Spokane
Stevens
Stevens
Stevens
Thurston
Wahkiakum
Walla Walla
Whatcom
Whatcom
Whatcom
Whatcom
Whitman
Yakima
Ada
Adams
Bannock
Bear Lake
Benewah
Bingham
Blaine
Blaine
Boise
Bonner
Bonner
Exist.
120
120
300
168
300
610
100
40
186
40
675
254
240
152
137
140
4
4
25
4
117
70
70
78
248
0
189
179
150
101
125
99
592
290
198
663
297
167
276
275
413
434
675
1265
Pot.
120
170
350
179
300
616
100
40
200
92
675
254
248
152
137
140
4
26
25
4
139
70
70
78
248
0
189
179
150
101
125
104
811
290
198
663
297
167
276
275
413
434
675
1365
Linear
Beach Feet
Exist.
275
1100
500
867
0
1450
400
900
900
1800
1030
300
0
500
1600
1715
150
40
100
0
40
300
300
300
849
0
700
800
1000
750
1150
800
5200
1960
400
0
300
1100
650
33
32
250
3830
6750
Pot.
275
1588
592
1028
0
1491
400
900
992
2145
1030
300
69
500
1674
1715
150
40
100
0
1040
300
300
300
1349
0
700
800
1000
750
1150
832
6640
1960
450
300
350
1100
750
85
32
250
3830
6800
Boat Ramps
Exist.
4
4
4
4
12
5
2
6
5
6
7
10
9
3
9
7
5
1
1
3
1
4
4
3
4
0
8
7
6
18
11
10
2
4
5
1
3
15
8
13
8
3
16
26
Pot.
4
7
4
5
12
5
2
6
6
8
7
10
9
3
9
7
5
2
1
3
2
4
4
3
12
0
8
7
6
18
11
10
11
4
6
1
4
15
11
14
8
3
16
28
River Miles
Exist.
800
241
80
265
281
241
40
100
178
45
7
260
285
275
334
340
61
94
50
75
119
219
250
100
174
114
263
40
413
180
60
639
728
79
345
266
241
159
130
0
407
504
152
310
Pot.
800
347
100
300
290
250
40
100
198
120
7
260
300
275
360
340
61
125
50
75
150
319
400
100
235
114
360
40
413
180
60
646
1041
79
373
290
283
159
240
104
407
509
152
325
(continued)
133
-------
TABLE A.4 (continued)
Recreation
Centroid
Number
49.0
50.0
51.0
52.0
53.0
54.0
55.0
55.1
56.0
57.0
58.0
58.1
59.0
59.1
60.0
61.0
62.0
63.0
64.0
64.1
64.2
64.3
65.0
66.0
67.0
68.0
69.0
70.0
71.0
72.0
73.0
74.0
75.0
76.0
76.1
77.0
78.0
79.0
80.0
81.0
81.1
82.0
82.1
83.0
Campsites
County
Bonnevil le
Boundary
Butte
Camas
Canyon
Caribou
Cassia
Cassia
Clark
Clearwater
Custer
Custer
Elmore
Elmore
Frankl in
Fremont
Gem
Gooding
Idaho
Idaho
Idaho
Idaho
Jefferson
Jerome
Kootenai
Latah
Lehmi
Lewis
Lincoln
Madison
Minidoka
Nez Perce
Oneida
Owyhee
Owyhee
Payette
Power
Shoshone
Teton
Twi n Fal 1 s
Twin Falls
Val 1 ey
Valley
Washington
Exist.
472
221
83
93
40
131
400
0
41
323
112
1013
182
180
340
458
47
324
15
200
200
80
22
95
1123
65
474
34
6
28
102
302
36
128
85
0
112
237
78
16
147
623
267
128
Pot.
472
221
83
93
40
131
400
0
41
423
162
1013
182
180
365
458
47
324
40
200
200
80
22
95
1123
65
524
34
6
28
102
302
36
128
85
0
112
237
78
16
147
623
267
128
Linear
Beach Feet
Exist.
100
525
0
50
150
0
0
0
0
155
431
2444
2340
260
100
0
725
0
250
500
25
100
100
0
5500
50
200
0
0
50
1465
1200
0
1100
0
0
0
0
0
0
0
9000
3350
150
Pot.
200
525
50
50
300
50
25
25
50
305
831
2444
2340
260
150
100
725
200
300
500
25
100
200
0
5700
50
400
0
0
100
1465
1200
50
1150
0
0
0
300
100
25
25
9000
3650
150
Boat Ramps
Exist.
60
8
0
1
4
10
1
7
0
9
1
4
7
1
5
8
5
3
1
0
0
0
0
1
82
1
5
3
0
0
4
10
2
4
6
0
10
0
1
4
5
12
5
0
Pot.
62
8
1
1
8
11
2
8
1
12
5
4
7
1
7
10
5
4
1
0
0
0
1
1
85
1
9
3
1
1
4
10
3
5
6
0
11
2
2
5
6
12
9
1
River Miles
Exist.
177
457
66
408
65
533
316
140
153
534
76
0
288
311
114
238
76
111
470
550
555
545
16
43
236
292
1003
150
31
30
31
243
58
174
149
78
104
682
51
107
83
374
320
179
Pot.
275
457
170
437
90
594
389
200
200
577
425
50
300
311
149
353
76
116
552
550
555
545
71
43
262
292
1053
150
91
58
31
243
90
574
174
78
124
716
82
167
150
374
375
219
(continued)
134
-------
TABLE A.4 (continued)
Recreation
r*Q nt Y*n "1 H
VsC 1 1 1* [ \J IU
Number
84.0
85.0
86.0
86.1
87.0
87.1
88.0
89.0
90.0
91.0
91.1
92.0
92.1
93.0
93.1
93.2
93.3
94.0
95.0
96.0
97.0
98.0
98.1
99.0
100.0
101.0
101.1
102.0
103.0
103.1
103.2
104.0
104.1
105.0
106.0
107.0
108.0
109.0
110.0
111.0
112.0
112.1
113.0
114.0
Campsites
County
Baker
Benton
Clackamas
Clackamas
Clatsop
Clatsop
Columbia
Coos
Crook
Curry
Curry
Deschutes
Deschutes
Douglas
Douglas
Douglas
Douglas
Gi 1 1 iam
Grant
Harney
Hood River
Jackson
Jackson
Jefferson
Josephine
Klamath
Klamath
Lake
Lane
Lane
Lane
Lincoln
Lincoln
Linn
Malheur
Marion
Morrow
Multnomah
Polk
Sherman
Til lamook
Til lamook
Umatil la
Union
Exist.
488
37
755
495
520
520
71
1525
221
1236
281
750
776
500
500
674
500
20
273
321
427
650
693
1750
1087
630
633
324
658
1200
200
800
538
861
273
1628
156
184
16
132
1100
1088
273
183
Pot.
488
37
830
495
520
520
71
1625
421
1236
281
750
916
584
585
874
700
20
273
371
447
650
693
1790
1087
730
633
324
788
1330
348
920
568
886
273
1628
156
184
16
132
1100
1088
273
183
Linear
Beach Feet
Exist.
8300
0
900
1000
11415
11415
0
2000
300
7750
3000
40
35
1300
1300
1450
1300
0
0
0
1280
700
700
4900
0
7080
7083
0
5000
5000
6608
150
50
4300
4725
7510
0
10218
1350
0
18000
18960
1300
10
Pot.
8300
940
1300
1000
11415
11415
0
2075
450
7750
3000
40
435
2100
2100
2210
2100
0
0
0
1280
700
700
5200
0
7800
7083
0
5400
5400
6938
150
50
5530
4725
7510
0
10218
2140
0
18000
18960
1300
10
Boat Ramps
Exist.
14
2
3
3
9
9
1
23
3
13
1
6
6
13
13
12
13
3
12
8
7
20
19
31
30
22
22
11
33
33
33
7
20
26
7
14
2
21
11
4
18
18
14
3
Pot.
14
2
4
3
9
9
1
25
5
13
1
6
7
16
15
15
15
3
12
8
7
20
19
32
30
25
22
11
36
36
35
7
20
29
7
14
2
23
14
4
18
18
14
4
River Miles
Exist.
827
155
375
295
165
169
308
131
552
200
206
169
85
150
670
25
70
382
1077
804
116
375
400
409
451
340
264
355
170
673
75
127
50
624
1897
460
460
130
172
282
175
174
752
524
Pot.
827
249
425
295
165
169
308
507
642
200
206
169
140
175
700
156
200
382
1120
1238
194
375
400
432
451
340
336
389
22
700
225
222
100
747
1935
493
493
147
251
282
175
177
842
535
(continued)
135
-------
TABLE A.4 (continued)
Linear
Recreation
Centroid
Number
115.0
116.0
117.0
118.0
119.0
County
Wai Iowa
Wasco
Washington
Wheeler
Yamhill
Camp si
Exist.
522
590
67
80
52
tes
Pot.
522
590
77
80
127
Beach
Exist.
400
2000
1200
0
0
Feet
Pot.
400
2000
1720
0
500
Boat
Exist.
4
8
2
0
0
Ramps
Pot.
4
8
4
0
2
River
Exist.
998
805
204
375
198
Miles
Pot.
998
805
256
375
290
County
Campsites
Beach Feet Boat Ramps River Miles
120.0
120.1
121.0
121.1
121.2
121.3
121.4
125.0
126.0
127.0
128.0
126.1
129.0
130.0
131.0
132.0
Lake
Lake
Flathead
Flathead
Flathead
Flathead
Flathead
Lincoln
Missoula
Canada1
Canada1
Missoula
Bear Lodge
Meagher
Cascade
Park
48
96
1
1
175
10
20
30
40
500
500
480
876
482
159
750
1100
1100
1
1
100
600
300
900
300
350
3300
350
4200
4500
900
900
7
8
4
3
7
4
4
3
3
4
4
13
19
9
4
14
55
55
96
58
72
16
120
50
50
100
100
70
50
64
40
120
Notes: Exist, means currently existing. Pot. means potential; that is,
the potential facilities (or river miles) that could be constructed if all
degraded rivers were improved so as to be acceptable for recreation purposes.
1These recreation centroids are near Calgary and Cranbrook, respectively.
136
-------
TABLE A.5
ANNUAL (1980) RECREATION VALUE BY ACTIVITY AND BY COUNTY FOR WASHINGTON, IDAHO,
AND OREGON
Zone
Number
1
2
3
4
6
9
10
11
13
14
15
16
17
20
23
25
29
31
32
34
35
36
39
42
46
47
49
52
53
55
57
59
64
67
68
69
70
74
75
County
Name Swimming
Adams $418,732
Asotin 317,286
Benton 694,835
Chelan 2,215,635
Clallum 2,792,041
Clark 5,219,251
Columbia 189,053
Cowlitz 2,057,886
Douglas 520,114
Ferry 572,054
Franklin 606,553
Garfield 143,368
Grant 2,010,921
ura^S 2,601,004
Harbor '
Island 5,103,889
Jefferson
4,309,672
King 49,635,416
Kitsap 2,808,435
Kittitas 6,747,085
Klickitat
1,334,830
Lewis 4.582,449
Lincoln 3,458,897
Mason 14,629,231
Okanogan 4,482,324
Pacific 359,415
J!end,-. 1,237,846
Oreille ' '
Pierce 18,545,658
San Juan 1,404,485
Skagit 4,982,385
Skamania 4,175,050
Snohomish
16,375,406
Spokane 13,261,349
Stevens 3,995,138
Thurston 7,317,709
Wahkiakum 968,438
Walla 10? 2Qg
Walla '
Whatcom 3,660,551
Whitman 1,506,345
Yakima 1,784,770
State $198,134,715
Total
Recreation Val
Camping
$124,046
267,561
744,426
4,477,158
2,105,443
4,166,888
436,056
5,256,482
859,498
1,043,430
582,571
59,728
3,740,331
5,089,433
9,601,347
3,615,155
16,920,861
2,637,427
6,415,688
1,305,933
5,351,179
2,903,928
13,323,855
5,776,672
2,190,611
2,958,325
9,979,171
3,119,350
6,578,156
4,068,523
9,365,677
6,895,249
3,900,172
6,468,939
231,069
1,368,908
4,476,638
1,542,352
3,972,679
$163,910,915
ue, Washington (in dollars)
Fishing
$825,649
310,729
496,187
1,539,314
1,457,025
2,644,397
489,887
3,308,244
484,039
542,865
500,445
409,595
1,312,042
2,211,118
2,400,678
1,996,718
14,558,351
1,087,164
2,571,265
1,020,827
2,044,047
2,054,917
6,965,910
2,846,955
744,379
925,770
1,904,041
532,618
2,953,124
2,883,744
5,086,977
8,856,214
2,976,602
2,872,549
1,598,016
765,048
2,014,450
1,111,546
838,726
$94,762,172
Boating
$674,596
204,062
564,788
1,609,433
1,637,269
6,081,738
242,627
5,319,961
221,079
322,250
439,460
81,671
1,122,036
4,254,056
13,171,954
2,964,559
115,215,125
3,859,918
5,671,063
1,020,862
6,991,453
906,117
18,191,191
1,566,587
1,141,501
639,492
22,029,498
1,127,575
7,846,645
2,242,283
19,330,802
10,521,165
2,991,068
11,579,364
1,596,378
763,027
3,589,988
1,724,077
1,605,125
$281,060,843
Total
$2,043,023
1,099,638
2,500,236
9,841,540
7,991,778
18,112,274
1,357,623
15,942,573
2,084,730
2,480,599
2,129,029
696,362
8,185,330
14,155,611
30,277,868
12,885,104
195,219,753
10,392,944
21,415,101
4,682,452
18,969,128
9,323,859
53,110,187
14,672,538
4,425,906
5,761,433
57,458,368
6,184,028
22,360,310
13,369,600
50,878,862
39,533,977
13,862,980
28,238,561
4,393,901
4,004,192
13,741,627
7,884,320
8,201,300
$737,868,645
(conti nued)
137
-------
TABLE A.5 (continued)
Zone
Number
76
77
78
79
80
81
82
84
85
87
88
89
90
91
92
93
95
96
97
99
101
102
103
104
105
109
110
111
112
113
114
115
116
117
118
119
120
122
123
124
125
126
128
130
Recreation Value, Idaho
County
Name Swimming
Ada $643,736
Adams
Bannock
Bear Lake
Benewah 1
Bingham
Blaine
Boise
Bonner 2
Bonnevil le
Boundary
Butte
Camas
Canyon
Caribou
Cassia
Clark
Clearwater
Custer
Elmore
Franklin
Fremont
Gem
Gooding
Idaho
Jefferson
Jerome
Kootenai 4
Latah
Lemhi
Lewi s
Lincoln
Madison
Minidoka
Nez Perce
Oneida
Owyhee
Payette
Power
Shoshone
Teton
Twin Falls
Valley
Washington
State $14
Total
40,860
223,012
95,777
,041,242
221,638
55,173
73,166
,211,064
102,547
376,725
42,735
71,696
386,587
26,197
224,741
27,653
167,255
103,848
317,244
102,925
20,087
334,305
101,542
277,789
300,407
112,146
,660,328
117,772
8,218
89,253
51,082
251,059
422,061
546,957
78,552
104,255
108,783
148,075
129,753
39,476
138,367
168,998
129,365
,849,336
Camping
$1,348,072
200,200
1,354,811
544,829
1,664,328
727,532
537,698
488,164
6,151,289
664,612
983,203
254,790
275,700
472,809
238,547
1,392,720
136,727
709,087
606,000
893,402
621,482
347,379
384,406
1,057,230
824,850
298,537
610,502
9,306,606
326,918
107,438
291,485
88,233
324,523
701,064
1,288,813
321,227
558,574
52,761
715,241
1,123,893
225,307
806,319
686,855
389,560
$41,447,118
Fishing
$1,279,777
150,935
1,153,465
603,709
753,164
1,025,614
337,267
321,526
1,274,625
688,426
430,045
493,668
461,566
1,106,917
440,539
2,424,434
378,111
304,967
388,627
1,045,508
663,081
308,287
817,416
951,653
685,628
1,326,688
979,517
1,929,019
230,153
74,139
325,064
494,576
1,359,088
1,174,084
537,271
959,115
844,756
758,055
1,599,766
409,826
517,499
1,410,276
399,642
455,427
$34,386,352
(in dollars)
Boating
$92,765
12,723
11,566
8,307
1,533,043
46,766
22,141
13,290
2,691,692
77,149
317,660
6,725
5,968
83,869
11,235
87,126
4,247
143,045
9,302
45,242
15,229
8,602
70,295
36,584
53,443
21,989
19,771
18,634,145
40,118
1,835
99,814
8,907
20,510
51,953
424,070
14,031
43,942
23,963
90,236
102,220
4,708
61,442
44,877
13,925
$25,225,203
Total
$3,354,350
404,718
2,742,854
1,252,622
5,001,777
2,021,550
952,279
896,146
12,328,670
1,532,734
2,107,633
797,918
814,930
2,050,182
716,518
4,230,132
546,738
1,324,354
1,107,777
2,301,396
1,402,617
684,355
1,606,422
2,147,009
1,952,710
1,987,621
1,721,936
34,530,098
714,961
191,630
805,616
640,798
1,955,180
2,349,162
2,797,111
1,372,925
1,551,527
943,562
2,553,329
1,765,692
786,990
2,416,404
1,300,372
988,277
$115,908,009
138
(continued)
-------
TABLE A.5 (continued)
Zone
Number
131
132
133
135
137
138
139
140
142
144
148
149
150
151
152
154
155
156
158
159
162
164
165
166
167
168
169
170
171
173
174
175
176
177
178
179
State
Region
Name Swimming
Baker $141,457
Benton 827,292
Clackamas
4,772,207
Clatsop 3,353,411
Columbia 912,365
Coos 175,528
Crook 110,386
Curry 172,808
Deschutes 480,344
Douglas 1,846,194
Gilliam 164,645
Grant 35,176
Harney 9,036
Hood
". 3,107,820
River ' '
Jackson 598,764
Jefferson 521,123
Josephine 95,934
Klamath 611,989
Lake 82,309
Lane 3,471,636
Lincoln 1,411,179
Linn 1,851,516
Malheur 166,984
Marion 1,493,100
Morrow 130,070
Multnomah
8,050,763
Polk 3,316,113
Sherman 350,726
Til lamook
4,017,140
Umatilla 365,126
Union 101,271
Wallowa 50,938
Wasco 1,634,881
Washington
3,145,591
Wheeler 53,209
Yamhill 2,176,145
Total $51,438,145
Total $265,008,995
Recreation
Camping
$561,255
1,252,484
10,898,672
5,539,193
1,957,309
993,108
536,669
539,296
3,634,461
5,250,715
333,351
503,063
194,990
5,045,580
2,021,986
3,194,512
1,148,556
1,782,220
909,666
7,317,266
6,308,622
4,341,859
355,532
5,265,461
808,591
4,697,102
906,166
1,342,707
8,290,208
828,568
540,853
384,261
3,517,436
2,003,162
341,281
2,255,131
$95,891,547
$300,057,296
Value, Oregon
Fishing
$200,539
1,667,586
3,131,003
1,553,691
1,685,883
197,613
216,667
211,894
804,946
1,662,190
451,784
205,665
81,409
1,541,053
731,808
438,121
345,897
568,538
352,077
2,249,034
1,683,258
1,218,805
473,956
1,001,303
427,914
2,784,334
1,890,496
802,698
1,809,872
373,757
293,411
114,082
1,166,457
1,726,816
221,735
1,602,844
$36,093,970
$165,669,098
(in dollars)
Boating
$63,442
5,599,918
1,663,320
1,401,502
570,635
79,706
43,073
14,001
324,188
805,572
175,736
78,217
8,944
1,836,999
223,571
552,449
140,261
213,087
114,146
2,723,584
1,607,926
1,492,862
26,483
817,479
110,449
7,293,007
2,241,450
444,574
2,105,897
279,471
74,768
21,527
857,965
1,160,209
28,802
588,034
$30,592,428
$336,035,293
Total
$966,693
4,307,280
20,465,202
11,847,797
5,126,192
1,445,955
906,795
937,999
5,243,939
9,564,671
1,125,516
822,121
294,379
11,641,452
3,576,129
4,706,205
1,740,648
3,175,834
1,458,198
14,761,480
11,110,985
8,905,042
1,134,066
8,677,343
1,481,024
22,825,206
8,374,225
2,940,705
16,223,117
1,846,922
1,010,303
570,808
7,176,739
8,036,778
645,027
6,622,254
$214,016,090
$1,066,770,682
139
-------
APPENDIX B
HOUSEHOLD SURVEY QUESTIONNAIRE
This appendix contains the questionnaire used by the Survey Research Center
at Oregon State. The telephone survey included 3,000 households and was
conducted in the Fall of 1980. Columns 1-4 on the code sheets are household
identification numbers; columns 5-8 are card numbers; and column 9 is a state
verification number. The responses to question one were coded in columns 10-11.
OREGON OUTDOOR RECREATION SURVEY
1.
2.
2a.
10-11 Number
99 DK, NA
12-13 Number
99 DK, NA
14-15 Number
99 DK, NA
During the past 12 months, how many persons,
including yourself, have lived in your household?
How many of these people are 18 years or older?
And, how many are under 18 years of age? (INT:
RESPONSE TO Q. 2 AND 2a MUST EQUAL TOTAL IN Q. 1)
3. I'd like to complete picture of your household. Some of these questions
concern each person, while others are about your household as a group.
Thinking about everyone who lived in your household during the past 12
months, I would like to list each person from the oldest to the youngest
just to make sure we are talking about everyone. (INT: STARTING WITH THE
OLDEST, GET ALL INFORMATION AND ENTER ON FIRST LINE. CONTINUE WITH EACH
FAMILY MEMBER DOWN TO THE YOUNGEST.)
Sex (Circle) Age
Person 1
Person 2
Person 3
Person 4
Person 5
140
Relationship to "R" First Name
16
19
22
25
28
Male
1
1
1
1
1
Female
2
2
2
2
2
17-18
20-21
23-24
26-27
29-30
-------
Person 6
Person 7
Person 8
Person 9
Person 10
Person 11
Person 12
31
34
37
40
43
46
1
1
1
1
1
1
1
2
2
2
2
2
2
2
32-33
35-36
38-39
41-42
44-45
47-48
Now I'd like to ask you some questions about your household's outdoor recreation
activities for the past 12 months.
4. Thinking back to the first of June 1980 to the present, how many trips, all
together, did you or any member of your household take for these four kinds
of outdoor recreation: swimming in a lake or river, boating, fishing, or
camping?
49-51
Number of trips
99 DK, NA
(INT: IF "NONE," WRITE 0 AND SKIP TO Q. 7)
The next series of questions refers only to the last trip you or someone in your
household took.
5. $
52-56
99 DK (SKIP TO Q. 6)
/day First, how much was the daily use fee, if
any, for the recreation facilities used?
(INT: IF NONE, WRITE 0 AND SKIP TO Q. 6)
5a. $
57-61
99 DK
/day What is the maximum daily use fee you would
be willing to pay for this recreation
facility rather than forego using it?
6. $
52-56
999 DK
About how much money did you spend
travelling to and from your home to the
recreation area on this last trip? This
includes meals, gas, oil, car rental or air
fare, and so forth. (Just your best
estimate please.)
6a. 1 Enjoyed travel time
2 Prefer to shorten
66 9 DK
Some people feel time spent travelling to a
recreation site is an inconvenience, while
others enjoy it. How about you? Did you
enjoy the time spent travelling on this
trip, or would you rather have shortened the
travel time?
141
-------
6b. $
67-70
About how much money would you be willing to
pay to shorten the total travel time for
this last trip by half?
(ASK OF EVERYONE)
7. 71-73
Number of trips
99 DK
Now, thinking back to the first of September
of last year to the first of June 1980, how
many trips, all together, did you or any
member of your houehold take for recreation
purposes? (INT: IF NONE, WRITE 0 AND SKIP
TO Q. 8)
Finally, for statistical purposes only, we have a few last questions about your
household.
8.
Town or City
999 Refused
First, in or near which town or city is your
home located?
9.
70-76
County
99 Refused; DK
And, in which
your home located?
10. 01 Less than $10,000
02 $10,000 to $14,999
03 $14,000 to $19,999
04 $20,000 to $24,999
05 $25,000 to $34,999
06 $35,000 to $40,000
07 over $40,000
99 Refused; DK
Would you please tell me if the total gross
income for your household in 1979 was ...
(READ LIST)
11. Is there anything else you would like to say about outdoor recreation?
(THANK YOU FOR YOUR COOPERATION)
142
-------
TABLE B.I
FREQUENCY DISTRIBUTION OF RECREATION TRIPS USING 1980 HOUSEHOLD SURVEY DATA
Oregon
Days
1
2
>2
Total
Proportion
Number of
Trips
273
130
100
403
Number of
Days
273
260
694
1227
Swimming
414
133
283
830
0.206
Boating
143
98
283
524
0.130
Fishing
182
320
484
986
0.245
Camping
10
485
1194
1689
0.419
Idaho
Days
1
2
>2
Total
Proportion
Number of
Trips
262
89
144
495
Number
Days
262
178
646
1086
of
Swimming
218
48
338
604
0.415
Boating
111
44
305
460
0.111
Fishing
576
247
630
1453
0.349
Camping
4
350
1290
1644
0.395
Washington
Days
1
2
>2
Total
Proportion
Number of
Trips
479
113
177
769
Number
Days
479
226
1181
1886
of
Swimming
748
250
1278
2476
0.315
Boating
470
211
982
1663
0.211
Fishing
398
337
952
1687
0.214
Camping
12
502
1528
2042
0.260
Note: The above estimates are based on a subsample of 313 households (123
from Washington, 100 from Oregon, and 90 from Idaho), but a total of 1767
recreation trips.
143
-------
ACKNOWLEDGEMENTS
The research for this report was conducted at the Environmental
Protection Agency, Corvallis Environmental Research Laboratory. I am grateful
to my EPA colleagues John Jaksch and Neils Christiansen for several
discussions during the developmental stage of the model. This work also
benefited from discussions with several recreation planners in the Pacific
Northwest at Federal and state agencies. I am grateful to Richard Walsh, John
Loomis, Russell Gum, Louise Arthur, Richard Adams, and John Duffield for their
review of the manuscript. I also thank Jack Gakstatter, the EPA Project
Officer for his assistance during the final two years of the study.
144
-------
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