xvEPA
United States
Environmental Protection
Agency
Office of Health and Ecological
Effects
Washington DC 20460
EPA-600/5-78-010
June 1978
Research and Development
The Recreation
Benefits of
Water Quality
Improvements
Analysis of Day
Trips in an
Urban Setting
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U S Environmental
Protection Agency, have been grouped into nine series These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields
The nine series are
1 Environmental Health Effects Research
2 Environmental Protection Technology
3 Ecological Research
4 Environmental Monitoring
5 Socioeconomic Environmental Studies
6 Scientific and Technical Assessment Reports (STAR)
7 Interagency Energy-Environment Research and Development
8 "Special" Reports
9 Miscellaneous Reports
This report has been assigned to the SOCIOECONOMIC ENVIRONMENTAL
STUDIES series. This series includes research on environmental management,
economic analysis, ecological impacts, comprehensive planning and fore-
casting, and analysis methodologies Included are tools for determining varying
impacts of alternative policies, analyses of environmental planning techniques
at the regional, state, and local levels, and approaches to measuring environ-
mental quality perceptions, as well as analysis of ecological and economic im-
pacts of environmental protection measures Such topics as urban form, industrial
mix, growth policies, control, and organizational structure are discussed in terms
of optimal environmental performance These interdisciplinary studies and sys-
tems analyses are presented in forms varying from quantitative relational analyses
to management and policy-oriented reports
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161
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EPA-600/5-78-010
June, 1978
THE RECREATION BENEFITS OF WATER QUALITY
IMPROVEMENT: ANALYSIS OF DAY TRIPS IN AN URBAN SETTING
by
Clark S. Binkley and W. Michael Hanemann
EPA Contract No. 68-01-2282
Project Officer
Dr. Dennis Tihansky
OFFICE OF HEALTH AND ECOLOGICAL EFFECTS
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
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DISCLAIMER
This report has been reviewed by the Office of Health and Ecological
Effects, and approved for publication. Approval does not signify that the
contents necessarily reflect the views and policies of the Environmental
Protection Agency, nor does mention of trade names or commercial products
constitute endorsement or recommendation for use. This report is available
for purchase from the National Technical Information Service, P. 0. Box 1553,
Springfield, Virginia 22161. The order number is PB257719.
ii
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ABSTRACT
Considerable past work has attempted to estimate the recreational
benefits which might accrue from water quality improvements. The
theoretical underpinnings of this work, however, are becoming increas-
ingly sus"pect. This report explores demand models, new to recreation
analysis, which are based on site characteristics and individual pre-
^ferences to estimate benefit measured by consumer's surplus.
The empirical findings of this study are based on a structured
^
survey of 467 representative households in the Boston SMSA. Our focus
O was specifically day trips to a system of Boston area beache3, but con-
o siderable additional data on willingness-to-pay, substitution between
.> sites and activities, water quality perception and general recreation
V behavior was developed as well. The reader will find an extensive
*-*c review of the post-war literature on recreation economics and water
r
' quality benefits.
ill
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TABLE OF CONTENTS
I. INTRODUCTION AND SUMMARY 1
II. RECREATION AND MEASURES OF ITS BENEFITS 8
1. The Recreation Experience 6
2. Quantifying the Recreation Experience 10
3. The Monetary Value of the Recreation 12
Experience
III. MULTIPLE SITE DEMAND MODELS FOR RECREATION SITES 28
1. The Multiple Site Demand Models in the 29
Literature
2. System Demand Models -- Nonstochastic 35
Choice
3. Stochastic System Demand Models 40
IV. SITE AND HOUSEHOLD SAMPLES, SURVEY S CHARACTERISTICS.. 44
1. The Network of Sites 45
2. Site Characteristic Variables 49
2.1 Economic Variables 51
2.2 Beach Characteristic Variables 53
2.3 Water Quality Variables 57
2.4 Factor Analysis of Water Quality 65
Variables
2.5 Subjective Measures of Site 71
Characteristics
3. The Household Survey 72
3.1 Sample Design 73
3.2 The Sample Population 78
3.3 The Survey Instrument 80
4. Measures of Attendance 84
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Page
V. DIRECT EMPIRICAL FINDINGS ON SITE CHOICE
AND WATER QUALITY PERCEPTION 88
1. Direct Questioning 88
1.1 The Favorite Site 89
1.2 Characteristics Important for Site 94
Choice
1.3 Not Visiting Closest Site 99
1.4 Importance of Various Water loi
Characteristics
1.5 Conclusions 103
2. Public Perception of Water Quality 105
2.1 Agreement Among Respondents 105
2.2 Accuracy of Perceptions 107
2.3 Ordinal Rankings Considered 112
2.4 Conclusions 116
VI. WILLINGNESS-TO-PAY 118
1. The Theoretic Basis for Willingness-to-Pay
Calculations 120
2. Tabular Analysis of Willingness-to-pay 126
3. Regression Analysis of Willingness-to-pay 132
4. Conclusions: Dollar Values of Willingness- 145
to-Pay in the Boston SMSA
VII. MULTIPLE SITE DEMAND FUNCTIONS 148
1. A Review of the Data 150
2. Some Determinants of Recreational Activity 157
3. Abstract Site Demand Functions 160
4. System Demand Functions 170
5. Benefit Calculation 174
6. Conclusions 176
VI
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Page
VIII. CONCLUSIONS
APPENDIX I: Site Facility Inventory Form 184
APPENDIX II: Water Quality Sampling 190
APPENDIX III: The Survey Instrument 191
Bibliography 205
vii
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LIST OF TABLES
NO. TITLE PAGE
II-l Water-Related Outdoor Recreation Activities 8
IV-1 Analysis of Available Recreation Sites 46
IV-2 Economic Variables 53
IV-3 Site Setting 54
IV-4 Water Quality Variables 58
IV-5 Water Quality Data 59
IV-6 Eigenvalues of Inferred Factors 66
IV-7 Varimax Rotated Factor Matrix 68
IV-8 Factor Score Coefficients 69
IV-9 Factor Scores by Site 70
IV-10 Subjective Variables: Summary Statistics 71
IV-11 Distribution of Sample Points Between Towns 75
IV-12 Comparison of the Boston SMSA Population
and the Sample 79
IV-13 Correlation Between Attendance Measures
Across Sites 85
V-l Reasons for Choosing Favorite Site 90
V-2 Cross Tabulations of Reasons for Choosing
Favorite Site and Income 92
V-3 Cross Tabulation of Reasons for Choosing
Favorite Site and Income 93
V-4 Important Characteristics for Site Choice 95
V-5 Most Important Site Characteristics
Tabulated by Education 97
viii
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NO. TITLE PAGE
V-6 Most Important Site Characteristics
Tabulated by Occupation 98
V-7 Distribution of Reasons for Not Visiting
Closest Site 100
V-8 Importance of Various Water Quality Characteristics 103
V-9 Distribution of Ratings of Water Quality for 28 Sites 106
V-10 Correlatives Between Water Quality Rating and
Water Quality Variables 108
V-ll Regression of Water Quality and Temperature
Ratings on Water Quality Parameters 110
V-12 Maximum Likelihood Estimates of Ordinally Discrete
Dependent Variable Model H5
VI-1 Distribution of Willingness to Pay 127
VI-2 Willingness-to-Pay by Transit Useage 130
VI-3 Willingness-to-pay by Participation in Fishing 131
VI-4 Some Regressions with WPT1 as Dependent Variable 136
VI-5 Correlation of Time and Distance Travelled to
29 Sites with Site Quality Variables 140
VI-6 Some Regressions with WTP2 as Dependent Variable
VI-7 Regressions with WPT3 as Dependent Variable 144
VII-1 Substitution Induced by Water Quality Decline 14.9
VII-2 Individual Site Visits and Mentions
VII-3 Total Attendance and Attendance from Sample
Households at Selected Sites 152
VII-4 Household Site Visitation Patterns 154
VII-5 Occurrences of Zero Expenditures for Site Visits
IX
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NO. TITLE PAGE
VII-6 Total Site Visitation as a Function of
Selected Socioeconomic Characteristics 158
VII-7 Probability of Site Visitation — Logit Model 165
VII-8 Abstract Site Demand Functions with Subjective
Quality Ratings 167
VII-9 Abstract Site Demand Functions with Objective
Quality Variables for 29 Sites 168
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LIST OF FIGURES
NO. TITLE PAGE
IV-1 Network of the Sites and the Study 48
IV-2 Sample Points and Sites 76
VI-1 Demand Curves for an Individual Recreation Site 124
XI
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I. INTRODUCTION AND SUMMARY
Recent years have seen a substantial increase in water-based
recreation at the same time the nation's rivers and lakes are
becoming seriously degraded. In response to the increasing water
pollution. Public Law 92-500, the 1972 Amendments to the Federal
Water Pollution Control Act was enacted. This law established as
a national goal "water quality which provides for the protection
and propogation of fish, shellfish and wildlife, and provides for
recreation in and on the water..." To help meet this objective,
$18 billion has been appropriated for municipal treatment works,
and consumer price increases from 1-5% are expected to support the
required industrial treatment. The Act represents one of the
largest public works programs ever instituted in the United States.
Objectives
This study is an inquiry into how water quality affects the
recreation objectives of the Act. While national estimates of the
recreation benefits stemming from water quality improvement could
help evaluate and administer the nation's water pollution control
program, such estimates were not the objective of this project.*
Our purpose is more limited. The principal objective was to
advance the methodology for estimating the recreation benefits of
water quality enhancement. To further this objective, data on the
recreation habits of.a sample of 467 Boston area households was
collected in the course of the project.
*One author [l] suggests over three-quarters of all water
quality benefits lie in recreation.
NOTE: Throughout this report references are cited by number cor-
responding to alphabetical chapter bibliographies. A general
bibliography is presented in Appendix IV.
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The research also explores some of the fringes of recreation
economics as well. We examine the importance of factors such as
setting, facilities and maintenance in site choice. The distinction
between benefits from water quality as a merit good are drawn-and
to a lesser extent quantified. Recreationists' perception of water
quality is compared with objective measures of water quality and
we investigate the potential for reducing the many dimensions which
define "water quality" to a smaller number of composite measures.
Methods in Brief
Three general phases complete the study. The first concentrated
on reviewing the recreation literature, and developing the theory
of multi-site demand models. Based on the models selected for testing,
a survey instrument was prepared, pre-tested and revised. A set of
fresh and salt water sites within a one day visit from the Boston SMSA
(about 50 miles) was delimited at this point in the project. The sites
were chosen to represent most of the daily recreation trips, and to be
close substitutes in terms of the activities available.
Data collection comprised the second phase. First, beach and
water quality characteristics for the system of sites were compiled.
From on-site visits, a beach quality catalog was completed by the
research team and water samples were taken and analyzed. During
December, the questionnaire' was administered to a representative sample
of 467 Boston SMSA households.* Nonresponse was eliminated by random
replacement (Section IV.3 details this procedure). Some respondents
choose not to answer certain questions, so the "no answer" response was
analysed separately for each questionnaire item.
*Originally the survey was to be conducted the first week in
September, immediately after the Labor Day closing of the outdoor
recreation "season." Clearance by OMB of the survey instrument took
much longer than expected, which necessitated the late starting date.
Details of the sample design, and a discussion of the biases which
may have been introduced by the delay are contained in Chapter IV.
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The last phase of the project involved extensive statistical
analysis of the survey data. First, the household characteristics
were tabulated to check for possible, obvious biases in the sample—
none were found. Then direct questions, concerning response to
water quality changes were analyzed. Next, simple tabulations of
visits, activities, and willingness-to-pay were made. At the same
time, a factor analysis of water quality parameters was performed
to examine the grouping of the variables across sites and develop
composite water quality indices. These in hand, we examined the
correlation between perceived water quality and actual water quality.
The third step in the analysis involved estimating (via multiple
regression) the determinants of willingness-to-pay and
recreation behavior. Finally, two multi-site models were specified
and estimated.
Outline of the Report
Seven more chapters complete the main body of this report.
The next chapter deals with some important background issues—the
definition and measurement of recreation activities and recreation
benefits. Five measures of recreation benefits are reviewed and
four are rejected. We choose to focus on a benefit measure based
on consumer surplus and demand analysis and its correlary in
survey research, willingness-to-pay. The chapter reviews the major
post-war literature on demand analysis applied to recreation research,
and codifies this research into a consistent theoretical framework.
Chapter III presents the theory of multiple site models and
describes the problems of empirically estimating these models and
retrieving consumer surplus measures from their parameters. It
also reviews two previous multiple site models found in the
economics literature.
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Chapter IV focuses on the mechanics of the study. It describes
how the network of sites was constructed, and reviews the character-
istics of the system. The water quality parameters used in the study
are described and justified, and a factor analysis reduction "of the
water quality variables is explored. This part of the report closes
with a discussion of the household survey and a comparison of the
sample with Boston SMSA population.
The principle empirical findings of the study are presented in
Chapters V, VI and VII. Chapter V first analyzes the response to
the direct questions concerning the determinants of recreation
behavior and finds that water quality is not among the most
important determinants of either site choice or demand. Chapter V
continues to examine the accuracy of subjective ratings of water
quality; to a large degree, public perceptions of water quality
do not match the objective measurements.
Chapter VI considers willingness-to-pay: its magnitude,
variation across subgroups of the sample and determinants. Despite
the finding of Chapter V that recreationists neither seem to
consider water quality in site choice, nor are able to perceive
objective water quality, respondents of all income groups, races
and educational levels are willing to pay between $20 and $26 per
family per year for water quality maintenance and improvements.
For the Boston SMSA, this may represent from $17 to $28 million per
year.
Empirical estimation of multiple site recreation demand models
is the subject of Chapter VII. After reviewing the data and
aggregate determinants of recreation behavior, an "abstract site"
model is estimated. Water quality seems to affect site choice
but not the number of visits once a site is chosen. Because this
model is not directly grounded in utility theory, retrieving consumer
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measures from its parameters is not possible. A second multiple
site model which has this property is specified, but attempts to
estimate it were constrained by the project budget.
Four appendices complete the report:
Appendix I: Site Facility Inventory Form
Appendix II: Water Quality Sampling-
Appendix III: The Survey Instrument
Appendix IV: General Bibliography.
CITED REFERENCES
1. Department of the Interior, Federal Water Pollution Control
Administration, "Delaware Estuary Comprehensive Study:
Preliminary Report and Findings," July 1966, Chapter 6.
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II. RECREATION AND MEASURES OF ITS BENEFITS
"The greatest gift is the power to estimate correctly
the value of things."
Francois de la Rochefaucauld
Maxims, No. 224. Cited in
Resources [28J.
The problem of "estimating correctly" the value of recreation
benefits, probably unknown to Rochefoucauld when he penned this
statement, requires three distinct steps:
(1) an exact definition of "recreation?"
(2) a metric for quantifying the recreation activities; and
(3) a transformation of the quantity of recreation into
dollar terms.
Each of these steps must further be relevant to the particular
problems of estimating benefits from water quality enhancement.
This chapter clarifies each of these three parts of benefit
quantification to form a suitable background for the methodological
and empirical chapters which follow. The first section below
delimits the recreation experience, and discusses the recreation
activities relevant to water quality improvements. The second
section develops measures to help quantify the recreation experience.
The last section reviews the metrics available for transforming
recreation experience into benefit measures.
1. The Recreation Experience
Recreation benefits can be delimited in the context of
Jordeninq's [16] taxonomy of water pollution abatement benefits.
He lists four categories:
(1) human health;
(2) production;
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(3) aesthetic; and
(4) ecological.
Our interest lies in the third category. According to the taxonomy,
this category includes water-based and water-oriented recreation,
property values and general aesthetic appreciation of water. Our
focus is limited to water-based and water-oriented activities.*
Specific activity and duration define the types of recreation
to be considered under this research. Outdoor recreational activities
can be divided into three types:
(1) those which depend on the existence of water
(water-based);
(2) those which may be enhanced by proximity to water
(water-enhanced); and
(3) all others.
Our concern is with the first two. Table II-l presents a participa-
tion analysis for these types of activities. Because of the importance
of water quality characteristics to water-based recreation, these
were the primary focus of the research. However, gross levels
of water pollution may affect the enjoyment of water-enhanced
activities, so picnicking, walking for pleasure and bicycling were
included in the analysis. Camping and hunting were eliminated
because, as explained below, their duration is typically longer
than these other activities.
This list of activities does not complete the specification
of recreation under study. The duration of the recreation experi-
ence must be addressed. Clawson and Knetsch [?] divide the recreation
experience into five parts: (1) anticipation; (2) travel to the
site; (3) on-site experiences; (4) travel from the site; and (5)
recollection.
*Property value changes are often used as a measure of benefits,
but then direct recreation and aesthetics are confused, and possibly
double counted. Section II.3, below, considers other empirical
and theoretic shortcomings of the property value approach.
8
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Table II-l-
Water-Related Outdoor Recreation Activities
1970
% Population Number of Recreation
Activity Participating Days x 10^ (% of total)
Water-Based
Swimming
Fishing (fresh & salt water)
Boating (including canoeing,
sailing, waterskiing)
Subtotal
Water-Enhanced
Picnicking
Walking for pleasure (including
hiking, nature walks)
Bicycling
Camping
Hunting
Subtotal
Total Water-Related
Total All Outdoor Recreation
46 1722
29 562
24 422
2706
49 542
48 2235
21 397
12 217
3391
6097
12,126
SOURCE: (1) Following N.L. Nemerow, H. Sumitano, &
Faro, [24].
(2) Bureau of Outdoor
Recreation, [sj.
(14.2)
( 4.5)
( 3.5)
(22.3)
( 4.5)
(18.4)
( 3.3)
( 1.8)
(28.0)
(50.3)
(100.0)
R.C.
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The experience itself (Phases 2-4) is taken to be as the
recreation activity. This approach is consistent with past studies
which include the cost of travel as part of the price of recreation.
The content of the on-site portion of the recreation activity
constitutes the major component of the recreation activity. In
order to derive appropriate benefit measures, it is important to
understand clearly the content of this phase, as many previous
studies confuse the purpose of the on-site recreational activity.
Fishing provides a good example of this confusion. The utility
of fishing is not necessarily related to the number of fish caught.
Benefit measures based on the market value of fish or increased
angling success may not reflect the qualities sought in a fishing
experience.* A noted outdoor writer, Ernest Schwiebert f29]
describes the experience:
"Many satisfying things are to be found along trout
water, and on hard pressed streams they help compensate
for lack of fish ... (the angler) remembers not only the
fish taken or lost but also the little things along
the stream. I remember the scores of ducks and geese
on a Yellowstone pond, the intense blue of the Wyoming
sky on those crisp September mornings and the doe and
fawn that crossed a Boardman riffle at twilight
in Michigan... A scoreless evening in the Catskills
was saved by the balmy pine scented wind that swept
down the Valley just at dusk. All of these things
mean as much as the fishing itself."
*Studies using these and other benefit measures are reviewed in
Section II.3, below.
10
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2. Quantifying the Recreation Experience
Traditional metrics for quantifying the magnitude of a recreation
experience are the user-day* or visit.** Theoretically at least,
the number of days per visit and the number of visits must be ascer-
tained simultaneously to derive user-days. Travel costs represent
a fixed cost of the activity, and must be amortized over a sufficiently
large number of days of the activity for the marginal value of the
activity to exceed its cost.
The anticipation phase of the recreation experience offers a
method for separating the interactions between the number of visits
and the duration of the visit. Essentially three broad classes of
recreational activities exist: day trips, weekend trips (two day
or three with Monday holidays), and longer vacation trips. These
differ in terms of the associated anticipation required, and hence
may be considered as essentially distinct although possibly similar,
classes of recreation. Then the unit of recreational activity is
defined separately for each class of recreation. For day trips the
»
unit is, equivalently, the number of trips or the number of days.
For weekend trips the appropriate unit is the number of trips.
For longer, vacation-related, recreation activities, the number
of user-days should be examined.
*Defined by D.E. Hawkins & B.S. Tindall, [l5], as (page 2),
"The presence of one or more persons on lands or .waters, generally
recognized as providing outdoor recreation, for continuous, inter-
mittent or simultaneous periods of time totalling twelve hours."
**Defined by Bureau of Outdoor Recreation [&], as (pages 1-4),
"A visit by one individual to a recreation development or area for
recreation purposes during a reasonable portion or all of a 24-hour
period. It is assumed that the average person participates in 2.5
activities during an average visit to a recreational area. Therefore,
2.5 activity occasions equal one recreation day."
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We chose to focus on one day trips. This focus eliminates the
theoretic quandary and empirical difficulties of estimating simultan-
eously the number and duration of visits. The possible travel distance
for one-day trips conveniently establishes a universe of sites for
sampling and survey. These low anticipation level recreation activities
will tend to eliminate any cultural differences in the desire or ability
to plan. Day trips from the Boston Area offer suitable variability
in water quality and site characteristics to assess the recreational
benefits of water quality enhancement. This limitation permits
careful analysis of urban water quality problems where the recreation
benefits of water pollution abatement appear to be greatest.
The major liability in this approach is the elimination of certain
wilderness settings where the sensitivity of demand to water quality
may be large. This limitation of the study necessitated dropping
camping and hunting, together comprising about 5% of total recrea-
tion days, from the research.
Our empirical analysis, therefore, relies on visits as the
principal measure of the amount of recreation. The specific defini-
tion of "visits" used in this analysis is discussed in Section IV.4
below.
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3. The Monetary Value of the Recreation Experience
The post-war literature on recreation benefit measures offers
six alternative approaches for transforming the recreation demand into
dollar values:
(1) gross expenditure;
(2) market value of fishing;
(3) income multiplier;
(4) property values;
(5) willingness-to-pay interview; and
(6) demand function (consumer surplus).
This section of the report reviews these methods and concludes by
arguing that consumer surplus estimates derived from demand functions
are the most appropriate measure for estimating recreation benefits.
The chapters below use this measure, and its survey research equi-
valent—willingness-to-pay—to estimate recreation benefits of
water quality improvements.
The Gross Expenditure Method
Much of the early literature, particularly, favored this approach,
whereby the benefits of recreation activity are measures by the
total costs incurred per recreationist, including travel and on-site
costs. The justification for this approach is that these costs
must represent at least a lower bound to the value which the recrea-
tionist places on the activity for otherwise, if it was worth
less than these costs to him, he would not undertake it. This argu-
ment is valid as far as it goes, but it does not go far enough. By
ignoring consumers' surplus, the gross expenditure method under-
estimates the value to the recreationist of his activities. The
understatement of benefits is serious because, when it comes to
calculating the net benefits of providing recreation facilities, the
only net benefits are the transfer payment component of costs, which
may be zero even for projects which yield positive net benefits
13
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when the latter are correctly measured. The gross expenditure
approach also leads to the well-known paradoxes that, when the
elasticity of demand is equal to or less than unity, an increase
in the quantity of recreation activity leads to a reduction in
benefit as measured by gross expenditure, which is contrary to
economic intuition. Note also that the use of the gross expendi-
ture approach begs the question of how to predict recreation
activity at a site.
Market Value of Fish
Crutchfield [8 ] argues the value of a sport fishery equals
to the market value of the fish it produced. This work incited
of a plethora of studies in agricultural and forestry experimental
stations throughout the country to estimate the market value
trout, salmon, bass, pickerel, pike, walleyes and so on. The
principal shortcomings of this method is that it excludes the bene-
fits of the recreation experience which are not related to filled
keels. The most obvious demonstration of this omission is the
extra money and time the angler expends beyond that required to
obtain the fish from the market.
A related methodology, explored principally by Stevens [30 & 31 ]
and Stovener [32], relates the benefits of water quality enhance-
ment to angler success. This procedure relaxes the assumption that
the value of the experience equals the market value of the fish
caught, but still insists that the value is proportional to the
number of fish caught. Where water quality improvements lead to
step changes in the type of fishing, the number of fish caught of
the preferred type may be significant. But this is an effect of
shifting the demand curves, not moving along it. The most important
step changes occur where water quality improvements lead to: (1)
establishment of sport fisheries where previously no fishing
existed, (2) replacement of carp and other coarse fish by bass
14
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and other warmwater species, and (3) introduction of salmonoid
habitat.
The Income Multiplier Method
In some studies it is quite common to find an estimate of
the increase in local income and production induced by an expan-
sion in recreation activity, usually calculated via a local input-
output matrix. (Recent examples are Reiling [28] , and Stoevener
[ 32] ). However, these estimates can be misleading. The existence
of indirect benefits depends largely on local conditions. The
method also assumes that there are locally underutilized resources
(i.e., the shadow price of the activity or commodity is zero).
If the resources used as inputs to the increased local production
would otherwise have been fully employed, there is no net gain in
the flow of goods and services available to society, merely a
transfer from one location to another. These estimates of induced
local income growth are valid only insofar as the regional distribu-
tion of income is a separate component of the objective function, and
long run federal policies designed to encourage regional development
are at least arguable.
The Property Value Method
This technique is widely used although, in our opinion, it
suffers from certain fundamental conceptual flaws. The pioneering
studies were done by Knetsch [17 ] , also David [ 10 & ll], Berger [21 ],
Darling [ 9 ], and Dornbusch [14]. Almost all of these studies
apply the "cross-section" model of land value-benefit assessment;
however, the Dornbusch study applies a "time series" model. The
analytical issue can be seen most clearly by considering the cross-
section model, which we discuss first.
15
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The central concept in this approach is the "rent-gradient
function" which expresses rent or property value at each location
as a function of its distance from a central feature, in this case
a water body. It is a well-documented empirical fact that, at
least within a certain radius, this function has a negative slope
i.e., land values are higher nearer to the water's edge. But
what inference can be drawn from these data?
First, we mention some well-known objections to the land
value method: it omits the benefits accruing to residents outside
the area, and there may be some double-counting if estimates
of recreation benefits obtained by this technique are added to
estimates obtained by some other technique, such as willingness-
to-pay interviews, a common practice (Berger, L2l], Darling [9],
Dornbusch [l4]). However, the objection which we emphasize
is that the land value method represents an illegitimate application
of partial equilibrium analysis.
Our argument is in two steps:
(i) As usually conducted, the land value method of analysis is
not an accurate measure of the change in land values because it
Ignores the impact on rents outside the vicinity of the area.
The conventional analysis proceeds as follows (for the case of
ex post facto analysis of a change in water quality). One
observes that land values in the vicinity of the water body are
higher than those at some distance from it, and that they decline
with the distance. One calculates the aggregate differential
in land values within some (often arbitrary) radius of the water
body, over the level of land values outside that radius, and
uses this differential as a measure of the benefits from the change
in water quality. This would be a reasonable procedure on the
assumption that (a) land values in the vicinity of the water body
were at approximately the same level prior to the change as the
16
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level of rents observed outside the vicinity of the water-body
after the change, and (b) land values outside the vicinity of the
water-body were approximately the same before the change as after
the change. It is very plausible that the second assumption is
false.(Berger [2l] for example, recognizes this, but proceeds to
ignore it.)
Intuitively, one would expect land outside the vicinity of the
water-body to become relatively less attractive after the change in
water quality and, therefore, to fall in price. This assumes a
fixed population of residents in the overall area. In
practice, this assumption might be violated because of population
increase. If the population of the overall urban area grew exo-
genously (i.e., from natural causes) the growth in the demand for
housing might keep rents outside the vicinity of the water-body
at their pre-quality change level. But clearly, this is an
irrelevant phenomenon and the appropriate datum for measuring the
benefits of the quality change is the pattern of rents which would
have occurred in the absence of the population increase. If the popula-
tion increase is endogenous (i.e., it is due solely to the water quality
change which causes a flow of immigrants to the urban area) , then
it may be that rents outside the vicinity of: the water body are
stabilized at their pre-quality change levels and the total rent
differential measured in the manner described above is an accurate
index of the change in land values within a general equilibrium
setting. However, we doubt whether the hypothesis of endogenous
population growth is applicable to most of the pollution abatement
situations studied .in the literature.
In the context of cross-section studies, the rent-equation is
misleading for analogous reasons; rents may fall in areas outside of
the environmentally improved region and, in consequence, rise less in
17
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that region than the regression equation predicts. The circumstances
in which this will happen can be described more rigorously in the context
of a theoretical model of location and rent determination which is
outside the scope of this study.
The Dornbusch methodology is slightly different, but it suffers
from analogous defects. In that study the change in property values
in areas where water quality has improved is regressed on distance
from the site and it is shown that the increase is greater close
to the site. But, in order for this finding to be meaningful, it
would have to be shown that the increase in land values would not
have occurred anyway even without the improvement in site quality,
say, because of an exogenous change in population or income. In
other words, the Dornbusch study does not show how much of the
increase is due to the change in water quality. (One way to do
this would be to undertake a similar study of the change in property
values at sites whose water quality had not changed and to use
these as a control group.) Moreover, the Dornbusch study does not
consider whether property values have fallen, or grown less rapidly
than would otherwise have happened, at sites outside the vicinity
of the water body.
This first argument is quite widely recognized. Our second
point is more often overlooked
(ii) Even assuming that one could accurately measure the change
in equilibrium rent gradients of all points in the area
occasioned by the change in water quality, this still would provide
no basis for measuring the social value of the improvement in
environmental quality. This can best be seen by considering the
following hypothetical, but not unreasonable, example. Consider a
community of 100 persons living in a town which contains, at one
end, a polluted lake, and, at the other, a flat plain. There is
space for 100 homes both on the lakeshore and on the plain but,
18
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since the lake is polluted, everyone prefers to live on the plain.
Land rents on the plain are $100 per acre (or per dwelling—it makes
no difference); on the lakeshore rents are only $10 per acre, since
no one likes to live there. Now the quality of water in the lake
is drastically improved and everybody wishes to live on the lake-
shore. Everybody moves to the lakeshore, nobody lives on the plain
and it so happend (there is no reason why this could not happen)
that rents are now $100 per acre on the lakeshore and only $10 per
acre on the plain.
The end result is that after the quality change there is no
net change in total rent payments. Yet we would certainly wish
to argue that there has been an increase in social welfare. (This
can be proved by revealed preference arguments: people would not
have moved home if they were not thereby better off.) Thus, it
is seen that the change in aggregate rent payments, even when full
allowance is made for rent changes outside the environmentally
improved area, provide no indication of the change in social welfare.
The reason why this is so is identical to the reason why gross
expenditure does not provide an adequate measure of the social value
of consumption (i.e., willingness-to-pay). In both contexts the
omission of consumers' surplus understates benefits. Furthermore,
in the present context, where there are shifts in the demand curve,
as well as in the supply curve, the change in expenditure bears
absolutely no relation to the change in the area under the demand
curve. Without knowing the demand curve explicitly one can infer
nothing from data on the change in equilibrium price and quantity.
Strotz [33] has recommended measuring the social benefit
from environmental quality improvements by summing the absolute
values of changes in rents at each point. However, it can be
shown that this result derives from the peculiar assumption of his
model and has no general validity. Also Lindsay [20] has recently
attempted to prove that the aggregate change in land values is an
adequate measure of social benefit of environmental quality
19
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using a linear programming assignment model. However, the
proof is based on certain quite limited assumptions and is not
generally valid.
The Willingness-to-Pay Interview Method
This technique was first applied by Davis [l2J, and subsequent-
ly, by Knetsch and Davis [l9], Berger [2l], Dornbusch [l4], and
Brown and Hammack [3], and others. In principal, this technique is
conceptually sound; however, its empirical value depends entirely
on the method of application and the degree of confidence that one
can have in the veracity (and accuracy) of interviewer responses.
Knetsch and David [24] cite reasons for believing that respondents
may both overstate and understate their true willingness-to-pay.
Since the method offers a correlate to consumer surplus
derived from demand function, willingness-to-pay questions were
implemented and analyzed from the survey research effort.
The Demand Function Approach
Hotelling [23] first suggested this approach in 1949 in a now
famous letter to A.E. Demeray, then Associate Director to the National Park
Service. During the post-war bidding for chunks of an expanding
federal budget, the park service decided a "monetary evaluation" of
park service facilities might both assist their management and
expand their budget. The park service asked ten of the nation's
leading social scientists and economists to comment on the feasibility
of such a study. The reviews were mixed and mostly forgotten, but
Hotelling drew on the work of Jules Dupuit, an 18th century French
engineer, who derived formulae for estimating the public benefits
of bridges, roads and canals, to suggest:
20
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"Let concentric zones be defined around each park so that
the cost of travel to the park from all points in one of
these zones is approximately constant. The persons
entering the park in a year, or a suitably chosen sample
of them, are to be listed according to the zone from
which they come. The fact that they come means that the
service of the park is at least worth the cost, and this
cost can probably be estimated with fair accuracy. If we
assume that the benefits are the same no matter what the
distance, we have, for those living near the park, a con-
sumers' surplus consisting of the differences in transportation
costs. The comparison of the cost of coming from a zone
with the number of people who do come from it, together
with a count of the population of the zone, enables us to
plot one point for each zone on a demand curve for the
service of the park. By a judicious process of fitting it
should be possible to get a good enough approximation to
this demand curve to provide, through integration, a
measure of the consumers' surplus resulting from the
availability of the park. It is this consumers' surplus
(calculated by the above process with deduction for the
cost of operating the park) which measures the benefits
to the public in the particular year. This, of course,
might be capitalized to give a capital value for the
park, or the annual measure of benefit might be compared
directly with the estimated annual benefits on the hypo-
thesis that the park area was used for some alternate
purpose."
The demand function approach has since been implemented
somewhat inaccurately by Trice and Wood [34], and authoratively
by Clawson and Knetsch [?]. Subsequently, it has been employed by
Lerner [l9], Ullman and Volk [35], Pankey and Johnston [25],
Dearinger [13], and Brown [4], and extended by Merewitz [22],
Stevens [30 & 3l], Boyet and Tolley [2], All of these formulations
have been in the context of the demand for a single site. This
approach may be summarized in the following equation :
where V is the number of visits made to a recreation site by
21
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individual i (or by the inhabitants of county i), P. is the
cost of reaching the site (including travel cost) for individual i
(or for a representative resident of county i) and Y. is a scalar
or vector of socioeconomic variables describing individual i (or
describing the residents of county i including, usually, the
county's population). In some early versions of the model, price
was not entered as a variable but instead distance was used as
a. surrogate. Stevens [30 & 3l] extended this model by adding an
index of site quality to the explanatory variables. The particular
index which he chose, angling success per day, is, as shown above,
oddly an indirect measure of site quality.
Generally, demand is estimated for a single site without con-
sideration for other sites, or all sites visited by the sample popu-
lation are combined, and a single equation is estimated. The latter
approach is essentially a "participation study" and is beyond the
scope of this report. The former approach suffers from a significant
short-coming, namely the so-called price dominance criteria.
The conventional procedure is to allocate recreation demand
among some new site and the existing alternative sites according
to a price dominance. Let P! by the cost to residents of county i of
visiting the old sites, and P'.' the cost of the new site. The
implicit criterion is that (i) if P!' > P!, nobody from location i
attends the new site while (ii) if P!' < P! everybody from that
place visits the new site, the total volume of attendance being
V!' = F(P!', Y.). In case (i), there is the same volume of recrea-
tion as before the-change, namely V! = F(P!,Y), and it is con-
centrated exclusively at the old sites. There is no economic gain
from the quality change for the residents of the county. In case
22
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(ii) nobody attends the old sites and the economic gain.consists
of the change in expenditures plus the change in consumers'
surplus associated with the change in prices from P! to PI'
This analysis can be justified in two ways: (1) if the new
site and the old sites offer exactly the same bundle of character-
istics and are identical in every way except for price/distance,
then the price dominance criterion should be valid; and (2)
if the new site offers a somewhat different bundle of character-
istics from those offered by the old sites, in other ways besides
price/distance, then the use of the price dominance criterion
involves an assumption that recreationists choices are made only
on the basis of price and are independent of other site character-
istics.
This empirical hypothesis was not substantiated. It was
tested by estimating appropriate demand functions for individual
sites with other site characteristics .besides price included
among the explanatory variables. Once these models have been
estimated, the hypothesis becomes a null hypothesis that non-price
related coefficients are zero. As seen in Chapter 5, this is
not the case.
One way around these difficulties is to estimate simultan-
eously demand functions for a system of competing sites which
form the universe of sites visited by the sample population.
Substitutions between sites are then explicitly estimated.
Although certain conceptual and empirical difficulties arise with
these models this is essentially the approach taken here. The handful
of recreation studies which employ this technique, and a theoretical
development of an improved multi-site model are contained in Chapter
III, below.
Having the demand equation, three procedures have been used to
estimate benefits, and two of these are incorrect. The most simple
is the dollar value of a user day. This is used by the federal govern-
ment in water resource project evaluation but omits the consumer
surplus enjoyed by some users.
23
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The second way of estimating benefits calculates the revenue
which could be gained by a non-discriminating monopolist. But, of
course, only a discriminating monopolist can price away all of the
"willingness-to-pay" for a good, so the result is inaccurate in a
manner similar to the first approach.
Consumer surplus measures the total willingness-to-pay for
the recreation activity. If the prevailing price is $5 per unit, and
a certain individual is just indifferent to consumption at a price
of $15, he enjoys a consumer surplus of $10. Ignoring income effects,
consumers' surplus equals the revenue which could be obtained by a
discriminating monopolist. In 1949, Retelling pointed out this fact,
but it has not be<=n considered by most recreation economists. Consumer
surplus is the theoretically correct measure of benefit, and is the
one used in this study.
One further note on benefit measurement from demand equations
is appropriate. Total benefit can be measured as the area under the
demand curve up to the prevailing price. If the good in question was
traded in a competitive market, the costs (producer revenue) could be
subtracted to estimate net benefits. However, recreation is not such
a good and the public sectors' market share position depresses the pri-
vate market and prices. Hence the costs are not the appropriate ones
to consider. Basically, the problem comes down to determining the
costs, both institutional and economic, required to achieve both adequate
water quality for recreation, and increased recreation itself. (As
seen below, the costs of additional facilities needed for recreation
may be large.) These costs could then be weighed against the benefits
to select the appropriate public policy. However, these costs, as
are the benefits, are highly sensitive to local conditions. Therefore,
neither net benefit calculations, nor nationwide benefit calculations
are appropriate for the research at hand. Instead, this study focuses
on total benefit measured by consumer surplus, and ignores the costs
of providing that recreation.
24
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CITED REFERENCES
1. A.J. Blackburn, "A Non-linear Model of the Demand for Travel,"
Chapter 8 in, R.E.Quandt (Ed.) The Demand for Travel;
Theory and Measurement, Lexington, Mass.: D.C. Heath,
1970.
2. W.E. Boyet & G.S. Tolley, "Recreation Projection Based on
Demand Analysis," Journal of Farm Economics #48
(Nov.-Dec. 1966): 984-1001.
3. Gardner Mallard Brown, Jr. & Judd Hammack, "A Preliminary
Investigation of the Economics of Migratory Waterfowl,"
in, Krutilla (ed.), Natural Environment Studies in
Theoretical and Applied Analysis, Baltimore: Johns
Hopkins University Press, 1972.
4. W.G. Brown, E.N. Castle, & A Singh, An Economic Evaluation
of the Oregon Salmon and Steelhead Sport Fisheries,
Corvallis: Oregon Agriculture Experiment Station, 1964.
5. Bureau of Outdoor Recreation, Department of the Interior,
The 1970*Survey of Outdoor Recreation Activities, Pre-
liminary Report, Washington, D.C.: GPO, February 1972.
6. Bureau of Outdoor Recreation, Department of the Interior,
Water-Oriented Outdoor Recreation in the Lake Ontario
Basin, Ann Arbor, Michigan: BOR, 1967.
7. M. Clawson & J. Knetsch, Economics of Outdoor Recreation.
Baltimore: Johns Hopkins University Press, 1966.
8. J.A. Crutchfield, "Valuation of Fishery Resources,"
Land Economics Vo. 38, No. 1 (May 1962): 145-154.
9. A.H. Darling, "Measuring Benefits Generated by Urban Water
Parks," Land Economics (February 1973).
10. Elizabeth David, "Lakeshore Property Values: A Guide to
Public Investment in Recreation," Water Rosources
Research Vol. 4, No. 4 (August 1968): 697-707.
25
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11. Elizabeth David, "The Exploding Demand for Recreational
Property," Land Economics Vol. 45 (May 1969): 206-217.
12. R.K. Davis, The Recreation Value of Northern Maine Woods,
unpublished Ph.D. Thesis, Department of Economics,
Harvard University, 1963.
13. John A. Dearinger, Esthetic and Recreational Potential of
Small Naturalistic Streams Near Urban Areas, Research
Report #13, Lexington, Kentucky: Water Resources Research
Institute, University of Kentucky, 1968.
14. D.M. Dornbush & S.M. Barrager, Benefit of Water Pollution on
Property Values, prepared for the U.S. Environmental
Protection Agency, San Francisco: David M. Dornbusch &
Company, Inc., August 1, 1973.
15. D.E. Hawkins & B.S. Tindall, Recreation and Park Yearbook
1966, Washington, D.C.: Recreation and Park Association,
1966.
16. David L. Jordening, "State-of-the-Art: Estimating Benefits
of Water Quality Enhancement," Office of Research &
Monitoring, U.S. Environmental Protection Agency,
Contract #68-01-0744.
17. J.L. Knetsch, "The Influence of Reservoir Projects on Land
Values," Journal of Farm Economics, Vol. 46: 520-538.
18- J.L. Knetsch & R.K. Davis, "Comparisons of Methods for
Recreatio'n," in A.V. Kneese & S.C. Smith (eds.)
Water Research, Baltimore: Johns Hopkins Press.
19. Lionel J. Lerner, "Quantitative Indices of Recreational Values,"
Water Resources and Economic Development of the West;
Economics in Outdoor Recreational Policy, Report #11,
Conference Proceedings of the Committee on the Economics
of Water Resources Development of the Western Agricultural
Economics Research Council, jointly with the Western
Farm Economics Association, University of Nevada, Reno,
1962, pp. 50-80.
20. John L. Lindsay & Richard A. Ogle, "Socioeconomic Patterns of
Outdoor Recreation Use Near Urban Areas," Journal of
Leisure Research Vol. 4 (1972).
26
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21. Louis Berger, Incorporated, Methodology to Evaluate Socioeconomic
Benefits of Urban Water Resources, prepared for the Office
of Water Resources Research, U.S. Department of the
Interior, East Orange, N.J.: Louis Berger, Inc., July 1971.
22. Leonard Merewitz, "Recreational Benefits of Water Resources
Development," Water Resources Research Vol. 2, No. 4
(Fourth Quarter, 1966): 625-639.
23. National Park Service, U.S. Department of Interior, "The
Economics of Public Recreation: An Economic Study of
the Monetary Evaluation of Recreation in the National
Parks," Land and Recreational Planning Division,
Washington, D.C., 1949.
24. Nelson L. Nemerow & Hisashi Sumitomo, "Benefits of Water
Quality Enhancement (Onondago Lake)," Water Pollution
Control Research Series/ 16110 OAJ 12/70, Washington,
D.C.: EPA, Water Quality Office.
25.. V.S. Pankey & W.E. Johnston, Analysis of Recreation Use
of Selected Reservoirs in California, Contract Report
#1, Plan Formulation and Evaluation-Studies—Recreation,
Sacramento: U.S. Army Corps of Engineers District,
May 1969.
26. S.D. Reiling, K.C. Gibbs, & H.H. Stoevener, Economic Benefits
from an Improvement in Water Quality, Socioeconomic
Environmental Studies Series, Environmental Protection
Agency, Washington, D.C.: GPO, January 1973.
27. Resources for the Future, Resources, No. 1.
28. Resources for the Future, Resources, No. 46
29. Ernest Schiebert, Matching the Hatch, New York: MacMillan, 1955.
30.. Joe B. Stevens, "Recreational Benefits from Water Pollution
Control," Water Resources Research Vol. 2, No. 2
(Second Quarter, 1966): 167-182.
31. Joe B. Stevens, "Recreation Benefits from Water Pollution
Control: A Further Note on Benefit Evaluation,"
Water Resources Research Vol. 1, No. 1 (First Quarter,
1967): 63-64.
27
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32.. Herbert H. Stoevener, et al., Multi-Disciplinary Study of
Water Quality Relationships; A Case Study of Yaquina
Bay, Oregon, Special Report 348, Corvallis: Oregon
State University, February 1972.
33.. R.H. Strotz, "The Use of Land Rent Changes to Measure Welfare
Benefits of Land Improvements," in The New Economics of
Regulated Industries; Rate-Making in a Dynamic Economy,
Los Angeles: Economics Research Center, Occidental
College, 1968: 174-186.
34. A.H. Trice & S.E. Wood, "Measurement of Recreation Benefits,"
Land Economics Vol. 34, No. 3 (Aug. 1958): 195-207).
35.. Edward L. Ullman & Donald J. Volk, "An Operational Model for
Predicting Reservoir Attendance and Benefit: Implications
of a Location Approach to Water Recreation," Papers
of Michigan Academy of Science, Arts and Letters 47 (1962):
473-484.
28
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III. MULTIPLE SITE MODELS FOR RECREATION DEMAND
Multiple site demand models offer one way to eliminate the
shortcomings of the more common single equation models reviewed
above. This chapter surveys the existing literature on systems
of demand equations for recreation sites and sets down some principles
for developing alternative demand models. Some of these alternative
models have been applied to our data on recreation behavior in the
Boston area, and the results are described in Chapter VII; others
impose extremely heavy computational requirements and for this
reason were not estimated.
The basic objective here is to model the demand for a set of
alternative recreation sites in such a way as to (i) allow for the
possibility of inter-site substitution, (ii) make explicit the relation-
ship between environmental quality conditions and inter-site demands,
and (iii) permit the explicit calculation of consumer's surplus mea-
sures of benefits from changes in site costs or environmental condi-
tions. As the next section shows, these objectives have not been
achieved by the existing multi-site models in the literature.
Section 2 sketches some non-stochastic models which do meet the
objectives. Finally, Section 3 discusses some stochastic choice
models which could be used for this purpose, and which explicitly
allow for the phenomenon of zero visitation rates for many of the
sites as well.
29
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1. The Multiple Site Demand Models in the Literature
To the best of our knowledge there have been only a handful of
recreation studies which attempt to estimate simultaneously the
demand for a network of competing recreation sites. These studies
may be divided into two groups. The first group may be called
allocation simulation studies, and the second, system demand
models.
The goal of the first type of model is to simulate the alloca-
tion of recreationists among a set of alternative sites using some
reasonable criterion, but one not necessarily based on a statistically
validated behavioral model of recreation choices. For example, in
one version of the Tadros-Kalter [lO,ll] model recreationists are
allocated among alternative sites on the basis of a travel distance
minimization subject to constraints on site capacity, time and
money expended on travel, and exogenous zonal recreation demands.
The model is solved using conventional linear programming
techniques. In another version of the Tadros-Kalter model, the
same constraints are used but the allocation criterion becomes one
of maximizing visitor day satisfaction, measured by the sum of
attendance at each site from each origin zone weighted by an index
of the attractiveness of the site to recreationists originating in
each zone. The attractiveness index turns out to be the available
recreation area at each site divided b/ its distance to each origin.
Hence the attractiveness maximization criterion is similar to the
travel distance minimization criterion of the first model.
The Ellis model [5 & 6J assigns recreationists to alternative
sites through a coinbination of travel cost/distance minimization and
site attractiveness. Total attendance at, each site is proportional
30
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to an index of its attractiveness. Subject to this constraint on
total attendance, site attendance by zone of origin is determined
by cost minimization using network theory techniques. The site
attractiveness index is a weighted sum of sub-indices of site
capacity, the quality of water resources at the site, and the
quality of the site's scenic setting. The weighting of these sub-
indices is not based on empirical estimates of behavioral choices
but appears to derive at least partly from calibration studies
designed to assure that the model provides a reasonable facimile
of observed recreation patterns.
It must be emphasized that neither the Tadros-Kalter models
nor the Ellis model can claim to be grounded in observed recreation
behavior. Both the cost minimization criteria and' site attractiveness
indices employed are assumptions which, although plausible, were
not validated by acceptable statistical techniques.
Finally, there is a recent paper by Baron and Scheckler [l]
which, though formally different from the Ellis study in its use
of network analysis, is a similar combination of travel distance
minimization plus an allowance for the differential attractiveness
o.f alternative sites. As in the Ellis study, this differential
attractiveness index derives from ad hoc calibration procedures
rather than a verifiable model of recreationists1 choice behavior.
None of these models, therefore, is of direct interest to us
since we wish to use formal statistical procedures to estimate the
behavioral relationships. In addition, none of these models is
based on utility theory and, therefore, the apparatus of consumers'
surplus analysis cannot be applied to derive benefit estimates.
31
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Now consider two system demand models, both intended for
statistical estimation and both at least tenuously related to
utility maximization theory. These are the models of Hurt and
Brewer [3] and Cicchetti et al^ [4]. The two models are, in fact,
virtually identical and differ only in the estimation techniques
used to implement them. Both involve the estimation of a set of n
equations (assuming n recreation sites) :
... (1)
where x. is the number of visits to site i by individual t,
(P-. ...P ) is a vector of the prices of the sites (travel costs,
etc . ) for this individual , and Y is a scalar or vector of such
variables as his household income. The system (1) is a natural
extension of the single site demand functions
Xlt = fllt'Yt
... (2)
* ,. = f [P ^./YU]
nt nL nt tj
which were discussed in Chapter II.
The Burt-Brewer and Cicchetti e_t al_ implementations of
are somewhat unsatisfactory for the present study on two counts, one
concerning the use of the model to obtain estimates of consumer's
surplus and the other concerning the problem of how differing water
quality conditions affect consumer's behavior. The first issue involves
some technical aspects of the theory of consumer demand only summarized
here. It is a fundamental theorem of consumer theory that if and only
if a- set of demand functions such as (1) satisfy certain conditions
on their first partial derivatives there exists a unique underlying
-------
utility function. Moreover, under these conditions, it is possible
to define and calculate measures of consumers' surplus for price
changes. The conditions to which we refer are that the cross-price
derivatives of the compensated demand functions be equal. In terms
of the ordinary demand functions—such as (1)—the conditions are that:
3x. 3x, 9x. 9x.
1*7 +xj *T= aij- +Xi3^ vi'j" - (3)
The conditions are sometimes, but mistakenly, taken to require that
the cross-price derivatives of the ordinary function be equal—that
is:
3x. 9x.
1*7 - IpJ" vi'j — (4)
This in fact is what Burt-Brewer and Cicchetti, et al both do
although for different reasons. Burt-Brewer [3] require the cross
price derivatives to be equal under the assumption that "income
elasticities among the outdoor recreation commodities are relatively
close in magnitude," an assumption they state but do not support or
test (although it seems likely for their application). Note that
these are the exact conditions when an unconstrained maximization
problem is posed (Hotelling showed this in 1932). Hence if total
expenditure on recreation is small relative to total income, then these
may be good approximations to the exact conditions.
Cicchetti et al L4 J analyze the integrability conditions in great
detail. They find small income elasticities of demand for downhill
skiing (a surprising result which they attribute to the use of in-
come data aggregated to the county level), but that the cross price
demand derivatives are not equal. They use a quasi-Bayesian approach
to reconcile the two sets of price elasticities (prior information
that the cross price terms were equal, sample information that they
are not) and proceeds as though the integrability conditions were
33
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satisfied. Thus, they set out to estimate (1) as a set of linear
functions in the variables P .. .P and Y, and impose the constraint
i~Vi
that the coefficient of P. in the i equation be the same as the
coefficient of P. in the j equation.
Although it is erroneous, the condition (4) has a certain con-
venience in that it causes the integral of the area under the
demand curves (1) between two price vectors to be path independent—
in the same way that the condition (3) causes the integral of the
area under the compensated demand curves to be path independent.
However, this is of dubious value because the relevant area for
measuring consumer's surplus is the area under the compensated
demand function and not that under the ordinary demand curve. It
is true that the latter area may be considered an approximation
to the former but as we shall show in the next section, it is possible
to adopt certain alternative specifications of (1) from which an
exact measure of consumer's surplus can be obtained with relative
ease.*
Note that when recreation demand is estimated separately from
demand for all goods, the Y of equation (3) is total expenditures
on recreation, not income. But neither Burt-Brewer nor Cicchetti
et al estimate the cross elasticities of demand (between sites)
with respect to total expenditures or recreation. Chapter VII
returns to this point.
So far, the discussion has considered only exact measures of
consumers' surplus. Willig [l3] has shown that when the income
(or in our case, recreation expenditure) is small, the errors in
ignoring the cross elasticity term of (3) are also usually small.
Rather than rely on this empirical serendipity, however, we choose
to specify, in Chapter VI, a model where exact measures are
possible.
*It would be possible to test this hypothesis using, for
example, a likelihood ratio test, although neither Burt-Brewer nor
Cicchetti et al bother to do this.
34
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The second point concerning the Burt-Brewer and Cicchetti et al
studies is less theoretical and is more directly concerned with the
practical value for water quality analysis of the demand systems
which they estimate. The equations in (1) do not contain environ-
mental quality variables as explicit arguments. The fact that site
conditions may differ and that this may influence recreationists' be-
havior is only acknowledged implicitly in these models. That is, if the
sites do not differ, or if they differ but the differences have no
influence on recreationists1 behavior, then we would expect all the
site demand functions to have the same own price coefficient and,
presumably zero cross-price derivatives; in effect we are back to
the single-equation general demand functions represented by equation
(1) in Section II-3. Otherwise, if the coefficients of different
equations are different, we may infer that this is because site
conditions differ and that these differences affect recreationists1
behavior, they are relatively unilluminating: they do not tell us
which aspect of the site conditions has the most effect on recreation
choices and whether this effect is large or small. They do not
directly enable us to predict the consequences of changes in site
conditions on recreation demand patterns, still less to measure the
benefits of these changes in a theoretically rigorous manner. One
way to achieve the first objective, if not the second, is to regress
certain of the fitted coefficients—for example the own price
conditions—on variables measuring site quality. Burt-Brewer and
Cicchetti do not do this, but it is an eminently feasible procedure.*
However, instead of doing this, we prefer to bring the environmental
quality variables directly into the demand equations; in the next
section we outline several methods for doing this.
*This procedure has been followed in a different context by
Parks & Barten [e] who were estimating a set of commodity demand
equations separately for several countries. Parks & Barten
wished to discover if consumer demand patterns were influences by
demographic structure and they investigated this by regressing
the coefficients of the fitted equations for each country on certain
demographic variables.
-------
2. System Demand Models—Nonstochastic Choice
We begin by elaborating on the remarks of the previous section
that to obtain exact measures of consumers' surplus from the Burt-
Brewer [3] or Cicchetti et al [4] type model a different specification
of (1) which is more easily reconciled with the theory of consumer
behavior must be adopted. It is true that there are relatively few
analytical demand functions which automatically satisfy the condi-
tions (3) and which, therefore, can be traced back to an underlying
utility function. Nevertheless, there are some functions with
this property and they have been used in studies of consumer behavior
over the last decade with some success. Among the most convenient
and widely used is the LINEAR EXPENDITURE SYSTEM, which actually
was introduced by Stone [9] more than twenty years ago.
Before describing this model and showing how it can be used
to model the demand for a set of recreation sites, it may be
useful to review some basic elements of consumer demand theory.
This will also enable us to clarify the distinction between the
models discussed in this section and those to be discussed in the
next section. Assume that the individual consumer has a utility
function defined over his comsumptions of n commodities,
u(x....x ) and that he arranges his purchases as though he
were solving the constrained maximization problem:
maximize u(x) subject to ZP.x.=Y ...(5)
X xil °
The Kuhn-Tucker theory introduces the multiplier A to derive
the first-order conditions for the stationarily of (5) as
36
-------
3u/3x. - XP. < 0 i=l...n ... (6a)
1 X ~~"
ZP.x. = Y ... (6b)
x. > 0 X > 0 — (6c)
x. • [au/BXi - XP^J = 0 i=l...n ... (6d)
The implication of (6d) is that if we knew that all n goods were
always going to be consumed in some quantity the n demand functions
could be obtained from the solution to the following equalities :
XPj^ = 0 i=l...n — (7a)
Y ... (7b)
which are a subset of the equations in (6) . Alternatively, if there
were m>n goods, but we knew that the same (m-n) goods would never be
consumed at any feasible prices and incomes, while the other n goods
always would be consumed, then we could obtain the demand functions
for the latter goods by solving (7); in effect we could ignore the
prices of the (m-n) goods which are never consumed. In practice,
as we shall see, neither of these assumptions is satisfied: by no
means all of the sites ate visited by each recreationist nor, on
the other hand, it is not necessarily true to say that if a person is
not visiting certain sites now then he would never visit them.
However, since it is vastly simpler to derive a set of demand
functions from (7) than from (6) we shall assume throughout this
section that (7) is the relevant set of equations for deriving a
system of demand functions from a specialized utility function. The
next section presents some demand models which are explicitly based
on (6).
37
-------
Return to the linear expenditure system. If we take as the
consumers' utility function the following specific formula
n
u(x) = .E bilog(xj,-c.) ... (8)
with Eb^=l, and solve the equation corresponding to (7), we obtain
the following demand functions
PJ I J J
Direct differentiation of these equations will show that they satisfy
condition (3). Moreover, an exact measure of the consumers' surplus
when prices change from P? to P' can easily be obtained from (8) and
(9). It is given by:
n /pi\bi
c = [Y-ZP?C.].II. [li\ - [Y-ZPJCJ.] ... (io)
J 1™-L I -fjQ I
* i'
The utility function (8) is a simple translation of the Cobb-Douglas
utility function.
u(x) = Tlx^i, Sb. = 1 ... (11)
The demand functions derived from the latter utility function are
... (12)
Thus, (11) and (12) can be regarded as limiting forms of (8) and (9)
when all the c.'s are zero. The effect of this restriction on
3
the c^'s is that there are no cross-price terms in the demand
functions for individual goods.
The problem to be resolved is how to generalize the equations
for the utility function such as (8) and (11) to deal with product
38
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quality as well as consumption quantities. The solution proposed
is to make the parameters of the utility function themselves a func-
tion of commodity characteristics. This, in turn, has the
effect of making the parameters of the demand curves a function
of commodity characteristics. To see how this works introduce a
set of variables Z. , i=l...n, k=l...m, representing the amount
IK
of characteristic k available at site i. Then, starting with the
utility function (11), we postulate:
(13)
u(x,Z) = nx.bi
1 .
b. = f.ffe.. ,...2. ]
i i1- il inr
The resulting demand functions are, of course, the same as (12) ,
with the functions f. (•) substituted for the b.'s. However, this
model is computationally inconvenient because we have to impose
the restriction that Ef^=l. In view of this, it is actually simpler
if we work with the more general utility function (2) and make the
c. *s functions of the commodity characteristics:
u(x,Z) = Eb.log(x.-c. )
... (14)
c. = f.[z.n ,...2. ]
i 3. il imj
There is no theoretical basis for choosing a specific form of
f. (•); for example, we could have
<=i - *io + £Wik2.k . . . (15a)
c=W+Wlog(Z.), ... (15b)
where (W. . . .W. ) are unknown coefficients to be estimated along
•10 im ^
with b. . However, it simplifies the computations greatly if
we assume that
W = W. , i=l — n, k=l...m.
39
-------
This assumption implies that, other things being equal, the effect
of a change in a given characteristic — say turbidity — is the same
for all sites. This does not necessarily mean that all sites are
equally attractive, because site characteristics are likely to be
different. Moveover, we have also left open the possibility that
the bi 's and W. 's are different across sites, so that even if all
1 10
sites had exactly the same characteristics and the same prices,
their demands could differ. With this assumption, .the site demand
functions implied by (14) and (15a) for the case of two character-
istics are:
Xi - Wio+WlZil+W2Zi2-bi- - " - "
3=1 3 Pi
... (16)
A similar set of demand functions would result if we used (15b)
instead of (15a). The estimation of these systems of equations
is discussed in Chapter VI.
40
-------
3. Stochastic System Demand Models
There are several stochastic choice models available in the
literature which could be used. For example, the multinomial logit
model assumes that the individual selects one of n alternatives—
in this case recreation sites—so as to maximize an explicit
utility function.* The observed output of this process is an
nxl vector with (n-1) zero elements corresponding to the rejected
alternative and one element containing the value "1" corresponding
to the alternative which is chosen. Blackburn [2] independently
developed a slightly more general model in which the output is an
(nxl) vector containing (n-1) zeros as before and, in the row
corresponding to the chosen alternative, the number of times the
preferred alternative is actually chosen (consumed).
Both these models are restricted to situations in which only
one alternative is chosen, and there is reason to believe that
is not the case with the choice of recreation sites. It is,
therefore, interesting to enquire whether a general stochastic
choice model can be written in which an arbitrary number out of
n alternatives is selected. Such a model could be based on the
full set of Kuhn-Tucker conditions for utility maximization
given the previous section. The method used makes some of the
parameters of the utility function (and hence the demand
function) stochastic variables. First, ignore the question of
commodity quality, since it can be incorporated relatively easily
along the same lines as in equations (15) above.
In order to allow for the case of zero consumption, the
utility function (8) must be slightly altered to ensure a bounded
derivative at the zero consumption point. As an example, the
*See Theil [12] and McFadden [? ].
41
-------
utility function could be
n ~
u(x) = E b.ln(l+x.) ... (17)
where the b. are random variables, depending partly on the site
characteristic Z. . Then (6) and (17) imply that the probability
of an observed individual consumption pattern in which, say, the
individual visits only the first m sites, the frequency of visita-
tion being V., i=l...m, while V.=0, i=m+l...n, is given by:
in -
•=1 b-
Pr ^ b. —3 m3 for all i=m+l...n
Y * &'!
b. (1+V )P
— = =m-jL for all i=l...m ? ... (18)
If a suitable distribution can be assumed for the b.'s, we can write
down the likelihood function based on (18) in closed form and apply
maximum likelihood estimation techniques. However, it is
clear that with (at least) 29 alternative sites the maximization
of this likelihood function will be computationally infeasible.
Therefore, the empirical work in Chapter VII relies on the non-
stochastic system demand models described in the previous section.
*The model would be feasible only with about 3-5 alternatives.
42
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CITED REFERENCES
1. Mira Baron & Mordechai Scheckler, "Simultaneous Determination
of Visits to a System of Outdoor Recreation Parks with
Capacity Limitations," Regional and Urban Economics
Vol. 3, No. 4 (1973): 327-359.
2. A. Blackburn, "A Non-linear Model of the Demand for Travel,"
Chapter 8 of The Demand for Travel: Theory and Measurement,
R.E. Quandt, Lexington, Mass.: D.C. Heath, 1970.
3. Oscar Burt & Durward Brewer, "Estimation of Net Social Benefit
from Outdoor Recreation," Econometrica Vol. 39, No. 5
(September 1971): 813-827.
4. Charles J. Cicchetti, A.C. Fisher & V. Kerry Smith, "An
Economic Evaluation of a Generalized Consumer Surplus:
The Mineral King Controversy," unpublished paper,
Natural Environments Program, Resources for the Future,
1975.
5. J.B. Ellis, "A System Model for Recreational Travel in Ontario:
A Progress Report," Ontario Joint Highway Research Program,
Report No. RR126, Ontario, Canada: Department of Highways,
July 1967.
6. J.B. Ellis & C.S. Van Doren, "A Comparative Evaluation of
Gravity and System Theory Models for Statewide Recreation
Travel Flow," Journal of Regional Science Vol. VI, No. 2
(1966).
7. D. McFadden, "Conditional Logit Analysis of Qualitative Choice
Behavior," in P. Zarembka (ed.) Frontiers in Econometrics,
Academic Press, 1974.
8. R.W. Parks & A.P. Barten, "A Cross-Country Comparison of the
Effects of Prices, Income & Population Composition on
Consumption Patterns," Economic Journal (September 1973).
9. Stone, The Measurement of Consumer's Expenditure and Behavior
in the UK, 1820-1938, Vol. 1, Cambridge University Press,
1953.
43
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10. M. Tadros & R.J. Kalter, "A Spatial Allocation Model for
Projected Outdoor Recreation Demand: A Case Study of
the Central New York Region," College of Agricultural
Experiment Station, "Search" Series No. 1, Department
of Agricultural Economics, January 1971.
11. M. Tadros & R.J. Kalter, "Spacial Allocation Model for
Projected Water Based Recreation Demand," Water Resources
Research Vol. 7, No. 4 (August 1971): 798-811.
12. H. Theil, "A Multinomial Extension of the Linear Logit Model,"
International Economic Review (October 1969).
13. R.D. Willig, "Welfare Analysis of Policies Affecting Prices
and Products," Memorandum #153, Center for Research
in Economic Growth, Stamford University, 1973.
44
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IV. SITE AND HOUSEHOLD SAMPLE, SURVEY AND CHARACTERISTICS
Chapters II and III outlined our methodological approach for
estimating the recreation benefits of water quality enhancement.
This chapter describes the data used to implement these methodologies.
The data needed for these approaches includes:
(1) a network of recreation sites which are potential
substitutes;
(2) data on the characteristics of the sites; and
(3) data on the number of visits by a representative
individual to each of the sites.
A number of recreation studies were reviewed to obtain the
requisite information from secondary material. These sources
included:
o National Park Service
o Forest Service
o Bureau of Outdoor Recreation
o Corps of Engineers
o Bureau of Sports Fisheries and Wildlife
o Massachusetts Department of Natural Resources
o Boston Metropolitan District Commission
o Boston Redevelopment Authority
o Metropolitan Area Planning Council (Boston's Area
A-95 agency)
None possessed the three requirements outlined above, so a data
collection effort was mounted. This included:
o establishing a network of water-based recreation
sites available for a one-day trip from the Boston
SMS A;
45
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o assembling water quality, cost and beach
characteristics data on these sites; and
o surveying a representative sample of Boston
SMSA households.
This chapter describes, in five parts, the data collection
effort. First, a system of sites is presented. Then the site
characteristics and v?ater quality variables and data are discussed.
This section includes a factor analysis designed to reduce the water
quality variables to an analytically more manageable number. Next,
the rationale and design of the household survey is presented.
Finally, to set the stage for the empirical results contained in
Chapters VI and VII, this chapter concludes with a discussion of
alternate measures of attendance.
1. The Network of Sites
Delimitation of the geographic extent of the study is the initial
step in defining a system of recreation sites for analysis. Ideally,
all possible sites available for one-day trips from the Boston inner
city would be included. Due to the lack of data on the recreational
habits of Bostonians, a surrogate to visitation—distance—was
arbitrarily employed to delimit the one-day trip region. This
region is roughly bounded by the New Hampshire border to the north,
the Cape Cod Canal to the sourth, Massachusetts Bay and the Atlantic
Ocean to the east, and Lake Cochituate to the west. It is enclosed
by a major circumferential highway, 1-495, and lies within 40 miles
of the Massachusetts State House.
Once the geographic extent of our study was defined it was
necessary to inventory the recreation sites available in that
area. One of the problems inherent in deriving an exhaustive water
recreation survey from the Boston Metropolitan Area is the
46
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multiplicity of sites. Besides the ocean frontage, Boston is
the locus of several rivers and their watersheds, and many natural
lakes and ponds. Our first attempt at a water site inventory
began with several good maps of the metropolitan area. It became
apparent that the number of small/ unmarked sites was large, and
that we should direct our efforts elsewhere.
The Department of Natural Resources of the State of Massachusetts
had conducted a state-wide open space survey in 1970* from which we
culled the water-recreation sites for the towns within the study
area. This inventory was supplemented by lists of the State of
Massachusetts Metropolitan District Commission (MDC) beaches, be&ches
from the Trustees of Reservations, state parks and forests, and
streams and ponds stocked by the Massachusetts Division of Fisheries
and Game. This inventory included over 200 swimming sites, nearly
200 fishing sites, and about 70 boating sites for the metropolitan
region. Table IV-1 presents the breakdown between types of
sites.
1
Table IV-1
Analysis of Available Recreation Sites
Area
Inside Route 128
Remainder of Study
Area
TOTAL
Number
Towns
38
77
115
of:
Sites
143
201
344
Number of
Swimming s
111
91
202
Sites 6ffering:
Fishing Boating
28
43
71
*Massachusetts Department of Natural Resources [is].
47
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Such a large inventory presents several major problems for our
methodology, however. The difficulty of analysis increases more
than geometrically with the number of substitutable sites. In addi-
tion, the survey would be unwieldly with so many locations. Many of
the sites are small, and used only by a very local constituent popula-
tion; further, it is difficult to collect data on facilities, character-
ists, and water quality from such a large number of sites. Because
of these difficulties, the focus of our site inventory turned to
a sample of sites in the study area which could account for a large
proportion of the area's recreation. However, the site-specific
visitation data required to delimit numerically the major sites is
sparse. One source* was used for this purpose, and a set of
eighteen major sites was developed. Our experience, however,
suggested a number of important sites were not represented. The
initial list was supplemented by major sites from the Massachusetts
Department of Natural Resources open space inventory. This com-
posite list was presented for review to a number of individuals
and agencies familiar with and knowledgeable about recreation in
Eastern Massachusetts. Reviewing agencies included:
Metropolitan District Commission
Metropolitan Area Planning Council
Massachusetts Department of Natural Resources
In addition, a private recreation planner with extensive experience
in Eastern Massachusetts reviewed our list.
During the course of the survey, this list of 31 sites was
supplemented by asking respondents what other sites they visited.
Another 14 sites or generic places (i.e., Cape Cod Beaches, New
Hampshire Lakes, etc.) were identified. The network of sites and
the study area are depicted in Figure IV-1. These site numbers are
used throughout the report to identify the sites.
*Metropolitan Area Planning Council [l5].
48
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Figure IV-1: Network of Sites
SJ
r
List of Sit3=J
1.
2.
3.
4.
S.
6.
7.
a.
9.
10.
11.
12.
13.
14.
IS.
16.
17.
18.
13.
20.
21
Kings Beach
Lynn Beach
Nahant Beach
Revere Beach
Shore Beach
Winthrop Beach
Constitution Beach
Cactle Island
Pleasure Bay
City Fault
L S M Street Beaches
Carson Beach
Mallbu Beach
Tenean Beach
Wollar,-.=-i Bnach
Sartasnet Beach
Wtngaersheeit Beach
Crane's Beach
Plum Island
Duxbury Beach
white Horse Beach
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
33.
39.
40.
41.
42.
Breakheart Reservation
Sandy Beach
Hough ton's Pond
Wright's Pond
Walden Pond
Stearns Pond
Cochxtuate State Park
Hopkinton State ParX
Esplanade/Storrow Lagoon
Charles Riv»r, between
Weeks & Anderson Bridges
New Hampshire Beaches, Lakes S Parks
Good Harbor
Gloucester Beaches in General
Dane Street Dei:h
West Beach
Hlngham Beach
Other North Shore Beaches
Other South Shore Beaches
Cape Cod Beaches
Lynch Park
Other Massachusetts Lakes 6 Ponds
SCALE IN MILES
O 5 1O 15 .20
• - recreation site
= - interstate highway
— - major US or ".ass.
highways
— - town boundary
49
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The sites in this set are, with one exception (Crane's Beach,
operated by the Trustees of Reservations and open to the public), pub-
lic facilities. It is well-known by recreation management that the
public provision of recreation facilities is subsidized, depresses the
private market for recreation. For our analysis this is important only
because the fees customarily paid are likely to be much lower than
the marginal social benefits of the facility, and estimates of
willingness-to-pay may, therefore, be biased downward. According to
one study [13] of the 229,423 acres of recreation lands in Eastern
Massachusetts, 46,551 acres, or 20.3%, are private. Private sites
number 779 or 14.7% of the 5,318 sites in the region. Private
ownership includes both profit and non-profit operations:
o private clubs
o Massachusetts Audubon Society
o Trustees of Reservations;
o Boy and Girl Scouts;
o YMCA and YWCA; and
o commercial recreation lands.
While there is significant incidence of private recreation in
the area, not all of these operations are entirely supported from
fees. Hence our estimates of willingness-to-pay may be understated.
2. Site Characteristic Variables
Site characteristics can be broadly divided into economic,
beach quality related, and water quality related. Each of these
groups are discussed separately below.
The site characteristics used in this study were culled out of
the literature on recreation participation and demand. In particular,
50
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Myles [is], Aukerman [2], David [5], Holman S Bennet [lO], and
Gamble & Meglie [9], contributed to this effort. Throughout we
have distinguished objective characteristics and perceived
characteristics. Objective characteristics are those, like water
temperature, which can be measured using known, accurate and
reliable techniques. Perceived characteristics reflect how people
believe the beach to be. The perception includes an assessment—
possibly erroneous—of the objective characteristics, and a reaction
to that assessment. No doubt, demand is more closely related to the
perceived characteristics than the ones only a scientist can measure.
And, in fact, the first step in our analysis tests whether or not
perceived and objective characteristics mesh. Unless the two
measures—objective and subjective—are collinear, inferences from
the relationships between demand and obj'ective water quality
measures may be misleading.
The contrast between perceived and objective water quality has
other interesting ramifications. Recall Clawson and Knetch's
five phases of the recreation experience. Anticipation of a recrea-
tion experience sets the expectations for the site characteristics
and activity content. Once on site, the perception of the site is
matched against the anticipation, and this contrast forms the
basis for recollection. In turn, that recollection, in large part,
determines future anticipation of a similar experience and hence
repeat demand. Equilibrium levels of demand should represent a
reasonable matching of expectation and perception. Therefore, to the
extent that only equilibrium demand is measured, inferences from
objective measures to preferences will be valid.
51
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Furthermore, any demand analysis can only address "iso-
anticipation" activities. In other words, exogenous considerations-
leisure time, family income, time of year, etc.—determine tradeoffs
between day trips, weekend trips, and vacation trips, but within
the anticipation classes, endogenous site characteristics, including
travel cost and price, prevail. Secondly, demand surveys must be
conducted in equilibrium conditions. Ideally, then, only users
with prior knowledge of the site should be surveyed, perhaps only
repeat users. Similarly, sites where relative changes in water
quality have occurred should be omitted from the analysis. A brief
investigation indicated that none of the sites in the sample had
undergone notable changes in water quality during the last few
years.
2.1 Economic Variables
These variables describe the costs incurred by the recreation-
ist prior to the on-site phase of the activity. They include the
costs of travel and entrance. Four variables were identified:
o Entrance/parking fee
o Travel time
o Travel cost
o Distance.
The first three of these were determined from the survey.
Entrance Fee; When your party goes to a beach you
might have some expenses just to get
onto the beach, such as parking or
entrance fees. For each site, about
how much are these expenses?
*Throughout the report, the particular question being analyzed
is repeated in the main text to aid the reader. A copy of the
complete survey instrument is contained in Appendix III.
52
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Travel Time
and Cost; A. For each site you mentioned in Question 2
(A & B) above, how did you or your group
get there?
a. walking d. bus
b. bicycle e. subway/streetcar
c. automobile £. taxi
b. other
B. About how long does it take to get there
that way? (in minutes)
C. How much does it cost to get there?
If by bus or subway or taxi, how much is
the roundtrip fare? If by auto, what was
the price of tolls? (the total cost for
the visiting group)
Distance; Distance was calculated as a straightline Euclidean
distance between the respondent's location and the site. This
was computed by plotting all the sample points and all the sites on a
large scale map. A quarter inch grid was overlaid and the coordinates
recorded. The distance from respondent i to site j was computed
from the formula:
where: (x,y). = Cartesian coordinates
of respondent i
(x,y). = Cartesian coordinates
3 of site j
and then scaled to miles.
Actual road milages are the best measure of distance, but
because of the large number of respondent-site combinations in
relation to the project budget, those computations were not possible.
An alternative is to scale straightline distances according to
the size of the road grid. It is easy to show that on a uniform
53
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grid the average distance equals about 20% more than the straight-
line distances. One could hypothesize a larger grid size as the
distance from the center city increases, and scale the distance
variable accordingly. Instead we chose to use, in the model
specifications, the straightline distance squared as a surrogate
for this phenomenon.
Table IV-2 presents the summary statistics for these
variables.
Table IV-2
Economic Variables
Variable
Entrance/Parking Fee ($)
Travel Time (Minutes)
Travel Cost ($)
Distance* (miles)
Mean Std.Dev.
1.04 3.77
32.87 22.25
.65 1.10
17.77 9.12
Skewness Kurtosis
6.040
1.447
2.441
.557
35.83
1.993
4.897
-1.293
*This distance is the average distance from the sample
points to the sites. It is not the distance traveled
averaged over all individuals.
2.2 Beach Characteristic Variables
Four dimensions of beach quality were defined:
o setting;
o facilities;
o quality; and
o crowding.
Data on these characteristics were collected two ways. First, the sites
54
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known at the time of the survey were catalogued using the form
contained in Appendix I. To reduce bias introduced by the personal
perception of the researcher who visited the site, only two
people were assigned this job. They inventoried together several
beaches to insure comparable interpretations. Second, respondents
were asked to rate the beach they attended most often according
to beach quality, beach facilities and crowding. Quality and
setting were lumped together because it was thought the two
would not be distinguished by respondents.
Setting;
Setting was determined from the questionnaire in the following
categories, in descending order toward less natural settings:
A. Surrounding Land Use
1. Natural
2. Agricultural
3. Low Density Residential (1 & 2 family homes)
4. High Density Residential (includes multi-family
buildings)
5. Commercial
6. Industrial
Table IV-3 shows the distribution of these settings across sites.
Setting
Natural
Agricultural
Low-Density
High-Density
Commercial
Industrial
Not Surveyed
Table IV-3
Site Setting
# of sites
12
0
Residential 13
Residential 1
3
3
12
Percent
27.3
0
29.5
2.6
6.8
6.8
27.3
55
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Facilities;
Facilities—bathhouses, picnic tables, etc.—related to all
water-oriented activities were inventoried. Initially we suspected
sites could be distinguished according to activities available,
but the facilities provided proved to be remarkably homogeneous across
sites, so the objective measures of facilities were omitted from
further analysis.
Of special interest to this study is our finding that facilities
seem to be rather important to recreationists. Of 467 respondents,
24.5% mentioned the presence of either changing rooms or lifeguards
as the most important determinant of characteristics toward their
choice of site. Hence, if water quality is enhanced, additional
capital and operating investments will be needed to obtain the
potential recreational benefits. This point is further amplified
by response to littering, pointed out below. Chapter V analyzes
the results in greater detail.
Quality;
Objective measures of beach quality are difficult to define.
Three were attempted. The first related to the physical descrip-
tion of the beach—composition, slope, nature of water bottom,
amount of water movement. The second included measures of
annoyance—presence of litter, natural debris, and flies. The
third was an indirect measure of quality—the frequency of
maintenance.
Data collection difficulties rendered these three measures
inadequate for analytic purposes. The necessarily subjective
judgements concerning beach topography were found to be inconsistent.
The inventory was made on different days of the week, so the
56
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judgements concerning littering (and crowding) were not consistent
cross-sectionally. Data on maintenance frequency was difficult
to obtain and largely incomplete. Because of these difficulties,
the analysis relies on perceived rather than objective quality
ratings.
When questioned about the most important characteristic in
choosing a site, the absence of litter was ranked first by 31.1% of
all respondents. This factor appears to be the single most important
factor in determining site preferences. The implications of this
finding are twofold. First, maintenance must be provided at any
new beaches opened due to water quality improvements. Second,
from the narrow standpoint of public recreation policy, money
might be more efficiently spent on maintenance of existing beaches
rather than improving water quality at any beach.
Crowding:
Crowding is a subjective assessment of the size and temporal
and spatial distribution of attendance in relationship to the
area of the site. Two approaches were tried to measure objectively
this variable. First, during the inventory, crowding at the sites was
rated by the project staff. Second, we sought secondary data on
attendance, particularly peak day attendance, to estimate crowding.
Total average and peak attendance data were consistently unavailable
for the sites. By and large, the agencies responsible for these
sites neither collected data nor kept records on attendance or crowding.
Because no systematic information on crowding was available, we were
forced to rely on the respondent's crowding ratings. Because crowding
is inherently a perceived characteristic, this may offer better
statistical fits, but it begs the question of "explaining" perception.
57
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2.3 Water Quality Variables*
Three main properties of water affect its suitability for
recreational use: hygenic factors, aesthetic factors and features
which indirectly influence nuisances. (The basic references for
this discussion are National Academy of Sciences [l7], and
Environmental Protection Agency [8].) Table IV-4 summarizes
the variables considered in this study and Table IV-5 presents
the data for the sites. Note that two parameters, Biological
Oxygen Demand (BOD) and Suspended Solids, which are commonly
considered in water quality analyses, were omitted from this
study. BOD was not determined because of the theoretical and
practical invalidity of cross-sectional comparisons between eco-
systems. Suspended Solids, commonly thought to be related in a
non-linear fashion to fish productivity, were partly accounted in
our turbidity measures. Note further, that observations are avail-
able for only 29 sites. These are the sites selected prior to the
household survey. Constructing a comparable data series for the
sites developed in the survey would not have been possible.
This section continues to describe the parameters selected
and explains the rationale for their includion. Appendix II
details the procedures used to measure the selected parameters.
*We are indebted to Dr. J.C. Morris, Gordon McKay Professor
of Sanitary Chemist-ry, Harvard University, for assisting in
identifying those water quality characteristics pertinent for
study. Further assistance in delimiting these parameters was
provided by Dr. Eraser Walsh and Dr. Alfred Ajami of Eco Control,
Inc., in Cambridge, Massachusetts. Under a subcontract to USR&E,
water quality samples were taken under the direction of Eco Control
and analyzed by that organization.
58
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Variable
Oil or grease
Turbidity
Color
Odor*
pH
Alkalinity
Total Phosphorus
Nitrate
Ammonia
Chemical Oxygen
Demand
Temperature
Fecal Coliform
Bacteria
Total Bacteria
Table IV-4
Water Quality Variables
Acronym
OIL
JTU
COLOR
PH
ALK
TPOS
NITR
AMMO
COD
TEMP
COLI
TBAC
Effect on
Water Quality**^
Jackson Turbidity
Units
APHA Platinum Cobalt
Standard
Threshold Odor Number
pH
m9/l as calcium
carbonate
mg/1
mg/1
mg/1
Degrees F
#/100 ml
#/100 ml
*Odor was dropped from the analysis because all sites
with the exception of Hopkinton State Park (#29)
had no detectable odor.
**"+" means higher values are associated with better
water quality, "-" means the opposite.
59
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Table IV- 5
Hater Quality Data
Site
No.
01
02
03
04
C5
u6
07
03
09
10
11
ll-
lS
14
15
16
17
ie
19
20
21
22
- 1
24
25
26
27
28
29
Mean
Std.IX.
Skevness
Kurtosis
Oil.
06.0
04.6
09.0
05.8
08.8
07.2
08.0
18.0
16.8
33.0
08.1
06.8
12.2
9.4
7.2
19.4
5.6
4.4
10.8
4.2
3.2
4.4
3.6
1.4
1.8
1.0
10.2
1.4
22.6
8.8
3.7
1.4
1.4
JTO
4
,2
4
1
0
2
3
6
4
8
10
6
3
16
14
4
0
0
0
6
5
0
6
4
4
2
14
14
23
6
6
I
1
COLOR
5
5
4
3
5
5
8
10
8
21
20
15
S
16
15
8
3
3
2
3
5
5
16
13
5
5
18
21
18
9
6
1
-1
ODOR
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
.
-
_
-
_
_
-
-
-
_
-
-
1
-
-
-
-
P«
8.0
8.0
8.1
8.0
7.9
7.9
7.9
8.0
8.1
7.9
7.9
8.0
7.9
7.9
7.9
8.1
8.0
8.0
8.1
8.0
7.9
6.1
7.7
6.8
7.4
7.2
7.0
7.7
6.7
7.7
.5
-1.9
2.7
ALK
112
111
111
101
103
123
103
112
106
106
108
110
106
105
106
116
108
108
110
109
114
3
43
8
26
10
10
26
10
84
43
- 1
- 1
TPOS
.03
.04
.04
.05
.06
.04
.09
.06
.06
.15
.09
.10
.06
.08
.17
.04
.04
.02
.02
.06
.04
.04
.•23
.09
.09
.02
.06
.05
.29
.08
.06
2.05
3.88
NITR
-
-
-
-
-
-
.02
-
.01
.17
.08
.01
.01
.04
.01
-
-
-
-
-
-
.12
2.20
.02
-
-
.02
-
.17
.10
.41
4.99
23.28
AMMO
.6
.3
.6
.6
.3
.2
.2
.3
.4
.3
.2
.3
.3
.4
.4
,2
.2
.2
.1
-
.2
.5
3.4
.6
1.0
.5
.8
.4
.6
.5
.6
4.1
17.3
COD
87
29
57
32
41
46
34
36
34
35
81
62
50
43
35
-
26
31
56
44
44
7
25
13
26
8
9
-
8
34
22
0
0
COLI
100
250
1500
100
7500
100
100
100
100
500
250
2000
250
9000
17500
2000
100
100
100
100
100
4000
2000
250
100
250
4500
500
5000
201:,
3790
3
8
TBAC
250
7500
7500
2500
20000
750
1000
100
1500
15 JO
2 SCO
2CCT:
2000
25300
40000
7500
100
ino
100
17500
1750
35000
45000
3000
125on
4000
1 3000
eooo
22500
10350
12764
1
1
TEKP
65.0
64. Q
65.0
66. C
66.0
66.0
66.0
67.0
66.0
70.0
69.0
68.0
68.0
67.0
65.0
64.0
68.0
62.0
60.0
65.0
65.0
69.0
68.0
69.0
71.0
70.0
72.0
70.0
72.0
67.0
2.8
- .2
- .1
-------
Hygenic Factors^
Factors such as pathogen populations, concentrations of
toxic substances, clarity, and other similar properties are
included. They are most important for direct contact recreation,
such as swimming, water-skiing and similar activities, but relate
also to secondary contact recreation like fishing, boating and
shellfishing. An important characteristic of many factors in
this category is that they do not change the perceived desirability
of the water and thus do not change utilization unless legal
limits are prescribed.
Fecal coliform population counts and total bacteria counts
were measured at each site. The possible presence of water-borne
pathogenic organisms is deduced usually from the count of fecal
coliform organisms, which are indicators of the fecal discharges
of man or other mammals. This group of 'organisms normally does not
multiply in the environment and tends to die out within about
a month after discharge from the human or animal body.
Currently, proposed EPA maximum limits on fecal coliforms
are 2000 per 100 ml average and a maximum of 4000 per 100 ml
for waters judged suitable for general recreational use and about
one-tenth this for waters designated for bathing or other contact
recreation. Table IV-5 reveals that readings higher than these
standards were found at several sites.
The presence of fecal coliforms or pathogenic bacteria or
viruses does not produce any change in the appearance of the water
and so tends not to alter acceptability by users unless legal
action occurs or s'trong publicity is given to the potentially
harmful condition of the water.
61
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Standard sewage treatment will reduce fecal coliform counts
8
in sewage by one or two orders of magnitude from about 10 per
100 ml. Chlorination of treated sewage will usually reduce
the counts to less than recreational water maxima.
Because of lack of suitable monitoring methods and other
important information, no viral limits are prescribed even though
these agents may survive chlorination levels that will kill fecal
coliforms. Shellfish will concentrate viruses from water and so
waters to be used for the recreational taking of shellfish are more
strictly controlled than other recreational waters.
Aesthetic Factors
These affect primarily the perceived desirability of the water
by the recreational user. They are sensory properties, including
color, turbidity, oil and grease content, odor and temperature.
On occasion properties in this category may also occur in category
(1) or (3). For a number of these properties the degradation in
quality can be related to the intensity of the property as with
color and odor, but this is not true for temperature, for
example. Most of these qualities are relevant, in one way or
another to both water-based and water-enhanced recreation.
The general appearance of a body of water is a strong factor
in its acceptance for recreational uses. Besides properties of
color, turbidity and floating plant growths, to be considered
individually, the term includes the presence of settleable or of
floating solids or oil matter. When these are from waste dis-
charges, they are not only visually objectionable but have other
adverse effects as well, such as coating the hulls of boats or
the bodies of swimmers.
62
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Settleable matter is obnoxious or deleterious because:
(1) if organic, it forms putrescible deposits that
produce hydrogen sulfide and other noxious
odorous substances during decomposition;
(2) if inorganic, it forms silt banks and tends to
destroy breeding areas for benthal aquatic
fauna, essential to fish life, and also egg-
hatching areas for many species of fish.
The clarity or transparency of water is directly related
to its use for bathing purposes. Drowning and other water
hazards increase greatly when bathers cannot be seen underwater.
The usual standard is a four-foot "Secchi-disk" transparency, but
turbidity is also commonly measured in "Jackson Turbidity Units."
Color affects clarity to some degree, but most impairment
of clarity is due to cloudiness or turbidity. Turbidity is
characteristic of certain waste discharges, such as those carry-
ing suspended clays or fibres, but may also be produced in the
water by excessive growth of algae. This last factor is by far
the most common one and is the primary basis for concern
about discharges qf phosphorus and nitrogen compounds.
High turbidity has also been found to have an adverse effect
on fish populations, but at low levels, increased turbidity
seems to increase fish yields. Attractiveness of water and
its turbidity seem nearly inversely related: so this may be one of
the best properties with which to relate water quality and recreational
use.
Industrial discharges of phenolic compounds, amines, or other
odorous substances may produce directly objectionable odor situa-
tions in bodies of water. Secondly, obnoxious odors may arise from
the anaerobic decomposition of organic sludge or benthal deposits.
Finally, algal or other heavy plant growths may produce odors as
part of their natural growth or during their bacterial decomposition
after death.
63
-------
Such odors may provide offensive conditions not only for those
in the water or close to it, such as bathers and boaters, but also
to picnickers, hikers and others attempting to use the water only
as an attractive amenity.
Improvements in water quality on the basis of odor elimina-
tion may be expected to occur in three stages: (1) immediately,
with the elimination of odorous waste chemicals; (2) with some delay
with the reduction in algal growths; and (3) with considerable
delay for the odors emanating from sludge deposits unless the body
of water itself is treated. Many organic substances similar to
those causing odors in water may also lead to tainting of fish flesh
with corresponding restrictions on this sort of recreational use.
Increase in temperature affects water quality for recreational
use in a number of ways: (1) it stimulates growth of algae and
other aquatic plants, thus accentuating the conditions produced by
such growth; (2) it may change the relative predominance of algal
or plant species to less attractive forms; (3) it has adverse effects
on fish populations; and (4) it may cause physiological disturbances
in swimmers. The last factor is the basis of the EPA standard that
recreational waters should not have temperatures exceeding 85 F
(30°C).
The acid or basic reaction of water, pH, is directly related
to recreational use for bathing, for waters with pH far from
neutral may lead to eye irritation. In addition, pH values far
from neutrality will give situations adverse to aquatic life.
Accordingly, water generally suitable for recreational use should have
pH 5.0 to 9.0, while acceptable bathing water should have pH 6.5 to
8.3, and deviations from neutrality (7) are a useful linear measure
of this effect.
64
-------
Indirect Nuisance Factors
There are two major subcategories of properties that indirectly
bring about nuisance or an undesirable environment: algal
nutrients that stimulate undesirable aquatic growths and substances
that directly or indirectly have adverse effects on aquatic life,
including fish. In this last subcategory are toxicants, oxygen-
consuming substances, temperature, silt-forming materials and
substances that cause tainting of fish flesh. Some of these were
described under Aesthetic Factors above. As with aesthetic properties,
the adverse effects here may discourage both water-based and water-
enhanced activities.
Excessive growth of algae, particularly in lakes, ponds, pools
and estuaries is a principal factor which impairs recreational
use of water. Often it is also a principal manifestation of the
intrusion of wastewater or polluting substances.
Algae require many elements and growth factors to achieve
maximum growth rates and maximum total production. Among them
are two forms of substance relatively scarce in most pristine
waters, but abundant in domestic sewage and other wastewaters.
These are combined nitrogen (ammonium ion, organic nitrogenous
material, nitrite or nitrate) and phosphate. When degradation in
water quality is the result of increased supply of these substances,
treatment for their removal may bring about sharp improvement in
water quality. Usually, it is phosphate that is the limiting material
in inland waters; in estuaries and the open ocean, combined nitrogen
tends to be more critical. The dry mass of algal material is 3 to
8%N and 0.2 to 0.8%P. The total amount of algal material that can be
produced at any one time is thus dependent on the amounts of combined
nitrogen and phosphate that are available.
65
-------
No specific acceptability limits have been set for these nutrient
substances, but acceptable limits of phosphorus for a situation where
it is a limiting constituent for nuisance growth are 0.025 mg per liter
of Phosphorus within lakes and reservoirs, 0.05 mg per liter at
inlets to lakes and reservoirs, and 0.10 mg per liter in flowing streams.
There is no way to deal adequately in a brief presentation
with the large numbers of substances, both inorganic and organic
and including radioactive materials, that may find their way on
occasion into natural waters and that may be inimical to recreation
uses because of toxicity either to man or to some forms of aquatic
life. Usually such substances are not directly detected by the user
and so tend to inhibit recreational possibilities by proscription
rather than by lessened seeming attractiveness. Occasions when any
of these types of substances are determining factors in recreation
use are rare enough except for catastrophic events—accidental spills
or deliberate illegal dumpings—that they generally need not be
considered individually in a first-order consideration of relation
of water quality to recreational use.
2.4 Factor Analysis of Water Quality Variables
The potential for reducing the number of water quality
variables was explored using a cross-sectional factor analysis.
(A good reference to the general technique is in Rummel [20].)
In addition to reducing the magnitude of the subsequent analytic
tasks, this analysis promised a composite index of water quality.
Prior to initiating the analysis, we hypothesized certain
relationships among the variables. First, the nutrient variables—
66
-------
total phosphate (TPOS), organic nitrogen (NITR), and ammonia (AMMO)—
would be highly intercorrelated. Similarly the two bacterial
variables—coliforms (COLI) and total bacteria (TBAC) would be
correlated, and the two measures of acidity/alkalinity—squared
deviations of pH from 7(pH) and alkalinity. Turbidity (JTU) and
color (COLOR) were hypothesized to correlate as well.
Beyond these obvious relationships further speculation was
difficult for reasons outlined in Section IV.2.3, above.
Temperature (TEMP) was expected to correlate with bacteria counts,
turbidity, and possibly the nutrient measures. Chemical oxygen
demand could correlate with oil and grease (OIL), the bacteria
measures and the nutrient measures.
The 29x12 data matrix transformed to standardized variables
was factored using the SPSS (Statistical Package for the Social Sciences)
Version 5.2 classical factor analysis routine. Four factors had
eigenvalues greater than one (Table IV-6) and the factoring was stopped.
The conventional varimax rotation performed.
Factor
1
2
3
4
Table IV-6
Eigenvalues of Inferred
Eigenvalue
4.59685
1.84255
1.80303
1.03523
Factors
Percent of Variance
49.5
19.9
19.4
11.2
At this point let us note a criticism commonly levelled on factor
analysis. The eigenvalues are a weighted combination of all water
quality variables even though only a few are emphasized in each factor.
In terms of standardized variates, the factor analysis accurately trades
off the influence of different water quality measures. But management
67
-------
alternatives may not impact the different water quality measures in a
standardized way, i.e., proportional to mean level, inversely propor-
tional to the standard deviation. Thus, in a prescriptive analysis,
some added computation would be required to use these factors as surro-
gates for direct water quality measures. However, since we do not
simulate the response of recreationists to specified changes in water
quality and certain sites, this difficulty does not arise.
The rotated factor matrix is shown in Table IV-7. It depicts
both the composition of each variable as a linear function of the
factors, and, since the factors are orthoganal, it shows the correlation
matrix of factors and variables as well. This matrix tells us
the composition of factors.
Factor 1 loads heavily on PH and ALK, as hypothesized. COD
also has a substantial correlation, equal to .56, and TEMP has
a large positive correlation (.74). This factor distinguishes fresh
and salt water sites by its high loading on alkalinity.
Factor 2 accounts for the nutrient variable, loading heavily
on NITR, AMMO, and TPOS. It also has a substantial correlation
with TBAC. This could be expected because the source of these
nutrients is principally domestic wastes, and because they are bene-
ficial to bacterial growth as well. This agrument also suggests
that a higher correlation with COLI would be expected.
The third factor represents the clarity measures—JTU and
COLOR. OIL also loads heavily, possibly as a surrogate or
suspended organic materials. TPOS and TEMP are both positively
correlated, which might represent the influence of algal growth
on turbidity and color.
Factor 4 is almost exclusively a bacteria factor, with loadings
of .90 and .79 on COLI and TBAC, respectively.
Table IV-8 shows the factor score coefficients which represent
the transformation between the standardized values of the variables
to the factor scores for a particular observation (site). In other
words, the cross product of the columns of this table with a row
of the standardized data matrix yields the factor score for that site.
These factor scores are presented in Table IV-9.
68
-------
OIL
JTU
COLOR
pH
ALK
TPOS
NITR
AMMO
COD
COLI
TBAC
TEMP
Table
Varimax Rotated
Factor 1
.19945
-.30753
-.31014
.89853
.97166
-.20549
-.04033
-.24947
.56333
-.00870
-.17298
.74402
IV- 7
Factor Matrix
Factor 2
-.09860
-.01743
.15834
-.12446
-.17796
.45742
.99361
.91755
-.04997
-.04961
.49110
.09180
Factor 3
.59208
.75006
.76775
-.14773
.03848
.64521
.07668
-.01047
-.00028
.21102
.06150
.41616
Factor 4
-.07898
. 36329
.17260
-.04908
-.08687
. 31424
.06023
. 08932
-.09096
.90023
.79158
-.04271
69
-------
I
OIL
JTU
COLOR
pH
ALK
TPOS
NITR
AMMO
COD
COLI
TBAC
TEMP
Table IV-8
Factor Score Coefficients
Factor 1
-.10537
.02241
-.02258
.27239
.95039
.11528
.11068
. 00819
-.16040
-.01242
.02510
.01702
Factor 2
-.01658
.11661
-.26698
.14010
-.10043
-.08479
1.38445
-.20316
. 06872
.15560
-.21013
.21583
Factor 3
-.05551
.36451
.24888
.32193
. 28964
.49527
..26472
-.24286
-.12032
.13901
-.49892
.42160
Factor 4
.08788
-.00152
. 06400
-.27116
.14454
-.11428
-.52784
.18315
.01611
.28402
.89755
-.31918
70
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Table iv-9
Factor Scores by Site
Site Number
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
Factor 1
. 330650
.770742
.671290
.536167
. 344646
.733737
.455647
.584022
.636439
.299133
.240946
.609568
. 310409
.450082
.707299
1.023437
.718979
.626749
.537515
.703423
.614024
-1.515222
-.016647
-1.965580
-1.517143
-1.985935
-2.057007
-1.197863
-1.649507
Factor 2
-.037110
-.357569
-.090507
-.150214
-.206782
-.119188
-.221862
-.180872
-.146644
-.021942
-.033968
-.473277
.053247
-.210344
-.506396-
-.395671
.134167
-.275875
-.213165
-.158402
-.125579
.127071
5.157724
-.463486
-.309996
-.066204
-.309797
-.417920
.020561
Factor 3
-.602331
-.632318
-.476255
-.424191
-.846099
-.233960
.273409
.574992
. 291845
2.052254
1.401489
.465519
.032738
.769322
.793623
-.018591
.066118
-1.001652
-1.289540
-.513387
-.247239
-1.747724
.066998
-.400823
-.834642
-1.220096
.265104
.933337
2.503201
Factor 4
-.492970
-.032098
-.048942
-.583751
1.301178
-.549294
-.686301
-.715547
-.696832
-.898088
-..811897
.553688
-.687993
1.717302
3.468664
.121545
-1.063389
-.363595
-.229208
.397690
-.448357
1.289062
.263602
-.556174
-.057191
-.556484
I
.432863
-.599095
.531601
71
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2.5 Subjective Measures of Site Characteristics
The objective measures presented above were supplemented by
perceived site characteristics from the household survey.
Respondents were asked:
For each site you visited would you please rate each
of the following characteristics on a scale from 1-5.
For this rating, 1 means bad, 2 means moderately bad,
3 is fair, 4 is moderately good, and 5 is good.
A. Water temperature
B. Water quality (clarity, color, weeds, odor, etc.)
C. Beach facilities (availability)
D. Beach quality (setting, maintenance)
E. Crowding.
Summary statistics of these ratings, by site and in total, are
shown in Table IV-10.
, . — _ — — .—._.,— ,._—.,
Table IV-10
Subjective Variables: Summary Statistics
Variable
Water Temperature Rating
Water Quality Rating
Beach Facilities Rating
Beach Quality Rating
Crowding Rating
Mean
2.656
2.881
2.703
3.207
2.838
Std.Dev.
.660
.929
.710
.832
.799
Skewness
-.652
.250
-.370
.592
-.427
Kurt os is
.607
-.611
.112
.835
.797
72
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3. The Household Survey^
As explained above, an extensive review of secondary informa-
tion sources revealed none was adequate to estimate the demand
and benefit models desired. The paucity of data indicated a survey
was required to assemble the information necessary for the
desired analyses. Several methods are available for obtaining
that sort of information. First, structured interviews with recrea-
tionists could be held at a sample of sites in the network.
This technique has been used in several previous studies of recreation
demand;* it has the advantage of being very convenient to organize
and relatively cheap. However, for our purposes, it is conceptually
unsound. We wish to focus on the recreational preferences of a
given population faced with a network of competing sites. We need
to know how often a representative member of that population attends
each of the different sites; we also need to know the preferences
of those persons who do not visit any site. Thus, for our purpose,
the relevant sample population is the population to which the
network of sites is available, not the population of users of
specific sites and alternatives.
Four types of population-oriented surveys are possible:
personal, telephone, mail and diary. The telephone survey would
have been used if the survey instrument had been brief (less than
five minutes for the interview). The problem of telephone owner-
ship bias is not important in a major metropolitan area. Mail
surveys offer a low cost method for obtaining responses to a longer
questionnaire, but significant problems of self-selection exist.
Telephone or personal follow-up could reduce, or at least quantify
the selection bias, but such follow-up proved to be not cost-
effective. The Bureau of Outdoor Recreation surveys are now done
*For example, Herbert H. Stoevener [21], S.D. Roiling,
K.C. Gibbs, and H.S. Stoevener [19] .
73
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by mail, and for most water-related recreation activities they report
comparable participation rates between mailed and personal interviews.
Although there have been several recreation mail surveys with
response rates well in excess of 50%, these surveys have generally
been directed to special interest populations such as licensed
fishermen and wilderness users. The general experience with mail
surveys directed to the public at large is much less encouraging;
with no follow-up the response rate is commonly in the range of
10%-15% and even with one or several follow-ups the response rate is
often less than 35%.
Finally, the diary method could provide more accurate responses,
more careful selection of respondents but may be difficult to
administer. Many consumer surveys are presently performed via
the diary method, and this approach should be examined further.
After evaluating the cost, reliability, timing and
response bias of the alternative technique, personal in-home
interviews were selected as the best medium to collect the needed
data. The details of the sample design are presented in the
first subsection below. Then the sample population is described
in relationship to the universe population. This section closes
with a discussion of the survey instrument.
3.1 Sample Design*
The objectives of the sample design were to produce a sample
of the Boston SMSA population which approximated the socioeconomic
characteristics and geographic dispersion of the SMSA's entire
population to meet simultaneously both objectives, a cluster point
procedure was adopted.
*The survey design, sampling, and fieldwork were completed
by Cambridge Survey Research, Inc. of Cambridge, Massachusetts,
under a subcontract to USR&E. We are particularly indebted to Mr.
John Gorman of that organization for his assistance in refining
the survey instrument and sample design.
74
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Households were the target respondents, and any available
adult member of the household was asked to respond. A probability
sample of about 500 interviews was determined which would produce
an approximation of the non-institutional population between the
ages of 14 and 65 of the Boston area SMSA. This would constitute
an overall sampling fraction of 500/661650 or about 7.6 households
per thousand. This is about the same sampling frequency as that
of the Harvard-MIT Joint Center for Urban Studies in a 1970 survey
of outdoor recreation and leisure activity in the Boston SMSA which
was conducted for the Massachusetts Department of Natural Resources.
Towns were picked as primary sampling units. Each town falling
in the SMSA was proportioned for a specific number of interviews
according to its population between the ages of 14 and 65. Some of these
towns were proportionately too small to warrant a sufficient number of
interviews to be sampled. A certain number of towns which were most
representative on demographic variables of all the towns were chosen
to be sampled. Twenty-three towns from the total 77 towns comprising the
SMSA were sampled. Table IV-11 shows the distribution of sample points
and respondents between towns, and Figure IV-2 shows a map of the sample
points and sites.
Each town was then systematically sampled. Towns were sub-
divided down to the Census block level. A sampling fraction was
computed for each town, and blocks were chosen at specific intervals
by the sampling fraction with a random start. Thus, within each town,
we had specific census tracts picked and specific blocks within that
census tract to be interviewed. Each block area was assigned a
•cluster of five interviews.
75
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Table IV-11
Distribution of Sample Points Between Towns
Town
Lynn 16
Saugus 11
Danvers 12
Beverly 2 3
Cambridge 18
Newton 17
Somerville 16
Wilmington 15
Framingham 25
Arlington 21
Natick 13
Norwood 13
Lexington 13
Maiden 16
Medford 20
Melrose 18
Hingham 21
Boston 116
Revere 17
Quincy 16
Brookline 25
Weymouth 23
Braintree 15
76
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Figure IV-2: Sample Points and Sites
SCALE IN MILES _
k o '~'>5 ~To 7s Jo
• - recreation site
— - interstate highway
— - major US or Mass.
highway
town boundaries
77
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This survey was administered in the respondents' homes during
December 1974 by supervised professional interviewers, specially
trained for this survey. We had planned to conduct the survey during
the first week in September (immediately after Labor Day which is
commonly considered the end of the summer recreation period), but a
three-month delay in obtaining OMB clearance which was completely
beyond our control forced postponing the survey until the first week
in December. The effect of this delay on the survey results is unknown,
but previous studies have found that respondents' recollections of the
recreation experience becomes more favorable as time passes. Subjective
quality ratings may, therefore, overstate true perceptions, possibly
accounting for the poor correlation between objective and perceived
quality found in the next chapter. No doubt, the accuracy of numeric
information, such as number of visits, expenditures, etc., suffered from
the deterioration of recall during the long hiatus.
Interviewers began at a randomly chosen starting point. A
skip pattern of housing units was also determined in order to
distribute the five clustered interviews evenly over the sample point.
Interviewers were instructed to keep a one-tor-one male/female ratio.
The person most qualified to speak regarding family activities was
designated as the proper respondent.
Where no one at the household selected was available for
interview, random replacement was used to find a substitute.
To 'find a substitute, the following pattern was employed until a
respondent was found. First, the housing unit on the right is
tried, then the one to the left, then the one across to the left,
then across to the right and finally, the housing unit directly
across is tried. Within the various cluster points substitutes
are not of concern because within the cluster, respondents and
non-respondents are statistically indistinguishable.
78
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Finished interviews were returned as they were completed,
and were checked and edited for accuracy. About 10 percent of
each interviewer's work was selected randomly and was validated
for authenticity.
3.2 The Sample Population
Selected socioeconomic characteristics of the sample of
respondents and the Boston SMSA population are presented in
Table IV-12. Median income of the two groups is nearly identical;
average income is within the error of projections in the poisson
distribution. The sample contains slightly more men than the
population as a whole, and in general, is better educated. The
racial composition of the sample is somewhat anomalous ,
because 20.8% of the respondents listed their race as "other
unspecified." This may have been a reaction to the question which
was designed to discriminate between-Irish and Italian Caucasion
as well as between Blacks from all Caucasians:
How would you describe your ethnic background?
a. American Indian
b. Asian-American
c. Black
d. Irish
e. Italian
f. Spanish Surname
g. Other Caucasian
h. Other (please specify)
The "Other" category is likely to include people of diverse
backgrounds (Russian, German, Jewish, Armenian, etc.) who would
normally describe themselves as "White."
79
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Table IV- 12
Comparison of the Boston SMSA Population
Number of Households
Family Income (?)
Median
Mean
Sex (%) of Respondent^
Male
Female
Education of Respondent
not completed high school
completed high school
some college
completed college
post-graduate
Race (%)
White
Black
Other
Sample
467
11,445
13,214
46.9
53.1
20.3
32.5
22.6
14.7
9.9
68.9
4.8
26.6
and the Sample
Boston SMSA
(1970)
661,650
11,449
13,284
45.5
54.5
35.6
36.8
4.9
8.1
7.6
94.5
4.6
.9
80
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3.3 The Survey Instrument
The survey instrument contained in Appendix III is designed
to elicit information on the sensitivity of demanci for water-
based recreation to changes in water quality. Three types of
behavior in response to altered water quality are explicitly
examined: substitutions between sites, substitutions between
activities (including non-water-based outdoor recreation), and
loss of benefit when no substitution occurs. This section
describes the general development of this instrument and then
concludes by discussion in detail the intent of each question or
group of questions.
The survey instrument was developed after a careful analysis
of the data required and review of previous similar recreation
surveys.*
*The survey instruments reviewed include those found in:
Boston Area Study; 1970 [ll].
Water Quality Criteria for Selected Recreational Uses; Site
Comparison L^J.
The Recreational Uses of Green Bay; A. Study in Human Behavior
and Attitude Patterns
Benefits of Water Pollution Control on Property Values [7],
Stream Quality Preservation Through Planned Urban Development [4],
A Case Study of Yaguina Bay, Oregon [21 J.
Economic Benefits from an Improvement in Water Quality [l9J.
Benefits of Water Quality Enhancement [is].
Transactions of American Fisheries Society [lj .
The Demand for Motorboat Use in Large Reservoirs in Arizona [l2].
An Economic Evaluation of the Oregon Salmon and Steelhead
Sport Fisheries
Metropolitan Washington Council of Governments Water Quality
Survey 1^22].
81
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Where specific questions have been adapted, the appropriate
references are presented in the more detailed discussion which
follows below. Based on these needs and the literature review,
an initial survey instrument was drafted. This draft was reviewed
internally by the project staff. Once suitable form and content
had been reconciled internally, experts in recreation planning
and survey research, not directly involved in the project, were
asked to review the instrument.* Based on this review, the
instrument was pretested and then finalized. The entire interview
required about one-half hour to administer.
The survey instrument is divided into three sections.
Part 1 generates the multi-site visitation data required to
estimate the demand model described elsewhere. Part II attempts
to measure directly the behavioral response to altered water
quality. In Part III, socioeconomic information on the respondent
and his household is developed to provide a backdrop for the required
analyses.
Part I, "Participation in Water-Based Recreation" generates
the information required to estimate statistically the benefits
from water pollution abatement. Question 2 elicits information
on the visitation by both the respondent himself and his household
to a system of sites in the Boston Study Area. Questions 3-6 obtain
the details of each visit including mode, cost and time of travel,
on-site expenditures and activities while on-site. Distance to
the site was, as explained above, calculated from a grid imposed
on the study area map. This data, along with the data on fixed
costs of recreation and socioeconomic identified in Part III
comprises the basis for statistically estimating the benefits of
water quality enhancement.
*We thank William Geizentanner, Janet Marantz, John Gorman
and Sherwin Feinhandler for their assistance in this review.
82
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Question 7 of Part I leads to the measurement of perceived
water quality and its relationship to recreation usage. This
question assesses the reasons for not visiting the closest site.
Utility is maximized with respect to distance at this point, so
the tradeoffs between other characteristics (beach facilities,
water quality, crowding, cost, etc.) can be more distinctly drawn.
Part II requests perceptions concerning site characteristics,
and response to changes in those characteristics. First a rating
is established in Question 1. This rating is used in con-
junction with objective measures of water quality to ascertain the
parameters which most directly affect perceived water and beach
quality. Question 2 defines the decision set of sites, and
obtains a ranking for those sites as well. Question 4 uses this
ranking to determine directly response to altered water quality,
beach characteristics, and so on.
The most frequently visited site is the focus of our probing.
Presumably the respondent is most familiar with this site, and in
some sense its mix of attributes optimizes his utility. First, the
predominant reason for visiting that site is determined. Then the
responses to declines (based on the ranking established in the pre-
vious question) in the quality of site characteristics and site
closing are elicited. This series of questions attempts to deter-
mine directly the site and activity substitutions which our demand
model infers. These questions provide both a check on the model
and also determine more detailed information on interactivity
substitutions.
More general questions on quality perceptions are asked in
Questions 5 and 6.* First, the importance of water quality with
respect to other site characteristics is established (Question 5).
Then, focusing on water quality, the relative importance of five
general parameters of water quality is established.
*These Questions are derived in part from Aucker;nan [2]
and Dornbusch [?].
83
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Part II closes with an assessment of the importance and
substitutability of various activities. Question 7 relates to water-
based activities, and provides the basis for turning the per-
ceptions of water quality into recreation water quality priorities.
Question 8 treats non-water-based activities to establish the basis
for activitiy substitution assessed in Question 4. Then Question 9
directly assesses the potential for substitution of water-based
and non-water-based activities. Part II concludes with a more
general open-ended question on the recreation provided in the system
of sites.
Part III, Identification, provides the respondent's
socioeconomic background for use in the demand modeling effort
and for analyzing the perceptions obtained in Part II. The age
ranges in Question 2 were chosen to reflect categories which
could affect recreational habits. Previous studies have found
income, occupation and education to influence recreational behavior,
and these data are solicited in Questions 4-8. The fixed costs
of recreation are determined in Question 9.* Recreation economists
have posited that the common omission of these fixed costs in
benefit research has artifically depressed estimates of the social
value of recreation.
Finally, Questions 10-13 relate to other exogenous determinants
of recreation participation. Question 10 asks for weekly and annual
leisure time. Questions 11 and 12 determine the potential from
travel to the recreation sites by automobile and public transit,
respectively. Lastly, previous research on recreation in the Boston
area suggests that ethnicity is an important determinant of site
choice. Question 13 elicits the information to test this hypothesis,
and control for its effect in our statistical analysis.
*This question is adapted from Reiling, Gibbs, and Stoevener [l9].
84
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4. Measures of Attendance
Our demand models use as a dependent response variable
measure of attendance at each site. Chapter II outlined some
of the characteristics of an adequate measure of demand, and
pointed out that our focus on one-day trips eliminated some of
the vaguaries of measuring activity duration. Initially,
five measures of visitation were considered:
(1) MNT: the number of times a site was mentioned
and for an individual, the binary variable
on whether or not a site was mentioned (number);
(2) PVS: the number of visits made to a site by the
respondent (person-visits);
(3) HVS: the number of visits to a site by anyone in
the respondent's household (person-visits);
(4) GVS: the number of household visits multiplied by
the average group size (person-visits); and
(5) VSDR: the number of household visits multiplied by
the average duration (person-hours).
All of these variables were derived in the obvious manner
from four questions:
The card shows some of the major fresh and salt
water beaches in the Boston Area. Could you
please tell me: (hand respondent site list)
A. Which sites did you personally visit, and
how many times did you visit each of those
sites. Are there any sites, town beaches, ponds
or other fresh or wait water areas, which you
visited that are not on this list? (Record
those sites and the number of visits to each.
Add visits and ask:)
So you personally visited a beach, lake or
stream about times this past summer?
B. Now I would like to find out about visits by
anyone in this household to fresh and salt
water beaches in the Boston Area. Could you
please tell me the number of visits by any
household member to each of these sites. Are
85
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c.
D.
there any sites, town beaches, ponds or other fresh
or salt water areas, which you visited that are
not on the list? (Record those sites and the
number of visits to each. Add visits and ask:)
So members of this household visited a beach,
lake or stream about times this past
summer.
About how long, on average, was spent at each
of the sites you listed in the two questions
above?
For each site about how many people from your
household, on average, made the trip?
The correlations between these variables is shown in Table IV-13.
The measures have similar distributions across sites, and display
a high degree of intercorrelation.
Table IV-13
Correlation Between Attendance Measures Across Sites*
MNT
PVS
HVS
GVS
PVS HVS GVS VSDR
.8100 .8350 .7823 .8692
.9605 .8413
.8836
.8916 .9608
.8454
*A11 coefficients are based on 43 observations,
and all are significant at the 5% level.
86
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CITED REFERENCES
1. American Fisheries Society, Transactions of American Fisheries
Society, Vol. 102, No. 2, April 1973.
2. R. Auckerman, "Water Quality Criteria for Selected Recreational
Uses - Site Comparisons," Thesis, University of Illinois,
1973.
3. W.G. Brown, E.N. Castle, & A. Singh, An Economic Evaluation
of the Oregon Salmon and Steelhead Sport Fisheries,
Corvallis: Oregon Agricultural Experiment Station,
1964.
4. R.E. Coughlin & T.P. Hammer, Stream Quality Preservation
Through Planned Urban Development, Socioeconomic
Environmental Studies Series, Environmental Protection
Agency, Office of Research & Monitoring, Washington, D.C.:
GPO, May 1973.
5. -Elizabeth David, "Public Perceptions of Water Quality," Water
Resources Research (June 1971).
6. Robert Ditton & Robert Goodale, Marine Recreational Uses of
Green Bay; A Study of Human Behavior and Attitude Patterns,
Technical Report No. 17, University of Wisconsin: Sea Grant
Program, December 1972.
7. D.M. Dornbusch & S.M. Barrager, Benefit of Water Pollution on
Property Values, prepared for the U.S. Environmental
Protection Agency, San Francisco, California: David M.
Dornbusch & Company, Inc., August 1, 1973.
8. Environmental Protection Agency, Water Quality Criteria Data
Book, Washington, D.C.: May 1971.
9. Hayes B. Gamble & Leland D. Megli, "The Relationship Between
Stream Water Quality and Regional Income Generated by
Water-Oriented Recreationists," Journal of Northeastern
Agricultural Economics, Vol. 1, No. 1 (Summer 1972).
10. Mary A. Holman & James T. Bennett, "Determinants of Use of
Water-Based Recreational Facilities," Water Resources
Research Vol. 9, No, 5 (October 1973): 1208-1218.
11. Joint Center for Urban Studies of the MIT-Harvard University
Survey Research Program, Boston Area Study: 1970
(Feb.-April, 1970).
87
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12. W.B. Kurtz, "The Demand for Motorboat Use of Large Reservoirs
in Arizona," Ph.D. dissertation, University of Arizona
1972.
13. Massachusetts Department of Natural Resources, Planning Office,
1970 Outdoor Recreation and Open Space Survey, October 1971.
14. L.D. Megli, W.H. Long, H.B. Gamble, An Analysis of the Relation-
ship Between Stream Water Quality and the Regional Income
Generated by Water-Oriented Recreationists. University
Park, Pa.: The Pennsylvania State University, Institute of
Research on Land and Water Resources, 1971.
15. Metropolitan Area Planning Council, Open Space and Recreation
Plan and Program for Metropolitan Boston, April 1969.
16. George A. Myles, Effects of Quality Factors on Water-Based
Recreation in Western Nevada, University of Nevada, Reno:
Agricultural Experiment Station, 1970.
17. National Academy of Sciences, Water Quality Criteria, Washington,
D.C.: Committee on Water Quality Criteria, 1972.
18. Nelson L. Nemerow & Hisashi Sumitomo, "Benefits of Water Quality
Enhancement (Onondago Lake)." Water Pollution Control
Research Series 16110 DAJ 12/70, Washington, D.C.: EPA,
Water Quality Office.
19. S.D. Reiling, K.C. Gibbs, H.H. Stoevener, Economic Benefits
from an Improvement in Water Quality, Socioeconomic
Environmental Studies Series, Environmental Protection
Agency, Washington, D.C.: GPO, January 1973.
20. R.J. Rummell, Applied Factor Analysis, Evanston: Northwestern
University Press, 1970.
21. Herbert Stoevener, et al, Multi-Disciplinary Study of Water
Quality Relationships; A Case Study of Yaguina Bay,
Oregon, Special Report 348, Corvallis: Oregon State
University, February 1972.
22. Westat, Inc., Metropolitan Washington Council of Governments
Water QuaIitj/_Su_rv_ey.' October 1973.
88
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V. DIRECT EMPIRICAL FINDINGS ON SITE CHOICE AND WATER
QUALITY PERCEPTION
In this chapter two types of analysis are used to detect the
response of recreationists to water quality. First respondents
were asked to rank water quality along with other determinants of
site choice. In general, this approach finds that proximity and
beach characteristics (facilities, cleanliness and setting) are
much more important than water quality in determining site choice.
If water quality improvements open sites close to major population
centers, then benefits may be generated.
Second, the relationship between objective measures of water
quality and the subjective water quality rating is probed in
Section V.2. Logic suggests that strong correlation between objective
and subjective measures is a necessary but not sufficient condition
for demand to show any response to changes in water quality. Despite
a rigorous analysis, of the data, we find weak, if any, association
between the objective and subjective measures. While the engineer
or public health scientist may measure improvements or declines in
water quality, the public will not, it seems, perceive those
changes.
1. Direct Questioning
Respondents were questioned directly concerning importance
of various factors, including water quality to their recreational
behavior. Four questions were posed:
89
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1.1 The Favorite Site
Let's talk about the beach, lake, or river
site you visited most. That was ,
site number (Hand Respondent Card D)
A. Why do you visit this site most often?
(Code most important reasons)
a. it is close
b. it is cheap
c. the water temperature is nice
d. the water quality is good
e. my family always came here
f. not too crowded
g. nice setting
h. beach is clean
i. nice facilities
j. my friends go there
k. other
This of all the questions is probably the best indicator
of behavior because the respondent considers and explains specific
rather than generic behavior. Responses to thi's question are
shown in Table v-1. Proximity is clearly the most important
factor (47.5%). That friends go there, what we describe as a
cultural factor, is the second most important reason (12.3%).
Factors related to the beach quality (lack of litter—10.3%,
and setting—11.7%) are the third and fourth most frequently
mentioned responses, but are much less important than proximity.
Water quality only gains 3.9% of the responses.
Response was tested against income, family size, education,
occupation, race, amount of recreational equipment, and the
amount of leisure time, automobile ownership, use of public
transit and vacation time. Only income and family size affected the
response distribution at a 5% level of significance. For all
family sizes, proximity is the most important reason cited. The
presence of friends is more important to larger families than
90
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Table V-l
Reason for Choosing Favorite Site
Response Number Percentage
a. it is close 170 47.5
b. it is cheap 2 .6
c. the water temperature
is nice 11 3.1
d. the water quality is
good 14 3.9
e. my family always
came here 17 4.7
f. not too crowded 13 3.6
g. nice setting 42 11.7
h. beach is clean 37 10.3
i. nice facilities 8 2.2
j. my friends go there 44 12.3
91
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smaller ones. Similarly, larger families respond to water quality
more readily than do smaller ones. These results are shown in
Table V-2.
Table V-3 shows the income cross tabulation. Again proximity
is always the most important reason, but declines in importance
with higher incomes. Conversely, the importance of beach cleanliness
increases moderately with higher incomes. The cell counts for
water quality are too small to discern with any confidence the
income trend, however.
92
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CO
Table V-2
Cross Tabulation of Reason for visiting
Favorite Site and Family Size
REASON: Fanily Size '* of a****>rs>
12 34 5 67 8 9 10
a. it is close
b. it is cheap
c. the water tempera-
ture is nice
d. trie water quality
is good
e. my family always
cane here
f. not toe crowded
g. nice setting
h. beach is clean
i. nice facilities
j. my friends go there
(5)
3.0
35.7
(0)
0
0
(0)
0
0
(0)
0
0
(2)
11.8
14.3
(1)
7.7
7.1
(2)
4.8
14.3
. (2)
5.4
14.3
(0)
0
0
(2)
4.S
14.3
(27)
16.0
42.4
(1)
50.0
1.6
(1)
9.1
1.6
(3)
21.4
4.7
(0)
0
0
(2)
15.4
3.1
.(8)
19.0
12.5
(13)
35.1
20.0
(0)
0
0
(9)
20.5
14.1
(22)
13.0
43.1
(0)
0
0
(0)
0
0
(1)
7.1
2.0
(2)
11.8
3.9
(0)
0
0
(9)
21.4
17.6
(8)
21.6
15.7
(2)
25.0
3.9
<7)
IS. 9
13.7
(52)
30.8
58.4
(0)
0
0
(4)
36.4
4.5
(3)
21.4
3.4
(3)
17.6
3.4
(1)
7.7
1.1
(12)
28.6
13.5
(6)
16.2
6.7
(2)
25.0
2.2
(6)
13.6
6.7
(26)
15.4
43.4
(0)
0
0
(1)
9.1
1.7
(5)
35.7
8.3
(5)
29.4
8.3
(2)
15.4
3.3
(2)
4.8
3.3
(6)
16.2
10.0
(4)
50.0
6.7
(9)
20.5
15.0
(16)
9.5
43.2
(1)
50.0
2.7
(2)
18.2
5.4
(0)
0
0
(1)
5.9
2.7
(5)
38.5
13.5
(5)
11.9
13.5
(2)
5.4
5.4
(0)
0
0
(5)
11.4
13.5
(8)
4.7
50.0
(0)
0
0
(1)
9.1
6.3
(2)
14.3
12.5
(2)
11.8
12.5
(0)
0
0
(2)
4.8
12.5
(0)
0
0
(0)
0
0
(1)
2.3
6.3
(8)
4.7
57.1
(0)
0
0
(0)
0
0
(0)
0
0
(0)
0
0
(0)
0
0
<2)
4.8
14.3
(0)
0
0
(0)
0
0
(4)
9.1
28.6
(2)
1.2
50.0
(0)
0
0
(1)
9.1
25. Q
(0)
0
0
(1)
5.9
25.0
(0)
0
0
(0)
0
L 0
(0)
0
0
(0)
0
0
(0)
0
0
(3)
1.8
37.8
(0)
0
0
(1)
9.1
12. 5
(0)
0
0
(1)
5.9
12.5
(2)
15.4
25.0
(0)
0
0
(0)
0
0
(0)
0
0
(1)
2.3
12.5
•Significant at 5% level, cells show number in ( ), row
percentage and colunn percentages.
-------
Table V-3
Cross Tabulation of Reasons*
For Choosing Favorite Site and Income
Income Class
REASON: _ ,456
a. it is close
b. it is cheap
c. tht water tenpev
ature is nice
d. the water quality
is good
e. my family always
f. not too crowded
1 '
g. nice setting
h. beach is clean
i. nice facilities
j. ray friends 90 there
(8)
8.9
10)
0
(1)
11.1
(2)
18.2
(1)
7.1
(0)
0
0
(4)
11.1
(2)
6.1
(3)
42.9
(3)
10.0
(15)
11.1
53 6
(0)
0
(0)
0
0
(1)
9.1
3 6
(0)
00
00
(2)
16.7
(0)
0
0
(2)
6.1
(0)
0
(8)
26.7
•>ft 7
(20)
14.8
c-> fl
(0)
0
o
(2)
22.2
4 3
(2)
18.2
4 3
(4)
28.6
8 7
(1)
8.3
(8)
22.2
17.4
(5)
15.2
10 9
(1)
14.3
2 2
(3)
10.0
6 5
(19)
14.1
5? a
(0)
0
0
(2)
22.2
5.6
(0)
0
0
(1)
7.1
2.8
(0)
0
, 0
(4)
11. 1
11.1
(8)
24.2
22.2
(0)
0
0
(2)
6.7
5.6
(16)
11.9
41.0.
(0)
0
0
(0)
0
0
(2)
18.2
5.1
(3)
21.4
7.7
(3)
25.0
7.7'
(4)-
11.1
10.3
<5>
15.2
12.8
(1)
14.3
2.6
(5)
16.7
12.8
(31)
23.0
56-4.
(0)
0
0
(2)
22.2
3.6
(4)
36.4
7.3
(1)
7.1
1.8
(1)
B.3
1.8
(7)
19.4
12.7
(5)
15.2
9.1
(1)
14.3
l~fi
(3)
10.0
-..- i'
7
(12)
8.9
44.4
(1)
50.0
3.7
(0)
0
0
(0)
0
0
(2)
14.3
7.4
(1)
8.3
3.7
(2)
5.6
7.4
(4)
12.1
14.8
(1)
14.3
3.7
<4>
13.3
14.8
8
(4)
3.0
28.6
(1)
50.0
7.1
(1)
11.1
7.1
(0)
0
0
(1)
7.1
7.1
(2)
16.7
14.3
(2)
5.6
14.3
(1)
3.0
7.1
(0)
0
0
(2)
6.7
14.3
9
(3)
2.2
42.9
(0)
0
0
(0)
0
0
(0)
0
0
(0)
0
0
(0)
0
0
OJ
8.3
42.9
(1)
3.0
14.3
(0)
0
0
(0)
0
0
10
(0)
0
0
(0)
0
c
(0)
0
0
(0)
0
0
(0)
0
0
(1)
8.3
100.0
(Oi
0
T>
(0)
0
0
(0)
0
0
(01
0
0
11
(}}
2.2
37.5
(ji
0
0
(1)
11.1
12.5
(0)
0
0
(1)
8.3
12.5
(1)
8.3
12.5
(2)
5.6
1C>. j
(Oi
0
10)
0
0
(«t
0
0
•Significant at 5% level, cells show number in ( ), row
percentages and column percentages.
-------
1.2 Characteristics Important for Site Choice
In choosing a site what are the three most
important characteristics?
a. presence of a bathhouse/changing room
b. absence of litter
c. presence of a lifeguard
d. presence of a marine/boat launching facility
e. stocked game fish/good fishing
f. a natural setting
g. water temperature
h. water appearance
i. presence of other beach facilities
j. cost (parking fees, entry fees)
k. proximity
1. where your friends go
m. where your family always went
n. other
We anticipated this question would yield less reliable results
than the first one since it is more vague and general. Table V-6
shows the response to this question. Here absence of litter is the
most important reason followed by the presence of beach facilities
(bathhouse, lifeguard) and a nice setting, water appearance,
rates, fifth, and proximity, sixth.
Several features of this response pattern are notable. The
most obvious is the relative lack of importance ascribed to proximity.
Two explanations suggest themselves. First, when considering the
generic question of motivation, respondents discount proximity,
although it is quite important to determine actual behavior. An
alternative hypothesis is that many more respondents understood
the meaning of "it is close" than knew the definition of "proximity."
The responses were tested against income, family size, race,
occupation, education, amount of recreational equipment, auto-
mobile ownership, amount of leisure time each week, vacation time
and use of public transit.
95
-------
Table V-4
Important Characteristics for Site Choice
Most
Characteristic
a.
b.
c.
d.
e.
f.
g-
h.
i.
j.
k.
I.
m.
n.
presence of a bathhouse/
changing rooms
absence of litter
presence of a lifeguard
presence of a marina/
boat launching facility
stocked game fish/
good fishing
a natural setting
water temperature
water appearance
presence of other
beach facilities
cost (parking fees,
entry fees)
proximity
where your friends go
where your family
always went
other
Important
# %
62
141
49
5
5
52
14
43
4
3
37
18
7
13
13.7
31.1
10.8
1.1
1.1
11.5
3.1
9.5
.9
.7
8.2
4.0
1.5
2.9
2nd
Most
Important
# %
28
109
48
12
5
• 37
38
71
16
31
17
16
5
11
6.3
24.5
10.8
2.7
1.1
8.3
8.6
16.0
3.6
7.0
3.8
3.6
1.1
2.5
3rd Most
Important
# %
33 7.6
48 11.0
37 8.5
6 1.4
10 2.3
42 9.6
26 5.9
74 16.9
I
16 3.7 i
43 9.8
44 10.1
25 5.7
14 3.2
19 4.3
96
-------
The null hypothesis of independent classification can be rejected
at the 5% level for education -a.nd occupation. The contingency tables
are presented in Tables V-5 and V-6, respectively. Higher levels
of education lead to a greater sensitivity to a natural setting. At
the same time, proximity becomes more important with increased
education. Because setting and proximity are inversely related,
this table suggests that respondents not understanding the definition
of "proximity" may explain, at least in part, the markedly differing
results from these two questions.
These results have two interesting implications, one method-
ological and one substantive. The first is that the wording of
the questionnaire is of great importance to subsequent findings.
Although our survey instrument was carefully developed, reviewed
and pretested, this anomaly persisted and seems to have made a
difference.
Secondly, facilities appear to be important to recreation demand.
Any recreation benefits from water quality improvements may not be
obtained unless further investments in beaches, changing facilities,
maintenance and lifeguards are made. Additional money, perhaps
raised through user fees, would be required to provide these facilities.
97
-------
Table V-'j
Tabulated by l.du'-at ion
Education
CHAKACTCRISTIC 1 2
a. presc'nce of a bath-
house/changing
b. absence of litter
c. presence of life-
guard
d. presence of a marina/
boat launching
facility
e. stocked game fish/
good fishing
f. a natural setting
g. water temperature
h. water appearance
i. presence of other
beach facilities
j. cost (parking fees.
entry fees)
k. proximity
1. where your friends
go
m. where your family
always went
n. other
(0)
0
0
(1)
.7
16.7
(2)
4.1
33.3
(0)
0
0
(0)
0
0
(1)
1.9
16.7
(0)
0
0
(1)
2.3
16.7
(1)
25.0
16.7
(0)
0
0
(0)
0
0
(0)
0
0
(0)
0
0
(0)
0
0
(1)
1.6
7.7
(5)
3.6
38.5
(2)
4.1
15.4
(0)
0
0
(0)
0
0
(1)
1.9
7.7
(0)
0
0
(0)
0
0
(0)
0
0
(0)
0
0
(2)
5.4
15.4
(1)
5.6
7.7
(1)
16.7
7.7
(0)
0
0
3456 7
(21)
34.4
17.9
(31)
22.3
26.5
(15)
30.6
12.8
(1)
20.0
.9
(3)
60.0
2.6
(7)
13.5
6.0
(7)
50.0
6.0
(11)
25.6
9.4
(1)
25.0
.9
(1)
33.3
.9
(7)
18.9
6.0
(8)
44.4
6.8
(1)
16.7
.9
(3)
23.1
2.6
(13)
21.3
15.9
(33)
23.7
40.2
(9)
18.4
11.0
(1)
20.0
1.2
(0)
0
0
(11)
21.2
13.4
(0)
0
0
(8)
18.6
9.8
(0)
0
0
(1J
33.3
1.2
(2)
5.4
2.4
(3)
16.7
3.7
(0)
0
0
(1)
7.7
1.2
(5)
8.2
17.9
(8)
5.8
28.6
(3)
6.1
10.7
(0)
0
0
(0)
0
0
(2)
3.8
7.1
(2)
14.3
7.1
(2)
4.7
7.1
(1)
2S.O
3.6
(0)
0
0
(3)
8.1
10.7
(0)
0
0
(2)
33.3
7.1
(0)
0
0
(17)
27.9
14.2
(36)
25.9
30.0
(9)
18.4
7.5
(3)
60.0
2.5
(1)
20.0
.8
(16)
30.8
13.3
(4)
28.6
3.3
(11)
25.6
9.2
(1)
25.0
.8
(0)
0
0
(11)
29.7
9.2
(6)
33.3
5.0
(1)
16.7
.8
(4)
30.8
3.3
(4)
6.6
4.8
(25)
18.0
30.1
(9)
18.4
10.8
(0)
0
0
(1)
20.0
1.2
(14)
26.9
16.9
(1)
7.1
1.2
(10)
23.3
12.0
(0)
0
0
(1)
33.3
1.2
(12)
32.4
14.5
(0)
0
0
(1)
16.7
1.2
(5)
38.5
6.0
Table shows cell count in ( ), row percentaqes and column percentages.
98
-------
to
Table Y-6.
Host Important site Characteristics Tabulated by Occupation
Occupation
Characteristic 1 2 3 4 5 6 7 8 9 10
a. presence of a bathhouse/changing
rooms
b. absence of litter
c. presence of lifeguard
d. presence of a narina/boat
launching facility
e. stocked game fish/good
fishing
f. a natural setting
g. water temperature
h. water appearance
i. presence of other
beach facilities
j. cost (parking fees, entry
fees)
k. proximity
1. where your friends go
«. where your fasdly always went
n. other
(15)
25.4
12.3
(37)
27.2
30.3
(15)
31.3
12.3
(0)
0
0
(1)
20.0
.8
(18)
34.6
14.8
(3)
23.1
2.S
(10)
23.3
8.2
(2)
50.0
1.6
(1)
33.3
.8
(13)
35.1
10 7
(2)
11.1
1.6
(1)
16.7
.8
(4)
30.8
3.3
(7)
11.9
9.5
(21)
15.4
28.4
(8) .
16.7
10.8
(2)
40.0
2.7
(1)
20.0
1.4
(7)
13.5
9.5
(2)
15.4
2.7
(13)
30.2
17.6
(0)
0
0
(0)
0
0
(7)
18.9
9 S
(3)
16.7
4 l
(0)
0
0
(3)
23.1
4.1
(2)
3.4 •
16.7
(5)
3.7
41.7
(1)
2.1
8.3
(0)
0
0
(0)
0
0
(0)
0
0
(0)
0
0
(0)
0
0
(2)
50.0
16.7
(0)
0
0
(0)
0
o
(1)
5.6
8 3
(0)
0
0
(1)
7.7
9.?
(13)
22.0
15.7
(27)
19.9
32.5
(10)
20.8
12.0
(0)
0
0
(2)
40.0
2.4
(9)
17.3
10.8
(4)
30.8
4.8
(4)
9.3
A R
(0)
0
0
(0)
0
O
(6)
16.2
7 2
(5)
27.8
fi O
(2)
33.3
2.4
(1)
7.7
1.2
(4)
6.8
7.8
(15)
11.0
29.4
(5)
10.4
9.8
(0)
0
0
(0)
0
0
(9)
17.3
1O.8
(4)
30.8
4.8
(6)
14.0
11. 8
(0)
0
0
(1)
33.3
2.0
(4)
10.8
7 a
(2)
11.1
3 9
(2)
33.3
3.9
(0)
0
0
(1)
1.7
4.3
(10)
7.4
43.5
(2)
4.2
8.7"
(0)
0
0
(1)
20.0
4.3
(3)
5.8
13.0
(0)
0
0
(2)
4.7
a. 7
(0)
0
0
(0)
0
O
(3)
8.1
13 O
(0)
0
o
(0)
0
0
(1)
7.7
4.3
(9)
15.3
34.6
(6)
4.4
23.1
(2>
4.2
7.7
(0)
0
0
(0)
0
O
(3)
5.8
11.5
(1)
7.7
3.8
(1)
2.3
3.8
(0)
0
0
(0)
0
o
(0)
o
n
(2)
11.1
7 7
(1)
16.7
s.a
(1)
7.7
3. a
d)
1.7
11.1
(4)
2.9
44.4
(0)
0
0
(0)
0
0
(0)
0
0
(1)
1.9
11.1
(0)
0
0
(3)
7.0
«.•»
(0)
0
o
(0)
0
o
(0)
0
o
(0)
0
o
(0)
0
0
(0)
0
o
(1)
1.7
16.7
(2)
1.5
33.3
(6)
10.2
16.7
19)
6.6
25.0
<2i (3>
4.2 1 6.3
33.3 8.3
(0)
0
0
(0)
0
0
(1)
1.9
16.7
(0)
0
0
(0)
0
Q
(0)
0
o
(0)
0
0
(0)
0
0
(0)
0
o
(0)
0
o
(0)
0
o
(3)
60.0
8.3
(0)
0
0
(1)
1.9
2.8
(0)
0
0
(4)
9.3
ill
(0)
0
n
(1)
33.1
2.8
(4)
10.8
11.1
(3)
16.7
ft 1
• (0)
0
0
(2)
15.4
5.6
Table shows call count in ( ), row percentages and colusn percentages.
-------
1.3 Not Visiting Closest Site
The third question asks the converse of the first one:
(If the respondent did not visit the closest site,
ask:) (Hand respondent Card B)
beach is the major recreation site closest
to your home, yet you did not mention having visited
it. Here are some reasons, which one best explains
why you did not visit that site?
a. not aware of that site
b. do not like the facilities
c. too crowded
d. beach too dirty
e. water too cold
f. water too dirty
g. don't own auto, not accessible by public transportation
h. too expensive
i. not interested in the activities available there
j. other (please specify)
Here we control for proximity to assess the rationale behind site
choice. The principal shortcoming of this question is that, since
the respondent does not visit the closest site, his knowledge of
it may be dated or secondhand.
Table V-7 shows the response distribution to this question.
It is remarkable, given the apparent importance of proximity to
attendance, that 60.2% of the respondents did not visit the closest
sites. Of course, the second most close site was, in many sample
clusters, quite close by. The importance of this finding is mitigated
somewhat by the widespread ignorance of the closest site (response a).
The ignorance hypothesis is further confirmed by the second most
important reason, "not interested in the activities available
there," because the beaches were offered quite homogenous activities:
swimming, boating, fishing, picnicking, bicycling, strolling and
informal sports were available at all, and only a few offer facilities
for tennis, basketball and other similar specialized sports.
TOO
-------
Table V-7
Distribution of Reasons for not
Reason
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
not aware of that site
do not like the facilities
too crowded
beach too dirty
water too cold
water too dirty
don't own auto/ not accessible
by public transportation
too expensive
not interested in the activities
available there
other
TOTAL
Visiting Closest
No.
69
14
31
24
0
32
2
'o
39
70
281
Site
Percent
24.6
5.0
11.0
8.5
0
11.4
.7
0
13.9
24.9
101
-------
Dirty water and crowding ranked third and fourth, respectively
as major deterents to attendance. The hypothesis that good water
quality does not encourage attendance, but bad water quality dis-
courages it suggests itself, but is not confirmed by the willingness-
f
to-pay analysis presented below. Judging from the low correlations
between water quality and water quality perceptions, "the water is
too dirty," may be another way of saying "I don't visit the site
because I am told it is not very nice." Hence a public agency might
'reduce attendance at a polluted site by identifying it as such. And,
the converse may also be true: water quality improvements may not in-
crease use unless there is adequate publicity that the beach is open
for swimming or that the water quality has been improved. This may be
particularly important for sites where water quality has been poor
for some time, such as the lower Charles River in Boston.
The obvious hypotheses concerning the effects of income, race,
education, occupation, automobile ownership, public transit usage,
vacation time, and leisure time on reasons for selecting a site
were tested via contingency tables and no effect was found to be
statistically significant at the 5% level. Once those who do visit
the closest site have been removed from the sample, it is easy to
see why those remaining do not differ along these socioeconomic lines,
but the income of those visiting the closest site is not statistically
different from the income of those who visit more distant sites.
1.4 Importance of 'Various Water Characteristics
The final direct question used to probe the relationship
between recreation behavior and water quality focused on the char-
acteristics people feel are important to good water quality:
Thinking of water quality, attractiveness of the
water for swimming depends on the color, odor,
clearness, amount of floating debris or scum, and
the amount of aquatic weeds. Which characteristic
102
-------
is the most important? 2nd most important? Please
rank these characteristics.
a. color
b. odor
c. clearness
d. floating debris
e. aquatic weeds.
Responses to this question are tabulated in Table V-8. Clarity
(the converse of turbidity) and the absence of floating debris appear
to be the most important parameters of water quality. These results
contrast with the observed ratings which show only color to be cor-
related with water quality perception (Section IV-4 above). In this
ranking color is next to last in importance. Several explanations
for this contrast are possible. The best is that this question, generic
rather than specific, is not a reliable indicator of perception. Another
is that because turbidity and color are intercorrelated (R -.72 for
our sample of sites) the two were confused in this question. In
other words, respondents did not understand the distinction between
color and turbidity. In hindsight it may have hindered the analysis
to include both.
The presence of aquatic weeds is of minor importance. This may
be due to the low incidences of eutrophication found in Boston's
cold weather climate.
103
-------
Table v-8
Importance of Various Water Quality Characteristics
Characteristic Most Important 2nd 3rd
4th Least Important
Characteristic #%#%#%#%#%
a. • color 39 8.4
b. odor 78 16.7
c. clearness 157 33.6
d. floating debris 157 33.6
e. aquatic weeds 15 3.2
73 15.6
142 30.4
78 16.7
115 24.6
38 8.1
78 16.7
130 27.8
75 16.1
80 17.1
76 16.3
145 31.0
64 13.7
82 17.6
56 12.0
88
110 23.6
26 5.6
54 11.6
28 6.0
217 46.5
-------
1- -> Conclusions
In sum, the responses to these questions do not seem to support
any hypothesis which relates recreation behavior to water quality.
They suggest proximity is the most important determinant of a site
choice. To the extent that improvements in water quality will open
up beaches proximal to large numbers of people, the water quality
improvement will lead to increased recreation benefits. This would
be the case in many urban places, and particularly Boston.
A secondary conclusion is that recreation behavior is not
overwhelmingly determined by socioeconomic variables. To a small
extent higher levels of SES may reduce the sensitivity to distance
and increase the propensity to visit the more distant, litter free
beaches in a natural setting. Larger family size suggests a greater
propensity to visit beaches where friends go.
Finally, the presence of facilities appears to be an important
factor in site choice. If so, improvements in water quality should
be accompanied by beach maintenance and capital investments to gain
recreation benefits.
105
-------
2. Public Perception of Water Quality
Do respondents agree on the quality of the water at individual
sites? Does the public perception of water quality match the
objective conditions? Which objective water qualith characteristics
affect most strongly the respondent's perception of site conditions?
These are the questions of this section.
The answers are the foundation for the demand models presented
in Chapter VI. In particular, a link between perceived and objective
water quality characteristics is a necessary but not sufficient
condition to establish recreation benefits from water quality
improvement.
2.1 Agreement Among Respondents
The first question presents the greatest analytical difficulties
gince there is at present no convenient methodology for assessing
the degree of nominal scale agreement among multiple raters. There
is a well-developed.methodology for the case of two raters involving
the kappa statistic but with more than two raters the only available
approach appears to be to compute the full set of (•?) pairwise agreement
statistics and to average them. This procedure can be applied when
there is a small number of raters but it is manifestly impractical with
several hundred raters.* Therefore, an informal analysis of the
rating distribution must suffice. The distributions of water quality
ratings for sites 1 to 29 are shown in Table V-9. With the exception
of sites 6, 22 and 23, the distributions seem to be reasonably tight.
Judging the degree of concensus by the percentage of total responses
"The problem of multiple raters is discussed in Fleiss [3] and
Light [&"]. Fleiss presents an application of the procedure described
in the text to a case with six observers. This problem is also
discussed briefly in Bishop e£ 4l [lJ-
106
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Table V-9
Distribution of Ratings of Water Quality for 28 Sites
Site
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
. 28
# of
Evaluations
24
44
98
119
10
13
14
27
7
9
11
12
13
5
41
124
57
86
45
28
18
34
23
18
24
46
8
20
% of Ratings in Category
1
12.5
15.9
9.2
37.0
20.0
23.1
42.9
25.9
14.3
22.2
18.2
16.7
30.8
20.0
34.1
4.8
0.0
3.5
6.7
3.6
0.0
26.5
26.1
50.0
8.3
4.3
37.5
20.0
2
29.2
34.1
17.3
29.4
20.0
15.4
28.6
44,4
28.6
33.3
18.2
33.3
38.5
20.0
29.3
12.1
3.5
3.5
13.3
3.6
5.6
14.7
34.8
16.7
16.7
17.4
12.5
15.0
3
29.2
31.8
33.7
22.7
30.0
15.4
7.1
18.5
42.9
33.3
54.5
41.7
23.1
40.0
26.8
28.2
12.3
11.6
26.7
21.4
16.7
23.5
21.7
22.2
29.2
23.9
12.5
30.0
4
16.7
15.9
27.6
8.4
20.0
38.5
14.3
3.7
14.3
0.0
9.1
8.3
7.7
20.0
9.8
30.6
40.4
45.3
35.6
21.4
38.9
14.7
0.0
5.6
33.3
34.8
25.0
20.0
5
12.5
2.3
12.2
2.5
10.0
7.7
7.1
7.4
0.0
11.1
0.0
0.0
0.0
0.0
0.0
24.2
43.9
36.0
17.8
50.0
38.9
20.6
17.4
5.6
12.5
19.6
12.5
15.0
NOTE: Rows sum to 100%, apart from rounding errors. The
modal rating in each row is underlined. Site 29 was
only rated by two respondents and is, therefore,
omitted. (l=bad, 3=fair, 5=good)
107
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accounted for by the modal response, the concensus is somewhat greater,
in general, for the sites with a higher modal water quality rating.
2.2 Accuracy of Perceptions
Given reasonably consistent ratings, the conceptually more
important question of the accuracy of respondent's perceptions of
water quality conditions can be considered. Before proceeding
with this issue, recall that the yardstick for measuring the accuracy
of public perceptions is the data obtained from our own water quality
survey. Every effort was made to make these samples as representative
as possible. With this caveat, consider Table V-10 which shows the
correlation between water quality rating and the 16 objective measures
of water quality. Negative correlations would be expected in all
cases. With the exception of color, none of the correlations are
statistically distinguishable from zero. The correlation between
perceived water quality and color is only, moderate, equalling -.377.
The low correlation might, of course, be due to the delay in implement-
ing the survey.
To obtain more detailed evidence on the accuracy of the
respondents' perceptions of water quality and, at the same time,
in order to examine the relative importance of different water quality
parameters in the formation of people's perceptions of water quality,
we regressed the water quality ratings for all sites on various
objective water quality variables. There are some statistical problems
with this procedure arising from the special nature of the dependent
variable. Firstly, the water quality rating (RWQUAL) is a discrete
variable; respondents were asked to rate sites on the integer scale
from 1 to 5. Because ordinary least squares regression does not
constrain the predicted value of the dependent variable to be an
integer, it is more difficult to assess the true degree of association
between the dependent and independent variables on the basis of the
filled regression equation. Secondly, it is possible to argue that
RWQUAL is not a cardinal but an ordinal variable: a person who rates
108
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Table V-10
Correlations Between Water Duality Rating and Water Quality
Variable
OIL
JTU
COLOR
PH
ALK
TPOS
NITR
AMMO
COD
COLI
TBAC
TEMP
FACTOR 1
FACTOR 2
FACTOR 3
FACTOR 4
Variables
Correlation
-.1100
-.0796
-.3777*
.1032
.0953
-.1553
-.1044
-.1752
-.0136
-.1340
-.0606
-.2550
.1211
-.0516
-.1986
-.0385
All figures are based on 29 observations (sites),
those with an asterisk are significant at the
5% level.
109
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a site at 4 certainly likes it more than a site which he rates at
2, but not necessarily twice as much more. Ordinary least squares
is not a desirable technique for handling this type of dependent
variable. Rather, it is preferable to use the maximum likelihood
estimation procedure which is described below.
We start, however, with some OLS regressions of RWQUAL on sel-
ected water quality variables and the composit water quality factors.
The results of these regressions are shown in Table V-ll. It is clear
that the water quality ratings are significantly affected by all the
water quality parameters, except OIL. The slope coefficients for
most variables have the signs which we would expect; the only exceptions
are the coefficients of squared pH deviations from a neutral value of 7,
and of temperature. The sign of the coefficient for temperature may be
an artifact of the sample since inner-harbor sites are both wanner and
more polluted than the more distant ones. The performance of the factor
scores as explanatory variables is somewhat disappointing: on the
whole, they do not perform any better than the water quality parameters
to which they are related. Factor 3, the clarity factor, performs best
as would be expected. The bacterial factor, Factor 4, also has an
adequate t-statistic% Among the most important parameters for explain-
ing water quality ratings are TURBIDITY, COLOR, PHOSPHORUS, AMMONIA,
and COLIFORM and TOTAL BACTERIA.* The explanatory power of the individual
equations is low, but this is partly to be expected because of the
discreteness of the dependent variable. We are thus led to the con-
clusion that, while there is a significant connection between objective
water quality conditions and the subjective water quality ratings, the
degree of association between them does not appear to be very great.
*The slope coefficients for TOTAL and COLIFORM BACTERIA appear
somewhat similar and, indeed, when RWQUAL is regressed on both vari-
ables, the hypothesis that they have the same slope coefficient
cannot be rejected.
no
-------
Table V-ll
Regression of Water Quality and Temperature Ratings on Water Quality
Parameters
(984 observations)
0.00254
(42.73) (0.36)
2
EWQUAL = 3.057 + 0.00254 OIL R =.000
RWQUAL = 3.256 - 0.0537 TURBIDITY R ='.024
(56.73) (4.88)
' 3.41 - 0.0529 <
(48.57) (6.11)
2.743 + 0.353
(22.08) (2.76)
RWQUAL = 3.41 - 0.0529 COLOR R2=.037
RWQUAL = 2.743 + 0.353 (PH-7)2 R2=.008
RWQUAL = 2.834 + 0.00263 ALKALINITY R2=.005
(24.44) (2.25)
2
RWQUAL = 3.499 - 7.6351 PHOSPHORUS R =.064
(53.2) (8.18)
2
RWQUAL = 3.096 - 0.3117 NITROGEN R =.006
(72.44) (2.45)
RWQUAL = 3.287 - 0.4665 AMMONIA R =.032
(59.17) (5.67)
2
RWQUAL = 3.244 - 0.00534 COD R =.007
(42.84) (2.64)
2
RWQUAL = 3.165 - 0.0000542 COLIFORM R =.022
BACTERIA
(64.19) (4.66)
RWQUAL = 3.215 - 0.0000164 TOTAL BACTERIA R =.021
(62.32) (4.53)
2
RWQUAL = 8.162 - 0.0773 TEMPERATURE R =.025
(7.95) (4.96)
RWQUAL = 3.037 + 0.0976 FACTOR 1 R =.004
(18.18) (2.02)
RWQUAL = 3.059 - 0.0794 FACTOR 2 R =.002
(71.82) (1.55)
RWQUAL = 2.964 - 0.2995 FACTOR 3 R =.024
(63.33) (4.89)
2
RWQUAL = 3.054 - 0.1681 FACTOR 4 R =.013
(72.18) (3.58)
2
RTEMP = 0.13 + 0.04082 TEMPERATURE R =.007
(0.12) (2.57
111
-------
A subsidiary issue, which can conveniently be analyzed in the
regression context, is the question of whether respondent's from
households which participated in boating or fishing might have a
different perception of water quality than other respondents. - This
could be tested by adding a dummy variable for participation in
these activities to the regression in Table V-ll but this would not
necessarily be the best procedure, since there is no presumption
that fishers or boaters rate sites higher or lower than the public
at large. Rather, the presumption is merely that they rate sites
differently from other people. To test this hypothesis, we
conducted separate regressions of RWQUAL on COLOR and COLI for
respondents from households which participated in boating and/or
fishing and for respondents from households which do not.* In
addition, we conducted a regression on the full posted sample.
The regression results are as follows:
FISHERS/BOATERS (551 Observations)
RWQUAL = 3.353 - 0.033 COLOR - 0.0000449 COLI R2=.037
(34.2) (2.54) (2.54) F = 10.65
SSR= 989.46
NON-FISHERS/BOATERS (429 Observations)
RWQUAL = 3.501 - 0.06203 COLOR - 0.00000381 COLI
(35.54) (4.45) (0.21) R =.06
F = 13.68
SSR= 636.98
FULL SAMPLE POOLED (980 Observations)
RWQUAL = 3.415 - 0.0448 COLOR - 0.0000277 COLI R =.043
(48.91) (4.70) (2.16) F = 22.16
SSR= 1632.09
*These explanatory variables were chosen as being among the most
important in the single variable regressions. Another variable which
we attempted to include is PHOSPHORUS, but it turned out that this
variable is highly collinear with COLOR and COLI, and, therefore,
it was dropped from the regression.
112
-------
Applying the standard Chow test for the equality of interceptor and
slope coefficients, we find that the hypothesis of homogeneity between
fishers/boaters and others cannot be rejected.
2.3 Ordinal Rankings Considered
A maximum likelihood estimation technique can explicitly allow
for the fact that the dependent variable may provide only an
ordinal raking of sites. The logic of the model is as follows. It
is assumed that.the respondent's true sentiment towards recreation
sites, W, is a function of certain variables, X, and a random
disturbance (representing, perhaps, random differences in tastes).
W± = Xt3 + V±. ... (1)
The variable, W, is a continuous, cardinal measure of preference.
However we do not observe it directly, instead we observe a discrete,
ordinal variable, Y, which is a function of W and of certain
"threshold" parameters, t.., t-, t,, t..
Y. =
1
Y. =
l
Y. =
i
Y. =
1
Y. =
1
1
2
3
4
5
if V^ •
if t± •
if t_ •
2
if V
if W. -
c t,
1
< W. < t^
i 2
« W. < t.
i 3
e W. < t.
i 4
c t..
4
The threshold parameters together with the coefficient vector 8
are to be estimated from the observed data on Y and X.
The model represented by (1) and (2) is flexible, in that it
specifically enables a test of the assumption that Y is cardinal:
if the estimated t. are (approximately) the integers from 1 to 4 we
113
-------
may conclude that Y is approximately a cardinal measure; in these
circumstances, the results from the OLS regressions presented
above would indeed be adequate. Otherwise, these conclusions
wouid not be warranted. The model is also plausible in that it
corresponds to the way in which one intuitively thinks of rating
site conditions; it seems quite likely that people's underlying
sentiments towards the sites are cardinal in nature but are then
mapped into a discrete, ordinal variable in the process of answering
the questionnaire.
In order to estimate the model it is necessary to make some
assumptions about the distribution of the random variable u in (1) .
It is convenient to assume that these variables are independently
and identically distributed, having a common normal distribution with
mean zero and variance a2. The resulting likelihood function is:
*et|x,Y) - P[
t,-x .e tv-x.e t -x.e
n
y=2
t -x e t -x.e
-VM - P C-V ]>• y I
J
where P[X] is the standard normal cumulative density function. In
this model o is not identifiable nor are all the threshold terms and
the intercept in (1). As normalizations we take o=t1=l; with this
assumption we can estimate both B and the differences (t.-t. ) up
to a multiplicative scale factor. The likelihood function is
maximized by an iterative procedure which converged very rapidly
in our experience . * Estimates of the variances and covariances of
the coefficients are obtained from the Hessian of the likelih»od
function at the final iteration. From these estimates, the standard
*The convergence criterion criterion was that successive
coefficient estimates must differ by less than .001 before the
iteration stops. With our data this always happened by the sixth
iteration.
114
-------
t-test for significance can be derived since the computed test
statistic asymptotically follows the t-distribution.
In order to implement the model, we focused on the relationship
between the objective measures of color and coliform bacteria
and subjective water quality relationships. The coefficient estimates
are shown in the upper panel of Table V-12 (with the absolute value
of the asymptotic t-statistic in parenthesis). It is noteworthy
that the three bounded ranges are roughly (though not exactly)
equally spaced, which tends to support the hypothesis that, at least
in its middle range, RWQUAL is a cardinal measure. We can test the
degree of association between the regressor variables and RWQUAL in
at least two ways. The method is to compute the predicted scores
using the estimated coefficients and see how many times the predicted
score matches the actual score. The results of this test are very
discouraging for the hypothesis of a strong correlation between
objective site conditions and subjective perceptions: the predicted
scores were all "1" (W ranged from -410 to -0.74), whereas only 155
of the 984 actual values of RWQUAL were 1. By this criterion, the model's
•
fit is very poor. An alternative procedure to perform an analogue
of the F-test in standard OLS regression to test the hypothesis is
that the slope coefficients are jointly zero. For this purpose, we
drop the regressor variables from the model while retaining the
constant term and re-estimate the model. The resulting coefficient
estimates are shown in Table V-12 in the lower panel. Although the
likelihood function is lower for the second model than for the first,
the difference is too small to be significant and hence we cannot
reject the hypothesis that the slope coefficients are indeed zero.*
*An alternative measure of association would be the multiserial
correlation coefficient between the predicted value of W and the
actual value of RWQUAL. See Cox [2],
115
-------
Table V-12
Maximum Likelihood Estimates of Ordinally Discrete Dependent
Variable Model
W = perceived water quality
W = 2.293 - 0.0353 COLOR - 0.00002328 COLI BACT
(32.96) (4.52) (2.21)
RWQUAL =1 if W < 1
=2 if 1 < W < 1.617
(39.01)
= 3 if 1.617 < W < 2.262
(43.73)
= 4 if 2.262 < W < 2.995
(48.34)
=5 if W < 2.995
- = 1541.48
W = 2.002
(41.46)
RWQUAL =1 if W < 1
= 2 if 1 < W < 1.605
(39.44)
= 3 if 1.605 < W < 2.32
(44.13)
* 4 if 2.32 < W < 2.947
(48.59)
=5 if W < 2.947
-i = 1562.48
116
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2.4 Conclusions
In sum, the hypothesis that water quality perceptions are not
linked to actual water quality cannot be rejected on the basis of
our data. Aside from data problems described elsewhere in this
report, the most obvious explanation of this result is that human
sensory perception of water quality is inaccurate. This is not
a surprising conclusion, particularly for the "invisible" contaminants
such as bacteria, algal nutrients, COD, etc. Perhaps our only per-
ception of water quality occurs when a beach is closed by the health
department. Alternately, this result may derive from some undis-
covered peculiarity of our sample of raters. In any case, this
conclusion jeopardizes the search for a link between levels of
water quality and demand.
117
-------
CITED REFERENCES
1. Y.M. Bishop, S.E. Renberg & P.W. Holland, Discrete Multivariate
Analysis, MIT Press, 1975.
2. N.R. Cox, "Estimation of the Correlation Between a Continuous
a Discrete Variable, Biometrics (March 1974): 171-178.
3. J.L. Fleiss, "Measuring Nominal Scale Agreement Among Many Ratios,"
Psychological Bulletin (1971): 378-382.
4. Haggestrom, Notes on Discriminant Analysis, Logistic Regression,
Rand Memorandum dated 4/3/74.
5. Yoel Haitovsky, Regression Estimation from Grouped Observations,
1973.
6. Richard J. Light, "Measures of Response Agreement for Qualitative
Analysis," Psychological Bulletin (1971): 365-377.
118
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VI. WILLINGNESS-TO-PAY
The willingness-to-pay survey method is frequently used for
determining the value of public goods. This method, in essence,
directly constructs a demand curve and its concomitant consumer
surplus integral. Davis [3] pioneered the approach in the recrea-
tion research, and subsequently many researchers have applied it
to the economics of water quality enhancement. Some of these
studies are reviewed in Chapter II. Presumably, willingness-to-pay
incorporates option demand and aesthetic benefits as well as the
benefits from actual recreation.
Bias in benefit estimates from willingness-to-pay surveys
are well known, but operate both to over- and under-state the goods'
true value. The "free rider" problem suggests that willingness-to-
pay will understate the true social value of the good. In the other
direction, the fact that the willingness-to-pay debts will never
come due could lead to extravagant estimates of value. To our
knowledge, no research has adequately sorted out the relative magni-
tude of these effects.
Three questions were designed to elicit the willingness of
respondents to pay for clean water for recreation:
WTP1
A. How much could the cost of visiting this site
be raised before you started visiting your
second most favorite site more:
a. $.50. e. $4.00
b. $1.00 f. $5-10.00
c. $2.00 g. more than $10.00
d. $3.00
119
-------
WTP2
B. Suppose that this site were to become very polluted
and the water quality would be reduced to a ranking
of 1. This could be avoided if sufficient funds
were raised to pay for the necessary clean-up. If
these funds were to be raised through a higher
entrance fee, how much would you be willing to pay
to prevent this decline in water quality?
a. $.50 e. $4.00
b. $1.00 f. $5-10.00
c. $2.00 g. more than $10.00
d. $3.00
WTP3
C. Suppose that the water quality could be made much
better (improved to a ranking of 5) if sufficient
funds were raised to pay for the necessary clean-up.
If these funds were to be raised through a higher
entrance fee, how much would you be willing to pay
to achieve the water quality improvement?
a. $.50 e. $4.00
b. $1.00 f. $5-10.00
c. $2.0'0 g. more than $10.00
d. $3.00
The analysis of these questions is in four parts. The first
section below outlines the principal theoretical underpinning need
for interpreting the responses to those questions. The next
section analyzes the responses to the three questions via con-
tingency tables. Mean willingness-to-pay is computed, and
variations across subgroups of the sample are examined. Contingency
tables are too restrictive to examine adequately the determinants
of willingness-to-pay on the possible non-linear functional
relationships involved. The third section uses OLS regression to
probe those relationships more deeply. The final part of this
chapter summarizes the major empirical findings and presents some
benefit estimations based on these findings.
120
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1. The Theoretic Basis for Willingness-to-Pay Calculations
Three measures of willingness-to-pay are available, correspond-
ing to the three survey questions reproduced above. This brief
and informal explanation of the theoretical infrastructure under-
lying these concepts is intended to define more precisely
what these questions measure and the distinctions between them.
A more formal analysis of willingness-to-pay (consumer surplus)
and specification of the demand curve is presented in Chapter VII
below.
The analysis starts with the individual's demand curve for a
given site, which we assume to be a function of some measure of the
cost of recreation at the site (including travel cost, entry fee,
etc.); we use the blanket term "price" to refer to this variable.
Temporarily ignoring the other variables which might affect the
demand for the site, draw the individual's demand curve as a function
of the price of the site; this curve is represented by the line
DD1 in Figure Vl-la. In this diagram, the recreationist is
assumed to face a price of OP for visiting the site and, at that
price, he makes OQ visits. Following the standard agrument of
elementary micro-economic testbooks, we assert that the area OPDAQ
may be taken as an approximate measure of the consumer's total
benefit from making OQ visits to the site, the area OPAQ measures
his expenditures for visiting the site, and the area PDA may be
taken as an approximate measure of his net benefit (consumer's
surplus) from visiting the site OQ times. This last area is
(approximately) the maximum additional amount which the individual
would be willing to pay for visiting the site OQ times rather
than not at all.
121
-------
Price
la
Price
H
D
# of visits
B
XT,
Q D'Q1 H1
lb
# of visits
Price
D
P"
P1
Po
# of visits
Q' Q° H1 D1
Ic
Figure VI-1: Demand Curves for an Individual Recreation Site
122
-------
What can be said about the determinants of this area? Holding
all other variables constant, it is larger when the price of the
site is lower (and the number of visits to the site larger). It
will also be affected by variables which shift the demand curve
DDr holding price constant. Thus, if recreation at the site is
a normal good and the individual's income rises, the demand curve
would shift outwards. This is illustrated in Figure Vl-lb.
If the individual's income rises (or if we are comparing two individuals,
one having a larger income than the other) the demand curve changes
from DD' to HH'; with price constant at OP, the net benefit increases,
the amount of the increase being the area ADHBA1. Similarly, if
some alternative site which the individual might visit as a sub-
stitute declines in quality, we would expect the individual's demand
for this site to increase and, with it, net benefit. Finally, if
the quality of this site itself is upgraded, we would expect his
demand to increase; assuming his demand curve shifts from DD' to
HH1 we may take the area as an approximate measure of his net
benefit from the improvement in quality. Conversely, if the site's
quality declines *and if the initial demand curve is taken to be HH',
this area is a measure or approximate measure of the disbenefit
arising from the quality change. Probably it is a function of the
magnitude of the quality change, but not necessarily of other
variables. However, it is possible that this area is a function of
the initial level of water quality or the initial number of visits
(if we assume, say, a declining marginal utility of water quality)
and it is not inconceivable that it is also a function of income
(if we assume that the marginal utility of site quality is not
constant with respect to income). Nevertheless it is quite possible
that these variables might not affect the magnitude of the net bene-
fit for water quality changes.
123
-------
With this background, we can consider more precisely what the
willingness-to-pay questions measure using Figure Vl-lb. Consider
the last measures, WTP3, the value of achieving water quality
increases is assessed. Here we ask the respondent to tell us
the maximum he would pay (i.e., P°P') to move his demand curve
from DD1 to HH1 (and implicity still consume OQ units of recreation).
His net benefit before and after the shift must be equal (or else
he would be willing to pay more) so the areas P'BH and P AD must be
equal. The net benefit he would receive if water were improved and
the'charges not levied is, therefore, P°A'BP'. This quantity is
proportional to P°P' and an estimate which understates its magnitude
is given by P°ABP'. Of course, this analysis assumes the demand
curves are approximately linear over the range considered and that
DD' and HH1 are parallel. Note that the parallel shift assumption
is the more critical one for recovering reasonable approximations
to the change in net benefits from the willingness-to-pay questions.
Ideally, we would like to determine the willingness-to-pay
over the entire season rather than the willingness-to-pay per
visit and then an exact measure of net benefit would be available.
But, the former is manifestly unreliable in a survey research
context. For any respondent, willingness to pay over the whole
season can be estimated by multiplying the reported willingness-
to-pay by number of the current visits. WTP2, the value of
avoiding water quality declines can be derived similarly.
Figure VI-lc has been constructed to help analyze the first
willingness-to-pay question, WTP1. This question asks how much the
cost per visit could be increased before the number of visits de-
clines, not necessarily to zero, but to some smaller number, and the
best substitute for that site is visited more often. When perfect
124
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substitutes are available, consumers' surplus vanishes. This
question in effect uses the implicit rates of substitution between
the two more preferred sites to compile the net benefit of the
most preferred site.
If the consumer is presently visiting the site Q° times, we
assume that if he visits it less he visits it Q1 times where
Q°-Q' is some integer (not necessarily unity) which depends on
the relative attractiveness of this site and the second most
favorite site. The situation is depicted in Figure VI-lc for
two different demand curves, DD' and HH1. Suppose, first, that
the true demand curve is DD'; with price P°, the- individual makes
Q° visits. The question, in effect, asks for the maximum length
(P'-P°) such that if price increased to P1, the individual would
begin to reduce the number of his visits.
The change in net benefit from this change in price and con-
sumption equals P°QOBP'. in general, this area depends on the
magnitude of the "minimum required reduction" Q°Q', which is un-
known to us. Assume the reduction is small (i.e., Q°Q' equals
unity) which is not implausible given the wording of the question.
Then the change in net benefit is bounded above by the quantity
(P°P')-Q°,-the reported willingness-to-pay multiplied by number of
visits prior to the price increases.
Observe that the net benefit depends strongly on the slope of
the demand curve. To see this compare the demand curves DD', and HH1
in Figure VI-lc. With the latter demand curve, the same starting
amount, and "minimum, required reduction," the answer to our question
would be P°P", a considerably larger amount than P°P'. But under
those conditions, and assuming that the demand curve is linear
over this range, then the percent error in the net benefit estimate
does not depend on the slope of the demand curve.
125
-------
We hypothesize that the magnitude of the price increase (pop1 or
WTP1) is positively related to the respondents household income
and the quality of the site, and negatively to the price of visiting
the site (measured by, say, travel time or distance). It may be
positively or negatively related to the total number of visits to
the site and the total number of visits to other sites.
126
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2. Tabular Analysis of Willingness-to-Pay
The responses to the willingness-to-pay questions are presented
in Table VI-1. Several results from this table are of interest.
First, the mean values of willingness-to-pay is greater than zero
(significant at the 5% level) for all three measures. In other words,
despite their inaccurate perception of water quality, respondents were
willing to pay to avoid it. This suggests that the principal benefits
of water quality improvements are essentially "conservation" oriented
rather than "use" oriented.
Second, the incremental value of the favorite site over the
second site is less than the value of either avoiding water pollution
or achieving water quality improvements (the difference is not, how-
ever, statistically significant at the 5% level). Since to avoid
the water quality deterioration, the person could shift to the
second site and not pay the added cost, this difference reinforces the
hypothesized non-usage (merit good, latent demand, option demand, or
aesthetic) benefit of water quality improvement. In fact, since we
have found only tenuous, at best, support for the relationship between
water quality and recreation behavior, we might speculate that most of
the willingness-to-pay is in these categories.
The third result is that willingness-to-pay is symmetric between
avoiding declines and achieving improvement in water quality. A three-
way contingency table shows a strong correlation between response to
WTP2 and WPT3 (i.e., the hypothesis of independence can be rejected at
the 5% level). This is not unexpected in survey research. Further-
more, the distribution means for WTP2 and WTP3 are nearly identical
and the standard deviation differs only by 1.1%, largely because most
respondents answered the questions identically. This similarity suggests
two hypotheses: either tastes are symmetric and the water quality
127
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TABLE VI-1
Distribution of Willingness to Pay
($ per visit)
$ .50
$1.00
$2.00
$3.00
$4.00
$5-10
> 10
Median
Mean
WTP1
#
128
84
68
26
17
16
13
%
36.0
24.0
19.4
7.4
4.9
4.6
3.7
1.083
1.978
Question
WTP2
ft
86
113
67
26
14
24
9
%
25.4
33.3
19.8
7.7
4.1
7.1
2.7
1.239
2.077
WTP3
ft
84
113
70
27
14
21
10
%
24.8
33.3
20.6
8.0
4.1
6.2
2.9
1.237
2.034
128
-------
rating equals 2.5 or tastes are nonsymmetric to account for water
quality ratings different from 2.5. As seen in Section IV 2.3 above,
the mean water quality rating equals 2.881, and is slightly skewed to
the right. A rating of 2.5 is not statistically different (at 5% con-
fidence) from the observed mean. Combined with the symmetry of re-
sponse to questions WTP2 and WTP3, the difference suggests avoiding
water quality declines is not so valuable as achieving water quality
improvements. This is contrary to the expressed preferences which
associated (negatively) site choice only with bad water quality and
find little if any response to good water quality. Again, we must
conclude that these willingness-to-pay questions measure something
outside recreational usage.
Previous studies have found willingness-to-pay for water
quality improvement to be related to income and education. Our
analysis is more limited, being confined to the recreation context,
but we still would expect a positive correlation between willingness-
to-pay and income, education and occupation. Too, we expected whites
to have higher levels of willingness-to-pay than blacks. None of
these hypotheses were confirmed at the 5% level.* No S-shaped curve
between income and willingness-to-pay, as suggested by some
authors could be discerned from the tables. A significant positive
correlation was found between family size and willingness-to-pay, but
this relationship disappeared when willingness-to-pay was computed
on a per capita basis.
This absence of correlation was surprising. Since our sample
SES characteristics are close to those for the SMSA as a whole,
these results suggest that the willingness-to-pay is uniform across
the population. The individual amounts are small, so perhaps they
do not constitute an adequately large portion of total income to
induce any differential effect.
*The next section probes these relationships in greater depth.
129
-------
Alternatively, in general, the poorer group of our sample live
closer to the lower quality inner city beaches. Conversely, the
more wealthy visit the better quality outer beaches more often.
Since there was substantial agreement concerning the perceived
water quality across the sites, we could postulate that the poor
are willing to pay more in proportion to their income than the
wealthy because they currently visit poorer sites and would like to
see them improve. However, then the wealthy should be willing to
pay more to avoid declines in their good sites and a positive income
correlation with WTP2 should exist. But no such correlation was
found-. Bolstered by the regression analysis in Section 3, Section 4
of this chapter returns to these conclusions.
A second set of hypotheses were formulated to examine the re-
lationship between willingness-to-pay and access to recreation.
Access included ownership of an automobile, amount of leisure time
each week, amount of vacation time per year, total amount of
recreation equipment owned and the use of public transit. We ex-
pected auto ownership to be negatively correlated and all the
others positively with willingness-to-pay. At the 5% level, only
transit usage was significant as shown in Table VI-2. Frequent
users of public transit may not have access to high quality sites,
and, therefore, perceive greater benefits from water quality im-
provements and disbenefits from declines.
The last subgroup examined were participants in various
•activities. We hypothesized that participants would be more
sensitive to water quality benefits than non-participants. For
swimmers, boaters, walkers and bicyclists, the hypothesis was
not proved. For fishermen, the hypothesis can be accepted at a
5% level of confidence, and the contingency table is shown in
Table VI-3.
130
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Table VI-2
Willingness to Pay By Transit Usage
a. $.50
b. $1.00
c. $2.00
d. $3.00
e. $4.00
f. $5-10.00
g. more than
$10.00
Never
(12)
14.1
18.2
(23)
20.4
34.8
(11)
16.4
16.7
(7)
26.9
10.6
(1)
7.1
1.5
(11)
45.8
16.7
(1)
11.1
1.5
Transit Use
Almost
Never
(14)
16.5
19.2
(27)
23.9
37.0
(20)
29.9
27.4
(5)
19.2
6.8
(2)
14.3
2.7
(3)
12.5
4.1
(2)
22.2
2.7
Occasionally
(7)
8.2
12.1
(27)
23.9
46.6
(11)
16.4
19.0
(6)
23.1
10. 3
(3)
21.4
5.2
(2)
8.3
3.4
(2)
22.2
3.4
Frequently
(52)
61.2
36.9
(36)
31.9
25.5
(25)
37.3
17.7
(8)
30.8
5.7
(8)
57.1
5.7
(8)
33.3
5.7
(4)
44.4
2.8
Table shows cell count in ( ), row percentages and
column percentages.
131
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Table VI-3
Willingness to Pay by Participation in Fishing
1 . Fishermen
2 . Non-Fishermen
1
(40)
28.2
31.7
(86)
41.3
68.3
2
(39)
27.5
46.4
(45)
21.6
53.6
3
(26)
18.3
38.2
(42)
20.2
61.8
4
(16)
11.3
61.5
(10)
4.8
38.5
5
(9)
6.3
52.9
(8)
3.8
47.1
6
(5)
3.5
31.3
(11)
5.3
68.8
7
(7)
4.9
53.8
(6)
2.9
46.2
Table shows cell count in ( ), row percentages
and column percentages.
132
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3. Regression Analysis of Willingness to Pay
For ordinary least squares regression analysis, it is conveni-
ent to continuous variables for both the dependent variable—willing-
ness to pay—and the independent variables. This assumption is not
strictly necessary—we shall relax it partially below—but it greatly
simplifies the analysis and it seems to be fairly reasonable in the
present case. The answers to the willingness to pay questions are
essentially ranges: the respondent who checks response (d)—$3~
may be presumed to be actually willing to pay some amount greater
than $2.50, but less than $3.50, and similarly with the other re-
sponses. Nevertheless, the ranges are relatively small, and there-
fore it is not unreasonable to use the midpoints of the ranges in
place of the unknown means. A similar argument applies to the in-
come variable. In doing this we arbitrarily take the (unknown) mid-
point of the last willingness to pay answer—"more than $10—to be
$15 and with the income variable we take the midpoint of the first
income class to be $2,500 and that of the last class to be $60,000.*
The properties of the resulting estimator have been analyzed
by Haitovsky [4]. He shows that they are biased in general,
but if the number of categories into which the 'dependent
variable is classified is the same as the number of categories into
which the explanatory variable is classified, the resulting estima-
tor will be the same as that obtained by using the (unknown) means
of the ranges instead of the midpoints. Cramer [2] has shown that
the latter estimator is unbiased, although inefficient. Haitovsky [4]
also shows that when the number of categories for the explanatory
variable is larger than for the number for the dependent variable—
*These values are actually closer to the mean of the first and
last groups computed from a Pareto distribution.
133
-------
as is the case when we regress willingness to pay on income—the
slope coefficient obtained by using the midpoints is likely to be
larger in absolute value than that obtained by using the means.
In addition, he shows that the loss of efficiency due to grouping
declines as the category size is smaller and as the population cor-
relation between the dependent and independent variable approaches
unity.
The other issue which we must address is the functional form
of the relationship between willingness to pay and its determinant.
We had no reason a priori to prefer any particular form. We there-
fore considered several different functional forms, including the
following:
I - - a + b/x. e.... -
II In y = a - b/x e = b/x
yx
III In y = a + bx e = bx
yx
IV In y = a + b In x e =b
yx
b
V y = a + b In x e = —
yx y
VI y = a + bx e = —
* yx y
where e = — I — 1 is the elasticity of y with respect to x.
yx dx \ y }
Form I, with b<0, is an ^"shaped function, intercepting the x-
axis at zero and approaching I/a asymptotically as x increases to
infinity. Form II with b>0 is an^/shaped function, passing through
the origin and approaching (a) asymptotically as x increases to in-
finity. Form III with b>0 is an—/shaped function, cutting the y-
axis at a. Form V with b>0 is shaped rather like Form I, except
that it cuts the x-axis at e and increases without bound as x
134
-------
increases. The shapes of the other two functions require no expla-
nation. When necessary, an appropriate criterion for choosing
among alternatives II, III and IV, or between V and VI is minimizing
the residual sum of squares from the fitted regression—or, equiva-
lently, maximizing the R statistic. However, in order to choose
between the three broad classes of functions (I), (II, III, IV),
(V, VI), with respectively l/y» In y andy as the dependent variable,
it is necessary to apply the likelihood ratio test suggested by Box
and Cox [i].
As before, we refer to the additional willingness to pay for
visiting the respondent's favorite site as WTP1, the willingness to
pay to prevent the site from becoming polluted as WTP2, and the
willingness to pay to obtain a higher level of water quality as
WTP3. Since these three measures pertain to different concepts,
there is no reason why they should be identical in value. In order
to test this, we regress one measure on the other; if the two mea-
sures were identical, the estimated intercept would not be signifi-
cantly non-zero and the estimated slope coefficient would not be
statistically different from unity. The regressions are performed
on the data subsets containing answers to both questions, for each
of the three pairs of measures. The results are as follows:
WTP2 = 1.031 + 0.5715 WTP1 R2 = .335 (275 obs.)
(5.88) (11.73)
0.983 + 0.547 1
(5.94) (12.48)
0.248 + 0.8662
(2.55) (31.4)
WTP3 = 0.983 + 0.547 WTP1 R2 = .362 (277 obs.)
WTP3 * 0.248 + 0.8662 WTP2 R2 = .772 (293 obs.)
The numbers in parentheses below the coefficient estimates are
t-statistics.
135
-------
Clearly, WTP2 and WTP3 are closer in value to each other than to
WTP1, but no pair of these measures is sufficiently close to be
considered statistically identical.
Determinants of WTP1
On the basis of the considerations outlined in Section 1, we
hypothesize that WTP1 is a positive function of income (INC), a
negative function of travel time (TIME) and distance to the site
(DIST), which are a large component of the site's "price", a posi-
tive function of the household's total number of visits to the site
(HVS), and a positive function of the site's quality. For the last
variable we can use either the respondent's subjective rating of
the site's characteristics or the "objective" water quality char-
acteristics.
The results of some bivariate regressions are shown in Table
VI-4. It turns out that there is little relationship between will-
ingness to pay and income. The two preferred equations—one of them
representing an S-shaped relationship—indicate that the relation-
ship is significant at the 90%, but not the 95% level. As hypothe-
sized, there is a positive relationship between the number of visits
and willingness to pay. Willingness-to-pay and travel time or distance,
which may be taken as proxies for price, are also positively associated,
an unexpected result. We discuss this result in greater detail below.
The next three sets of regressions show that there is a
strongly significant relationship between willingness-to-pay and
*In fact, our of the 293 cases where the respondent provided data
on both WTP2 and WTP3, the response was the same in 251 cases; in
24 cases WTP3 exceeded WTP2 and in 18 cases WTP2 exceeded WTP3.
All.the intercepts are significantly different from zero, and
slope coefficients are less than unity at the 95% level.
336
-------
Table Vl-4
Some Regressions with WPT1 as Dependent Variable
INCOM^ (256 observations)
0.9854
(13.37) (1.78)
1177.
(1.64)
* FORM I. 1/WTF1 = 0.9854 + 988.47/INC R2-.012 f=3.12
* FORM II. In(WTPl) = 0.3672 - 1177.28/INC R2-.01 f=2.68
FORM IV. In(WTPl) = -1.017 + 0.13431n(INC) R2«.009 f=2.21
(1.19) (1.49)
HOUSEHOLD VISITS TO SITE (308 observations)
FORM V. WTPl = 1.57 + 0.31141n(HVS) R2«0.13 f=4.05
(4.63) (2.01)
* FORM VI. WTPl = 1.92 + 0.0191 • HVS R2=.013 f=4.19
(9.33) (2.05)
DISTANCE FROM SITE (290 observations)
FORM I. 1/WTP1 = 1.02 + 0.1535/DIST R2=.01 f=3.02
(19.12) (1.74)
0.029 -I- 0.0:
(0.38) (3.87)
* FORM VI. In(WTPl) - 0.029 -I- 0.0274 • DIST R2-.049 f=14.95
FORM VI. In (WTPl) = 1.767 4- 0.0442 • DIST R2-.013 f=3.67
(7.07) (1.92)
TRAVEL TIME (293 observations)
FORM I. 1/WTPl = 0.979 + 1.395/TIME R2=«.011 f=3.19
(16.7) (1.79)
-0.405 + 0.21
(1.93) (3.38)
•FORM IV. In(WTPl) - -0.405 + 0.20661n(TIME) R2*.038 1=11.43
FORM VI. WTPl = 1.82 + 0.00995TIME R2=.015 f=4.52
(7.12) (2.13)
RATING OF WATER QUALITY (303 observations)
FORM I. 1/WTPl = 0.8441 + 0.519/RWQUAL R2=0.39 f=12.27
(11.52) (3.50)
* FORM III. In(WTPl) = -0.2105 + 0.1485 • RWQUAL R2=.05 f=15.78
(1.59) (3.97)
FORM VI. WTPl = 1.141 + 0.3223RWQUAL R2=.022 f=6.91
(2.63) (2.63)
RATING OF BEACH QUALITY (303 observations)
FORM I. 1/WTPl - 0.9085 + 0.4698/RBQUAL R2=.02 f=6.13
(11.85) (2.48)
-0.295 + 0.15:
(1.85) (3.67)
il + 0.38811
(1.46) (2.85)
* FORM II. In(WTPl) = -0.295 + 0.1535RBQUAL R2=».043 f=13.46
FORM IV. WTPl = 0.761 + 0.3881RBQUAL R =.026 f=8.1
137
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Table VI-4 (CONTINUED)
Some Regressions with WPT1 as Dependent Variable
RATING OF CROWDING (308 observations)
0.965 + 0.2273/
(12.67) (1.59)
-0.0197 + 0.(
(0.15) (2.41)
FORM I. 1/WTP1 = 0.965 + 0.2273/RCROWD R2=.008 f=2.51
* FORM III. In/WTPl) = -0.0197 + 0.094RCROWD R2=".019 f=5.82
FORM VI. WTP1 - 1.296 + 0.2906RCROWD R2=.017 f=5.35
(2.31)
FACTOR 4 (245 observations)
FORM I. 1/WTP1 = 1.0277 - 0.00924/FACT4 R2=.016 f=3.91
(21.48) (1.98)
0.2943 + O.Oi:
(4.9) (2.2)
5.5088
(2.31)
* FORM II. In(WTPl) = 0.2943 + 0.0129/FACT4 R2=.019 f=4.83
FORM VI. WTP1 - 2.131 -t- 0.5088 • FACT4 R2=.021 f=5.33
pH (245 observations)
= 1.
(20.92) (1.4)
FORM I. 1/WTP1 = 1.033 -I- 0.0125/pH R2-.008 f=1.96
* FORM II. In(WTPl) = 0.2902 - 0.0186/pH R2=.011 f=2.76
(4.68) (1.66)
TURBIDITY (187 observations)
* FORM I. 1/WTP1 = 0.965 -t- 0.5268/TURB R2-.059 f=11.57
(12.24) (3.4)
-0.24 + 0.2S
(3.15) (3.79)
FORM IV. .In(WTPl) = -0.24 + 0.28221n(TURB) R2=0.72 f=14.38
FORM VI. WTP1 = 1.101 + 0.1468 • TURB R2=-.OS2 f-10.23
(3.79) (3.2)
COLIFORM BACTERIA (245 observations)
* FORM III. In(WTPl) = 0.2036 + 0.0000341 - CBACT R2=.014 f=3.37
(3.33) (1.84)
FORM VI. WTP1 = 1.8802 + 0.0000135 - CBACT R2=.022 f=5.56
(9.99) (2.36)
NOTES: 1. The absolute values of the t-statistic are given in
parentheses below the coefficient estimates.
2. The critical values at the 95% level for the t-
and f-statistics are respectively 1.96 and 3.84.
3. An asterisk denotes the functional form which is
preferred on the basis of the likelihood ratio test.
138
-------
perceived site quality, as measured by the rating of water quality,
beach quality and crowding.* However, the relationship between
willingness to pay and "objective" water quality is tenuous at best.
Many objective water quality measures, such as the sites' scores
for Factors 1, 2 and 3 and such variables as alkalinity and color
bear no significant relationship to willingness to pay. Those vari-
ables which do have a significant slope coefficient, such as pH
(measured in terms of squared deviations from the value of 7), tur-
bidity and coliform bacteria, have a positive coefficient instead
of a negative one (it should be remembered that larger values of
these variables signify a greater degree of pollution). The only
exception is the site scores for Factor 4 (which are positively
correlated with bacteria counts); the regressions equation using
Forms I and II indicate a significant negative relationship with
willingness to pay, while the equation using Form VI indicates a
significant positive relationship. This last result is difficult to
interpret since it is unlikely that recreationists can perceive
bacteria, let alone a composite water quality factor which loads
heaving on the bacteria count.
The divergence between the results obtained using subjective
ratings of site characteristics and objective measures of water
quality reaffirm one's doubts concerning the accuracy of the re-
spondent's perception of water quality conditions at the Boston
area sites.
There remains the question of the positive slope coefficient
in the regressions of WTP1 on TIME and DIST. Larger values of
these variables, signifying a higher cost of access to the site,
and should be associated with smaller amounts of willingness to
pay. One explanation for the positive slope coefficients is that
the more distant sites are of a better quality than the closer sites,
so that distance is serving as a proxy for site quality. That this
*These variables are here treated as being continuous, cardi-
nal variables. The appropriateness of this assumption was discussed
more fully in Section V 2.3, above.
139
-------
explanation has some validity is shown by the correlation coeffi-
cients between distance and various site quality variables dis-
played in Table VI-5. * In order to examine the relationship be-
tween willingness to pay and distance, allowing for the separate
effects of site quality, consider these regressions of WTP1 on both
distance and quality variables:**
In(WTPl) = -0.323 + 0.0301 DIST + 0.1617 RWQUAL
(1.9) (.69) (3.89)
R2 = .066 F = 9.03
In(WTPl) = -0.288 + 0.0329 DIST + 0.1328 RBQUAL
(1.51) (.73) (2.73)
R2 = .039 F = 5.18
In(WTPl) = -0.296 + 0.0024 TIME + 0.1509 RWQUAL
(2.07) (1.59) (3.62)
R2 = .073 F = 10.123
In(WTPl) = -0.289 + 0.0031 TIME + 0.1253 RBQUAL
(1.64) (2.07) (2.69)
R2 = .053 F = 7.13
It seems from these regression equations that, even when the effects
of site quality are removed, there is still a somewhat positive re-
lationship between willingness to pay and distance. The same con-
clusion holds when income, which is positively correlated with both
distance and willingness to pay, is held constant, as can be seen
from the following regressions:***
*These correlation coefficients are computed from the full set
of data on household visits to all sites, rather than merely the
visits to the favorite site.
**These regressions are based on 260 observations? the notation
and display is the same as in Table VI-1.
***These regressions are based on 226 observations.
140
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Table VI-5
Correlation of Time and Distance Travelled to 29 Sites With Site Quality Variables
Distance
In
(Distance)
Time
TIME
.453
.407
1.000
FACTOR 1
.218
.208
.087
FACTOR 2
-.093
-.129
FACTOR 3
-.214
-.232
-.099 1 -.130
1
FACTOR 4
-.210
-.235
-.109
Bacteria
-.304
-.347
-.179
Color
-.347
-.376
-.148
Turbidity
-.263
-.275
-.135
Rating of
Water Quality
.395
.371
.110
Rating of
Beach Quality
.202
.185
.072
Rating of
Crowding
.278
.252
.119
Household
Income
.125
.155
.053
NOTE: "Bacteria" is the arithmetic mean of Coliform and Total Bacteria.
All the correlation coefficients are significantly different from zero
at the .01 level; there are about 900 degrees of freedom for all but the
last column, for which there are about 750 degrees of freedom.
-------
In(WTPl) = -0.242 + 0.0139 DIST + 0.1301 RWQUAL - 353.15/INC
(1.31) (1.56) (2.69) (.48)
R2 = .076 F * 6.1
In(WTPl) = -0.242 + 0.0024 TIME + 0.1422 RWQUAL - 520.18/INC
(1.31) (1.56) (3.12) (.71)
R2=.076 F = 6.1
Thus, it seems possible that respondents place a positive pre-
mium on more distant sites, even when the effects of site quality
and income are removed. There are two possible explanations for
this phenomenon. The most obvious explanation is that respondents
visit those sites for their natural setting, lack of crowding, or
other site characteristics not included. Another explanation is
based on the specialized definition of the WTP1 variable, discussed
in Section 1 above; it may be that the length (Q0-^1) in Figure VI-lc
is larger for more distant sites than for nearer sites; that is,
if the household is to reduce the number of its visits to its fa-
vorite site, the minimum reduction is larger for more distant sites.
The alternative explanation is that recreation sites, like certain
other commodities, may be subject to the Veblen effect: consumers
are willing to buy larger quantities of the higher priced good.
Determinants of WTP2
The results of some regressions of WTP2 on various explanatory
variables are shown in Table VI-6. Willingness to pay to avoid
very polluted site condition appears to be an increasing function
of income, although the confidence intervals on this result are
wide. Also, increases in present site conditions tend to increase
WTP2. From the fact that functional form III has the best fit of
all six forms, we may infer that willingness to pay elasticity ac-
tually increases with quality of present site conditions, which re-
futes the diminishing marginal utility of water quality hypothesis
142
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Table VI-6
Some Regressions with WTP2 as Dependent Variable
INCOME (247 observations)
0.8492 + 12
(12.26) (2.33)
0.185 + .0000
(1.7) (1.82)
-1.1571 + .1602
(1.37) (1.79)
EATING OF WATER QUALITY (292 observations)
= 0.825 + 0.3828
(11.68) (2.7)
III. ln(WTP2) = -0.0549 + .1188 • RWQUAL R2-.034 f-10.32
IV. ln(WTP2) - 0.05083 + 0.26581n(FWQUAL) R2-.027 f-8.05
(.46) (2.84)
RATING OF BEACH QUALITY (294 observations)
I. 1/WTP2 = 0.8109 -t- 0.529/RBQUAL R -.032 f-9.96
I. 1/WTP2 - 0.8492 + 1253.57 • 1/INC R2-.033 f-5.42
III. ln(WTP2) = 0.185 + .00001113 . INC R2-.013 f*3.3
IV. ln(WTP2) = -1.1571 + .1602 In(INC) R2-.013 f-3.2
I. 1/WTP2 = 0.825 + 0.3828/RWQUAL R2-.025 f-7.32
(11.39) (3.11)
-0.162 + 0.133
(1.08) (3.33)
III. ln(WTP2) - -0.162 + 0.1319 - RBQOAL R2-.037 f-11.1
IV. ln(WTP2) = -0.0338 + 0.291n(RBQOAL) R -.025 f«7.36
(.25) (2.71)
PARTICIPATION IN FISHING/BOATING (303 observations)
III. ln(WTP2) - 0.209 + 0.2094PART R2-.014 f-4.26
(2.80) (2.06)
VI. WTP2 = 1.838 + 0.6497PART R -.014 f»4.16
(7.85) (2.04)
DISTANCE/TIME, WATER QUALITY RATING AND INCOME (226 observations)
III. ln(WTP2) = -1.113 + 0.0116DIST + 0.0815KWQUAL -t- 0.1171n(INC) R2=.05
(1.29) (1.29) (1.72) (1.25) f-3.92
III. ln(WTP2) = -1.276 -1- 0.000794TIME + 0.1014 RWQUAL + 0.13441n(INC) R2-.04S
(1.49) (0.51) (2.28) (1.46) f-3.46
143
-------
suggested above. In addition, we have regressed WTP2 on a dummy
variable PART, which takes the value 1 of members of the respon-
dents' household engaged in boating and/or fishing, and the value
0 otherwise. As we might expect, participation in these activities
increases the respondent's willingness to pay to avoid pollution by
about 20% over nonparticipants. Finally, as with WTP1, there is
some evidence of a positive relationship between distance and will-
ingness to pay, even when water quality rating and income are held
constant.
Determinants of WTP3
The results of some regressions ofWTP3on several explanatory
variables are shown in Table VI-J. The most important finding is
that willingness to pay to obtain an improvement in water quality
increases with present site quality. This is completely counter-
intuitive: we had hypothesized that willingness to pay would be
greatest when existing site conditions were very poor, because visi-
tors to such sites would have the greatest amount to gain, both ab-
solutely and relative to the starting position. The finding that
the reverse seems to be true suggests that the taste for water
quality increases with the respondent's exposure to it. In terms
of utility theory, we are suggesting that the marginal utility of
water quality may increase with "consumption" of water quality,
at least within the range covered by the present sample.
144
-------
Table VI-7
Regressions with WTP3 as Dependent Variable
INCOME (247 observations)
0.9007 -
(12.97)
0.2871
(2.71) (.57)
I. 1/WTP3 = 0.9007 + 736.33/INC R2=.008 F=1.87
III. ln(WTP3) = 0.2878 + 0.00000344 INC R2=.001 F=0.33
IV. ln(WTP3) = -0.1737 + 0.05441n(INC) R =.002 F=0.38
(.21) (.62)
RATING OF WATER QUALITY (292 observations)
I. 1/WTP3 = 0.819 + 0.3544/RWQUAL R2=.023 F=6.81
(11.77) (2.61)
0.0093 + 0.10;
(.07) (2.82)
III. ln(WTP3) = 0.0093 + 0.1023 RWQUAL R2=.027 F=7.97
•IV. ln(WTP3) = 0.1058 + 0.22291n(RWQUAL) R2=.02 F=6.03
(1.0) (2.46)
RATING OF BEACH QUALITY (295 observations)
I. 1/WTP3 = 0.7908 + 0.5281/RBQUAL R2=.035 F=10.5
(11.38) (3.24)
0.088 + O.lli
(.60) (2.98)
III. ln(WTP3) = -0.088 + 0.116 RBQUAL R2=.029 F=8.87
IV. ln(WTP3) = 0.0171 + Q.26161n(RBQUAL) R2=.021 F=6.31
(.13) (2.51)
145
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4. Conclusions; Dollar Values of Willingness to Pay in the
Boston SMSA
Willingness to pay for water quality exceeds zero despite the
generally poor perception of water quality. The evidence suggests
that the net benefits implied by this do not necessarily derive
from the direct usage of the water, but may also be based on an
option demand character of water quality. Bostonians appear to
value conservation.
Willingness to pay to either achieve water quality improvements
or avoid water quality degradation increases with better site qual-
ity. In other words, the value of improving/maintaining good sites
is greater than that for poorer sites. This finding holds once in-
come and distance (setting) effects are removed as well. It sug-
gests there are increasing returns to water quality improvements.
Because the costs of water pollution abatement typically display
increasing marginal costs, this finding implies that much higher
levels of water quality contact than previously thought may be so-
cially efficient.
From the response to the willingness-to-pay questions (WTP2 or
WTP3), a dollar value of water quality improvements (or cost of de-
clines) can be estimated from the formula developed in Section 1.
Recall these estimates probably overstate the true net benefits.
We assume our sample is representative of the Boston SMSA population,
and no adjustments are needed to account for variation due to social,
economic or other factors. On the average, responding households
made 20.75 visits to a recreation site during the period. Valued
at the median willingness-to-pay figure (1.259) this implies a value
of about 26.11 per household per year for water quality improvements.
This equals $17.3 million per year for the 1970 Boston SMSA
146
-------
population. Using the mean figure of $2.065, the per capita figure
becomes $42.85 per year, and the SMSA figure rises to 28.4 million
per year. Because the data are categorical, confidence bands for
these estimates cannot be simply calculated. But the distribution
is skewed to the right, so any equal probability confidence inter-
vals would find deviations to the high side more likely. Remember
that this value is not necessarily generated by direct recreation
usage alone, but also by the conservation value of achieving and
maintaining good quality water in the Boston area.
147
-------
CITED REFERENCES
1. G.E.P. Box and D.R. Cox, "An Analysis of Transformations,"
Journal of Royal Statistical Association Series B (1964) :
211-252.
2. J.S. Cramer, "Efficient Grouping, Regression and Correlation
in Engle Curve Analysis., Journal of American Statistical
Association (1964): 233-250.
3. R.K. Davis, The Recreation Value of Northe'rn Maine Woods,
unpublished Ph.D. thesis, Department of Economics,
Harvard University, 1963.
4. Yeol Haitovsky, Regression Estimation from Grouped Observations,
1973.
148
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VII. MULTIPLE SITE DEMAND FUNCTIONS
The formal economic analogue to willingness-to-pay is
consumer's surplus measured from an appropriately specified
demand function. Our analysis focuses on multiple site demand
systems because substitutions between the sites were significant.
Table VII-1 showg the response to a direct question on
substitutions:
Let's talk about the beach, lake or river si'te you
visited most, that was , site
number .
If water quality became much worse (declined
to a ranking of 1), what would your response be?
a. still visit the same beach as much
b. visit that site less frequently and some
other site more (specify which one below)
c. visit that site less frequently and parti-
cipate in some other non-water-based
recreation more (specify which activity
below).
d. participate in outdoor recreation less,
no change in other leisure
e. participate in outdoor recreation less
and indoor recreation more.
Most (56.9%) respondents would shift to their second most favorite
site. Over three-quarters of all respondents would continue to
participate in water-based activities at the system of sites
under study.
149
-------
Table VII-1
Substitution Induced by Water Quality Decline
Response No. Percent
a. still visit the same beach as much 83 20.9
b. visit that site less frequently
and some other site more 226 56.9
c. visit that site less frequently
and participate in some other
non-water-based recreation more 53 13.4
d. participate in outdoor recreation
less, no change in other leisure 21 5.3
e. participate in outdoor recreation
less and indoor recreation more 14 3.5
Five sections complete the demand analysis. The first
section discusses in a qualitative way demand at the system of sites.
Section 2 presents some aggregated regressions which focus more
specifically on the determinants of recreation behavior. These
sections, combined with the background matter presented in previous
chapters, set the stage for the demand modelling of sections 3 and 4.
Section 3 employs the abstract site demand functions pioneered in
transportation economics to estimate the functional relationships
between site characteristics and site demand. However, the speci-
fication does not permit recovery of an exact measure of consumers'
surplue (net benefit), so Section 4 considers a system of demand
equations derived explicitly from a utility model. Unfortunately,
estimation of these equations, a complex operation, exceeded the
level of the project's resources. This model is left specified
but not estimated. The last section presents benefit estimates
from the abstract site model, and comments on benefit estimates
from the system demand model.
150
-------
1. A Review of the Data
Table VII-2 shows the number of mentions and visits for each site
in our survey. The first column contains the number of households who
visited each site at least once during the summer of 1974; the second
column gives the total number of visits to the site by these households.
The median number of visits to a site, computed from the third column
of the table, is 7 visits per household. For reasons to be explained
below, the statistical analysis will be focused mainly on sites 1-29;
these sites account for almost 80% of the total number of mentions but
only 66.6% of the total number of household visits. Thus the excluded
sites appear to have a somwhat higher average visitation rate per house-
hold. In fact, however, this is misleading because some of the excluded
sites are really composites of individual sites. If we adjust for this,
the average visitation rates for the included and excluded sites would be
fairly similar.
To get some feel for the coverage of the sample Table VII-3 presents
a comparison of the site attendances generated by the respondents to our
questionnaire and estimates of total attendance at selected sites for
which data is available. The data in second column of the table was ob-
tained by multiplying the number of household visits to each site by the
average group size and summing this over all respondents. The data in the
first column comes from a variety of sources. Attendance figures were
generally not available at the head office of the MDC or at other official
agencies in Boston, but some data was available from staff at the sites
when we visited them. The quality' of the data is unknown: some of it
comes from a survey conducted in 1969; in other cases the data is based
on parking and entrance fee receipts. Taking this data at face value, ob-
serve that the households in our sample generated 0.13% of the estimated
total attendance at these sites. This may be compared with the ratio be-
tween our sample population and the total Boston area population, which
157
-------
1
Site
1
2
3
4
5
6
7
8
9
1Q
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
*32
33
*34
35
36
37
*38
*39
*40
41
*42
*43
All Sites
lean
Table VII-2
Individual Site Visits and Mentions
# of Mentions
21
45
98
112
9
15
14
30
7
11
9
11
11
4
30
115
51
74
43
23
15
34
14
17
20
47
8
22
2
24
43
12
10
4
9
4
4
27
24
18
11
49
6
1163
2.49
# of Household Visits
150
306
681
906
98
68
188
107
22
44
209
121
57
16
382
948
256
306
167
77
80
212
162
216
312
180
26
143
15
294
556
102
71
8
94
74
96
408
300
119
141
937
30
1685
20.74
(2)/(l)
7.1
6.8
6.9
8.1
10.9
4.5
13.4
3.6
3.1
4.0
23.2
11.0
5.2
4.0
12.7
8.2
5.0
4.1
3.9
3.3
5.3
6.2
11.6
12.7
15.6
3.8
3.3
6.5
7.5
12.3
12.9
5.7
7.1
2.0
10.4
18.5
24.0
15.1
12.5
6.6
12.8
19.1
5.0
8.3
9.0
NOTE: Column (1) excludes those respondents who mentioned a site
for the purpose of rating its characteristics but did not
actually visit it.
An Asterisk denotes those "sites" which are actually groups
of individual sites; each mention refers to a different
individual site and/or different respondent.
152
-------
Table VII-3
Total Attendance and Attendance from Sample Households
Site
1
2
3
4
5
6
7
9
10
12
15
16
18
22
23
24
27
28
29
TOTAL
At Selected Sites
(1)
Estimated
Annual
Attendance
-QO^ visitor
days)
\
t 2000
6400
350
750
500
1
r 2500
)
750
2700
140
150
175
750
40
120
105
17,430
(2)
Attendance
by Sample
Households
(visitor
days)
428,
957
1998
5124
2021
289
881
92
90
384
1628
3370
1246
918
991
602
84
662
141
21,911
(3)
Percent of
Total
Attendance
Generated by
Sample
0.17
0.08
0.58
0.04
0.18
0.02
0.22
0.12
0.89
0.61
0.57
0.08
0.21
0.55
0.13
0.13
NOTE: Column (2) is number of visits by household members to
sites multiplied by average group size.
Column (3) contains fractions of one percent.
153
-------
amounts to about 0.06%. The comparison suggests that the households
in our sample could be responsible for more recreation visits than the
average household in the Boston area. However, this conclusion must be
treated with considerable caution, for the total attendance estimates are
not reliable. Some of these figures date back to 1969 and others
are only guesses of numbers of automobiles, so that they understate
present attendance levels. On the other hand, it should be noted that
the attendance may have been generated by a population larger than that
of the Boston metropolitan area, since they may contain visits by tourists
from elsewhere in the state or from out of state.
The next issue to be considered is how many sites each household
visits. We pointed out in Chapter III that certain statistical site de-
mand models could be applied only if it were believed that each indivi-
dual visited one and only one of the alternative sites. It is there-
fore important to check the validity of this assumption. Table VII-4
shows the distribution of the number of sites visited by respondents.
It is clear that the assumption is not valid: two thirds of the sample
visited more than one site in the summer of 1974. In fact, that mean
number of sites visited was 2.5 sites per household, and the median and
modal number was 2 sites. Thus we must rule out those models which pre-
suppose the choice of a single site.
In fact, two types of demand models were estimated. The explana-
tory variables in one type include income and household structure and
the own price and quality variables for the site; in the other type
of models, besides these variables, there are also the prices and
quantities of the other (n-1) sites. In order to generate the data on
subjective site quality ratings necessary for the implementation of the
second type of model we included questions in our questionnaire asking
respondents to rate the quality of other sites which they knew about but did
not visit. Unfortunately, these questions were not very successful and,
154
-------
Table VII-4
Household Site Visitation Patterns
# of Sites
Visited
0
1
2
3
4
5
6
7
.8
9
10
11
t of
Occurrences
56
106
114
69
54
21
17
10
8
3
2
1
155
-------
for one reason or another, most respondents did not answer them. Thus,
while we have 1312 site cards, each representing the metnion of one site
by one respondent, only 148 cards represent the mention of sites which the
respondent did not visit but where he was willing to rate site quality.
To all intents and purposes, then, we do not have subjective ratings of
the sites which respondent did not visit. Since most respondents visited
only 2 or 3 sites, this rules out the majority of the sites where we
wish to model demand. Accordingly, if we wish to include a full set of (n-1)
other site variables in each demand equation, we have to use the objective
measure of water quality obtained from our water samples from 29 sites.
This is why we are forced to exclude sites 30-43 from most of the
statistical anlaysis.
The same problem arises with the price variable. However, there
are some additional considerations. The questionnnaire asks how much it
costs respondents to gain access to a site in parking or entrance fees.
It also asks how much respondents spend once they are at the site. As
Table VII-5 shows, most persons said that they incurred no expenditures
for access—about 73% of the mentions indicate a zero price—and about
one third of the respondents said they had no on-site expenditures. We
cannot tell how accurate these responses are: since the interviews were
administered three months after the end of the summer recreation season, it
is possible that the respondents have underestimated their true expenditures.
In view of these difficulties, we have decided throughout this chapter to
replace price with distance, which is easily computed for all sites.
This is a quite common practice in recreation studies and is justified
if travel and access costs are proportional to distance. That this
might be so is suggested by the following regression of access costs,
as reported by respondents, on distance (in miles):
Price = 0.0949 + 0.04086 Distance R = .012 F = 22.35
(1.06) (4.73) (1214 observations)
156
-------
Table VII-5
Occurrences of Zero Expenditures for Site Visits
Site
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
All Sites
# of Mentions
21
45
98
112
9
15
14
30
7
11
9
11
11
4
30
115
51
74
43
23
15
34
14
17
20
48
8
22
2
24
43
18
10
4
9
4
4
27
24
18
11
49
6
1164
# of Mentions with Zero
Expenditures
for Access
20
35
56
94
8
13
12
29
7
11
9
10
7
0
30
81
27
30
29
14
10
34
13
16
20
45
5
9
1
24
42
9
3
4
9
3
4
24
17
11
11
5
241
On-site
11
32
45
54
6
12
10
20
5
8
3
4
7
1
28
51
29
41
30
15
9
25
9
15
18
39
7
18
2
22
41
8
6
2
8
3
4
20
23
5
8
1
408
NOTE: This table excludes those respondents who mentioned
a site for the purpose of rating its characteristics
but did not actually visit it.
157 156
-------
2. Some Determinants of Recreation Activity
Although the following sections present demand functions for in-
dividual sites, it is interesting to consider how the total number of
sites visited or the total number of visits to all sites per household
is affected by various socio-economic and demographic factors. Some
regressions with thse dependent variables are shown in Table VII-6.
The first equations deal with household income and structure. KIDS is
the number of persons aged 17 and under in the respondents' household;
PEOPLE is the total number of persons of all ages in the household.
We might expect that the number of children in the household would have
a stronger effect on the scope of the household's beach recreation activ-
ity than the total size of the household. The opposite appears to be
the case:* in no case was the slope coefficient significantly different
from zero for KIDS. Also, it appears that the household income has no in-
fluence on the total number of visits to all sites by household (although
it does affect the total number of sites visited—richer families are
likely to visit more sites than poor families). However, the relationship
is fairly weak and is complicated by the collinearity between household
income and size.**
•
The next two regressions deal with racial differences in recreation
activity. IRISH is dummy variable taking the value 1 if the respondent
described himself as having an Irish background. ITALIAN is a dummy vari-
able for respondents with an Italian background and OTHER CAUCASIAN is a
dummy variable for other Caucasiaru backgrounds. Thus the slope coefficients
represent differential effects relative to respondents from minority groups—
American Indian, Asian-American, Black and Spanish Surname. In the regres-
sions of both numbers of visits to all sites and number of sites visited
*Similar results were obtained when we used a dummy variable taking
the value 1 if there were children and 0 if there were none, in place of
the continuous variable KIDS.
**In these regressions we have replaced missing household income values
with the sample mean, $14,137. This is the so-called zero-order regression
method—see Afifi and Elashoff [l ]; in the present context it produces
unbiased but inefficient estimates.
158
-------
Table VIJ-6
Total Site Visitation as a Function of Selected Socioeconomic Characteristics
(462 observations)
8.309 + 0.71
(.37) (.30) (2.08)
15.012 - 1373.79/INC + 1.4628
(3.86) (.08) (2.13)
# VISITS = 8.309 + 0.71171n(INC) + 1.4317 PEOPLE R2=.01 F=2.41
# VISITS = 15.012 - 1373.79/INC + 1.4628 PEOPLE R2=.01 F-2.37
# SITES = 0.116 + 0.24281n(INC) + 0.1736 KIDS R2«.008 F-1.74
(.08) (1.58) (.89)
2.611 - 2099.74/INC + 0.1783
(13.26) (1.82) (.92)
0.39 + 0.17461n(INC) + 0.1141
(.27) (1.12) (2.55)
2.203 - 1654.43/INC + 0.1142
(8.67) (1.43) (2.55)
# SITES - 2.611 - 2099.74/INC + 0.1783 KIDS R2-.009 F-2.14
# SITES = 0.39 + 0.17461n(INC) + 0.1148 PEOPLE R2=.02 F»4.59
# SITES = 2.203 - 1654.43/INC + 0.1142 PEOPLE R2=.022 F=4.98
INC = 11266.4 + 732.145 PEOPLE R2«.035 F-16.75
(13.5) (4.09)
# VISITS = 13.94 + 16.02 IRISH +5.2 ITALIAN +5.4 OTHER CAUCASIAN
(3.20) (3.01) (0.95) (1.13) -
R =.026 F=4.07
# SITES = 1.98 + 0.95 IRISH +0.77 ITALIAN +0.38 OTHER CAUCASIAN
(6.89) (2.7) (2.13) (1.22)
R =.022 F=3.38
# VISITS = 10.30 + 3.213 AUTO OWNERSHIP R =.002 F=.73
(5.33) (0.85)
M4 + 0.448 ;
(9.51) (1.81)
# SITES = 2.14 + 0.448 AUTO OWNERSHIP R =.007 F=3.29
2
# VISITS = 19.46 + 0.527 DAYS WORKED PER WEEK R =.000 F=.16
(4.78) (0.39)
..973 + 0.188 1
(7.4) (2.15)
2
# SITES = 1.973 + 0.188 DAYS WORKED PER WEEK R =.01 F=4.6
159
-------
the hypothesis that the slope coefficients are all zero—if there is
no difference in the recreation behavior of minority and other groups—
is rejected at the .05 level. However, in the first regression, it is
clear that only the Irish have a significantly different recreation be-
havior—on average they make 16 more visits per household—while
Italian and other Caucasian respondents have the same behavior as minor-
ity group respondents. In the case of the number of sites visited, both
Irish and Italian, but not other Caucasians, have a significantly differ-
ent behavior from minority groups; moreover, the hypothesis that Irish
and Italian respondents have the same behavior cannot be rejected at the
.05 level.
The remaining regressions show that automobile ownership has some
effect on the number of sites visited, but not on the total of visits to
all sites; and also that the length of the working week has a similar ef-
fect. However, the sign of the relationship is the opposite of
what we might expect—it appears that longer working weeks lead to a lar-
ger number of sites being visited. In some regressions not reported here,
we found no relationship between the length of paid vacation and the to-
tal number of visits to all sites or the total number of sites visited.
This is not surprising since our data pertains to day trips and we might
expect vacation length to influence more extended trips but not day trips.
160
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3. Abstract Site Demand Functions
The demand functions presented in this section differ from the
demand functions to be discussed in the next section in two ways.
Firstly, the demand functions presented in this section contain only
own price and quality variables. Secondly, they are not derived from
an explicity utility function.* On the other hand, the demand func-
tions in this section differ from those estimated by Clawson and Knetch
[5 ], and those who have copied their methodology in that instead of
estimating separate demand functions for each site or for groups of
sites and included site quality explicity as an explanatory variable.
The demand functions thus resemble the "abstract mode" demand functions
pioneered in transportation economics by Quandt and Baumol L^J- The
functions which we estimate have the following form
vit = f[dit'V cit'Yt
where V. is the number of visits to a site i by an individual t, d.
is the distance traveled (a proxy for price) for individual t in visiting
site i, Z. is a vector of "objective" characteristics of site i, C.. is
a vector of characteristics of site i as perceived by individual t, and
y is a fector of characteristics pertaining to individual t, such as
household income and composition.
At this point we must deal with the question of zero visitation
rates. As Table VII-4 indicates, nobody in our sample visits all of the
possible sites and indeed, most people visit very few of them. We re-
*In Section 3 of Chapter 3 we suggested a specific utility function
which would lead to demand functions containing only own price and quality
variables—see equation (13) of Chapter 3. However, as we pointed out,
these particular demand functions require a form of constrained estimation
which would be very burdensome computationally, and we have not attempted
to estimate them.
161
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marked in Chapter III that the problem of zero visitation rates can be
incorporated into stochastic choice system demand models, but it would
be prohibitively expensive to apply such a model when there are so many
alternative sites. It is relatively easier to deal with this phenomenon
in the context of the ad-hoc demand functions represented by (1) . Since
there are 4627 respondents in our sample and 29 sites (at least), (V )
would be a vector with 13,543 (= 467 x 29) rows. 912 elements of (V. )
would be non-zero—this is the number of mentions corresponding to sites
1-29, as listed in Table VII-1—and the remainder would be zero. The obvious
estimation method would be Tobit analysis.* Unfortunately, however, the
data sets involved are too large to be handled by the conventional Tobit
programs. The alternative is a two-step procedure suggested by Goldberger
[ 6 ], in which the analysis is broken down into two issues.** The first
issue is what determines whether a given individual visits a given site
at all. We can think of the dependent -variable, V. , as being a dummy
variable which takes the value 1 if individual t makes at least one visit
to site i, and the value zero otherwise. Thus (V. ) is a 13543 x 1 vector
of 1's and O's. The second issue is: given that an individual visits a
site, what determines how many times he visits it? In this case, the anal-
ysis is restricted to the subject of cases where visits are actually made,
and the dependent variable, V. , is a 912 x 1 vector containing the (non-
zero) numbers of visits by each household to each site.
The two-stage procedure does not necessarily produce the same coeffi-
cient estimates as the theoretically preferable Tobit analysis, but is is
the best alternative available. Moreover, as Goldberger [ 6] points out,
it is somewhat more flexible than the Tobit procedure because it allows us
to specify different.sets of regressors in the two stages of the estimation.
Thus the factors which determine the probability of an individual's making
any visit to a site need not be the same as those which determine how many
*See, e.g., Goldberger
**Goldberger
162
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visits he makes to those sites which he does visit. We intend to ex-
ploit this opportunity; indeed it is necessary for us to do so because,
as noted in Section 1, subjective site ratings are generally available
only for those sites which respondents actually visited. Thus these
variables can be included in the second, but not the first stage regres-
sion. Moreover, in our opinion, certain socio-economic variables such
as household income and size are not likely to influence whether an indi-
vidual visits a random site, although they are likely to influence how
many visits an individual makes to a site which he does visit*" There-
fore, we propose to exclude these two variables from the first stage re-
gressions.
The first-stage regressions, although computationally more conven-
ient than Tobit analysis, are by no means problem free. The dependent
variable in those regressions is a dummy variable and OLS is not a natural
estimation method in these circumstances. The normal practice is to use
maximum likelihood estimates based on some specification of the random pro-
cess which generates the 1's and O's, the most common specifications being
the Probit and the Logit models. The two models are quite similar but.
Since the latter is more convenient for reasons to be explained below, we
.adopt it here. The idea behind Logit (and Probit) analysis is similar to
the idea behind the discrete dependent variable model presented in Chapter
III. We assume that there is an underlying unobserved continuous variable
W given by
W = a + £x.B. + u .,. (2)
and the observed dichotomous variable V is generated from W by the rule
This statement may not be strictly true in the light of the results
reported in Section 2. An alternative statement, which may be more accept-
able, is that the influence of household income and size on the probability
that an arbitrary individual visits an arbitrary site is less interesting
than the influence of these variables on the number of visits made by an
individual to those sites which he docs visit.
163
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Thus if H ( • ) is the cumulative distribution function of the random
variable u, we have:
P = Prob[v-l] - H[-a - Ex.6.]
(1-P) = Prob[v-o] = l-H[-a - Ex.B.]
If u is assumed to be normally distributed, we have the Probit Model;
if u is assumed to follow the logistic distrubtion, we have the Logit
model. In the latter case we observe that
109
and
, -a-Ex. B.
1 + e 3 ")
For either model the likelihood function is
H H[-a-Zx.6.] n (l-H[-a-Ex.3.]) ... (4)
V =1 3 D v. =0 D -1
it it
It would be possible to obtain maximum likelihood estimates of the
coefficients (Jx.6. ) on the basis of (4) but, given the size of our data
set, this would be very expensive. Instead we shall avail ourselves of
a much simpler computational procedure suggested recently by Haggerstrom
I 7 J, on the basis of work by Halperin, Blackwolder and Verter [8j.
The latter authors show that maximum likelihood estimates of the parame-
ters of the Logit model in practice are very close to the coefficient
estimates obtained by discriminant analysis. Haggerstrom points out that
discriminant analysis coefficients can be obtained from a relatively sim-
ple transformation of ordinary least squares regression coefficients us-
ing a dummy-dependent variable. Thus, while OLS by itself is not an appro-
164
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priate technique for handling dummy dependent variables, the OLS co-
efficient estimates when suitably transformed provide a good approxima-
tion to the maximum likelihood estimates of the Logit coefficients, and
the OLS t and F statistics may reasonably be used to test hypotheses
about the Logit coefficients. It should be noted that, although the
predicted values of the dependent variable obtained using OLS are not
constrained to lie between 0 and 1, the predicted values of the depen-
dent variable obtained from the transformed OLS coefficients do satisfy
this constraint. Haggerstrom shows that, if (a,6.) are the OLS coeffi-
* A -*
cient estimates and ( a,g. ) the discriminant analysis coefficient esti-
mates the required transformation is:
§,- «.
o = log (Pi/P2) + C[a-Jj] + JCn'1 - n'1]
where C = n/SSR, SSR being the sum of squared residuals from the OLS
regression n. is the number of cases in which the dependent variable
takes the value 1 (i.e. 912), n2=n-n=12,486, P =n /n, and P =n /n.
For the reasons mentioned above, we decided that the most impor-
tant regressor variables for the. first stage analysis were the distance of
individual t from the site i and some measures of water quality at site i.
On the basis of the regression analysis of willingness to pay and the ac-
curacy of subjective perception of water quality parameters reported else-
where, we decided to confine our analysis to three parameters—color, coli-
form bacteria counts and phosphorous content. When we came to implement
the OLS regression of a dummy variable for site visitation we found
'that, even using OLS, the data set exceeded the capacity of the pro-
grams available to us, so we restricted ourselves to no more than two
regressions and truncated the data set at 11,000 observations. The
results of these regressions are shown in Table VII-7. The regression
coefficients have the signs which we would expect and are significantly
different from zero: the greater the distance and the more polluted a
site (in terms of color, coliform bacteria or phosphorus) the lower the
165
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Table VI 1-7
Probability of Site Visitation — Logit Model
Variable
CONSTANT
DISTANCE
PHOSPHORUS
COLI
COLOR
R2
F
SSR
n/SSR
OLS
Estimate
0.1682
(25.6)
-0.00433
(11.5)
-0.7332
(13.95)
.022
120.42
727.91
Discriminant
Estimate
-1.245
-0.06543
-11.0799
15.11
OLS
Estimate
0.1094
(22.73)
. -0.003
(8.18)
-0.00000315
(4.97)
.007
39.12
739.12
Discriminant
Estimate
-2.0437
-0.04465
-0.0000469
14.88
OLS
Estimate
0.1944
(27.79)
-0.00533
(13.73)
j
-0.00803
(17.26)
.031
176.38
721.25
Discriminant
Estimate _
-0.392
-0.08129
-0.1232
15.25
n = 11,000; n = 803; HZ = 10,197
log(P /P ) + 2£l~ I ] - 3.768
x * ^ *i_ n^
166
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probability that a respondent visits it. The impact of objective water
quality conditions on the probability that a site is visited at least
once is unambiguously established by these results,
However, when we come to the second stage regressions—the OLS
regression of the number of visits by members of a respondent's house-
hold to each site which it visits—we reach a rather different conclu-
sion. Tables VII-8 and VII-9* presents the results of several regressions
of this variable on various sets of regressors including alternatively
subjective water quality ratings and objective measures of water quality.
The other variables are distance from site (DIST), household income** and
size (INC, PEOPLE) and a dummy variable, ACCESS, which takes the value 1
if the site is accessible by public transportation and the value 0 other-
wise. *** Several results stand out in these regressions. DIST always has
a significant negative coefficient and although the coefficient of INC is
unstable in sign and frequently insignificant—at least partly because of
the colinearity with PEOPLE—in the preferred equations it is positive and
fairly significant. As we might expect, household size and accessibility
to public transport always have a positive effect on the number of visits
to a site although these slope coefficients are not always significant.
The most important findings concern the relative performance of
subjective and objective measures of water quality as explanatory vari-
ables. Subjective water quality rating always has a significant positive
coefficient—respondents make more visits to a site which they consider
to be of higher quality. This is not a surprising conclusion, although
* "There are 819 rather than 912 observations because 93 site cards
contain no water or beach quality ratings.
** As with the regressions presented in section 2, we have replaced
missing income values with the mean income of $14,317.
*** In Tables VTT-7 and VII-8 an asterisk marks the preferred equation. The
choice between functional forms is based on the Box & Cox [ 3] maxi-
mum likelihood criterion.
167
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Table VI1-8
Abstract Site Demand Functions with Subjective Quality
Ratings
(819 observations)
VISITS = 4.226 + 7903.46/INC + 0.8649 RWQUAL - 0.3775 DIST
(2.76) (1.53) (2.68) (5.73)
+ 2.2461 ACCESS - 0.3804 PEOPLE
(2.63) (2.13) R -.076 P=13.32
VISITS = 5.431 - .00000675 INC + 0.8567 RWQUAL - 0.3889 DIST
(3.79) (.14) (2.65) (5.89)
+ 2.2323 ACCESS + 0.3346 PEOPLE R -.073 F»12.82
(2.61) (1.86)
VISITS = 11.441 - 0.671n(INC) + 0.8567RWQUAL - 0.3811 DIST
(1.84) (1.00) (2.66) (5.77)
+ 2.2376. ACCESS + 0.3665 PEOPLE R2=.074 F=13.033
(5.76) (2.60)
In(VISITS) = 1.363 + 512.653/INC + 0.0745 RWQUAL - 0.0464 DIST
(10.39) (1.16) (2.7) (8.23)
+ 0.088 ACCESS + 0.0172 PEOPLE R2=.103 F=18.573
(1.2) ' (1.12)
In(VISITS) = 1.375 + 512.887/INC + 0.0776' RWQUAL - 0.0077 RBQUAL
(9.93) (1.16). (2.61) (.27)
- 0.0463 DIST + 0.0875 ACCESS + 0.0175 PEOPLE R =-103 F=15.473
(8.22) (1.20) (1.14)
*ln(VISITS) = 13.607 -I- 0.0000072 INC + 0.0759 RWQUAL - 0.0485 DIST
(11.13) (1.78) (2.76) (8.62)
2
+ 0.0861 ACCESS + 0.00856 PEOPLE R =-105 F=18.98
(1-18) (5.56)
In(VISITS) = 1.409 + 0.003041n'(INC) + 0.0741 RWQUAL - 0.0472 DIST
(2.65) (.05) (2.69) (8.36)
+ 0.087 ACCESS + 0.0138 PEOPLE R =.101 F=18.275
(1.19) (0.90)
168
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Table VII-9
Abstract Site Demand Functions with Objective Quality
Variables for 29 Sites
VISITS = 5.83 + 7693.71/INC + 0.0000344 COLl + 0.0526 COLOR
(3.92) (1.48) (0.26) (0.57)
- 0.3025 DIST + 1.9361 ACCESS + 0.426 PEOPLE R =.068 F=9.901
(4.67) (2.21) (2.38)
VISITS = 5.525 + 7110.52/INC - 0.000054 COLI + 0.044 COLOR
(3.69) (1.37) (0.44) (0.4)
+ 24.217" PHOSPHORUS - 0.2935 DIST + 1.8 ACCESS
(1.68) (4.52) (2.05)
2
+ 0.387. PEOPLE R =.071 F=8.907
(2.14)
VISITS - 7.023 - 0.00001105. INC + 0.0000352 COLI + 0.0531 COLOR
(5.07) (0.23) (0.26) . (0.57)
- 0.3133.DIST + 1.9239 ACCESS + 0.3843 PEOPLE R =.066 F=9.52
(4.84) (2.20) (2.14)
In(VISITS) = 1.54 + 495.99/INC + 0.0000146 COLI - 0.00318 COLOR
(12.12) (1.12) (1.29) (0.4)
- 0.0408 DIST + 0.0514 ACCESS + 0.0222 PEOPLE R2=0.96 F=14.424
(7.36) (0.69) (1.45)
In(VISITS) = 1.54 + 494.95/INC + 0.0000144 COLI - 0.00335 COLOR
(12.02) (1.11) (1.17) (0.36)
+ 0.043. PHOSPHORUS - 0.0407 DIST + 0.0152 ACCESS
(0.03) (7.33) (0.68)
2
+ 0.0221. PEOPLE R =.096 F=12.35
(1.43)
*ln(VISITS) = 1.541 + 0.00000672' INC + 0.0000143 COLI - 0.00279 COLOR
(13.05) (1.65) (1.27) (0.35)
+ 0.426: DIST + 0.0494 ACCESS + 0.014 PEOPLE R =.098 F=14.7
(7.72) (0.66) (0.91)
In (VISITS) = 1.59 + 0.0021. In(INC) + 0.0000146 COLI - 0.0031 COLOR
(2.98) (0.04) (1.3) (0.4)
- 0.0416 DIST + 0.0505 ACCESS + 0.0188 PEOPLE R2=.095 F=14.2
(7.5) (0.68) (1.22)
169
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the direction of causation is ambiguous. It might be best to regard
site ratings as jointly endogenous variables together with site
visitation rates, the true exogenous variables being the objective
measures of site quality. However, there is very little relationship
between objective measures of site quality and the frequency with
which a site is visited. The coefficients of COLOR, COLI BACT and
PHOS are usually insignificant and frequently of the "wrong" sign.
The data provides little evidence that objectively better sites
are visited more frequently, other things being equal.
Thus, we may conclude that if a site has a better water quality
there is a higher probability that a household taken at random
will visit it at least once but, given that the household does visit
the site, there is little reason to believe that the site is visited
more frequently than other sites of lower water quality. On the
other hand, households make more visits to sites which they believe
to be of a higher quality—or perhaps the converse is true: households
believe that the sites which they visit often are better than those
which they visit rarely. This discrepancy is similar to that observed
•
in the analysis of willingness-to-pay; households were willing to
pay more for sites which they believed to be of a higher quality,
but not necessarily for sites wihich objectively had a higher
quality. It is consistent with our finding in Chapter 5 that
subjective site rating match up with objective site conditions only
imperfectly.
170
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4. System Demand Functions
Chapter 3 suggested the following model for deriving site demand
functions based on p characteristics Z. . :
U = Zb.log(V.-c.) ... (la)
P
c. = W. + , E, W. Z., ... (Ib)
i 10 k=l k ik
The demand functions obtained from this utility model are:
3iibJ
where V is the number of visits to site i by individual t. The
standard practice in consumer demand theory is to normalize the b.'s
so that Zb.=l, in which case (2) can also be written in expenditure
form as
This function is nonlinear in the parameters b. and c. (or,
equivalently, in the parameters b. and W. , W ). Two alternative
JL 1O X,
estimation procedures are available: a maximum likelihood estimation
procedure due to Parks [10] and less sophisticated iterative two-
part procedure due to Stone [12J. Because of its computational
simplicity, we shall follow Stone's procedure here. This procedure
»
is based on the fact that, for a given set of values of the parameters
b., equations (2) and (3) are linear functions of c. (or,
171
-------
equivalently, of W. and W), while for a given set of values of the
i-O is.
parameter c., these equations are linear functions of b.. Stone's
method is to iterate between OLS estimates of b,, for given values
of c., and OLS estimates of c.r for given values of b..
At this point we have to face the fact, hitherto neglected,
that we are actually dealing with a subset of commodities—namely,
expenditures on recreation sites—rather than with the whole set
of consumption items. This raises the question of whether the
theory developed for the latter situation can be applied here.
The answer is that the general theory does carry over to the case
of a subset of commodities if the consumer's utility function is
assumed to be appropriately separable. There are various concepts
of separability which we might invole; without going into detail, we
may state that an underlying idea of these concepts is that the
marginal rate of substitution between -any pair of recreation sites
should be independent of the consumer's level of consumption
of any other commodity besides recreation sites.* This is a strong
requirement, but not an entirely unreasonable one. If it is
accepted, and if the relevant portion of the consumer's utility
function dealing with the utility from beach recreation is given
by (1), then the site demand functions are indeed given by (2) or
(3), with one change. Site depand depends on the prices of the n
sites and on the total expenditure on beach recreation, rather than
income. Thus, the variable, Y, in (2) or (3) must be taken as
standing for total expenditure on water-oriented recreation. This
variable is then endogenous to the consumer's choice process, and is,
therefore, a function of the prices of both recreation sites and (in
general) all the other commodities as well as income. Instead of
trying to model the determinants of recreation expenditure explicitly,
we shall employ the assumption commonly used in Engle curve analysis
*See, for example, Pollak [ll].
172
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that there is relatively little variation in the prices of non-
recreation goods faced by our sample households; hence, we may
postulate some simple relationship between expenditure on beach
recreation (Y) and income, such as
or
Y » d + d.INC ... (4a)
o i
Y = d + d,ln (INC) ... (4b)
o 1
If we substitute (4a) or (4b) into (2) or (3) we have a fully specified
system of demand equations for recreation sites, under the
separability assumption.
There are still some complications due to the fact that, for the
reasons outlined in Section 1, we do not have good price data.
Because of this deficiency, we have chosen to use distance as a
proxy for price and, as we observed in the previous section, this
seems to be a good substitute. However, in the context of system
demand models, this substitution causes some problems because it
means that the "adding-up condition" no longer applies—i.e., it is
no longer true that for each individual, the sum of the left-hand
side variables in Equation (3) over all sites is exactly equal to
Y, the total expenditure on water-oriented recreation. The adding-up
condition in practice has an important role in the estimation of
(2) or (3) both with the maximum likelihood procedure and with Stone's
method. In the latter case it helps to ensure that £b.=l without
the need for constrained estimation techniques. Without this assump-
tion, therefore, we must either use constrained OLS estimation, which
is computationally difficult or simplify the model further. We have chosen
the latter alternative. Specifically, we have assumed that
b.=b i=l...n ... (5)
173
-------
and, without any loss of generality, we have taken b=l. Accordingly,
the term (b./£b.) in (2) is replaced by (1/n), n being the number of
sites. Since we have in effect suppressed b. as a parameter, the only
parameters to be estimated are the c.'s (i.e., W. ,W ); as we noted
X _LO JC
above, with the values of b. known, equations (2) or (3) are linear
in the latter variables and a single-stage OLS estimation may be
applied. We have, thus, removed the need for iterating on the
coefficient estimates, thus greatly reducing the computational difficulty.
The model which we propose to estimate is given by (2), (Ib),
(4) and (5). We have chosen to use as site characteristics COLOR
and COLIFORM; thus, there are 33 coefficients to be estimated:
29 W. 's—one for each site; W, , the coefficient of COLOR; W0, the
10 1 2
coefficient of COLI; and the parameters d and dn in (4). We
o 1
have 912 observations from which to estimate these coefficients,
corresponding to the site cards with non-zero visits. Assuming that
we share the specification (4a), the actual estimating equations are:
P.
P.V. - W. P. f^-) - .§.W. -3- + W, {Z,.P. f?-=-) + .E.Z. .P.. }
11 10 i v n ' 37*1 30 ._n 1 li i v n ' j|si I] ;j/n
+ w (2 P j""1 + r z P }
2 2i i ^ n * j£i 2i j/n
d° dl
+ — + — INC i»l...n (6)
n n
Unfortunately, despite several attempts to model (6), we
were unable to do so. The reason was that the data were highly
collinear leading to a nearly singular cross-product matrix which
could not be inverted. One possible solution may be to group
neighboring sites of similar quality so that there is a smaller
set of sites differing more in their locations. This would cause
the matrix of price (distance) variables to be less collinear and
174
-------
simultaneously reduce the number of parameters to be estimated.
Also, it is possible that maximum likelihood estimation of a less
specialized version of the model might prove to be more successful.
There is ample scope for further research on the specification and
estimation of the model, but this was beyond the scope of this
project.
5. Benefit Calculation
The only rigorous method to obtain empirical measures of
willingness-to-pay for changes in recreation site quality is to
estimate a set of demand functions which can be shown to derive from
a specific utility function and, using the coefficient estimates,
to calculate the resulting change in the area under the compensated
function. If the utility function is that given by (1), the
corresponding formula for the consumer's surplus associated with
a change in site quality is given by Formula (1) in Chapter 3,
with the c. terms replaced by equations (Ib) above. Since we
are not presently able to estimate this demand model, we are unable
to apply this methodology to calculate the benefits of changes
in water quality.
We are forced, instead, to rely on the abstract site demand
functions described in Section 3. Since these demand functions
are not derivable from an explicit utility function, there is no basis
for calculating measures of consumer surplus. All that we can do
with these demand functions is to predict the impact of
water quality changes in site visitation. The only solution is to
use some ad hoc metric such as the Principals and Standards estimate
that one visitor day is "worth" $.75-$2.50; alternatively, we
could value visits at the average willingness-to-pay plus
transportation costs as expressed by the respondents to our
175
-------
questionnaire. As an illustration of this procedure, suppose
that the coliforro bacteria, count at a site declines from the
average ( 2000) to the minimum across the samples, 100. Assuming
that an individual lives five miles from the site; using the
coefficients in the fourth column of Table VII-7, we calculate
that the probability that the individual will visit the
site changes from:
1+e
or
,0.086 (COLI=2000)
°-094
-------
6. Conclusions
This chapter provides interesting additional evidence for some of
the points argued elsewhere in the report. First, persons with large
families or families with higher incomes tended to visit our sample
beaches more frequently than other families. Family ethnic background
also appears to influence recreation behavior.
Second, substitution between sites is a significant aspect of
recreation behavior in the Boston sample of households and sites. Most
respondents visited two or more sites during the summer. Under direct
questioning, most cited inter-site substitution as their most likely
response to a change in water quality at their favorite beach. Any-
where proximal sites are close substitutes, perhaps most urban areas,
inter-site substitution is likely to be an important phenomenon. Thus,
single site demand models are not altogether appropriate for either
demand forecasting or benefit estimation. We specified a system demand
model to account explicitly for this behavior, but were not able to
complete its estimation with the resources available to us. This is a
fruitful area for further research.
Finally, poor water quality at a site appears to reduce the pro-
bability that a randomly selected household will visit the site at all,
but does not influence the number of visits to the site given that it
is visited at least once. Hence, water quality changes impact recreation
behavior principally through inter-site substitutions; this reinforces
the need for systems demand models. On the other hand, higher perceived
water quality is significantly associated with more visits, but the dir-
ection of causation is by no means evident. Again we must conclude that
while subjective ratings of water quality match only poorly objective
measures, Bostonians seem to value maintaining and improving the area's
waters for recreational uses.
177
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1. A.A. Afifi and R.M. Elashoff, "Missing Observations in Multi-
variate Statistics II. Point Estimation in Simple Linear
Regression," Journal of the American Statistical Association
(March 1967): 10-29.
2. M.R. Anderberg, Cluster Analysis for Applications, Academic
Press, 1973.
3. G.E.P. Box and D.R. Cox, "An Analysis of Transformations," Journal
of Royal Statistical Association Series B (1964) : 211-252.
4. C.J. Cicchetti, A.C. Fisher, V. Kerry Smith, "An Economic
Evaluation of a Generalized Consumer Surplus: The Mineral
King Controversy," unpublished paper, Natural Environments
Program, Resources for the Future, 1973.
5. M. Clawson & J. Knetsch, Economics of Outdoor Recreation,
Baltimore: Johns Hopkins University Press,1966.
6. A. Goldberger, Econometric Theory, New York: John Wiley fi Sons,
1966.
7. Haggestrom, Notes on Discriminant Analysis, Logistic Regression,
Rand Memorandum, dated 4/3/73.
'8. M. Halperin, W.C. Blackwalder & J.C. Verter, "Estimation of the
Multivariate Logistic Function: A Comparison of the
Discriminant Function and ML Approaches," Journal of Chronic
Diseases (1971): 125-158.
9. R.E. Quandt & W.J. Baumof, "The Demand for Abstract Transport
Modes: Theory & Measurement," Journal of Regional Science
(1966): 13-26.
10. R.W. Parks & A.P. Barten, "A Cross-Country Comparison of the
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Consumption Patterns," Economic Journal (September 1973).
178
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11. Pollak, Robert, "Subindexes in the Cost of Living Index,"
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179
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JO. CONCLUSIONS
Where did this research take us? The conclusions of the study,
presented in each of the chapters below, can be summarized in three
parts. First, we explore a number of methodological issues related
to recreation demand analysis and the benefits of water quality en-
hancement. Of particular importance is our theoretical work incorporat-
ing substitution between sites in formal demand models and using these
models to derive benefit estimates. Hopefully, our work in this area
will help other researchers as they try to clarify some of the issues
treated in this study, and the broader questions of water quality
management.
Second, we use these models to analyze day recreation trips in
the Boston SMSA, with particular emphasis on how changes in water quality
'would influence recreation behavior. These empirical results are of
interest to national and regional water quality planning and management,
and may also be useful to recreation planners.
Finally, both the methodological and empirical findings of this
research suggest several areas where additional research is critical
for resolving the issues of this report.
1. Empirical Findings
Perceived Water Quality Does Not Seem to be Related to Actual
Water Quality. Bacteria counts, nutrients and so on are not perceived
by human senses. Turbidity and color are perceived moderately well by
recreationists, but with only a low degree of reliability. Reputations
of beaches as being good or bad may be a much more important determinant
of water quality perception than the actual quality of the water itself.
This conclusion tends to undermine any causal links between recreation
behavior and water quality.
180
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Recreation Behavior Is Not Strongly Linked to Objective Measures
of Water Quality. No evidence was found to reject this null hypothesis.
On the contrary, under direct questioning, water quality appears to
follow behind proximity, beach cleanliness, setting and beach facilities
in importance to site choice or attendance. These findings are con-
firmed in the multiple site demand analysis. Some evidence suggests
that good water quality is important in determining which sites are
visited, but not the number of visits to the site. In light of this
finding, the principal benefit, in terms of recreational usage, of
water quality improvements in urban areas such as the Boston SMSA would
be to reopen beaches which are proximal to large population concentrations.
Despite the Insensitivity of Recreation Demand to Water Quality,
Respondents in the Boston SMSA were Willing to Pay from Between $20
to $26 Per Family Per Year for Improved Water Quality. The willingness-
to-pay persists across income groups, occupational levels, and amount
of education. Water quality appears to be a merit good of significant
value. Perhaps, then, attempts to quantify benefits on the basis of
consumption are misguided. Water quality, like democracy or national
*
defense, are "goods" desired for their own conservation.
Willingness-to-Pay Seems to be Correlated with Water Quality.
That is, people are willing.to pay more to maintain water quality
at a site with good water quality than at a site with poorer water
quality. Over the range of water quality represented in the sample of
sites, there are, therefore, increasing returns to water quality.
This finding may be of significant practical importance in water quality
planning since the incremental costs of water quality improvements tend
to increase as higher levels of water quality are attained.
181
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Finally, Where Water Quality Improvements Expand Recreation
Opportunities, Adequate Facilities and Maintenance Must be Provided
to Gain The Benefits. People are sensitive to beach cleanliness and
minimal beach facilities, such as a changing room. These must-be
provided to gain the potential benefits of water quality enhancement.
Coordination with parks and recreation departments, generally
institutionally separated from water quality agencies, must be
established and maintained, and adequate funds for these new respon-
sibilities must be insured.
2. Methodology
Multiple Site Demand Models which Provide Exact Measures of
Benefits as Measured by Consumer Surplus can be Specified.
Traditional recreation demand studies ignore intersite substitu-
tions; existing multiple site demand models do not meet the technical
economic criteria for consumer surplus computations. A model which
meets these conditions was specified. Estimation of its parameters
was attempted but was unsuccessful. Methods for dealing with the
attendant problems are outlined.
Factor Analysis can Effectively Reduce the Number of Dimensions
of Water Quality, but the Resulting Factors are not Better
"Explainers" of Recreation Behavior than the Variables From Which
they are Drawn. Cross-sectional data on twelve water quality
measures could be reduced to four factors which "explained" most
of the variance in the data. These factors have natural inter-
pretations. However, certain of the original variables perform
as well as the factors in the statistical analysis relating water
quality perception and recreation demand to water quality variables.
182
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3. Avenues for Further Research
Why do People Care About Water Quality if they are not Sensitive
to Consuming its Uses? This conservation ethic seems to be behind
much contemporary environmental concern. Methods for measuring its
value and weighing it in the political calculus could provide the
basis for more efficient natural resource management. Further, a more
precise statement of its nature might help clarify the issues con-
cerning environmental preservation on one hand, and resource exploita-
tion on the other.
Improved Methodology for Estimating System Demand Equations
for a Large Number of Similar Goods is Needed. In the large, multi-
equation techniques are very expensive and are capable of handling
only a limited number of alternatives. The problem lies both in exist-
.ing software, and the statistical techniques in use. In the small,
further work on the model specified in this study could proceed by
aggregating sites to some (much) smaller number of representative
sites.
Finally, the Analysis Should be Extended,to Non-urban Areas.
While at present most of the nation lives in or close to major cities,
there is some evidence that those demographic trends are shifting, and
significant exurbanization has occurred during the late 1960's, and
through the 1970's. How does this affect recreational needs and their
relationship to water quality? Less urban areas typically have higher
levels of water quality than urban areas, so the recreational usage may
not be constrained by water quality, and conservation value may be
less as well.
183
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APPENDIX I. SITE FACILITY INVENTORY FORM
SITE CATALOG
1. Site Name
2. Address
3. Owner or Manager
4. What fees are charged (list purpose & amount)
ACCESS & PARKING
5. Rapid Transit: route name/no.
6. Bus: route name/no.
7. Auto Road: route name/no.
8. Distance to major highway (miles)
9. Number of parking spaces
SETTING
10. Urban Rural
11. Surrounding Land Use
a) low density residential (1 & 2 family homes)
b) high density residential (includes multifamily
buildings)
c) commercial
d) industrial
e) agricultural
f) natural
184
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12. If Natural Land Use, select from below categories
a) not applicable
b) salt marsh or other wet lands
c) wooded or forest
d) mountainous of cliffs
13. Type of Body of Water
a) ocean or great lake
b) lake or pond
c) river
d) stream
SIZE
14. . Water frontage (in feet)
15. Beach area
16. Water surface area (if appropriate)
17. Total site area
BEACH CHARACTERISTICS
18. Material
a. sand
b. gravel
c. grass or ground cover
d. rocks
e. paving
185
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19. Describe transition from land to water
a. gradual, sloping
b. abrupt
20. Describe nature of v;ater bottom
a. muddy
b. sand
c. rocks
d. vegetation
21. Water movement
a. no movement
b. slow movement
c. rapid
22. Presence of flies or other insects
a. none b. some c. many
FACILITIES
23. What special facilities are available for swimming
a. bathhouse
b. raft'or float
c. diving board
d. delimited swimming area
e. life guards -(how many? )
f. other
186
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24. What special facilities are available for boating?
a. marina
b. boat launch ramps (how many? )
c. boat rental facilities (what kinds of
boats? )
d. services and supplies
e. gasoline
f. other
25. What special provisions or facilities are provided
for fishing?
a. program of fish stocking
b. list type of fish
c. suppliers (of bait, etc.)
26. What non-water based facilities are provided?
a. playground
b. game areas
number of tennis courts
number of ball fields
other
c. number of developed camp sites
d. amusement park or other facilities
e. number of miles of walking trails
187
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USER CONVENIENCE FACILITIES
27. Which and how many of each of the following•sanitary
facilities are provided?
a. drinking fountains
b. sinks or water for washing
c. flush toilets
d. pit toilets
e. litter containers
EATING FACILITIES
28. What picnic facilities are available?
a. size of area in acres
b. number of picnic tables
c. number of fireplaces
d. number of grills
e. number of shelters
f. total square feet of sheltered area
29. How far it it to the nearest
a. Restaurant?
1. on-site
2. distance in miles
b. Concession Stand?
1. on-site
2. distance in miles
188
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29. c. Food Store?
1. on-site
2. distance in miles
SITE USE
30. Are attendance or other usage data available?
yes no
31. Annual number of visitors
32. Number of visitors on a peak day
33. What is the number of groups in 100 sq.ft. of site
area? a. b.
34. Estimate number of visitors
35. In your opinion/ is this site crowded (scale of 1
to 3)?
MAINTENANCE
36. Are any facilities in need of repair? List
37. In your opinion, is the site littered? (on a scale
of 1 to 3)
38- HOW often is trash removed and trash barrels emptied?
a. more than once a day
b. daily
e. less than daily
39. What is the number of pieces of litter in a 3 foot
square area? Select three random areas
a. b c
189
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APPENDIX II. WATER QUALITY SAMPLING
WATER QUALITY SAMPLING
Water quality samples were taken at all the sites over the
two-day period, September 12-13, 1974. Both days were sunny
with ambient day time air temperatures between 65° and 80 F.
After rinsing the sample bottles with the water at the site,
two one-liter samples were taken from a depth of approximately
one foot in water at least three feet deep. The sample bottles
were kept in an ice chest until delivered to the laboratory for
analysis.
The analysis was performed by Eco-Control, Inc. of Cambridge,
Massachusetts. The methods used to analyze the water samples
for the parameters chosen were those recommended in the
"Compendium of Analytical Methods" prepared'in 1973 by the MITRE
Corporation for the Environmental Protection Agency (PB-228 425).
In general, the methods recommended come from "Standard Methods
for Examination of Water and Waste Water," 13th Edition, American
Public Health Association, Washington, D.C. (1971).
190
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APPENDIX III. THE SURVEY INSTRUMENT
SURVEY OF WATER-BASED RECREATION
191
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CARD
a. yes/b. no Reasons
PART I; PARTICIPATION IN WATER-BASED RECREATION
Hello, my name is _ , and I am taking a public
opinion survey for Urban Systems Research and
Engineering', Inc. I'd like to ask 'you some questions
about the types of recreation you or members of this
household participated in last summer, and the
recreation areas you might have visited. (Last
summer is the 15 weeks between Memorial Day — May 27 —
through Labor D ay — September 2 . )
(1) First of all, last summer in the Boston Area did
any members of your household:
A. go swimming
B. go boating
C. go fishing
D. go picnicking
E. go bicycling
P. go someplace especially to walk or stroll
If not, why not?
REASONS: a. not interested
b. don't know how
c. don't have the appropriate equipment.
d. too expensive
e. water too dirty
f . water too cold
g. good places too crowded
h. good places too far away
i. don't own auto, good places can not
be accessed by public transportation
j. lack of time
k. poor health
1. other (please specify) _
G. What other types of recreation did members of
your household engage in this summer?
(IP NO ACTIVITIES RECORDED, SKIP TO PART II, Q.2)
192
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(2) The card shows some of the major fresh and salt
water beaches in the Boston Area. Could you
please tell me:
A. Which sites did you personally visit, and
the number of times you visited each of those
sites.. Are. there any sites which you visited
which "are not on this list? (Record those
sites and the number of visits to each.
Add visits and ask:)
So you personally visited a beach, lake or
stream about times this past summer?
B. How I would like to find out about visits by
anyone in this household to fresh and saltwater
beaches in the Boston Area. Could you please
tell me the number of visits by any household
member to each of these sites. Are there any
sites which you visited which are not on the
list? (Record those sites and the number of
visits to each. Add visits and ask:)
So members of this household visited a beach,
lake or stream about times this past
summer.
C. About how long, on average, was spent at each
of the sites you listed in the two questions
above?
a. less than one hour
b. over one hour but less than three hours
c. over three hours but less than six hours
d. more than six hours
(3) Travel;
A. For each site visited, how did you get there?
a. walking e. subway
b. bicycle f. taxi
c. automobile g. other
d. bus
B. About how long does it take to get there that
way? (in minutes)
C. How much does it cost to get there?
If by bus or subway or taxi, how much is the
roundtrip fare? If by auto what was the price
of tolls? (the total cost for the visiting group)
193
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(4) Expenditures;
For each site, about how much does it cost when
your party goes there? (total cost for the group)
parking
entry
food
liquor
other (includin'g rentals, gasoline for boats, etc.)
Add and Record Total/Visit
(5) For each site about how many people from your
household, on average', make the trip?
(6) Activities;
For each site you visit.what activities do you
participate in? (Record the most important
activities up to three.)
a. swimming e. strolling
b. boating f. bicycling
c. fishing g. picnicking
d. sunbathing h. other
(7) If the respondent did not visit the closest site,
ask:
beach is the major recreation site
closest to your home, yet you did not mention having
visited it. VJhy not?
REASONS: a. not aware of that site
b. do not like the facilities
c. to crowded
d. beach too dirty
e. water to cold
f. water too dirty
g. don't own auto, not accessible by
public transportation
h. too expensive
i. not interested in the activities
available there
j. other (please specify)
194
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PART II: PERCEPTION
(1) For each site you visited would you please rate
it on .a scale from 1-5. For this rating, 1 means
bad, 2 is moderately bad, 3 is fair, 4 is moderately
good, and 5 is good.
A. water temperature
B. water quality (clarity, color, weeds, odor, etc.)
C. beach facilities (availability)
D. beach quality (setting, maintenance)
E. crowding
(2) Are there any sites with which you are familiar,
but did not visit this summer? If so, which are
they and would you please rate in a similar
fashion those sites.
(3) Are there any sites which you have visited this or
other seasons, or are familiar with, which you do
not intend to visit again? If so, please list the
sites and why you do not intend to use them.
Site ft Reasons•
REASONS:
__ __ a a. too crowded g. poor beach facilities
___ b. too far away h. non-auto access too poor
c. too expensive i. change in activities
d. water too cold. j. other (please specify)
e. water too dirty
f. beach too littered
(4) Let's talk about the beach, lake, or river site you
visited most. That was , site number .
Site ft Reason
A. Why do you visit this site* most often?
REASONS: a. it is close
b. it is cheap
c. the water temperature is nice
d. the water quality is good
e. my family always care here
f. not too crowded
g. nice setting
h. beach is clean
i. nice facilities
j. my friends go there
k.. other
195
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B. If water quality became much worse {declined
to a ranking of 1) what would your response
be?
a. still visit the same beach as much
b. visit that site less frequently and some
other site more (specify which one)
c. visit that site less frequently and
participate in some other non-water-based
recreation more (specify which activity)
d. participate in outdoor recreation less,
no change in other leisure
e. participate in outdoor recreation less,
and indoor recreation more
C. If beach facilities became much worse (de-
clined to a ranking of 1) what would your
response be?
a. still visit the same beach as much
b. visit that site less frequently and some
other site more (specify which one)
c. visit that site less frequently and
participate in some other non-water-based
recreation r.ore (specify which activity)
d. participate in outdoor recreation less,
no change in other leisure
e. participate in outdoor recreation less,
and indoor recreation more
O. If beach quality became much worse (declined
to a ranking of 1) what would your response be?
a« still visit the same .beach as irruch
b. visit that site less frequently and seme
other site more (specify which one)
c. visit that site less frequently and
participate in some other non-water-based
recreation core (specify which activity)
d. participate in outdoor recreation less, no
change in other leisure
e. participate in outdoor recreation less and
indoor recreation more
196
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E. If crowding became much worse (declined to
a ranking of 1}, what would your response be?
a. still visit the same beach as nuch
b. visit that site less frequently and some
other site more (specify which one)
c. visit that site less frequently and
participate in some other non-water-based
recreation more (specify which activity)
d. participate in outdoor recreation less, no
change in other leisure
e. participate in outdoor recreation less and
indoor recreation more
F. If this site were closed, what would your
response be?
a. visit the site that you now visit second
most often and still go to the beach as
often as before
b. visit second most frequently visited site
more, but reduce total number of visits
c. visit all sites now visited more, but
reduce total number of visits
d. participate in non-water-based outdoor
recreation more (specify which activity)
e. participate in outdoor recreation less,
ao change in other leisure
f. participate in outdoor recreation less and
indoor recreation core
6. Bow much could the cost of visiting this site
be raised before you started visiting your
second most favorite site more?
a. $.50 e. $4.00
b. $1.00 f. $5-10.00
c. $2.00 g. more than $10.00
d. $3.00
B. Suppose that this site were to become very pol-
luted and the water quality would be reduced
to a ranking of 1. This could be avoided if
sufficient funds were raised to pay for the
necessary clean-up. If these funds were to be
raised through an entrance fee, what is the most
you would be willing to pay to prevent this
decline in water quality?
a. $.50 e. $4.00
b. $1.00 f. $5-10.00
C. $2.00 g. more than §10.00
d. $3.00
197
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I. Suppose that the water quality could be made
much better (improved to a ranking of 5) if
sufficient funds were raised to pay for the
necessary clean-up. If these funds were to
be raised through an entrance fee, what is
the most you would be willing to pay to
achieve the water quality improvement?
a. $.50 e. $4.00
b. .$1.00 f. $5-10.00
c. $2.00 g. more than $10.00
d. $3.00
1st ___ (5) In choosing a site what is the most important
2nd characteristic? 2nd most important? 3rd most
3rd important?
a. presence of a bathhouse/changing room
b. absence of litter
c. presence of a lifeguard
d. presence of a marine/boat launching facility
e. stocked game fish
f. a natural setting
g. water temperature
h. water appearance
i. presence of other beach facilities
j. cost (parking fees, entry fees)
k. proximity
1. where your friends go
m. where your family always went
n. other
1st (6) Thinking of water quality, the attractiveness of
2nd the water for swiraiaing depends on the color, odor,
3rd clearness, amount of floating debris or scum, and
4th _, the amount of aquatic weeds. Which characteristic
5th is the most important? 2nd most important?
Please rank these characteristics.
a. color
b. odor
C. clearness
d. floating debris
e. aquatic weeds
198
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(7) What is your favorite water-related activity?
DO NOT READ RESPONSES
a. swimming
b. boating (canoeing, sailing, etc.)
c. fishing
d. wading
e. water skiing
£. picnicking by water
g. bicycling by water
h. walking/strolling by water
i.' other (please specify)
1st (8) What other, recreation activities have members of
2nd your household engaged in this summer? (rank
3rd according to preference) DO NOT READ RESPONSES
a. swimming, in a pool
b. tennis
c. field sports (softball, baseball, football)
d. basketball
e. golf
f. picnicking
g. walking for pleasure
b. bicycling
i. outdoor spectator sports
j. indoor recreation activities
k. other (please specify) ____________________
1st (9) Of all the recreational activities we have discussed,
2nd including both those related to water and those
3rd not, what do you do most often? 2nd cost often?
3rd most often?
a. swimming
b. boating
c. fishing
d. wading
e. water skiing
f. other water-based (please specify) _____________
g. swimming, in a pool
h. tennis
i. field sports (softball, baseball, football)
j. basketball
k. golf
1. picnicking
m. walking for pleasure
n. bicycling
o. outdoor spectator sports
p. indoor recreation activities
q. other non-water-based (please specify)
199
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(10) Among the water-based activities covered in this
interview, are there any which you would enjoy
doing but do not get to as much as you would
like to in the Boston Area?
(Record Response Below)
PART III; PERCEPTION
(1) Bow many people are in the household? Could you
tell me how many fall into each age category?
Number Age Range
A. 0-6 (pre-school)
B. 7-13 (elementary school-junior high)
C. 14-17 (high school/too young to drive)
D. 18-25 (college age)
E. 26-65
F. 65
(2) Who is the Respondent?
_____ A. Sex ~ a. male
b. female
B. In which of these groups is your own age?
a. 0-6 (pre-school)
b. 7-13 (elementary school--unior high)
c. 14-17 (high school/too yuung to drive)
d. 18-25 (college age)
e. 26-65
f. 65
_____ C. Which of these best describes your status
in this household?
a. grandparent
b. father
c. mother
d. sibling
e. other relative
f. live alone or with unrelated individuals
200
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(3) Which letter corresponds to the total household
(including children) annual income after taxes,
in other words, the total take-home pay?
a. 0-4999 g. 20,000-24,999
b. 5000-7499 h. 25,000-29,999
c. 7500-9999 i. 30,000-34,999
d. 10,000-12,499 j. 35,000-40,000
e. 12,500-14,9-99 k. greater than 40,000
f. 15,000-19,999
(4) What is the occupation of the principal income
earner?
a. Professional, Technical, and Kindred
b. Managerial
c. Production Superintendent/foreman
d. Skilled Laborer
e. Unskilled or Semi-skilled
f. Clerical/Secretarial
g. Retired
h. Student
i. Ho'usewife
j. Other (please specify)
(5) What is your occupation?
a. Professional, Technical and Kindred
b. Managerial
c. Production Superintendent/foreman
d. Skilled Laborer
e. Unskilled or Semi-skilled
f. Clerical/Secretarial
g. Retired
b. Student
i. House v/ife
j. Other (please specify)
(6) What is the highest level of educational attain-
ment represented in the household?
a. elementary/junior high school
b. some high school
c. completed high school
d. some college (including junior college)
c. vocational/technical school
f. completed college
g. post-graduate
201
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_^ (8) What is the last grade in school you yourself
completed?
a. elementary/junior high school
b. some high school
c. completed high school
d. some college (including junior college)
e. vocational/technical school
f. completed college
g. post-graduate
(9) Do you own any of the following equipment? If
so, please estimate its approximate original
retail cost and the year purchased.
Original Retail Year
Cost Purchased Item
$__, A. Boat
$__, B. Outboard Motor
$__, C. Boat Trailer
$__, D. Other Boat Equipment
$ E. Fishing Tackle (rod, reel, tackle box, etc.)
$ __ __ ^* Fishing Licenses
$ G. Backpack
$ H. Water skis
$ I. Special Clothing (wetsuit, waders, etc.)
$ __ __ __ J. Bicycle
$ K. Cooler
$__, . L. Other Items (please specify)
(10) Leisure Time
A. How many days per week dees the principal
income earner usually work?
a. less than four
b. four
c. five
d. six
e. seven
_____ B. How long is his or her paid vacation (# weeks)?
a. none
b. up to one week
c. over one week, up to two weeks
d- over two weeks, up to three weeks
e. over three weeks, up to one month
f. over one month, up to two months
g. over two months
202
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(10) Do you own an automobile? If yes, how many?
a. No, none
b. Yes, 1
c. Yes, 2
d. Yes, 3
e. Yes, more than 3
(11) A. How often do you or anyone in this house-
hold' use public transportation?
(highest -level in household)
a. never
b. almost never
c. occasionally
d. frequently
B. About how far away is the nearest subway
or bus stop?
a. 1 block (1/8 Edle)
b. 2 blocks (1/4 mile)
c. 3 blocks (3/8 mile)
d. 4 blocks (1/2 mile)
e. more than 1/2 mile
(12) How would you describe your ethnic background?
20J
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MCORD1HG
sires
2. Lynn Beach (Lym)
3. Nahant Beach (tfahant)
4. Severe Beach C*.evere)
S. Shore Eeach (Revere)
6. Wlnthrop Beach (Wintfcrop)
. Constitution Eeach (Orient
Heights) Beach (Boston)
B. Castle Island (Boston)
9. fleasure Bay (Boston)
10. City Point (Boston)
11. L 4 M Street Beaches (Beaton)
12. Car son Eeach '(Boston)
11. Halitu (Savin Hill)
Beach (Boston)
14. Tenaan Beach (Boston)
IS. Hollaston Beach (Quincy)
17. Vinqa«rsh«ek Eeach (Gloucester)
18. Crane 'i Beach (Ipswich)
19. Hum Island (Kevfcury)
20. Ouxburv Beach (Duxbur>*)
21. White Horse Beach (Plymouth)
21. BreaUieirt Reservation (Saucus)
21. Sandy Beach (Upper Mystic
lake) (Winchester)
24. Bcmgh ton's Pond (Blue Hill*
Reservation) (Miltor.)
25. Wright's Pond (xedfocd)
26. Valden Pond (Concord)
27. Stearns Pond (Harold Parker
State Forest) (Ar.dover)
28. Cochituate State Park (Natick)
29. Hookinton State' Park (Hockinton)
JO. Csplanade/Storrcv laaocn (Boston)
31. Charles River, between Weeks
and Anderson Bridges (Cambridge)
32. Spy Pond (Arlington)
OTHER (please) specify)
33.
34.
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204
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BIBLIOGRAPHY
Ad Hoc Water Resources Council. "Evaluation Standards
for Primary Outdoor Recreation Benefits." Supplement
to Senate Document No. 97 of the 87th Congress,
Policies, Standards, and Procedures in the Formation/
Evaluation/ and Review of Plans for Use and Develop-
of Water and Related Land Resources.U.S. Executive
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1 REPORT NO.
EPA-600/5-78-010
3. RECIPIENT'S ACCESSION* NO.
PB257719
4. TITLE AND SUBTITLE
The Recreation Benefits of Water Quality
Improvement: Analysis of Day Trips in an
Urban Setting
5. REPORT DATE
June 1973 issuing date
6. PERFORMING ORGANIZATION t
7. AUTHOR(S)
Clark S. Binkley, W. Michael Hanemann
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Urban Systems Research & Engineering, Inc.
1218 Massachusetts Avenue
Cambridge, Mass. 02138
10. PROGRAM ELEMENT NO.
1HA094
11. CONTRACT/GRANT NO.
68-01-2282
12. SPONSORING AGENCY NAME AND ADDRESS
Office of Health and Ecological Effects - Wash., DC
Office of Research and Development
U.S. Environmental Protection Agency
Washington, DC 20460
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
EPA/600/18
15. SUPPLEMENTARY NOTES
16. ABSTRACT
Considerable past work has attempted to estimate the recreational benefits
which might accrue from water quality improvements. The theoretical underpinnings of
this work, however, are becoming increasingly suspect. This report explores demand
models, new to recreational analysis, which are based on site characteristics and
individual preferences to estimate benefit measured by consumer's surplus.
The empirical findings of this study are based on a structured survey of
467 representative households in the Boston SMSA. Our focus was specifically day
trips to a system of Boston area beaches, but considerable additional data on willing-
ness-to-pay, substitution between sites and activities, water quality perception and
general recreation behaviour was developed as well. The reader will find an extensive
review of the post-war literature on recreation economics and water quality benefits.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
Recreation
Demand
Regression Analysis
Ranking Order
Factor Analysis
Water Quality
Willingness-to-pay
Benefits
Perceived Water Quality
Objective Water Quality
3 DISTRIBUTION STATEMENT
Release to Public
19. SECURITY CLASS (This Report)
21. NO. OF PAGES
265
20 SECURITY CLASS (Thispage)
unclassified
22. PRICE
EPA Form 2220-1 (9-73)
«U.S. GOVERNMENT PRINTING OFFICE: 1978 260-880/77 1-3
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