, nited States
r'.nvironmental .'
Xgency
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anoing and Evaluation
. .ashington DC 20460
"I "tester 198«
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2JU12ooU21
Model Estimating the
Economic Impacts of Current
Levels of Acidification on
Recreational Fishing in the
Adirondack Mountains
-------
A Model Estimating the
Economic Impacts of
Current Levels of Acidification
on Recreational Fishing in the
Adirondack Mountains
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A MODEL ESTIMATING THE ECONOMIC IMPACTS OF
CURRENT LEVELS OF ACIDIFICATION ON
RECREATIONAL FISHING IN THE ADIRONDACK MOUNTAINS
Prepared for:
Dr. Ronald Nesse
Acid Deposition Assessment Staff
National Acid Deposition Task Force
and
Dr. Thomas Lareau
Benefits Staff
Economic Analysis Division
United States Environmental Protection Agency
Submitted by:
Daniel M. Violette
Energy and Resource Consultants, Inc.
P.O. Drawer O
Boulder, Colorado 80306
(303) 449-5515
May, 1985
TRAV1
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TABLE OF CONTENTS
Page
ABSTRACT vi
1.0 INTRODUCTION 1-1
2.0 INCORPORATING SITE CHARACTERISTICS IN TRAVEL COST MODELS .. 2-1
3.0 PROJECT DATA 3-1
3.1 The New York Anglers' Survey, 1976-1977 3-1
3.2 Adirondack Lake and Pond Survey 3-6
3.3 Integration of the Anglers' Survey and the Lake and Pond
Survey 3-8
3.4 Site Selection 3-9
4.0 THE MODEL 4-1
4.1 Participation Model 4-1
4.2 Estimation of Per Mile Travel Costs 4-4
4.2.1 Per Mile Travel Cost Estimation Results 4-8
4.2.2 Estimated Travel Costs: Conclusions 4-12
4.3 Travel Cost Model 4-15
4.3.1 TOBIT Procedures Applied to Total Fishing Days 4-19
4.3.2 Ordinary Least Squares Applied to Total Fishing Days 4-25
4.3.3 Brook Trout Fishing Day Travel Cost Model Analyses 4-28
4.4 Second Stage Analysis of the Characteristics of
Fishing Sites 4-29
4.5 Travel Cost Model Estimates: Conclusions 4-35
5.0 RECREATIONAL FISHING RESOURCE VALUATION 5-1
5.1 Estimate of Damages from Acidification Using the
Travel Cost Model 5-1
5.2 Estimating the Damages from Acidification Using the
Participation Model 5-12
5.3 Comparison of Participation Model and Travel Cost Model
Estimates of Damages 5-13
REFERENCES R-l
11
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LIST OF TABLES
Page
3-1 Project Data 3-2
3-2 Fishing Site Names 3-4
4-1 Participation Models using Total Fishing Days at a Site as the
Dependent Variable 4-3
4-2 Participation Models using Brook Trout Fishing Days as the
Dependent Variable 4-5
4-3 Regression Results using Total Site Travel Expenditures per day as the
Dependent Variable 4-9
4-4 Regression Results using Expenditures on Oil and Gas as the
Dependent Variable 4-11
4-5 Regression Results using Total Travel and Site Expenditures per day as the
Dependent Variable 4-13
4-6 Summary of Estimated Expenditures per Mile per Day 4-15
4-7 Travel Cost Model using Total Days as the Dependent Variable:
Estimated with a TOBIT Procedure 4-20
4-8 Travel Cost Model Using Total Days as the Dependent Variable:
Estimated by Ordinary Least Squares 4-26
4-9 Travel Cost Model using Brook Trout Fishing Days as the Dependent Variable:
Estimated with a TOBIT Procedure 4-29
4-10 Travel Cost Model using the Natural Log of Brook Trout Fishing Days
as the Dependent Variable: Estimated with a Tobit Procedure 4-31
4-11 Second Stage Generalized Least Squares Runs on the TOBIT Estimated
Parameters from the Total Fishing Day Equations 4-33
4-12 Generalized Least Squares Runs on the Ordinary Least Squares Parameters
from the Total Day Equations 4-34
5-1 Current Recreational Fishing Values in the Adirondack Mountains,
per year 5-4
5-2 Losses of Fishable Lake Area Due to Acidification 5-5
5-3 Valuation of Resource Losses Due to Acidification:
Moderate Acreage Loss Scenario 5-7
111
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LIST OF TABLES
(continued)
5-4 Valuation of Resource Losses Due to Acidification:
High Area Loss Scenario 5-8
5-5 Valuation of Resource Losses Due to Acidification:
Moderate Area and Catch Rate Loss Scenario 5-9
5-6 Valuation of Resource Losses Due to Acidification:
High Area and Catch Rate Loss Scenario 5-10
5-7 Estimates of Damages Resulting from Current Levels of
Acidification 5-14
iv
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LIST OF FIGURES
Page
3-1 Mapping of Sites 1 through 24 used in the Travel Cost Model 3-3
4-1 Expected Relationship Between the OLS Estimates, TOBIT Estimates,
and the TOBIT Generated Expected Values 4-23
5-1 Measurement of Consumer Surplus Losses Caused by Acidification 5-2
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ABSTRACT
The purpose of this project was to estimate the parameters of an economic model that
can be combined with information on the current extent of fresh water acidification to
produce economic estimates of damages in the Adirondack Mountains of New York State.
One traditional approach for estimating the economic value of recreational sites has
been to use the travel and on-site costs incurred by visitors as proxy measures of the
price paid to use that site. Early travel costs studies focused on changes in the supply of
sites, i.e., the addition of a new site or the loss of an existing site. However, the estima-
tion problem faced by this project is different. Acidification not only changes the num-
ber of sites available for fishing, but also changes important characteristics of fishing
sites. As there are approximately three thousand lakes and ponds in the Adirondack
Ecological Zone, a lake by lake analysis was not possible. Instead, each site was viewed
as a geographic area containing a number of lakes. Sites were characterized by the num-
ber of lakes they contained with certain characteristics. Possible site characteristics
include the number of acres of cold water, two story, or warm water lakes. In this
framework, acidification could change the area of cold water lakes able to support fish
populations. The estimation problem is to determine how a change in these site charac-
teristics will affect the value of a site as a recreational fishery. Both a site characteris-
tics based travel cost model and a simpler participation model were used to obtain
estimates of the use values of recreational fishing in Adirondack lakes and the reduction
in use values due to acidification were also estimated. The estimates of damages result-
ing in current levels of acidification ranged from approximately $1 million to $12 million.
It should be emphasized that travel cost models are only able to estimate use values.
Reviews of the possible magnitude of non-use values indicates that non-use values may
be larger than use values.
VI
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1.0 INTRODUCTION
The purpose of this project is to estimate the parameters of an economic model that can
be combined with information on the extent of the current effects of fresh water acidifi-
cation to produce economic estimates of damages. A travel cost model is applied to
fishing sites in the Adirondack Mountains of New York State. A travel cost model uses
information on travel costs to develop estimates of the value of that site; however, these
models only estimate a portion of the total benefits derived from the aquatic resources
available at each site. The economic value of a site is a combination of both use and
non-use values. A travel cost model only estimates use values. Estimates of non-use
values must be obtained from other methods. Reviews of the possible magnitude of non-
use values indicate that non-use values may be larger than use values.
The Adirondack Mountain region was selected for this study because of the availability of
survey data relating current levels of acidification to the presence or absence of desir-
able gamefish populations. Acidic deposition is commonly viewed as a regional problem
since large areas in the eastern United States and Canada have elevated levels of deposi-
tion (National Research Council, 1983). However, from the perspective of damages to
fish populations, the fresh water effects of current levels of acidic deposition are
expected to occur in narrower geographic areas. Two factors must interact before fish
populations will experience adverse effects from acidic deposition first, the water-
sheds must be exposed to elevated levels of acidic deposition; and secondly, the water-
sheds must be sensitive to the increased hydrogen ion deposition (U.S. EPA, 1983). Even
though broad regions are exposed to elevated levels of acidic deposition, sensitive lakes
and streams are grouped into smaller areas. The regions containing sensitive lakes in
New York are essentially limited to the Adirondack and Catskill Mountains, and the
Hudson Highlands (U.S. EPA, 1985). Within these regions, the waters that tend to be the
most susceptible to acidification effects are the high altitude brook trout ponds and
streams (Schofield, 1982).
See Fisher and Rancher (1983) for a review of this material.
1-1
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Past analyses of user damages to recreational fishing caused by acidification (Crocker et^
al., 1981 and Menz and Mullen, 1982) have estimated economic losses to be extremely
small. The primary reason for these findings is the small number of affected ponds rela-
tive to the total lake and pond acreage in the Adirondack Mountains. The rationale for
this result is that, even though there are some lakes that are being affected by acid
deposition, the number of anthropogenically acidified lakes is not large enough to sub-
stantially affect the available fishing opportunities. Another way of stating this is that
there are enough substitute lakes available for fishing, so that the loss of a limited num-
ber of gamefish populations does not have a large effect on the overall recreational use
value of the aquatic resource in the Adirondack Mountains. In a recent study, Peterson
(1983) estimated that a decrease in sulfate deposition of 25 percent would increase
gamefish habitat in the sensitive Adirondack Mountains and Catskill-Hudson Highlands by
only five percent. Assuming that only waters in the Adirondacks and Catskills are
affected at current deposition levels and extrapolating to New York State, the statewide
increase in gamefish habitat resulting from a 25 percent decrease in sulfate deposition is
found to be less than one percent. The general order of magnitude of these estimates
indicates that if all fishing sites are considered substitutes, estimates of damages likely
will be small.
Because previous estimates of damages have been small, this study has been framed to,
where possible, provide an upper-bound of consumer surplus damages related to acidifica-
tion in the Adirondack Mountains. This approach was followed in order to provide policy
makers and economists with estimates that indicate the largest probable loss of recrea-
tional fishing use values attributable to acidification. Results, presented in Chapter 5,
indicate that consumer surplus losses associated with acidification are small. Because
the analysis used assumptions that biased the calculations to provide an upper-bound
damage estimate, the size of the consumer surplus losses supports the interpretation that
recreational use value losses associated with acidification of ponds and lakes in the
Adirondack Mountains are relatively small. Again, it is important to recognize that use
values are only a portion of the overall value of an aquatic resource.
One issue of importance to the damage assessment that was not adequately addressed in
this project is whether the sensitive, threatened lakes constitute a unique resource. Even
though the area of threatened lakes is a small fraction of all fishable waters, it may
represent a unique resource for which other fishing sites are less than perfect substi-
tutes. In particular, the threatened lakes are largely small, high altitude book trout
1-2
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ponds. These ponds may provide a relatively unique recreation experience. Some of
these lakes must be hiked to, and offer more of a combined wilderness/fishing experience
than do other fishing sites. A number of these high altitude ponds have already been
acidified or are in danger of acidification at current deposition rates (Colquhoun et al.,
1984). While these ponds make up only a small portion of total fishable acreage, they
may have a disproportionately high value to, at least, some recreationists.
A traditional approach for estimating the economic value of recreational sites has been
to use the travel and on-site costs incurred by visitors as proxy measures of the price
paid to use that site. Early travel costs studies focused on changes in the supply of sites,
i.e., the addition of a new site or the loss of an existing site. However, the estimation
problem faced by this project is different. Acidification not only changes the number of
sites available for fishing, but also changes important characteristics of fishing sites. As
there are approximately three thousand lakes and ponds in the Adirondack Ecological
Zone, a lake by lake analysis was not possible. Instead, each site was viewed as a
geographic area containing a number of lakes. Sites were characterized by the number
of lakes they contained with certain characteristics. Possible site characteristics include
the number of acres of cold water, two story, or warm water lakes. In this framework,
acidification could change the area of cold water lakes able to support fish populations.
The estimation problem is to determine how a change in these site characteristics will
affect the value of that site as a recreational fishery.
Two data sets were identified that contain data useful for an analysis of Adirondack
lakes the New York Anglers' Survey and the Adirondack Ponded Waters Survey. The
New York Anglers' Survey contains data on fishing activity throughout the state; how-
ever, the Adirondack Ponded Waters Survey only contains data on lakes and streams in
the Adirondack Ecological Zone. As a result, the geographic scope of the study was
necessarily limited to this area. This may not pose a significant problem for a national
assessment of damages, since documented^ damages to recreational fisheries at current
levels of deposition have largely been limited to the Adirondack Mountain region. Lakes
and streams in other regions of the U.S. are sensitive to acidic deposition and may have
suffered some damage. Nevertheless, at the current level of acidification most docu-
mented effects on recreational fisheries in the United States are occurring in the
Adirondack Mountains.
1-3
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2.0 INCORPORATING SITE CHARACTERISTICS IN TRAVEL COST MODELS
This chapter will discuss, in general terms, potential approaches to incorporate site
characteristics within a multiple site travel cost model. The recent literature contains
several approaches for incorporating site characterisitics within a travel-cost frame-
work. Prominent applications incorporating site characteristics into a travel cost model
are Vaughan and Russell (1982); Desvousges, Smith and McGivney (1983); Morey (1981,
1985); Greig (1983); and Brown and Mendelsohn (1984). This literature includes several
diverse approaches, each with certain strengths and weaknesses. The use of site charac-
teristics in travel cost models is a recent development. As a result, new applications and
techniques are currently being researched.
The problem of incorporating site characteristics within a travel cost model can be illus-
trated using a conventional Burt and Brewer (1971) type travel cost model. This "conven-
tional" travel cost model estimates a separate demand equation for each fishing site.
These demand functions for "n" fishing sites are shown below.
Site 1 equation: Vlq = B1Q+ Bn Pu + B12 P12+ ... +Blq Plq + C^ Sqj + U (2-1)
Site n equation: Vnq = BnQ + Bnl Pnl + Bn2 Pn2 + . . . + Bnq Pnq + Cnj Sqj + U
where:
V- = the visitation rate to site i from origin q, usually measured in visitors per
10,000 people
Pjq = the price of visiting i from origin q in terms of travel and time costs.
B- = the regression coefficients on the price variables
S_j = socioeconomic variables for origin q
Cn* = regression coefficients on socioeconomic variables
U = random term
2-1
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For example, the data necessary to estimate the site 1 equation are the visitation rate,
and the travel costs from each of the q origins to the site. The underlying assumption is
that the visitation rates to site 1 will be lower for origins more distant from site 1; that
is, as the costs of traveling to site 1 increase the visitation rate will decline.
In this specification, the own price* of visiting that site whose demand equation is being
estimated is included. Also included are the prices of visiting other substitute fishing
sites. This specification takes into account the cost of traveling to substitute fishing
sites.
In this conventional model, it is not possible to examine how the characteristics of the
site affects the visitor's demand function. The equation for each site is estimated
separately. As a result, there can be no variability in the characteristics of just one
site. Several different approaches for incorporating site characteristics within a travel
cost framework have appeared in the recent literature. These new methods can be
classified into three basic approaches:
1) The varying coefficient travel cost model as characterized by
Vaughan and Russell (1982), and Desvousges, Smith and McGivney
(1983);
2) The explicit utility function characterized by Morey (1981) and Grieg
(1983);
3) The hedonic travel cost model as developed by Brown and Mendelsohn
(1984).
A variant of the varying coefficient travel cost model was selected for this application.
The characteristics of the available data posed problems for the other two approaches.
The appropriateness of these alternative methods for this application are reviewed in
Violette(1983).
The varying coefficient travel cost model approach is similar to that used by Vaughan
and Russell (1982), and Desvousges, Smith and McGivney (1983). This approach utilizes a
two step framework. The first step estimates a separate visitation-travel cost equation
* For example, the own price in the site 1 equation is the price of visiting site 1. Thus,
own price effects can be contrasted with substitution effects resulting from the prices of
visiting other sites.
2-2
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for each site. The second step uses the regression coefficients from the step one equa-
tions as dependent variables and regresses these coefficients on the site characteristics.
To use a simple example, the conventional Burt and Brewer visitation demand function
for site "i" is:
Viq = Bio + Bil Pi2 + + Biq Piq <2'2>
where Vjq is the visitation rate from origin q to site i and P^ is the travel cost from
origin q to site i. Since a separate equation is estimated for each site, there are "i" dif-
ferent estimates of each coefficient. These regression coefficients represent the rela-
tionship between travel costs and visits. The variability in the magnitude of the regres-
sion coefficients in the different site equations may be due to the relative desirability of
the site in terms of the site's characteristics. This can be tested in the second step
regressions where the regression coefficients are regressed against the characteristics of
each site:
BiO = A00 + A01 zli + + A0k zki
Bil = A10 + All zli + + Alk zki
B- = A + A Z + ... + A Z (2-3)
where Zk^ is the level of the k^ characteristic at site i. This two step procedure can be
combined into an equivalent one step method by substituting equation 2-3 into equation
2-2 to yield:
Viq = (A00 + A01 Zli + " + A0k zkP + ^A10 + All zli + + Alk zkP Pil * *
+ Piq' (2"4)
Equation 2-4 includes both site characteristics and travel costs as interaction terms.
This equation can be estimated using data pooled across sites.
Using ordinary least squares in this two stage procedure will introduce heteroskedasticity
into the error term of the second stage regressions. The second stage regression using
only one site characteristic as the dependent variable is:
2-3
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The dependent variable Bi0 is an estimated regression coefficient from the first stage
regression; therefore, the error term for the regression shown as equation (2-5) is
influenced by the error in the estimated coefficient. This introduces heteroskedastieity
in the regression equation error term. Simply stated, if the estimated variance of B^g
from the stage 1 regression is large (i.e., Bi0 is estimated imprecisely) this will influence
the error term in the regression shown in equation (2-5), This can be corrected by using
generalized least squares (GLS) procedures where the estimated standard errors for the
rt
regression coefficient from each site are used as the correcting weights.
The two applications of varying coefficient travel cost model cited previously (Vaughan
and Russell, 1982 and Desvousges, et ah, 1983) found site characteristics to be signifi-
cant in the second stage regression equations. The available data and nature of the
estimation problem makes this application somewhat different from these previous appli-
cations. For example, Vaughan and Russell (1982) used a sample of fee fishing sites in
the Northeastern United States. These sites were typically widely dispersed geograph-
ically making it unlikely that visitors to one site would have visited another of the sites
included in the data set and, even if they had, there was no way to learn this from the
data. The Desvousges, et aL_ (1983) visitation data were obtained from 46 U.S. Army
Corps of Engineering recreation sites. Again, these sites were scattered throughout the
United States. These applications can be contrasted to the Adirondack region where all
of the sites are located in a small region. This results in a visitation data set where
many fisherman have visited more than one site.
Because of available data it was desirable to use a variant of this two stage approach.
Instead of using ordinary least squares techniques to estimate the coefficients of the
first stage site demand equations, a Tobit procedure was used. The Tobit procedure
takes full advantage of the available data on individual fishermen. First used in Tobin
(1958), it estimates both the probability of an individual visiting a site as well as the
number of days the individual will spend at that site, given that a visit is made. Taken
2 For more detail see G. Saxonhouse (1977).
2-4
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together, these two estimates can be used to calculate the expected value of days spent
at each site for each individual.
The procedure used to incorporate site characteristics within this travel cost model is
very similar to the varying coefficient travel cost model as depicted by equations (2-2)
and (2-3). The only difference is that the first stage regression coefficients of equation
(2-2) are estimated using a Tobit procedure. In the second stage, these regression coeffi-
cients are used as the dependent variable and regressed against the site characteristics
using a generalized least squares procedure to correct for heteroskedasticity. This pro-
cedure will be discussed in more detail in Section 4.3.
2-5
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3.0 PROJECT DATA
There were two main data sources for this project. These were the 1976-1977 New York
Anglers' Survey and the Adirondack Lake and Pond Survey (Ponded Waters Survey). Both
data sets were compiled by the New York State Department of Environmental Conserva-
tion (NY DEC). Data used in the project are listed in Table 3-1. The site boundaries are
shown in Figure 3-1. Names for the sites, based on a prominent water or geographic
feature, are shown in Table 3-2. The balance of this section presents a short discussion
of the Anglers' survey and the Ponded Waters survey, the procedures used to integrate
these two data sets, and the criteria used to define the sites.
3.1 THE NEW YORK ANGLERS' SURVEY, 1976-1977
The New York Anglers' Survey for 1976-1977 is the most recent data source from which
information on fishing activity and travel costs can be compiled for the Adirondack
Mountains. The Anglers' Survey consisted of a questionnaire mailed to a three percent
sample of fishermen licensed in New York State between October 1, 1975 and September
30, 1976. The questionnaire elicited responses about fishing activity in New York State
between April 1, 1976 and March 31, 1977. Of the 25,564 questionnaires mailed, 11,721
responses were received.
The questionnaire consisted of three major sections: one - fishing activities, expendi-
tures, and preferences; two - attitudes and opinions; and three - participant background.
The first section examined fishing activities, expenditures and preferences. This section
collected data on where, for how long, for what species, and by what methods the
respondent fished. Data on expenditures per fishing location for that year and for total
equipment expenditures were also requested. Questions relating to preferred species,
reasons for fishing and what makes a fishing trip successful were included in this sec-
tion. The attitudes and opinions section of the Anglers' Survey was mainly concerned
with New York's fisheries management programs, procedures and regulations.
3-1
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Table 3-1
Project Data
Angler Specific Data;
o Number of days spent fishing at each site (from Anglers' Survey)
o Years of fishing experience (from Anglers' Survey)
o Annual income (from Anglers' Survey)
o Travel expenditures on gas and oil (from Anglers' Survey)
o Total expenditures in transit to site including gas and oil, food and drink, lodging,
and other (from Anglers' Survey)
o Total expenditures at the site including food, lodging, gas and oil, guide fees, and
other (from Anglers' Survey)
o Number and species of fish caught (from Anglers' Survey)
o Distance from residence to each site (compiled from regional maps)
Site Characteristic Data:
o Total acreage of ponded waters in that site (from Ponded Waters Survey)
o Acres of private waters in the site (from Ponded Waters Survey)
o Net acreagetotal minus private acres (from Ponded Waters Survey)
o Acreage of ponds with warm water fisheries (from Ponded Waters Survey)
o Acreage of ponds with two story fisheries (from Ponded Waters Survey)
o Acreage of cold water and brook trout ponds (from Ponded Waters Survey)
o Total fishing days spent at each site (computed from Anglers' Survey)
o Average daily catch rate (computed from Anglers' Survey)
o Average daily catch rate of brook trout (computed from Anglers' Survey)
3-2
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Figure 3-1
Mapping of Sites 1 through 24 Used in the Travel Cost Model
(Dotted lines are 15 minute quadrangles, solid lines are either
site boundaries or the boundary to the Adirondack Ecological Zone)
180 190 200 210 220 230 240 250 260 270
3-3
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Table 3-2
Fishing Site Names1
List of Sites
1 Chateaugay Lakes
2 Black Lake
3 Lake Ozonia
4 Meacham - St. Regis Lakes
5 Union Falls Pond
6 Lake Bonaparte
7 Cranberry - Tupper Lakes
8 Saranac Lakes
9 Lake Placid
10 Long - Blue Mountain Lakes
11 Mt. Marcy
12 Paradox Lake
13 Still water Reservoir
14 Fulton Chain
15 Raquette Lake
16 Indian Lake
17 Thirteenth Lake
18 Schroon - Brant Lakes
19 Lake George
20 Southwest Corner
21 Piseco - Pleasant Lakes
22 Peck Lake
23 Great Socadanga Lake
24 Saratoga Lake
1 Site selection was based on several factors including lake and pond geography, accessi-
bility of an area based on the location of paved roads, and the number of observations
available for statistical analysis.
3-4
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The participant background section elicited information on fishing background, whether
or not the respondent belonged to a fish and game club, other recreational activities, and
household income. A summary of the Anglers' Survey appears in Kretser and Klatt
(1981).
Since the 1976-77 Anglers' Survey gathered information on fishing throughout New York
State, it was necessary to select only observations on fishing trips to the Adirondack
region. Fishing locations in the Anglers' Survey are identified by name of water and
county. Relevant observations for this project were chosen by selecting only those fish-
ing locations in Adirondack counties. The counties included are: Clinton, Essex,
Franklin, Fulton, Hamilton, Herkimer, Lewis, Saint Lawrence, Saratoga and Warren. This
resulted in data on 3015 individual anglers and 6053 fishing visits.
The 6053 visits by individuals were to 760 different fishing sites, 504 of which were lakes
and ponds, the remainder being rivers and streams. Since adequate site characteristic
data were available only for lakes and ponds, the effective sample size was further
reduced to data on visits to the 504 lake and pond locations.
Data on expenditures in transit to the site and at the site were requested by the Anglers'
Survey although not all individuals reported these expenditures. Travel expenditure data
were available for 62.3 percent of the 6053 sites, and on-site expenditure data for 57.3
percent of these sites. Expenditures on equipment were also requested, but improperly
coded and entered onto the tape, thereby making this data unuseable.
The Anglers' Survey contained no data on distances traveled to each site or time spent
traveling to the site. Distance data was estimated using Zip Codes included in the
Anglers' Survey.1
Socioeconomic and other respondent background data contained information on household
income, date of birth, years of education, and years of fishing. Other questions in this
section concerned whether the individual had a preferred species to fish for, whether or
not the respondent was a member of a fish and game or other sportsmen's club, and his or
her participation in other recreational activities. A number of attitudinal questions were
Given the large number of observations, this was a time consuming task.
3-5
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also included examining the individual's reasons for fishing, factors important to a
successful fishing trip, and limiting factors for respondents who do not fish as often as
they would like.
3.2 ADIRONDACK LAKE AND POND SURVEY
Site characteristic data was obtained from the Adirondack Lake and Pond Survey
(ponded Waters Survey). This data base includes information on 3,506 ponded waters in
the Adirondack area. The Ponded Waters Survey is not entirely comprehensive; not every
ponded water in the Adirondack area has a complete record. For example, there are only
2,409 pH records in the most recent chemistry survey data for those waters which have
been surveyed. Also, not all lakes and ponds are surveyed each year. The most recent
survey for a particular pond or lake may have been last year, or it may have been 20 or
more years ago. Only 1,217 of the 2,409 pH records date from 1960 to the present. The
New York State Department of Environmental Conservation (NY DEC) is continuing to
update this data base.
The data in the Adirondack Lake and Pond Survey refers to ponded waters only. Stream
fishing is also important in the Adirondacks. There are approximately 5,000 miles of
coldwater fishing streams in the Adirondacks, with about 3,500 miles of these open to
public fishing (Pfeiffer, 1979). Over 700 miles of warmwater fishing streams also exist,
with approximately 480 miles open to public fishing (Pfeiffer, 1979). Unfortunately,
stream characteristic data are not as readily available as ponded water data. Miles of
streams open to public fishing appears to be available on a county basis, but may be
difficult to obtain on a more disaggregated basis. Some acidification data is available
for select streams (Colquhoun, et al. 1981, 1984), and a new report on stream acidifica-
tion in the Adirondacks will be released by the NY DEC in 1985. As a result of the lack
of adequate stream and river chemistry and fish population data, this report does not
consider potential effects to stream and river fishing opportunity.
The data in the Ponded Waters Tape consisted of seven files, each of which had several
record types. Only three of these files were relevent to this project. These files contain
^ This survey is continually updated. The survey used in this analysis was the version
available in February, 1984.
3-6
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the most recent pond, chemistry and fish data. Waters are identified on each record in
each file by their watershed code and pond number. A Fortran program was developed to
create a single file in a fixed format containing only the information desired. The
Ponded Waters Survey has an entry for the USGS 7-1/2 minute quadrangle location of all
but 9 of the 3506 waters listed. As a result, 7-1/2 minute USGS quadrangles were chosen
to form the basis of a site.
Of the general site characteristics, surface area and elevation were most commonly
available, existing for at least 80 percent of the waters. Shoreline length could be a
useful alternative to surface area, and is listed as a variable in the Tape's documentation,
but did not exist for any waters. Another potentially useful characteristic listed in the
documentation, but for which no data exist, is the distance from a pond or lake to the
nearest public road or trail. This accessibility measure could have been quite useful.
The public or private ownership classifications may be useful to limit the number of
ponds, or surface area in a site, to those open to public use.
The current management class of a water can be useful for determining the different
types of fishing opportunities available within a site, and their relative importance.
Management classifications in the survey included warm water, two story, cold water and
brook trout fishery classifications. Although only 38 percent of the waters were cate-
gorized by management class, these waters comprise 87.7 percent of the total measured
surface area. Thus, this variable may be used with a reasonable level of confidence.
Two issues surround the relevance of the pH and alkalinity data which are available. One
is the fact that much of the data, perhaps a large portion, may be old and thus no longer
accurate. Secondly, pH data existed for only 35 percent of measured surface area and
alkalinity for only 52 percent. As a result, estimates of the effect of acidification on
fishable acreage of ponds made by others were used in this analysis. Other National Acid
Precipitation Assessment Program research has calculated the change in fishable acres
due to acidification.^
3 In this report, NAPAP funded work by Dr. Joan Baker at North Carolina State
University was used to obtain estimates of how acidification will affect the acreage of
water available for fishing.
3-7
-------
Since 7-1/2 minute quadrangles were chosen as site components, the data extracted from
the original Ponded Waters tape for each pond or lake needed to be aggregated by
quadrangles. Site characteristics were defined in terms of surface area. For a
quadrangle containing a number of lakes and ponds, a number of characteristics, includ-
ing total surface area, were described. Surface area was further analyzed by elevation
and fishery management class. Surface area was divided by elevation into acres below
1500 feet, acres between 1500 feet and 2000 feet, and acres above 2000 feet. Surface
area was also broken down by ownership category.
3.3 INTEGRATION OF THE ANGLERS' SURVEY AND THE LAKE AND POND SURVEY
The Anglers' Survey and Ponded Water Survey used different methods for identifying par-
ticular water bodies and a mapping from one code to the other was necessary. Individual
waters in the Ponded Waters Survey are identified by a watershed and pond number com-
bination. For the Anglers' Survey, a water name and county was supplied by respond-
ents.^ However, NY DEC personnel cautioned against a one-to-one mapping of waters
due to concern that anglers may not have accurately reported where they fished.
Anglers may believe they are at one lake or pond when they are actually at a different
lake. They may also use a name for the lake which is different from the official name
for that lake. Also, there can be several lakes within a county with the same name. In
these cases NY DEC personnel had to use their judgement, based on knowledge of popular
fishing areas and species availability in these waters, in coding fishing locations. Since
both the Gazatteer and the Ponded Waters Survey include identification of the 7-1/2
minute USGS quadrangle in which a water's outlet lies, the fishing locations from one
survey to the other were mapped on the basis of 7-1/2 minute quadrangles. As a result,
even if the fisherman gave the name of a nearby lake in error, his visit will still be
mapped to the correct site as long as both lakes are in the same 7-1/2 minute quadrangle.
A code was created by the NY DEC for identifying waters in the Angler Survey which
consisted of locating the water in the report, Characteristics of New York Lakes, Part 1
Gazatteer of Lakes, Ponds and Reservoirs (Greeson and Robison, 1970). This was done
by coding each water by a number where the first two digits indicated the page and the
second two digits the line of the Gazatteer listing the water name and location. The
result was a time consuming process where each lake or pond in the Anglers' Survey had
to be be looked up by hand in the Gazatteer and matched to a lake with hopefully the
same name and location in the Ponded Waters Survey.
3-8
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3.4 SITE SELECTION
Site definition raised several issues. One of these issues has already been discussed,
namely the problem of not being able to cross-reference waters between the Anglers' and
Ponded Waters Surveys on a one-to-one basis. The use of 7-1/2 minute quadrangles may
mitigate this problem. However, the use of 7-1/2 minute quadrangles poses other
problems. Most importantly, the 7-1/2 minute quadrangle associated with any lake or
pond refers to the quadrangle in which that water's outlet lies. For large bodies of
water, this quadrangle can be several miles from where an angler actually fished. In
other cases, a group of lakes may cross several quadrangle boundaries yet still exist in
relatively close proximity with easy access from one to the other, making this group of
lakes a reasonable candidate for a site (destination). There are few major roads within
the Adirondacks, thus accessibility was another site determinant.
The issues mentioned above were considered when aggregating the individual 7-1/2
minute quadrangles into larger sites. The sites were constructed by grouping together as
geographically homogeneous 7-1/2 minute quadrangles as was possible, given the best
judgment of the project investigators. If the outlet of a lake was in one 7-1/2 minute
quadrangle while the body of the lake was in a neighboring quadrangle, both quadrangles
were included in the same site. Sites were also constructed to include groups of similar
lakes, such as the Saranac Lakes. Another consideration was the highway system where
quadrangles having a common access were included in the same site. From an empirical
viewpoint, there have to be enough sites for sufficient degrees of freedom in the second
step regression. A site specification resulting in 24 sites was ultimately decided upon
(see Figure 3-1).
3-9
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4.0 THE MODEL
This chapter is divided into three sections. Section 4.1 presents a simple participation
model. A participation model relates recreational activity to the supply and quality of
recreation opportunities available at different sites. Compared to travel cost models,
participation models have less stringent data requirements and assumptions. Participa-
tion models do not use data on travel costs and, therefore, the assumptions required for
travel costs to serve as the basis for calculating consumer surplus based values for the
recreation activity do not have to be imposed. However, participation models do not
have the ability to infer values for the resource, but show how participation is expected
to change as recreation opportunities increase due to improved water quality. If the
value of additional recreation days can be inferred from other sources, then an estimate
of the value of the improved water quality can be obtained by multiplying the increase in
recreation days times their daily value.
An empirical model designed to estimate the value of the resource for recreational fish-
ing is presented in Sections 4.2 and 4.3. Section 4.2 takes advantage of the data availa-
ble on expenditures to obtain an estimate of the average per mile travel cost incurred to
produce one fishing day. The ability to estimate this dollars per mile per fishing day
travel cost is important for the analysis since the visitation data from the Anglers' Sur-
vey is expressed in terms of fishing days spent at a site and the survey did not contain
information on whether these days were taken during one trip, two trips or many trips.
Section 4.3 presents the estimation of the relationship between travel costs and fishing
days at each site. Section 4.4 incorporates the characteristics of the site into the travel
cost framework.
4.1 PARTICIPATION MODEL
The first step in the analysis of the visitation data was to estimate a simple participation
model. As was discussed above, participation models have less stringent data require-
ments and assumptions than do travel cost models, but entail the loss of the ability to
4-1
-------
infer values from the estimated model. This model relates the number of fishing days
at each of the 24 sites to selected characteristics of the site. Site characteristics used
include measures of fishable acres of lakes and ponds, and the total catch rate defined as
the average number of fish caught per fishing day at each site. The site characteristics
are the variables that are affected by acidification. In this participation model, travel
costs and distances traveled were not considered, but they are incorporated into the next
phase of the analysis procedure. Once this model is estimated, it is possible to calculate
the change in fishing days due to a change in the site characteristics.
The results of the participation model runs are shown in Table 4-1. The coefficients on
the fishable acreage variables are significant in all runs and the magnitudes of the coef-
ficients were consistent across the different specifications. The coefficients on the
acreage variables ranged in magnitude from .061 to .0978, with the majority of the coef-
ficients clustered between .0845 to .0978. The one exception was the coefficient on the
acres of cold water in equation 2 which had a negative sign, but was not significant.
These data show a relationship between the total number of fishing days spent at a site
and fishing opportunities as measured in fishable acreage.
The total catch rate variable did not perform as well as the acreage variables. The catch
rate variable was significant in two of the specifications, but the magnitude of the coef-
ficients varied considerably from 49.8 to 199.4. The lack of stability of the coeffi-
cients on the catch rate variable would tend to make predictions based on this variable
less reliable than predictions based on the acreage variables.
The plausibility of the coefficients' magnitudes for the acreage variables can be
examined by performing calculations using regression equation 1 from Table 4-1. The
mean values across all 24 sites for the variables total days, acres of warm water, and
acres of two story ponds are 1145.8 days, 451.6 acres of warm water, and 364.5 acres of
two-story ponds. Using these values to depict an "average site," the effect on total fish-
ing days of a 10 percent reduction in fishable acreage can be calculated as:
Xh *
days = .0958 x (451.6) + .0845(364.5)
= 74.06 days
* This is discussed in more detail in Freeman (1979), Chapter 8.
4-2
-------
Table 4-1
Participation Models using Total Fishing Days at a Site as the Dependent Variable
(t-values are in parentheses)
#-
Total Net
Regression Park Park
Number Acres Acres
1 * *"""" ~*~"
2. -
3. - .0978
(5.66)
4.
5. .061
(3.16)
Warm
Water
Acres
.0958
(4.44)
.0972
(4.59)
Two
Story
Acres
.0845
(3.80)
.0851
(3.90)
Acres at
less than
Cold 1,500 feet in
Acres Elevation
-.540
(-1.33)
_
.076
(4.16)
Total
Catch
Rate
42.04
(.418)
49.84
(5.04)
199.4
(1.97)
-85.1
(.84)
7.44
(.62)
R2
.60
.635
.615
.55
.32
Overall
F
9.49
7.849
16.03
8.23
5.01
-------
The predicted result of a 10 percent reduction in f ishable acreage at the "average" site is
a reduction of 74 fishing days, or a 6.5 percent reduction in fishing days at the site.
One problem that may limit the usefulness of these results is the lack of significance of
the cold water acreage variable. Acid deposition may be expected to largely affect cold
water lakes and ponds and to have a much smaller effect on warm water and two-story
lakes and ponds. To further examine this particular issue, a second set of participation
models were estimated. Rather than using total fishing days as the dependent variable in
this model, a new variable defined as brook trout fishing days was used. This variable
was constructed by taking all the days at each site where survey respondents reported
catching at least one brook trout. Other species of fish may have been fished for and
caught as well, but if brook trout were caught, then these days were classified as brook
trout days.
The result of the participation models using brook trout days at each site as the depend-
ent variable are shown in Table 4-2. In contrast to the participation models using total
fishing days, the cold water acres variable in this model had the appropriate sign and a t-
value of 1.38. Although the t-value is low, it is significant at the 80 percent confidence
level with a two-tailed test and significant at the 90 percent level with a one-tailed
test. The catch rate variable was significant and stable in magnitude across the specifi-
cations examined. These models indicate that a reduction in the brook trout catch rate
from four fish per day to three fish per day would reduce the number of fishing days at
that site by approximately 37 days. Also, the coefficient on the cold water acres
variable was similar in magnitude to the coefficients on the warm water and two-story
acreage variables in the total fishing day participation models. This suggests that it may
not be unreasonable to use a value of .08 to .09 for the estimated loss in fishing days due
to the loss of one surface acre of water, whether the acre represents warm water, two-
story, or cold water ponds.
4.2 ESTIMATION OF PER MILE TRAVEL COSTS
The data contained in the New York Anglers' Survey present certain problems for use in a
travel cost valuation model, but they also have certain advantages relative to the type of
data commonly used in travel cost models. One problem with the Anglers1 Survey data is
that it contains information on the number of days spent at a site rather than the number
4-4
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Table 4-2
Participation Models using Brook Trout Pishing Days as the Dependent Variable
(t-values in parentheses)
Regression No.
1.
2.
3.
Cold
Water
Acres
.088
(1.38)
Two
Story
Acres
.0086
(2.67)
Brook
Trout
Acres
.0224
(1.32)
.004
(.224)
Acres at
Greater than
2000 ft in
Elevation
.005
(.225)
Brook
Trout
Catch
Rate
37.81
(2.22)
32.55
(1.67)
37.98
(2.88)
R2
.445
.239
.309
Overall
F
5.08
3.15
3.13
-------
of trips made to a site. This is the reverse of the problem typically faced by travel cost
models where there is data on the number of visits, but generally no information on the
duration of the stay. A positive aspect of the Anglers1 Survey is that it contains travel
expenditures reported by the individual. This expenditure data can be used to obtain
estimates of the per mile travel costs. These estimates may be preferable to estimates
from external sources such as the often used American Automobile Association's (AAA)
estimates of average travel costs, since they may better represent the individual's per-
ceived travel costs (i.e., the costs on which individuals base their fishing location
decisions). Another advantage of this particular data set is that it contains information
on individuals who visited each site as well as those who chose not to visit the site. The
decision by an individual not to visit a site provides useful information that can be in-
corporated into the estimation of the visitation equation.
One concern with the New York Anglers' Survey is that it only contains data on the num-
ber of days spent at a pond or lake. As a result, having a fisherman indicate that he
spent eight days at a pond or lake does not provide any information on whether this was
one eight-day trip, two four-day trips or four two-day trips. Depending on the number of
trips taken to provide the eight fishing days at the pond or lake, the travel costs
associated with those eight fishing days could be very different. For example, if the lake
is 100 miles from the respondent's residence, and assuming travel costs of ten cents per
mile, then one round trip would cost $20.00. If the eight days at the site represented one
trip, then the total travel costs to produce those eight fishing days would be $20.00, or
$2.50 per day. If the eight fishing days were the result of four two-day trips, then the
total travel cost would be $80.00, or $10.00 per fishing day.
This problem results in potentially large measurement errors in the estimated travel
costs. It could be solved if there were data on the number of trips and length of trips.
With such data, separate models could be estimated for trips of different lengths. The
problem faced by this analysis is not dissimilar from other travel cost applications that
have used data containing information on the trips to a site, but not the number of days
at a site. One commonly used procedure to address this problem is to use only trips of
short distances that most likely represent one-day outings, and then assume that all days
spent at the site are one-day trips. This option is not desirable for this application as the
purpose of the model is to obtain an estimate of the total use value of the resource.
Using a subset of data that represents only one-day trips could result in an under-
estimate.
4-6
-------
Given the New York Anglers' Survey data set, the best option for the dependent variable
in the travel cost model was the number of days at the site. For this dependent variable
to be most meaningful in a travel cost model framework, an estimate of the travel cost
incurred per day is desirable. As was shown above, the travel cost required to produce
one fishing day will vary depending on the length of the trip. In turn, the length of trip
could be expected to depend on the distance to the site, the individual's income and other
factors such as the individual's fishing experience. The underlying problem is whether
the travel cost per day can be estimated given data on the distance to the fishing site,
and the number of days spent at the site. Fortunately, the New York Anglers' Survey
contained selected data on expenditures. The Anglers' Survey asked the following
questions:
o What amount was spent on travel to and from each fishing location in
each category:
food, drink and refreshments
- lodging
- gas and oil
- fares on buses, airlines, etc.
- Total expenditures on travel
o What amount was spent at each fishing location on:
- food, drink and refreshments
- lodging
gas and oil
- guide fees
- access and boat launching fees
- Total expenditures at the site
The goal of the statistical analysis presented in this section was to utilize this
expenditure data to obtain an estimated travel cost per mile per fishing day. If the
travel costs associated with one fishing day can be estimated, then the data on days at a
site can be successfully used as the dependent variable in a travel cost model. It was ex-
pected that the travel costs per mile per day at a site would vary depending on the length
of trip. For example, if a fisherman were to travel 150 miles to reach a site, it is likely
that he would spend a greater number of days at the site than if he only had to travel 50
miles to reach the site. The higher fixed costs that have to be incurred to reach the
4-7
-------
more distant fishing sites would result in these costs being incurred only if the number of
days spent at the site were sufficient to offset the travel costs. For example, assume
that out-of-pocket travel costs are ten cents per mile. If a 50 mile travel distance is
associated with one-day trips, then the 100 miles traveled round trip would result in a
total cost of $10 to yield one fishing day. The travel cost per mile per fishing day would
be $10 !-(100 mile * 1 day) = $.10. If 100 mile travel distances (200 miles round trip) are
typically associated with three-day trips, then the travel cost per mile per fishing day
would be $20 t-(200 miles * 3 days) = $.033. This implies that the travel costs associated
with producing one fishing day, for this example, would be 3.3 cents per mile for a three-
day trip.
4.2.1 Per Mile Travel Cost Estimation Results
The equations used to estimate the per mile travel costs all had the same basic specifica-
tion. Travel expenditures per day were expressed as a function of distance to the site,
the individual's income, and the number of years the individual had been fishing:
Travel Expenditures per Day = Bj(Distance) + B2(Income) + B3(years fishing exper-
ience)
The coefficient B^ on distance has the dimension of dollars per mile per day. If signifi-
cant, Bj can be used as an estimate of the travel costs per mile per fishing day. The
data were disaggregated into subsets of visits to sites that were 0 to 75 miles, 0 to 150, 0
to 225, and greater than 225 miles from the fisherman's residence. Equations using data
on visits to sites 75 to 150 miles, and 150 to 225 miles were also estimated. Table 4-3
presents the estimation results using total travel expenditures per day as the dependent
variable. These results are encouraging. The coefficient on the distance variable is
highly significant in all equations except for visits to sites where the distance traveled is
greater than 225 miles. However, this is not surprising in that trips of this length are
more likely to be influenced by factors other than travel costs, in particular, income. As
can be seen from Table 4-3, the income variable was significant only for the longer trips.
The regression equations in Table 4-3 also show the expected relationship between travel
cost per mile per day and the distance traveled to the site. The average cost per mile
per day is higher for the shorter trips, reflecting that trips of short distances likely are
associated with fewer days spent at the site:
4-8
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Table 4-3
Regression Results Using Total Site Travel Expenditures per day
As the Dependent Variable
(t-values in parentheses)
CD
Regression No.
1.
2.
3.
4.
5.
6.
Sites 0 to 75 miles from
Residence
Sites 0 to 1 50 miles
Residence
Sites 0 to 225 miles
Residence
from
from
Sites greater than 225 miles
from Residence
Sites 75 to 150 miles from
Residence
Sites 1 50 to 225 miles from
Residence
Distance
(t-value)
.66E-01
(8.11)
.55E-01
(9.78)
.4398E-01
(10.128)
.544E-02
(.377)
.238E-01
(9.50)
.97E-01
(2.05)
Income
.234E-01
(1.395)
.153E-01
(.6999)
.24E-01
(.9137)
.138
(2.38)
.482E-01
(1.98)
.6376
(.37)
Years
Experience
1.28
(-1.77)
.418E-03
(.296E-01)
.234E-01
(1.42)
-.082
(-2.07)
.156E-01
(1.02)
.132
(1.86)
Constant R2
(2.67) .077
1.50
(2.44) .067
1.3349 .0635
(1.956)
6.95
(1.65) .028
2.59
(4.17) .049
-12.48
(-1.39) .033
Overall
F
24.22
32.63
36.62
3.04
33.465
2.87
-------
Distance Traveled to Site Estimated Travel Costs (t-value)
0-75 6.6£ per mile per day
(8.11)
0 - 150 5.5£ per mile per day
(9.78)
0-225 4.4£ per mile per day
(10.13)
greater than 225 .05)6 per mile per day
(0.38)
There is one anomaly in the estimated travel costs shown in Table 4-3. The regression
equation #6 on trips of 150 to 225 miles shows an estimated per mile travel cost that is
larger than those from the equations for visits of 0 to 75 and 75 to 150 miles. One pos-
sible explanation for this could be a clustering of trips with travel distances near the
lower end of the 75 to 150 mile range; however, additional analysis of the data would be
useful in interpreting this result. Still, the travel costs for the 0 to 75, the 0 to 150, and
the 0 to 225 trip distance subgroups show the expected relationship and these regressions
would not be as sensitive to the clustering of trip distances within each range. The
results of these regressions show a declining relationship between trip distance and travel
cost per mile per day.
A second set of regression equations were estimated using only oil and gas travel ex-
penditures per fishing day rather than total travel expenditures. These costs may better
represent the variable costs of traveling, since food and lodging would have to be pro-
vided on a trip of any distance. The same independent variables were used in the estima-
tion. The results are shown in Table 4-4. Again the results are encouraging. The
coefficients on the distance variables are significant in all equations, except for the
visits to sites of greater distances:
Distance Traveled to Site Estimated Oil & Gas Travel Costs (t-value)
0-75 5.8£ per mile per day
(7.84)
0 - 150 3.9d per mile per day
(9.71)
0 - 225 2.5£ per mile per day
(8.58)
greater than 225 -.OOSji per mile per day
(.36)
4-10
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Table 4-4
Regression Results Using Expenditures on Oil and Gas
As the Dependent Variable
(t-values in parentheses)
Regression No.
1.
2.
3.
4.
5.
6.
Sites 0 to 75 miles from
Residence
Sites 0 to 150 miles from
Residence
Sites 0 to 225 miles from
Residence
Sites greater than 225 miles
from Residence
Sites 75 to 150 miles from
Residence
Sites 150 to 225 miles from
Residence
Distance
(t-value)
.579E-01
(7.84)
.39477E-01
(9.71)
.248E-01
(8.58)
-.326E-03
(-.36E-01)
.1015E-01
(6.42)
-.372E-01
(-1.369)
Income
.258E-01
(1.72)
.2527E-01
(1.515)
.2864E-01
(1.63)
.104
(2.85)
.489E-01
(3.21)
.423E-01
(.726)
Years
Experience
-.467E-01
(-1.679)
-.1069E-01
(-1.06)
.7488E-02
(-.689)
-.4035E-01
(-1.59)
-.0061
-.627)
.952E-02
(.2335)
Constant R2
.834 .078
(1.935)
1.46 .0717
(3.29)
2.1665 .05
(4.75)
4.855 .03
(1.827)
2.626 .028
(6.71)
11.97 .0092
(2.335)
Overall
F
23.09
33.016
26.779
3.21
19.267
.798
-------
A third set of regression equations were estimated using total costs (travel and on-site)
divided by days at the site. These equations were estimated for comparison purposes and
as a consistency check. These estimates include expenditures at the site and are not
appropriate for use as travel costs. Still, these estimates are informative. The coeffi-
cient on the distance variable is still dimensioned in dollars per mile per day. Also, it is
possible that site expenditures may be related to distance. If a greater distance is
traveled, then more activities may be required to make the time spent at the site worth
the incremental travel costs. Although this hypothesis is weak theoretically and is
entirely dependent upon the marginal utility and cost of activities available at the site
visited, it is easily tested with this data. The results of these regressions are shown in
Table 4-5. Again, the coefficient on the distance variable was significant except for the
longer trips and declined in magnitude as trips of longer duration were included:
Distance Traveled to Site Estimated Total Costs (t-values)
0-75 17.0£ per mile per day
(6.15)
0-150 16.1£ per mile per day
(8.03)
0-225 10.9^ per mile per day
(9.20)
greater than 225 4.6<4 per mile-day
(1.7)
Another result worth noting from the regressions presented in Table 4-5 is that income
was a more important variable for explaining total costs per day than for explaining
travel costs only. It seems intuitively plausible to have high recreation expenditures at
the site correlated with high individual incomes.
4.2.2 Estimated Travel Costs; Conclusions
The results of the travel cost estimation are encouraging and indicate that reasonable
estimates of travel costs to provide a fishing day can be obtained. As expected, these
costs tended to vary with the length of trip. In most travel cost models, the per mile
travel cost comes from a source such as the American Automobile Association's pub-
lished estimates of average travel cost per mile. This travel cost per mile estimate
4-12
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Table 4-5
Regression Results Using Total Travel and Site Expenditures per day* as the Dependent Variable
(t-values in parentheses)
Regression No.
1.
2.
3.
4.
5.
6.
Sites 0 to 75 miles from
Residence
Sites 0 to 150 miles from
Residence
Sites 0 to 225 miles from
Residence
Sites greater than 225 miles
from Residence
Sites 75 to 1 50 miles from
Residence
Sites 150 to 225 miles from
Residence
Distance
(t-value)
.17
(6.15)
.0251
(1.58)
.0465
(1.70)
.054
(6.78)
.161
(8.03)
.1089
(9.20)
Income
.0136
(.232)
.227
(2.47)
.294
(2.64)
.1739
(3.40)
.1107
(1.31)
.1158
(1.566)
Years
Experience
-.066
(-2.08)
.089
(1.41)
.01
(.1439)
-.827E-03
(-.0257)
-.22E-01
(-.4452)
.0187
(.416)
Overall
Constant Rz F
3.57 .0676 13.91
(2.16)
11.01 .0216 378
(2.47)
4.90 .0324 3.25
(.611)
10.56 .0305 20.33
(8.95)
1.93 .065 22.45
(.867)
3.56 .0723 30.56
(1.856)
DF
576
517
292
1938
955
1176
*Dependent Variable is the individual's total expenditures on travel to the site (includes gas and oil, food and lodging in
transit), plus the cost of lodging, food and activities at the site divided by the number of days spent at the site.
-------
poses problems due to the large variability in per mile costs that results from the varia-
bility in age and type of vehicles).2 The estimates obtained from the regression equa-
tions reported in this section are based on reported expenditure data and, although
subject to error, are probably no worse than those used in other travel cost studies.
These estimates may even be preferred in that they may better represent the individual's
perceived travel costs since they are based on expenditure data supplied by the respond-
ent. In addition, individuals use perceived travel costs when making their site selections.
The estimation results are summarized in Table 4-6. The range of estimates for travel
costs per day for sites of different distances was quite narrow. The per mile total travel
costs ranged from 6.6 cents per mile per day for nearby sites (0 to 75 miles) to 4.4 cents
per mile per day as more distant sites were included in the sample (0 to 225 miles). The
estimates for only the oil and gas portion of travel costs were slightly less, ranging from
5.8 to 2.5 cents per mile per day.
2 For example, Vaughan and Russell (1982) use the AAA estimate of 7.62 cents per mile.
4-14
-------
Table 4-6
Summary of Estimated Expenditures per Mile per Day
(t-values in parentheses, units are cents per mile per fishing day)
Distance to Site
0 to 75 miles
0 to 150 miles
0 to 225 miles1
Greater than 225 miles
Estimated Total
Travel Costs
6.6
(8.11)
5.5
(9.78)
4.4
(10.13)
.05
(.34)
Estimated
Oil and Gas
Travel Costs Only
5.8
(7.84)
3.9
(9.71)
2.5
(8.58)
-.003
(.36)
Estimated
Total Costs:
Travel and Site
17.0
(6.15)
16.1
(8.03)
10.9
(9.20)
4.6
(1.7)
These travel cost estimates for trips of 0 to 225 miles were used in Chapter 5.0.
4-15
-------
4.3 TRAVEL COST MODEL
Several different techniques to estimate a relationship between travel costs and fishing
days were considered. As mentioned previously, the data available for this project are
different from the data typically used in travel cost models. To briefly review, the data
set contained information on individuals, the distances from the individuals' home to each
of the 24 sites, and the number of days that the individual spent at each of the 24 sites.
The fewest number of individuals visiting any site was 30. In estimating the site demand
function, the typical travel cost model would only use data on individuals that have
actually visited the site. This would result in observations on a sample of 30 individuals
being available for the least visited site. However, using data on only those individuals
that have actually visited the site ignores a substantial amount of information, namely
the travel distance to the sites and characteristics of the individuals that did not visit
the sites. For many of these individuals, the price in terms of travel costs to sites not
visited may have been too high relative to the costs of visiting other sites. This informa-
tion is pertinent to the analysis and should not be omitted from the estimation. As a
result, it is desirable that the travel cost models for each site be estimated using the
entire data set.
A data set that contains observations on individuals who purchased the commodity (i.e.,
made a trip to the site), as well as on individuals who did not purchase the commodity, is
termed a "limited" data set.** The data set is "limited" in that the dependent variable is
not observable over the entire range. In this case, the dependent variable is fishing days
at each site and is observable only when a trip to that site has been made. Therefore,
the dependent variable is observable only when it is greater than zero. The regression
model is:
D = BX + u; (4.1)
where "D" represents the number of days spent at the site. D is observed only if D is
greater than 0. Therefore, the model is:
3 This discussion follows Maddala (1977), pp. 162-164.
4-16
-------
D = BX + u, if BX + u > 0, which implies u > - BX
or (4.2)
D = 0, ifBX + u<_0
Applying ordinary least squares (OLS) regression techniques to only those observations
for which D > 0 results in biased estimates. The residuals in this equation will not satisfy
the OLS assumption that the expected value of the error term is zero (i.e., E(u) = 0). If
some specific assumptions are made about the distribution of the residuals, then
maximum likelihood techniques can be used to estimate the parameters. If it is assumed
that u has a normal distribution with a zero mean and variance o » then the joint
distribution of the observations is:
D .-BX . -BX .
L = n i f ( 1 V n F(-)
2 (4,3)
where f(') is the standard normal density function and F(') is the cumulative normal
density. The first term corresponds to those individuals for which D^ is greater than 0,
and, therefore, is known. The second term corresponds to those individuals for which all
that is known is that D^ is less than or equal to 0. The earliest application of this tech-
nique was by Tobin (1958).
The use of OLS techniques rather than the maximum likelihood techniques discussed
above will result in biased estimates of the coefficients. If OLS is applied to the data
and Dj = 0 is used for those individuals who did not visit the site, there will be many non-
visitors with a resulting concentration of observations at Dj = 0. The absence of any
negative Dj's in the sample will tend to keep the estimated regression equation above the
zero axis over the relevant range of the X's, but it will also tend to flatten the estimated
curve. This results in the estimated number of days spent at the site being underesti-
mated for individuals with a low travel price (i.e., short distance between the site and
individual), and overestimated for individuals with a higher travel price.
A TOBIT procedure is recommended to correct for this bias. The TOBIT analysis takes
into account both the individual's likelihood of visiting a given site and the number of
days spent at the site, given that the individual decides to visit the site. These two
4-17
-------
values taken together can be used to calculate the expected value of days at each site
for each individual. The TOBIT procedures also produce consistent estimates of the
regression coefficients in equation 4.1. In this analysis, both TOBIT and OLS estimates
of the regression coefficients are derived and compared.
A separate travel cost equation for each of the 24 sites was estimated. In each case, the
dependent variable was the number of days spent at the site. The independent variables
were the distance to the site, the individual's income, and the individual's years of fishing
experience. Distance to the site rather than an actual travel cost estimate was used as
an independent variable to allow for sensitivity analysis around the estimated per mile
travel cost. If information on the marginal value of time (e.g., wage rates) across the
individuals in the sample had been available, then it might have been desirable to include
an estimate of actual travel time costs to determine the relative influence of each cost
on the decision to take a fishing trip. Since both the out-of-pocket and time value com-
ponents of travel costs are expressed on a per mile basis in this analysis, using distance in
miles as the independent variable provides the most general formulation.
One advantage that the use of travel costs rather than distance traveled as the inde-
pendent variable could provide is that the non-linear relationship between travel distance
and per mile per day travel costs found in Section 4.2 could have been explicitly incorp-
orated into the analysis. For each individual, a different per mile travel cost to each
site, depending on that individual's distance from the site, could have added to the data
set. However, the robustness of the per mile travel cost estimate over the entire 0 to
225 mile range,* the fact that to perform any sensitivity analysis around travel costs
would have required the re-estimation of the entire set of site equations, and the time
and budget constraints of the project resulted in the decision to use distance rather than
actual travel costs as the independent variable.
Only observations on individuals within 225 miles of the site were used in this analysis.
There were two reasons for this. First, trips of over 225 miles are more likely to be mul-
tiple purpose trips, which would result in interpretation problems. Second, the estimates
of travel costs presented in Section 4.2 showed that the number of days spent at a site
* The high level of significance, i.e., low standard error, implies that this estimated
travel cost could be used as an average value for travel costs for trips of up to 225 miles
distance without introducing an uncomfortably large amount of error.
4-18
-------
were largely independent of the amount of money spent on travel when the distance
traveled was greater than 225 miles. 1,040 observations remained after deleting visits to
sites that required a one-way trip of greater than 225 miles. Prior to estimating the
travel cost model for all of the sites, preliminary analyses were performed on three
sites. These results showed that when the own price (i.e. travel cost) to each site and the
substitute prices to the other 23 sites were included in the regression equation none of
the travel cost coefficients were found to be statistically significant.^ It was decided to
include only the own price in each travel cost equation. The omission of cross-price
effects should result in the estimates of damages due to acidification being over
estimated. Since previous estimates (Menz and Mullen; 1982 and Crocker et al., 1981)
have been very low, an estimate that is biased on the high side, if still found to be low,
should provide useful policy information.
4.3.1 TOBIT Procedures Applied to Total Fishing Pays
The TOBIT procedure in the SHAZAM econometric software package was used to esti-
mate the model. Table 4-7 presents the estimated regression coefficients obtained by
using this TOBIT procedure and total fishing days at a site as the dependent variable.
Table 4-7 shows that the distance variable was highly significant in most of the equa-
tions. The coefficients on the distance variable were significant at the 1 percent level in
eighteen out of the twenty-three estimated equations. The distance variable was not
significant or had the wrong sign in the equations for sites 10, 16 and 20.6 Inspection of
these sites showed that the total number of fishing days at these sites was in the lower
half of the data set. The coefficients on the income and the years of fishing experience
variables were generally not significant. The R-squares were low, typically varying
This outcome was probably the result of multicollinearity across the distance variables.
The inclusion of the travel distances to each of the 24 sites for all individuals provides
many possible linear combinations of .these variables that might result in a singular or
near singular X'X matrix. There are other methods of including substitutes. One
approach would be to reduce the dimension of the distance data set by using principal
components. This would require a different set of principal components to be calculated
for each site. This is due to the fact that the set of 23 substitute sites is different, by
one site, for each of the 24 sites.
c
The equation for site 13 was not estimated due to an error in the program that merged
the distance data and the site characteristics data. The merging of the data sets
involved two large data bases and was expensive.
4-19
-------
Table 4-7
Travel Cost Model using Total Days as the Dependent Variable:
Estimated with a TQBIT Procedure
{t-values in parentheses)
Site*
1
2
3
4
5
6
7
8
9
10
11
12
14
15
Distance
-.3946
(7.71)
-.2752
(8.32)
-.0780
(3.52)
-.1794
(6.51)
-.1772
(5.63)
-.8122
(7.92)
-.0726
(2.40)
-.2350
(5.72)
-.2877
(6.34)
.1266
(2.62)
-.0777
(3.38)
-.1638
(3.18)
-.1304
(3.81)
-.0842
(3.11)
Income
-.0727
(.19)
-.4038
(1.67)
.1205
(.76)
.0928
(.55)
-.1298
(.56)
.1421
(.28)
.0843
(.53)
.0969
(.40)
.2334
(.99)
-.5379
(2.36)
-.0304
(.26)
.2017
(.84)
.3542
(2.47)
.0903
(.87)
Years Fishing
-.2661
(1.20)
.1052
(.88)
-.0302
(.30)
-.1008
(.95)
.1254
(5.63)
-.8122
(7.92)
-.0726
(2.40)
-.2350
(5.72)
.4359
(2.90)
.1250
(1.14)
.0038
(.05)
-.0345
(.23)
.1484
(1.59)
.0363
(.58)
Constant
-10.457
(1.25)
-1.5800
(.26)
-24.371
(5.30)
-10.915
(2.58)
-25.871
(4.32)
1.4610
(.11)
-26.931
(5.22)
-25.511
(3.59)
-38.819
(5.43)
-53.252
(7.46)
-16.996
(4.80)
-41.044
(5.44)
-31.192
(5.77)
-18.249
(4.73)
R2*
.083
.077
.0018
.035
.06
.074
.009
.077
.079
.001
.011
.006
.013
.007
*Note: R2 between observed and predicted values.
4-20
-------
Table 4-7
Travel Cost Model using Total Days as the Dependent Variable:
Estimated with a TOBIT Procedure
(continued)
Site #
16
17
18
19
20
21
22
23
24
Distance
-.0024
(.11)
-.1915
(3.53)
-.2301
(3.07)
-.3893
(10.24)
.0543
(1.12)
-.1912
(4.25)
-.3626
(6.62)
-.4553
(10.85
-.3262
(10.04)
Income
-.2005
(1.75)
-.0731
(.35)
.0944
(.28)
.6607
(4.75)
-.1903
(.66)
-.0816
(.43)
-.0584
(.37)
-.1374
(.95)
.0428
(.32)
Years Fishing
-.0432
(.73)
-.0072
(.06)
-.0174
(.09)
.0915
(1.04)
.2764
(1.78)
.1727
(1.59)
-.0794
(.90)
.1884
(2.31)
-.0935
(1.22)
Constant
-19.036
(5.56)
-26.191
(3.65)
-55.701
(5.22)
-9.9139
(2.21)
-68.586
(7.94)
-27.370
(4.41)
.2548
(.05)
1.6300
(-38)
.1331
(.03)
R2*
.0006
.0119
.007
.058
.004
.0117
.038
.098
.027
Note: R2 between observed and predicted values.
4-21
-------
between .01 and .10 for those equations where the distance variable was significant.
n
While low, these R-squares are not atypical for travel cost models.
The regression coefficients in the TOBIT model should be interpreted a little differently
than conventional OLS regression coefficients. In the TOBIT procedure, an index "I" is
created which is a function of the independent variables, I = XA; where A is a vector of
normalized coefficients:
In = A0 + AiXln + A2 X2n + . . . + Ak Xkn; (4.4)
where In is the value of the index for the nth individual given the values of the Xk's for
that individual. These Ak normalized coefficients can be transformed into estimates of
the regression coefficients the Bi's by multiplying the Ai's by the calculated
standard error of the estimate:
(BQ, B!, . . . , Bk) = (0- A0, a Alf . . . ,°" ' Ak); (4.5)
where o is the standard error of the dependent variable.
The coefficients presented in Table 4-7 are transformed normalized coefficients, or the
B^ regression coefficients. One intuitive explanation of the meaning of these regression
estimates is that they are consistent estimates of the same regression coefficients that
would have been estimated by OLS, if the data set was not truncated at zero; that is, if
both positive and negative values of the dependent variable "DAYS" could have been
observed. Recall that the OLS procedures applied to the truncated data set produces an
estimate of the slope that will be biased downwards due to the many observations where
the dependent variable is zero. As a result, the TOBIT coefficients should always be
larger in magnitude than regression coefficients estimated using OLS.
A graphical depiction of the relationship between the expected relationship between the
OLS estimates, the TOBIT estimates and the calculated expected values using the TOBIT
procedures is shown in Figure 4-1a. The OLS estimated relationships is line segment BD
and is shown to be flatter than the TOBIT maximum likelihood estimate. The expected
^ For example, see Brown and Mendelsohn (1984) and Desvousges, Smith and McGivney
(1983).
4-22
-------
Figure 4-1
Expected Relationship Between the OLS Estimates, TOBIT
Estimates, and the TOBIT Generated Expected Values!
Figure 4-la - Standard TOBIT, OLS
Relat ionship
Days
Expected Value
Estimate
OLS Slope Estimate (ED)
TOBIT Maximum Like-
lihood Slope Estimate
D Distance
Figure 4-lb - Relationship when the probabilities of an individual visiting the site
are less than .5 for all distances
D Distance
This figure is similar to Figures 3a and 3b in Tobin (1958).
4-23
-------
value locus is also shown in Figure 4-1 a. Each individual has some positive probability of
visiting each site; however, this probability is lower the greater the distance to the site.
For sites that are very distant, the probability may be close to zero. The expected value
locus shown in Figure 4-1 a is this probability multiplied by the expected number of fish-
ing days at that site, given the individual visits to the site. This conditional expectation
Q
can be calculated from the following equation:
where:
o E (Dn ( ln) is the expected value of the number of days at a site given
the value of the index (In) for that individual;
o In is the value of the index calculated from I = AX, i.e., equation 4.4;
o a is the standard error of the dependent variable;
o f () and F () are the marginal and cumulative normal density func-
tions.
As is shown in Figure 4-la, this method of calculating the expected value locus results in
a nonlinear relationship. The expected value locus will always be above the TOBIT maxi-
mum likelihood equation (i.e., segment AC). At the left where the probabilities of visit-
ing a site are high, the expected value locus will approach AC asymptotically. At the
right where the probability of visiting a site approaches zero, the expected value locus
will approach the line segment CD, which will be the horizontal axis in cases where the
limiting value is zero.
Given the above explanation, some further analysis of certain peculiarities of the TOBIT
regression results are possible. An examination of the coefficients estimated for site 1
in Table 4-7 shows that all of the coefficients are negative. This fact combined with the
realization that the values of all the independent variables are positive results in any
8 This equation is derived in Tobin (1958) and Goldberger (1964).
4-24
-------
predicted number of fishing days from this model being negative. However, this result is
consistent with the TOBIT interpretation presented above. There are two factors that
must be considered when interpreting this outcome. First, the regression coefficients
are used to calculate an index that in turn is used to calculate the probability of an
individual taking a trip. This index is positive whenever the probability of taking a trip
exceeds fifty percent and is negative whenever the probability is less than fifty per-
cent.9 This result for site 1 indicates that the probability of any one individual taking a
fishing trip to that particular site is less than .5; however, the expected value for fishing
days will still be positive. This outcome is illustrated in Figure 4-1 . ° A second point
that should be considered when interpreting the TOBIT coefficients for site 1 is the large
standard errors of the coefficients on the non-distance variables. These make the actual
intercept in Figure 4-1 very uncertain. This interpretation is important for calculating
consumer surplus and willingness-to-pay estimates, and will be readdressed in Chapter 5.
4.3.2 Ordinary Least Squares Applied to Total Fishing Days
In spite of the fact that OLS estimates are biased, OLS was applied to the data sets to
provide information on the strength of the relationship between fishing days and distance
to the site. The OLS estimates provided a useful point of comparison as there is an
explicit theoretic prior expectation of the relative magnitudes of the OLS and TOBIT
regression coefficients.
The OLS estimates are presented in Table 4-8. As in the TOBIT analysis, only sites
requiring trips of less than 225 one way miles were included in the data set. The results
in Table 4-8 show that the distance variable was highly significant in most of the equa-
tions. The coefficients on the distance variable were significant at the 1 percent level in
eighteen out of the twenty-three estimated equations. The distance variable was not
significant for sites 3, 10, 12, 16 and 20. The income and the years of fishing experience
variables were generally not significant. The R-squares were low, typically varying
between .01 and .06 for those equations where the distance variable was significant.
9 See Tobin (1958), page 34 and Goldsmith (1983) footnote 19, page 39.
*Q A similar result was found by Deegan and White (1976) where their TOBIT regression
coefficients only yielded negative values for the dependent variable over the entire range
of Xj, with the other Xj held constant at their means.
4-25
-------
Table 4-8
Travel Cost Model Using Total Days as the Dependent Variable:
Estimated by Ordinary Least Squares
(t-values in parentheses)
Site #
1
2
3
4
5
6
7
8
9
10
11
12
13*
14
15
16
Distance
-.0158
(6.72)
-.0178
(6.45)
-.0012
(1.02)
-.0076
(5.92)
-.0133
(6.06)
-.0235
(5.60)
-.0104
(3.51)
-.0347
(6.76)
-.0168
(5.82)
.0052
(1.18)
-.0040
(3.38)
-.0064
(1.59)
NA
-.0157
(3.96)
-.0091
(3.40)
-.0010
(.58)
Income
-.0066
(.41)
-.0254
(1.84)
-.0027
(.32)
.0036
(.52)
-.0074
(.57)
-.0047
(.23)
-.0060
(.25)
-.0065
(.25)
-.0082
(.57)
-.0167
(1.28)
-.0021
(.37)
-.0048
(.26)
NA
.0088
(.58)
.0050
(.63)
0.0054
(1.00)
Y0ars Fishing
-.0139
(1.48)
.0075
(.93)
.0008
(.16)
-.0007
(.18)
.0114
(1.52)
.0082
(.69)
.0157
(1.89)
.0014
(.09)
.0174
(2.07)
.0109
(1.43)
-.0016
(.49)
-.0076
(.70)
NA
.0112
(1.27)
-.0019
(.41)
-.0005
(.16)
Intercept
3.3441
(6.86)
3.3922
(6.77)
.4533
(1.73)
1.21
(5.43)
2.0050
(5.00)
3.4523
(4.91)
1.5810
(3.23)
5.5683
(6.64)
2.0850
(4.62)
-.1924
(-36)
.75
(4.13)
1.4612
(2.46)
NA
1.9952
(3.33)
1.32
(3.83)
.4222
(1.82)
R2
.0468
.0445
.0012
.033
.0369
.0303
.0155
.0436
.0355
.0044
.0118
.0031
NA
.0172
.0113
.0014
* The equation for site 13 was not estimated due to an error in the program that merged
the distance data and the site characteristics data.
4-26
-------
Table 4-8
Travel Cost Model Using Total Days as the Dependent Variable:
Estimated by Ordinary Least Squares
(t-values are in parentheses)
(continued)
Site #
17
18
19
20
21
22
23
24
Distance
-.0182
(2.94)
-.0229
(3.19)
-.0439
(6.63)
.0022
(1.08)
-.0137
(2.64)
-.0180
(5.38)
-.0486
(7.56)
-.0316
(5.52)
Income
-.0158
(.98)
-.0033
(.13)
.0717
(2.44)
-.0093
(.93)
-.0310
(1.59)
-.0153
(1.43)
-.0719
(2.27)
-.0155
(.53)
Years Fishing
.0058
(.61)
.0257
(1.68)
.0335
(1.94)
.0126
(2.15)
.0281
(2.44)
-.0023
(.36) '
.0248
(1.33)
-.0156
(.91)
Intercept
2.4106
(3.38)
2.1425
(2.35)
3.9322
(4.23)
-.1677
(.55)
1.9496
(2.74)
2.3041
(5.79)
6.5822
(6.93)
5.2824
(6.15)
R2
.0102
.0126
.0498
.0062
.0152
.0291
.0579
.029
4-27
-------
Comparing the OLS results to the TOBIT results, the magnitudes of the coefficients con-
form to theoretic expectations. The absolute magnitudes of the TOBIT coefficients are
greater than the OLS estimated coefficients. Also, the calculated t-values and R-
squares were higher for the TOBIT equations.
Brook Trout Fishing Day Travel Cost Model Analyses
The participation models presented in Section 4.1 indicated that brook trout fishing days
might be better analyzed separately. If possible, this could prove useful since acid
deposition is expected to have a greater impact on the high altitude lakes that provide
much of the unique brook trout habitat. As with the participation model, a new brook
trout fishing days variable was defined. This variable was constructed by taking all the
days at each site where the individual reported to have caught at least one brook trout.
Other species of fish may have been fished for and caught as well, but if brook trout
were caught, these days were classified as brook trout days.
This brook trout fishing day variable was used as the dependent variable in a TOBIT re-
gression. The TOBIT procedure requires the use of iterative numerical methods. When
brook trout days were used as the dependent variable, a number of the equations did not
converge after the default number of iterations. As a result, TOBIT estimates were not
able to be obtained for many of the sites. Table 4-9 presents the estimates for those
sites where convergence was achieved. The fact that many equations did not converge
may be explained by the limited number of non-zero observations. When total fishing
days were used as the dependent variable, the sites with the least number of non-zero
observations still had 30 non-zero observations out of 1,040 total observations. When
only brook trout fishing days were used, several sites had less than 10 non-zero observa-
tions. Table 4-9 shows that only five sites achieved convergence and, of these five, only
three had significant coefficients of the right sign on the distance variable. The
R-squares of these equations were substantially lower than those found for the TOBIT
results shown in Table 4-7. One interesting finding is that, where the coefficient on the
4-28
-------
Table 4-9
Travel Cost Model using Brook Trout Fishing Days as the Dependent Variable:
Estimated with a TOBIT Procedure
(t-values are in parentheses)
Site # Distance
6 -.9785
(3.34)
9 -.3667
(2.93)
10 .2447
(1.62)
11 -.1160
(2.11)
12 .0315
(.38)
Income
.6716
(.44)
-1.5920
(1.57)
.5675
(1.18)
.2602
(1.16)
.1096
(.29)
Years Fishing
.9690
(1.14)
.6671
(1.89)
.2559
(1.29)
-.0421
(.27)
-.0070
(.03)
Constant
-94.926
(2.39)
-53.748
(3.08
-86.855
(4.46)
-37.776
(5.05)
-76.104
(5.99)
R2
.0044
.009
.0039
.007
.0022
4-29
-------
distance variable is negative and significant, it is similar to the magnitudes of the
coefficients in the total days equations presented in Table 4-7:
Brook Trout Fishing Total Fishing Day
Day Coefficients Coefficients
(t-value) (t-value)
Site 6 -.978 -.812
(3.34) (5.63)
Site 9 -.367 -.287
(2.93) (6.34)
Site 11 -.116 -.078
(2.11) (3.38)
The similarity in the magnitude of these coefficients may mean that it is less important
to separately estimate a travel cost model for brook trout fishing days.
A semi-log specification for brook trout fishing days was also estimated. The results of
this TOBIT estimation are presented in Table 4-10. The semi-log specification produced
a modest improvement more equations converged and the statistical results in terms
of t-values, expected signs on the distance coefficients, and R-squares were slightly
improved.
4.4 SECOND STAGE ANALYSIS OF THE CHARACTERISTICS OF FISHING SITES
The coefficients of a travel cost model using both TOBIT and OLS procedures were esti-
mated following procedures discussed in Section 4.3. As discussed in Chapter 2.0, these
travel cost models do not explicitly take into account site characteristics. Travel cost
models do estimate the travel and time costs that an individual is willing to pay to visit a
site. These willingness-to-pay amounts can be calculated from the coefficients on the
independent variables in the visitation equation for each site. It seems likely that sites
with more desirable recreational characteristics, such as fishing opportunities and catch
rate, would attract fishermen from further distances. This should show up in the relative
magnitudes of the estimated coefficients on the distance variable in the site equations.
Also, the participation models estimated in Section 4.1 showed the number of visitor days
to be positively related to site characteristics such as pond acreage and total catch rate.
This section presents results obtained by regressing the coefficients from each site
equation on selected characteristics of that site. Two site characteristics were used:
fishable acreage and total catch rate. The equation that was estimated is:
4-30
-------
Table 4-10
Travel Cost Model using the Natural Log of
Brook Trout Fishing Days as the Dependent Variable:
Estimated with a Tobit Procedure
(t-values are in parentheses)
Site # Distance
1 -.0435
(3.45)
3 -.0201
(3.06)
9 -.0544
(2.91)
10 .0459
(1.59)
11 -.0255
0.91)
12 .0135
(1.25)
14 -.0466
(2.83)
15 -.0236
(1.22)
Income
.0781
(.82)
-.0041
(.08)
-.2330
(1.55)
.0977
(1.08)
.0798
1.54)
.0243
(.45)
.0490
(.78)
.0463
(.80)
Years Fishing
-.0852
(1.31)
.0248
(.88)
-.363
(.09)
.099
(1.88)
.032
(.86)
-.004
(.12)
-.018
(.50)
.016
(.44)
Constant
-9.54
(4.10)
-6.01
(.478)
-8.20
(3.13)
-15.8
(4.29)
-9.43
(5.19)
-11.5
(6.10)
-7.75
(3.49)
-9.67
(3.94)
R2
.043
.017
.011
.003
.007
.005
.007
.001
4-31
-------
By = AQ + AJ (Acres)j + A2 (Catch Rate).
where By is the ith parameter (either a coefficient or intercept from the j site equa-
tion. Two parameters were used as the dependent variable in this second stage. The
first was the coefficient on the distance variable (i.e., BJJ), the second was the inter-
cept. The demand curve intercept was defined as:
B2j (Mean Income Value) + B^j (Mean Experience Value) + 84;.
This composite variable represents the intercept of a demand equation relating fishing
days to distance, holding the other variables constant at their mean values. It would
have been possible to estimate each coefficient and intercept as a function of the site
characteristics; however, the income and experience variables were not significant in
most of the site equations. As a result, these coefficient estimates would have large
standard errors and, at best, would be imprecisely estimated. This would make statis-
tically significant estimates of the effects of the site characteristic levels on these
coefficients unlikely and the results hard to interpret. Given this situation, only the
above composite inter-cept was regressed against site characteristics. Since this inter-
cept is the actual demand curve intercept, this was felt to be appropriate.
The results of regressing both the coefficient on the distance variable and the intercept
against two site characteristics net acres and total catch rate are shown in Table
4-1 la. Two other specifications were also estimated. The results of these are shown in
Table 4-llb. The GLS procedure discussed in Chapter 2 was used in both instances.
Table 4-12 presents similar GLS estimated equations for the parameters from the OLS
estimated travel cost equations.
In Tables 4-11 and 4-12, the site characteristics have t-values that are small. Still, a t-
value of 1.27 is significant at the 10 percent level for a one-tailed test and 20 percent
for a two-tailed test. The coefficients on the site characteristics in the intercept
equation have the expected sign. As fishable acres and catch rates decline, intercept
moves downward, reducing the consumer surplus obtained from the site. The coefficients
on the site characteristic in the equation using the stage one distance coefficient as the
independent variable did not have the expected sign. In general, the composite effect of
reductions in the level of the site characteristics was a reduction in consumer surplus
because the influence of the change in the intercept was large enough to outweigh the
4-32
-------
Table 4-11
Second Stage Generalized Least Squares Runs on the TOBIT Estimated Parameters
from the Total Fishing Day Equations
(t-values)
a. Base Equations
Dependent
Variable
Coefficient on
Distance Variable
Intercept
Net
Park Acres
-.692* 10~5
(1.80)
.597 x 10~3
(1.27)
Total
Catch Rate
-.007
(1.01)
4.81
(2.47)
Constant
-.116
(-1.27)
45.01
(10.15)
R2
.161
.225
b. Additional Trial Specifications
Dependent
Variable
Coefficient
or Distance
Variable
Acres less
than 1 500 feet
Elevation
-.519+ 10"5
(1.36)
Warm
Water
Acres
Two
Story
Acres
Total
Catch
Rate
-.0056
(.2907)
Constant
-.129
(1.89)
R2
.108
Intercept
.623 x 10"3
(1.38)
.211 + 60~3
(.449)
3.07
(1.13)
32.14
(3.15)
1.34
4-33
-------
Table 4-12
Generalized Least Squares Runs on the Ordinary Least Squares Parameters
from the Total Day Equations
Dependent Net Total
Variable Park Acres Catch Rate Constant R
Coefficient on -.852 x IO"6 -.254 x 10~2 +.583 x 10~2 .178
the Distance (1.91) (1.48) (.797)
Variable
Intercept .135-t-lO"4 .253 .740 x 10"1 .235
(2.44) (1.04) (.072)
4-34
-------
effect from the change in the distance coefficient. For calculating the changes in con-
sumer surplus associated acidification, only the effect of site characteristics on the
intercept of each site's demand curve was used. This is consistent with the objective of
selecting assumptions that would lead to a high estimate of damages as was discussed in
Chapter 1.
4.5 TRAVEL COST MODEL ESTIMATES: CONCLUSIONS
The statistical results presented in this section show a strong relationship between visitor
days at a site and the travel distance to the site. The analyses provide estimates that
can be used to estimate the consumer surplus derived from each fishing site; however,
only the most basic specifications have been estimated and additional analyses would be
desirable.
Additional analysis may be beneficial in several areas. One could examine alternative
functional forms including semi-log and Box-Cox specifications. A second issue warrant-
ing additional analysis would be the opportunity cost of time. To examine this issue, an
estimate of the individual's marginal valuation of time is needed. Most often, the
individual's wage rate is used as an estimate of the value of time. Unfortunately, the
Anglers' Survey does not include information on the individual's wage. It would be pos-
sible, however, to perform an analysis similar to that contained in Section 7.4 of
Desvousges, Smith and McGivney (1983).
Desvousges, et ah (1983) used a model that predicts the wage rate given the individual's
annual income, occupation and related characteristics. They found the variation in
estimated wage rates from the mean wage level to be approximately 50 percent.
Given the potential magnitude of other errors in the model, the error due to not captur-
ing differences in individual's marginal valuation of time does not seem overwhelming,
but it also should not be minimized. The present formulation of the model, where
distance rather than a specific travel cost is entered into the model, allows alternative
cost per mile values to be calculated using varying travel and time costs.
Another important issue concerns the current inability to estimate a separate model for
brook trout fishing days. The TOBIT procedures applied to brook trout fishing days failed
4-35
-------
to converge on a set of coefficients for most of the sites because of too few non-zero
observations. This could potentially be remedied by redefining the sites and using
alternative numerical techniques. Since the brook trout fish population is the fishery
most threatened by acid deposition, a separately estimated brook trout travel cost model
may be useful.
4-36
-------
5.0 RECREATIONAL FISHING RESOURCE VALUATION
Several procedures can be used to provide estimates of the value of damages (i.e.,
reduced benefits) to recreational fishing in the Adirondack Mountains from current levels
of acidification. Section 4.3 discussed the relationships between demand curves based on
OLS estimated regression coefficients, TOBIT estimated regression coefficients, and the
expected value locus calculated from the TOBIT coefficients. A consumer surplus
estimate associated with each of the sites can be calculated using each of these demand
curves. Of these three options, the most appropriate curve to use for estimating the
consumer surplus is the TOBIT based expected value locus, since this estimate takes into
account both the probability of visiting the site and the estimated number of days at a
site given that a trip is taken. In addition to the travel cost model, estimates of damages
from acidification can be derived from the participation model presented in Section 4.1.
The reduction in benefits due to the effects of acidification can be estimated by examin-
ing the difference between the consumer surplus estimates in the current state and the
pre-acidification stated Figure 5-1 illustrates this benefits calculation. The shaded
area in Figure 5-1 is a measure of the dollar value of the damages to recreational
fishermen that have resulted from acidification.
5.1 ESTIMATE OF DAMAGES FROM ACIDIFICATION USING THE TRAVEL COST
MODEL
Estimates of the value of each site, using the travel cost model results, were obtained by
using the routine in the SHAZAM econometrics software package that produces the ex-
pected value locus. These expected value curves were estimated holding the values of
1 This consumer surplus measure is termed the Marshallian consumer surplus. It is not a
perfect welfare measure, but it is an adequate approximation for this application. Other
consumer surplus measures are available, but Freeman (1979) concludes that the differ-
ences among these measures are "small and almost trivial for most realistic cases."
5-1
-------
Figure 5-1
Measurement of Consumer Surplus Losses Caused by Acidification
Quantity
(Fishing
Davs)
P* Price
(Travel Cost)
DC is the demand curve in the current situation where acidification has reduced the
fishing opportunities available at the site.
D is the demand curve given that there is no acidification.
* ACS is the change (i.e., reduction) in consumer surplus due to acidification.
5-2
-------
the income variable and fishing experience variable constant at the means of the sam-
ple. This resulted in a schedule for each site that shows the increase (decrease) in the
expected number of fishing days the "average" individual would spend at a site as his
distance from the site decreases (increases), other things held constant.
The estimated total willingness to pay and consumer surplus for each site is shown in
Table 5-1. These are based on an out-of-pocket travel cost estimate of 4.4 cents per
mile (from Table 4-6) and an opportunity of time cost of 9.06 cents per mile. The time
cost was based on an assumed average driving speed of 40 miles per hour, and the de-
flated mean hourly wage of a sample of fishermen from Desvousges jit al. (1983). The
time cost was calculated as being two thirds of the wage rate to reflect the fact that
some individuals may obtain enjoyment from the drive and, therefore, time in transit
should not be valued at the full wage rate. Table 5-1 shows the value for the current
recreational fishing experience in the Adirondacks to be 261 million dollars per year.
The next step in the analysis is to obtain an estimate of the losses that may have resulted
from current levels of acidification. The second stage equations (shown in Table 4-9)
that regressed the TOBIT regression coefficient on the characteristics of the sites can be
used to show how the value of the resource has changed due to increased acidification.
These estimates are based on analyses conducted by Dr. Joan Baker as part of the
National Acid Precipitation Assessment Program (NAPAP), and are based on research
that is still in progress.2 Table 5-2 shows some sites to have experienced greater levels
of acidification than others. This is due to a number of factors, including: differing
amounts of acidic deposition; the varying sensitivity of the lakes in a site to elevated
hydrogen ion loading; and the distribution of gamefish populations.
The reductions in fishing opportunities shown in Table 5-2 can be translated into an esti-
mated economic loss by using the site characteristic equations from Table 4-9. These
characteristic equations can be used to calculate how the TOBIT estimated regression
coefficients change as a result of these site characteristic changes. The new TOBIT
regression coefficients are then used to estimate a new expected value locus. New will-
ingness-to-pay estimates can be calculated from these new curves. The difference be-
n
Caveats to these estimates are presented in the Appendix.
5-3
-------
Table 5-1
Current Recreational Fishing Values in, the Adirondack Mountains per year
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
TOTAL
Expenditure*
7,294.5
8,483.8
4,157.5
3,228.4
5,870.5
6,586.6
7,784.2
13,615.6
5,679.1
(*)
2,415.6
6,569.0
N.A.
7,557.9
4,417.9
2,610.1
5,649.7
7,469.4
18,583.9
(*)
8,881.9
3,691.4
18,429.6
16,657.0
165,580.3
Consumer
Surplus1
3,033.0
2,912.6
1,267.5
1,489.8
2,510.4
4,038.1
4,373.6
6,334.5
2,934.3
(*)
1,147.1
3,698.7
N.A.
3,054.7
2,120.4
2,082.4
2,181.0
3,785.0
10,285.3
(*)
3,982.7
3,053.6
17,460.4
13,400.6
95,146.1
Total
Willingness
To Pay1
10,327.5
11,396.4
5,425.0
4,718.2
8,380.9
10,624.7
12,157,8
19,950.1
8,613.4
(*)
3,562.7
10,267.7
N.A.
10,612.6
6,538.3
4,692.5
7,830.7
11,254.4
28,869.2
(*)
12,864.6
6,745.0
35,890.0
30,057.6
260,726.4
Total
Willingness
To Pay Per
Fishing Day
107
104
118
97
98
105
107
96
96
(*)
75
103
N.A.
80
75
88
66
64
79
(*)
71
78
85
81
85
Consumer
Surplus Per
Fishing Day
31
26
27
31
29
40
38
30
32
24
37
N.A.
23
24
39
18
21
28
{*)
22
35
41
36
31
1
Thousands of 1984 dollars per year
* These sites had a positive coefficient on the travel cost variable.
5-4
-------
Table 5-2
Lasses of Fishable Lake Area Due to Acidification
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
Total Area (km2)
27.023
(*)
61.510
22.595
28.126
7.008
145.445
16.591
23.404
55.165
12.545
22.146
71.019
25.750
39.235
14.529
36.319
30.654
4.654
62.679
27.265
17.411
125.79
(*)
Percent Reduction
Moderate Loss Estimate
Scenario 1
0.0
(used site 6 estimates)
.1%
2.2%
.1%
5.3%
.2%
1.0%
.3%
0.0
5.1%
.2%
17.7%
7.5%
.2%
.2%
.5%
1.1%
0.0
12.0%
.6%
20.2%
0.0
(used site 23 estimates)
High Loss Estimate
Scenario 2
0.0
4.3%
32.0%
.1%
10.6%
8.6%
19.5%
.3%
16.7%
10.4%
32.0%
21.3%
7.5%
.2%
2.7%
3.4%
3.3%
0.0
27.7%
7.4%
28.3%
0.0
* These sites lie outside the Adirondack Park boundaries. Dr. Baker's data set did not
have information on these sites.
5-5
-------
tween the original willingness-to-pay or consumer surplus estimates represents the
change in the value due to the change in characteristics; in this case, fishable acres of
water.
Two site characteristics were incorporated in the TOBIT analyses presented in Section
4.4. They were net fishable acres and the catch rate in the remaining fishable acres at
that site.3 It was assumed that the percentage change in net fishable acres due to acidi-
fication is equal to the percentage change in total fishable area estimated by Dr. Baker.
How acidification at these levels actually influences the catch rate at a site is
unknown. As a result, several assumptions regarding the catch rate were made. Tables
5-3 and 5-4 show how the value of the recreational fishing resource changes assuming
that the catch rate is unaffected by whatever acidification has occurred. Tables 5-5 and
5-6 assume that acidification reduces the average catch rate experienced by fishermen
at the site by the same proportion as fishable area. The resource value changes
presented in Tables 5-3 through 5-4 may be summarized as follows:
1) The estimated current value of the recreational fishing sites in terms
of total willingness to pay is 260.7 million dollars per year. The esti-
mated current consumer surplus is 95.1 million dollars (Table 5-3).
2) Using the moderate acreage loss estimate and assuming no change in
catch rates, acidification is estimated to have resulted in a decline in
the resource value of 2.1 million dollars per year and reduced con-
sumer surplus of .76 million dollars per year (Table 5-3).
3) Using the high acreage loss estimate and assuming no change in catch
rates, acidification is estimated to have resulted in a decline in the
resource value of 9.2 million dollars per year and a reduced consumer
surplus of 3.3 million dollars per year (Table 5-4).
4) Using the moderate acreage loss estimate and assuming that the
catch rate declines proportionately, the estimated decline in the
resource value is 10.5 million dollars per year and the loss of con-
sumer surplus is 4.4 million dollars.
5) Using the high acreage loss estimate and assuming a proportionate
change in catch rate, the estimated decline in the resource value is
26.9 million dollars and the loss in consumer surplus is 11.6 million
dollars.
* Estimates were available for the amount of lake area that would no longer support a
fish population, but catch rates at remaining fishable lake acreage might also be reduced
by acidification.
5-6
-------
Table 5-3
Valuation of Resource Losses Due to Acidification:
Moderate Acreage Loss Scenario
($ x 103 per year, 1984 dollars)
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
OTALS
Current
Willingess
To Pay
10,330
11,400
5,420
4,720
8,380
10,620
12,160
19,950
8,610
(*)
3,560
10,270
N.A.
10,610
6,540
4,690
7,830
11,250
28,870
(*)
12,860
6,740
35,890
30,060
260,760
Willingness
to Pay
Given No
Acidification
10,330
11,570
6,150
4,860
8,380
10,930
12,190
19,970
8,620
(*)
3,570
10,270
N.A.
10,760
6,600
4,690
7,850
11,270
28,870
(*)
12,900
7,140
35,890
30,060
262,800
Losses
0
170
730
140
0
310
30
20
10
(*)
10
0
N.A.
150
60
0
20
20
0
(*)
40
. 400
0
2
2,110
Current
Consumer
Surplus
3,030
2,910
1,270
1,490
2,510
4,040
4,370
6,330
2,930
(*)
1,150
3,700
N.A.
3,050
2,120
2,080
2,180
3,780
10,280
(*)
3,980
3,050
17,460
13,400
95,110
Consumer
Surplus
Given No
Acidification
3,030
2,960
1,470
1,540
2,510
4,160
4,390
6,340
2,940
(*)
1,160
3,700
N.A.
3,100
2,140
2,080
2,190
3,790
10,280
(*)
3,990
3,240
17,460
13,400
95,870
Consumer
Surplus
Losses
0
50
200
50
0
120
20
10
10
(*)
10
0
N.A.
50
20
0
10
10
0
(*)
10
190
0
£
760
These sites had a positive coefficient on the travel cost variable.
5-7
-------
Table 5-4
Valuation of Resource Losses Due to Acidification:
High Area Loss Scenario
{$ x 103 per year, 1984 dollars)
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
TOTALS
Current
Willingess
To Pay
10,330
11,400
5,420
4,720
8,380
10,620
12,160
19,950
8,610
(*)
3,560
10,270
N.A.
10,610
6,540
4,690
7,830
11,250
28,870
(*)
12,860
6,740
35,890
30,060
260,760
Willingness
to Pay
Given No
Acidification
10,330
13,030
6,190
5,670
8,380
10,980
13,320
22,240
8,620
(*)
3,600
10,940
N.A.
10,760
6,600
4,790
7,920
11,280
28,870
(*)
13,180
7,290
35,890
30,060
269,940
Losses
0
1630
770
950
0
360
1,160
2,290
10
(*)
40
670
N.A.
150
60
100
90
30
0
(*)
320
550
0
0.
9,180
Current
Consumer
Surplus
3,030
2,910
1,270
1,490
2,510
4,040
4,370
6,330
2,930
(*)
1,150
3,700
N.A.
3,050
2,120
2,080
2,180
3,780
10,280
(*)
3,980
3,050
17,460
13,400
95,110
Consumer
Surplus
Given No
Acidification
3,030
3,400
1,490
1,850
2,510
4,180
4,830
7,150
2,940
(*)
1,160
3,960
N.A.
3,100
2,140
2,130
2,200
3,800
10,280
(*)
4,080
3,320
17,460
13.400
98,410
Consumer
Surplus
Losses
0
490
220
360
0
140
460
820
10
(*)
10
260
N.A.
50
20
50
20
20
0
(*)
100
270
0
£
3,300
* These sites had a positive coefficient on the travel cost variable.
5-8
-------
Table 5-5
Valuation of Resource Lasses Due to Acidification:
Moderate Area and Catch Rate Loss Scenario
($ x 103 per year, 1984 dollars)
Site
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
1?
18
19
20
21
22
23
24
OTALS
Current
Willingess
To Pay
10,330
11,400
5,420
4,720
8,380
10,620
12,160
19,950
8,610
(*)
3,560
10,270
N.A.
10,610
6,540
4,690
7,830
11,250
28,870
(*)
12,860
6,740
35,890
30,060
260,760
Willingness
to Pay
Given No
Acidification
10,330
13,410
7,740
5,210
8,390
11,740
12,200
20,230
8,640
(*)
3,970
10,270
N.A.
22,430
6,620
4,720
7,870
11,310
28,870
(*)
12,930
9,530
35,890
30,060
282,360
Losses
0
2010
2320
490
10
1120
40
280
30
(*)
410
0
N.A.
710
80
30
40
60
0
(*)
70
2,790
0
0.
10,490
Current
Consumer
Surplus
3,030
2,910
1,270
1,490
2,510
4,040
4,370
6,330
2,930
(*)
1,150
3,700
N.A.
3,050
2,120
2,080
2,180
3,780
10,280
()
3,980
3,050
17,460
13.400
95,110
Consumer
Surplus
Given No
Acidification
3,030
3,540
2,080
1,870
2,520
4,510
4,390
6,430
2,940
(*)
1,290
3,700
N.A.
3,230
2,150
2,090
2,190
3,810
10,280
(*)
4,000
4,630
17,460
13.400
99,540
Consumer
Surplus
Losses
0
630
810
380
10
470
20
100
10
(*)
140
0
N.A.
180
30
10
10
30
0
(*)
20
1,580
0
0.
4,430
These sites had a positive coefficient on the travel cost variable.
5-9
-------
Table 5-6
Valuation of Resource Losses Due to Acidification:
High Area and Catch Rate Loss Scenario
($ x 103 per year, 1984 dollars)
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
TOTALS
Current
Willingess
To Pay
10,330
11,400
5,420
4,720
8,380
10,620
12,160
19,950
8,610
(*)
3,560
10,270
N.A.
10,610
6,540
4,690
7,830
11,250
28,870
(*)
12,860
6,740
35,890
30.060
260,760
Willingness
to Pay
Given No
Acidification
10,330
15,770
8,140
7,760
8,380
12,910
13,520
22,860
8,690
(*)
4,400
13,280
N.A.
11,320
6,620
5,050
8,070
11,440
28,870
(*)
13,550
10,780
35,890
30.060
287,690
Losses
0
4,370
2,720
3,040
10
2,290
1,359
2,910
80
(*)
840
3010
N.A.
710
80
360
240
190
0
(*)
690
4,040
0
0_
26,939
Current
Consumer
Surplus
3,030
2,910
1,270
1,490
2,510
4,040
4,370
6,330
2,930
(*)
1,150
3,700
N.A.
3,050
2,120
2,080
2,180
3,780
10,280
(*)
3,980
3,050
17,460
13.400
95,110
Consumer
Surplus
Given No
Acidification
3,030
4,320
2,280
3,200
2,510
5,060
4,920
7,400
2,940
(*)
1,470
5,000
N.A.
3,230
2,150
2,250
2,250
3,850
10,280
(*)
4,210
5,510
17,460
13.400
106,720
Consumer
Surplus
Losses
0
1,410
1,010
1,710
0
1,020
550
1,070
10
(*)
320
1,300
N.A.
180
30
170
70
70
0
(*)
230
2,460
0
£
11,610
These sites had a positive coefficient on the travel cost variable.
5-10
-------
There are a number of factors that must be considered when interpreting these results.
First, the correct measure of benefits for use in a benefit-cost analysis of acidification is
the change in consumer surplus.
Second, the data set used in the analysis only includes information on visits to lakes.
Streams in the Adirondack Mountains were not examined due to the lack of data on the
characteristics of the streams and uncertainty regarding the actual fishing location.
Data in the Anglers' Survey indicated that approximately one third of fishing trips listed
a stream as the final destination.
Third, sites 10, 13 and 20 were not assigned a value. Site 13 was not valued due to an
error in the computer program that combined the data in the Anglers' Survey and the
Ponded Waters Survey. Sites 10 and 20 had the wrong sign on the coefficients on the
travel cost variables. As a result, willingness-to-pay estimates for these sites were not
available from the statistical analysis. These sites certainly have some value. An
examination of the data presented in Table 5-2 shows each of these sites is susceptible to
acidification with the high estimates of fishable acreage losses being 16.7 percent, 21.3
percent, and 27.7 percent respectively. Thus, the exclusion of these sites in the value
estimates contained in this report biases the estimated effects of acidification down-
ward. Because of the estimated sensitivity of site 13 to acidic deposition, it could be
argued that a substantial fraction of acidification damages have not been captured. To
evaluate this hypothesis, changes in willingness to pay and consumer surplus values were
estimated using the estimated relationship between fishing days and a site's fishable
acreage and catch rate (equation 3 from Table 4-1), and the average willingness to pay
and consumer surplus values calculated for the remaining sites using the travel cost
model. The results of this analysis suggest that the omission of site 13 causes an under-
estimate in the consumer surplus values ranging from $7,000 to $14,000. In light of the
uncertainty surrounding the aggregate consumer surplus losses, these damages are not
likely to represent a serious downward bias to the estimates.
Fourth, the travel cost model in its present version does not explicitly take into account
the substitutability of fishing sites. This will tend to result in estimates of losses that
are overstated. See Section 5.3 for a more complete discussion of this point.
Fifth, the travel cost analysis considered only trips that have a one-way distance of 225
miles or less. This was done to avoid including multi-purpose trips where fishing may not
5-11
-------
have been the primary reason for the trip. Th4 inclusion of these trips would have biased
the estimates and made the results uninterpretable. Still, these trips represent fishing
days spent at the site that have value. In scaling the sample estimates up to a population
estimate, it was assumed that fishing days from trips of distances greater than 225 miles
resulted in the same consumer surplus as shorter trips. The actual consumer surplus
resulting from fishing days taken as part of a multi-purpose trip could be either greater
or smaller than that estimated from the shorter trips. Still, over 70 percent of the
fishing days were from trips of less than 225 miles.
5.2 ESTIMATING THE DAMAGES FROM ACIDIFICATION USING THE PARTICIPATION
MODEL
The participation model developed in Section 5.1 can be used in conjunction with the
resource value estimates from Table 5-1 to estimate the damages from acidification.
The participation model found a robust relationship between the number of fishing days
spent at a site and fishing opportunities measured by fishable acreage and fishing success
measured by the total catch rate. Equation 3 from Table 4-1 presents the estimated
relationship between fishing days and a site's f ishable acreage and catch rate:
Fishing Days = .0978 (Net Park Acres) + 199.4 (Catch Rate) + intercept
(5.66) (1.97)
The R-square for this equation was .615. The moderate loss due to acidification scenario
from Table 5-2 resulted in an average reduction in fishable acreage of 3.2 percent and
the high loss scenario resulted in an average acreage reduction of 10 percent. The mean
values across all sites for net park acres and catch are 7,420 and 3.47 respectively.
Using these mean values to represent the average site, the effect of acidification on
total fishing days for this average site can be calculated. Then, the average willingness
to pay ($85) and consumer surplus ($31) per fishing day from the travel cost model (see
Table 5-1) can be used to calculate an estimate of damages. Four scenarios are eval-
uated.
Scenario 1 Assumes moderate acreage losses and no change in catch
rate, causing a reduction of 56,000 fishing days across all sites. Estimated
5-12
-------
damages expressed as willingness to pay and consumer surplus are 4.8 and
1.7 million dollars per year respectively.
Scenario 2 Assuming high acreage losses and no change in catch rate, a
reduction of 173,000 fishing days across all sites is estimated. Estimated
damages expressed as willingness to pay and consumer surplus are 14.7 and
5.4 million dollars per year respectively.
Scenario 3 Assuming moderate acreage losses and a proportionate change
in catch rate, a reduction of 109,000 fishing days is estimated. Estimated
damages expressed as willingness to pay and consumer surplus is 9.3 and 3.4
million dollars per year respectively.
Scenario 4 Assuming high acreage losses and a proportionate change in
catch rate, a reduction of 340,000 fishing days across all sites is esti-
mated. Estimated damages expressed as willingness to pay and consumer
surplus are 28.9 and 10.5 million dollars per year respectively.
5.3 COMPARISON OF PARTICIPATION MODEL AND TRAVEL COST MODEL
ESTIMATES OF DAMAGES
The damage estimates derived in terms of reduced consumer surplus from both the travel
cost model and participation model are presented in Table 5-7. The estimates derived
from the two models are quite similar in magnitude. There is no clear reason to prefer
one set of estimates over the other. The use of average values in the participation model
poses some problems, but are reasonable approximations for the modest changes in site
characteristics examined in this study. One favorable attribute of the participation
model results was the robust statistical relationship that was found between fishing days
and site attributes. The statistical relationship found in the second stage of the varying
coefficient travel cost model was less robust.
5-13
-------
Table 5-7
Estimates of Damages Resulting from Current Levels of Acidification
($ x 106 per year, in 1984 dollars)
Assumed
Acidification
Scenario
Estimated
Consumer Surplus
Losses from the
Travel Cost Model
Estimated
Consumer Surplus
Losses from the
Participation Model
1. Moderate acreage losses and
no change in catch rate
.8
1.7
2. High acreage losses and
no change in catch rate
3.3
5.4
3. Moderate acreage losses and
proportionate changes in
catch rate
4.4
3.4
4. High acreage losses and
proportionate changes in
catch rate
11.6
10.5
5-14
-------
REFERENCES
1. Baker, J., and T. Harvey. 1984. "Critique of Acid Lakes and Fish Population Status
in the Adirondack Region of New York State," Report under U.S. EPA grant, pre-
pared for NAPAP Project E3-25.
2. Brown, G. and R. Mendelsohn. 1984. "The Hedonic Travel Cost Method", Review of
Economics and Statistics.
3. Burt, O.F. and D. Brewer. 1981. "Estimation of Net Social Benefits from Outdoor
Recreation", Econometrica 39, p. 813-827.
4. Colquhoun, James, Walter Kretser, Martin Pfeiffer. 1984. Acidity Status Update of
Lakes and Streams in New York State. New York State Department of Environ-
mental Conservation, Albany, NY.
5. Colquhoun, J., J. Symula, and R.W. Karcher, Jr. 1982. "Report of Adirondack
sampling for stream acidification studies-1981 supplement." New York State
Department of Environmental Conservation, Technical Report 82-3.
6. Colquhoun, J., J. Symula, M. Pfeiffer, and J. Feurer. 1980. "Preliminary report of
stream sampling for acidification studies 1980." New York State Department of
Environmental Conservation, Technical Report 81-2.
7. Crocker, T.D. et al. 1981. "Methods Development for Assessing Acid Deposition
Control Benefits." Report under U.S. EPA Grant #R80697201Q, prepared for the
Office of Explanatory Research.
8. Deegan, J. and K.J. White. 1976. "An Analysis of Nonpartisan Election Media
Expenditure Using Limited Dependent Variable Methods," Social Science Research,
June, p. 127-135.
9. Desvousges, W.F., V.K. Smith and M.P. McGivney. 1983. A Comparison of Alterna-
tive Approaches for Estimating Recreation and Related Benefits of Water Quality
Improvements, U.S. Environmental Protection Agency, Economic Analysis Division,
Washington, DC, EPA-230-04-83-001.
10. Fisher, A. and R. Raucher. 1984. "Intrinsic Benefits of Improved Water Quality:
Conceptual and Empirical Perspectives," in Advances in Microeconomics, Vol. 3, V.
Kerry Smith and A. DeWitte, eds. JAI Press, Grenwhich, CT.
11. Freeman, A.M., III. 1979. The Benefits of Environmental Improvement; Theory and
Practice^ The Johns Hopkins University Press, Baltimore, MD.
12. Goldberger, A. 1964. Econometric Theory. Wiley Pubs., New York (Chapter 5).
13. Goldsmith, A. 1983. "Household Life Cycle Protection: Human Capital Versus Life
Insurance," The Journal of Risk and Insurance, XL (March), 473-486.
14. Greeson and Robison. 1970. "Characteristics of New York Lakes, Part 1
Gazatteer of Lakes, Ponds and Reservoirs," Report of the New York Department of
Environmental Conservation.
R-l
-------
15. Grieg, P.J. 1983. "Recreation Evaluation Using a Characteristics Theory of Con-
sumer Behavior", American Journal of Agricultural Economies, 65: 90-97.
16. Kretser, W.A., and L.E. Klatt. 1981. "1976-1977 New York Anglers' Survey Final
Report," New York Department of Environmental Conservation, May.
17. Maddalla, G.S. 1977. Econometrics, McGraw-Hill, New York.
18. Menz, F.C. and J.K. Mullen. 1982. "Acidification Impacts on Fisheries", presented
before the Division of Environmental Chemistry, American Chemical Society, Las
Vegas, April.
19. Morey, E.R. 1985. "Characteristics, Consumer Surplus, and New Activities,"
Journal of Public Economics V. 26, 221-236.
20. Morey, E.R. 1981. "The Demand for Site-Specific Recreational Activities: A
Characteristics Approach", Journal of Environmental Economies and Management
8: 345-371.
21. National Research Council. 1983. Acid Deposition Atmospheric Processes in
Eastern North America. National Academy Press, Washington, DC.
22. Peterson, D.C. 1983. "Estimated Changes in Fish Habitat Resulting From Changes
in Acid Deposition," prepared for the Economic Analysis Division, U.S. EPA,
November.
23. Pfeiffer, M. 1979. "A Comprehensive Plan for Fish Resource Management within
the Adirondack Zone." FW-P142 (12/9), New York State Department of Environ-
mental Conservation, Albany, NY.
24. Samples, K.C. and R.C. Bishop. 1983. "Estimating the Value of Variation in
Anglers' Success Rates: An Application of the Multiple Site Travel Cost Method,"
Working Paper, February.
25. Saxonhouse, G.R. 1977. "Regressions from Samples Having Different Character-
istics," Reyjej^oj^c^nomic^n^Sta^istics, 59: 234-237.
26. Schofield, Carl L. 1982. "Historical Fisheries Changes in the United States Related
to Decreases in Surface Water pH." In: Acid Rain/Fisheries. Proceedings of an
International Symposium on Acidic Rain and Fishery Impacts on Northeastern North
America. Raymond E. Johnson (ed.). American Fisheries Society, Bethesda, MD.
27. U.S. EPA. 1985. Personal Communication with James Olmernik, Corvallis Envi-
ronmental Research Laboratory, U.S. EPA, Corvallis, OR.
28. U.S. EPA, 1983. The Acidic Deposition Phenomenon and its Effects; Critical
Assessment Review Papers. Volume n Effects Sciences. Public Review Draft.
Office of Research and Development. EPA-600/8-83-016B.
29. Vaughan, W.S. and C.S. Russell. 1982. "Valuing a Fishing Day: An Application of a
Systematic Varying Parameter Model," Land Economics, 58: 450-463.
30. Violette, D.M. 1983. "Travel Cost Methods Incorporating Site Characteristics For
Use in Estimating the Recreational Fishing Benefits of Reduced Acid Deposition,"
presented at Society of Government Economists, Annual Meeting of the American
Economics Association, San Francisco, December.
R-2
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APPENDIX
-------
North Carolina State University
Acid Deposition Program
Varsity Dmc Iff » »
igh, NO z^ioii School of r orest Kesourccs
'y-^-js-'u February 1, 1985
Dan Violette
Energy and Resource Consultants FEB 8
P.O. Box Drawer 0
Boulder. CO 80306 £?" - "OURCC
r, r, ^w..^i... !KC.
Dear Dan;
In response to your request for estimates of loss of flshable 'acres' in
the Adirondacks as a result of acidification, I have prepared the attached
table based upon the information in the FIN (Fish Information Network)
database and in the draft report prepared for NAPAP project E3-25 {Baker, J.
and T. Harvey. 1984. Critique of Acid Lakes and Fish Population Status in the
Adirondack Region of New York State, draft report to the U.S. Environmental
Protection Agency). It should be clear that these are preliminary estimates.
Because of the quick turn around time required to provide numbers for your
draft report, our approach has been very simple. Better estimates should be
available by late February for inclusion in your final draft.
The numbers in the attached table are derived from evaluations of all
available data (current and historic) on fish populations in the Adirondacks
in FIN and from the assessment of fish community status as described in Baker
and Harvey (1984). Briefly a rating of fish community status of 3, 4, or 5
for a given lake indicated that several to all species have disappeared from
the lake overtime, apparently as a result of acidification. A rating of 2 was
considered marginal; one or two species have apparently declined in abundance
and/or disappeared from the lake but neither the evidence for loss of
populations nor the indications of the potential influence of acidification
are particularly strong. Ratings of 0 or 1 were indicative of "healthy1 fish
communities and no adverse effects as a result of acidification. The
'reasonable1 estimates of fishable acres lost in the the table are based on
the number and surface area of lakes with fish community status rated 3, 4, or
5. The 'high' estimates are based on lakes with fish community status rated
2, 3, 4, or 5. Note that we have not, at this time, zeroed in specifically on
game species. Such information will, however, be available for your next
series of model runs.
The fraction of lakes with adequate fish survey data (historic and
current) for assessment of fish community status is, unfortunately, quite
small. Thus, it was necessary to extrapolate from our sample of lakes in FIN
with adequate data to all lakes in the Adirondacks. Lakes with 'adequate'
data (particularly surveys of fish populations pre-1970) tend to be larger,
and have a higher pH. To partially adjust for this bias, lakes were
K'urtfi C,m>ltMil Sltttr thin>?<*ny is Norlli C>m>'»iii i uriguiul /unJ-)('.i>il Iri>lilutit»i
,<»./ i» .. iM'.ififutnt in*litntiun of ! lit' lt>i>l>ei»tly i>/ Nortli C>i>tifm><
-------
PRELIMINARY estimates of flshable
result of acidification
acreage1 lost in the Adirondack* as a
Total in Region
Number Surface
Reg ion+
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
r\f
or
Lakes
61
0
182
130
66
131
331
105
17
62
83
156
315
96
51
49
199
58
45
308
45
121
84
0
A i**o ^
f\i ca
(km2)
27.023
0
61.510
22.595
28.126
7.008
145.445
16.591
23.404
55.165
12.545
22.146
71.019
21).7t>0
39.235
14.529
36.319
30.654
4.654
62.679
27.265
17.411
125.790
0
Estimates of 'Acreage' (km2)
'Reasonable1 'Hi
Total
0
-
0.050
0.500
0.013
0.371
0.309
0.174
0.062
0
0.644
0.053
12.545
1.920
0.097
0,023
0.171
0.351
0
7.527
0.158
3.523
0
* '
0
-
0.1*
2.2
<0.1*
5.3*
0.2
1.0*
0.3*
0
5.1
0.2
17.7
7.5
0.2*
0.2*
0.5
1.1
0
12.0
0.6
20.2
0
^
Total
0
-
2.634
7.225
0.013
0.743
12.473
3.233
0.062
9.191
1.308
7.092
15.154
1.920
0.097
0.398
1.225
0.557
0
17.376
2.021
4.927
0
lost
9h'
*
0
-
4.3
32.0
<0.1*
10.6*
8.6
19.5
0.3*
16.7
10.4
32.0
21.3
7.5
0.2*
2.7
3.4
3.3
0
27.7
7.4
28.3
0
TOTAL
2695
876.863
28.491
3.2*
87.649
10. OJ
+ Refer to attached figure
* Refer to letter for
tion
-------
nc &' Situ i through 2i L'tcd In tht Trivtl Celt Kod«i
(totted lln§* »rt )£ mlnuU quidrtngtd, lolld l!nt» *r« *lth»r
e!te tuuntferli* or th« t&uncJery to the
Adlrcncitck Ecologies) 2on«)
1EO 190 200 210 220 230 240 260 260 270
Lakes in FIN in the areas shaded could not be included in the estimates ot acreabe
because of uhe lack of information on T-2 minute
-------
Dan Violette
Page 2
February 1, 85
classified Into four strata based on lake area and elevation. These strata
were originally designed for estimating the number of acidic lakes in the
Adirondacks {Table 4, Baker and Harvey 1984). Again, because of time
limitations we assumed that this stratification would also be appropriate for
extrapolations regarding fish community status. We will check this assumption
prior to providing final estimates.
Numbers in the table denoted by asteriks were, however, derived slightly
differently. In all cases, procedures outlined above Indicated zero acreage
lost for these regions (i.e., no lakes in the sample with "adequate1 data had
fish community status rated 3 to 5, or 2 to 5, as appropriate for the
'reasonable1 estimate or 'high' estimate, respectively). In these regions,
however, several lakes with no historical survey data and thus for which fish
community status could not be rated, had current fish survey data suggesting a
loss of fish populations as a result of acidification. Specifically, no fish,
or only brown bullhead were caught but the habitat appeared suitable for brook
trout and in some cases the lake had been stocked with brook trout in the
years immediately preceeding the survey {coded 7 and 8). It was therefore
presumed that the original estimate of zero acreage lost was too low.
Instead, the estimates of percent acreage lost are based simply on the surface
area of lakes coded 7 or 8 divided by the total area of lakes in the sample.
These estimates were not adjusted by stratifying the sample by area and
elevation due to time limitations. In all cases but one, the new estimates of
acreage lost were quite small. For region 6, however, the surface area of
lakes coded 7 or 8 represented 10.6% of the total surface area of the sample.
Thus the 'reasonable* estimate of acreage lost was arbitrarily set at one-half
of 10.6% (or 5.3%).
The table deserves one final note. Although the percentages of lake area
impacted may be reasonably accurate, the surface area totals listed in the
table are probably under-estimates. Lakes with surface area undefined in FIN
(122 of the lakes in the Adirondack Ecological Zone) and lakes for which we
could not identify the region in which they occurred (refer to the attached
figure), could not be included in these totals.
I hope these numbers will be of some use. At the same time, please
remember that these are preliminary estimates, to be used with caution. The
problems and uncertainties associated with estimating the numbers of fish
populations in the Adirondacks lost as a result of acidification are discussed
in greater detail in Baker and Harvey (1984).
Slacerely,
/I
^J
Joan P. Baker
Aquatic Research Coordinator
NCSU Acid Deposition Program
JBP/rw
cc: John Malanchuk
------- |