AN ABSTRACT OF THE THESIS OF Ching-Kai Hsiao Doctor of Philosophy

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AN ABSTRACT OF THE THESIS OF
Ching-Kai Hsiao
in
for the degree of
Agricultural
Resource
and
Doctor of Philosophy
Presented
Economics
on
April 30, 1985.
Title:
An Evaluation of Alternative Estimates of Demand
for and Benefits from Oregon Salmon Sport Fishing.
Redacted for privacy
Abstract approved:
William G. Brown
The main objective of this study was to estimate the
demand
sport
for
fishing.
travel cost method was used
The
primary technique for demand analysis.
estimates
salmon
and net econcinic benefits from Oregon
Several
as
the
empirical
of consumer surplus per trip and per fish
were
obtained from different estimation methods.
The
differences
different
versions
observation
travel
bias
this
cost
travel
the
approaches produced higher
than
costs
economic
of
among
benefits
economic
were
method
Empirical results indicated that the individual
assessed.
estimates
net
in
the zone average approach
of
net
are believed to be due in part to
the
caused by travel cost
of
surplus
reported
when
These higher estimates
were used.
benefits
problem
consumer
bias
measurement
was
instrumental variable approach.
dealt
with
error.
by
However,
using
the
Higher
resulted
estimates
from
observations
function
net
use
of
economic
unadjusted
individual
demand
recreational
for fitting the
(Ulo)
also
benefits
because this approach does not account
declining
the
for
participation rates for the more distant zones.
Therefore,
it
observations
the
the
of
recommended
is
individual
the
that
be adjusted to a per capita basis,
probability
participation be linked to
of
that
or
UlO
the
estimates of demand in order to compute valid estimates of
net economic .benef its.
A
and
quality
hedonic
variable was incorporated into
regional
and
marginal
Average
travel cost models.
values of the primary site and substitutes sites thus were
directly derived from the demand equations.
Estimates
computed
from
changed
and
total and average consumer
of
the
very little with the addition of
quality
regional
variables in the more
travel cost models.
model
cost
traditional travel
surpluses
substitute
the
completely
specified
This finding indicates that
the traditional travel cost model may be basically
for
estimating
However,
total
additional
and
were
average
research
on
consumer
robust
surplus.
recreational
other
activities is needed to see if estimates of total consumer
surplus
remain
from
the
relatively
variables
traditional travel cost
stable
when
quality
model
and
always
substitute
are included in a regional travel cost type
specification.
of
Unfortunately,
the numerical estimates of value per
were
trip and per fish from the hedonic travel cost model
rather
unstable
and
should
questionable for this study.
marginal
values
be
considered
Similarly,
somewhat
the estimates of
per fish from the regional
travel
cost
model did not seem very reasonable,
being only about one-
fourth
fish.
appears
of
the average
value
per
Therefore,
it
that the more complex regional and hedonic travel
cost models require more and better quality data to
more accurate estimates of marginal values per fish.
yield
An Evaluation of Alternative Estimates of Demand for
and Benefits from Oregon Salmon Sport Fishing
by
Ching-Kai Hsiao
A THESIS
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Doctor of Philosophy
Completed
Commencement
April 30, 1985
June 9, 1985
APPROVED:
Redacted for privacy
Professor of Agricultural and Resource Economics
in charge of major
Redacted for privacy
Head of Department of Agricultural and Resource
Economics
Redacted for privacy
Date thesis is. presented
April 30, 1985
Typed by Shih-Ya Yeh and Ching.-Kai Hsiao for
Ching-Kai Hsiao
ACKNOWLEDGEMENTS
This
study
was made possible by the
and assistance of many people.
encouragement
Gratitude and appreciation
are due to the members of the graduate advisory committee,
Dr.
Richard Adams, Dr. William Brown, Dr. Dale Mcfarlane,
Dr.
Wesley Musser, and Dr. David Thomas, who assisted the
completion of this thesis. A special thanks is extended to
Dr. William Brown for his guidance and assistance as major
professor.
I
would like to dedicate this thesis to my
parents
for
their understanding and support, to my son 1-Ming for
his
encouraging smile,
Shih-Ya,
whose
and especially to my lovely
emotional support and
were essential to completing this study.
constructive
wife
help
TABLE OF CONTENTS
Chapter
Page
INTRODUCTION
Statement of the Problem
Objectives
Methodology
Source of Data
Outline for Presentation of Research in this
Study
THE
THEORETICAL
IN
CONSIDERATIONS
SPECIFICATION OF DEMAND FOR OUTDOOR
RECREATION
A Model of Demand Analysis for Outdoor
Recreation
The Specification Problem
The Identification Problem
Evaluation Methods of Demand for Outdoor
Recreation
Comparison of Various Evaluation Methods
Measures of Consumer Welfare
The Travel Cost Method
1
2
7
8
9
10
SOME
EMPIRICAL ESTIMATES OF SINGLE SITE TYPES OF
TRAVEL COST DEMAND FOR OREGON SALMON ANGLING
Estimated Zone Average Travel Cost Demand
Fresh-Water Salmon Sport Fishing
Ocean Salmon Sport Fishing
Theoretical
Relationships Between Angler
Benefits and Fish Catch
Relation of Estimated Angler Benefits to
Salmon Catch
Effect of Other Factors Upon
Estimated
Benefits Per Fish
Estimated Adjusted Individual Travel Cost
Demand
Fresh-Water Salmon Sport Fishing
Ocean Salmon Sport Fishing
Estimated Unadjusted Individual Travel Cost
Demand
Fresh-Water Salmon Sport Fishing
Ocean Salmon Sport Fishing
DISCUSSION AND APPRAISAL OF SEVERAL VERSIONS OF
THE TRAVEL COST METHOD
Individual
Observations
Versus
Zonal
Averages
Reasons
for Declining
Participation
Rates
13
14
17
20
22
22
26
30
34
34
35
40
41
44
49
54
55
59
60
61
63
65
66
68
TABLE OF CONTENTS (cont.)
Chapter
Page
Effects of Distance Upon Participation
Rate in Ocean Salmon Fishing
Measurement Errors in Travel Cost Variable
Sources and Consequences of Measurement
Errors
The Instrumental Variable Approach
74
81
82
85
INCLUSION
OF QUALITY VARIABLES IN THE TRAVEL
COST MODEL
Using
Regional Travel Cost Models to
Estimate the Benefits from Fresh-Water
Salmon Fishing
Regional Travel Cost Method
Estimation
of Regional Travel
Cost
Demand Model
Use of the Hedonic Travel Cost Model
to
Estimate the Value of Site Characteristics
Hedonic Travel Cost Method
Estimation of Hedonic Travel Cost Demand
Model
SUMMARY AND CONCLUSIONS
91
91
92
96
103
104
109
116
BIBLIOGRAPHY
129
APPENDIX A
139
APPENDIX B
140
APPENDIX C
144
APPENDIX D
145
APPENDIX E
150
APPENDIX F
156
LIST OF TABLES
Page
Table
1
2
3
4
5
6
Estimated net economic benefits and catch
for Oregon fresh-water salmon sport anglers
average
zonal
in
1977,
upon
based
participation rates per capita
39
Estimated net economic benefits and catch
f or Oregon fresh-water salmon sport anglers
individual
in
1977,
based
upon
participation rates per capita
57
Observations
zones
generated for three
distance
70
Estimated consumer surplus to ocean salmon
sport anglers of Oregon, based upon four
different methods of estimation
80
Estimated consumer surplus to ocean salmon
anglers of Oregon, based upon observed
travel cost variable and its instrumental
variable
89
Estimated net economic benefits for Oregon
fresh-water salmon sport anglers in 1977,
based upon regional travel cost method
98
7
A comparison of consumer surplus values for
fresh-water salmon sport fishing, estimated
by various models using reported travel
117
costs
8
A comparison of consumer surplus values for
ocean salmon sport fishing,
estimated by
various models using reported travel costs 117
9
A comparison of consumer surplus values for
ocean salmon sport fishing, estimated by
119
various models using measured distance
F-i
Some
regression results and .the estimates
Gum-Martin consumer surplus for Oregon
157
fresh-water salmon angling in 1977
of
AN
AND
EVALUATION OF ALTERNATIVE ESTIMATES OF DEMAND FOR
BENEFITS FROM OREGON SALMON SPORT FISHING
I.
Leisure
is
one
INTRODUCTION
of the
fast
growing
industries.
Almost all Western and Eastern countries maintain research
centers
on
leisure (Kaplan,
1975).
the
In 1958,
U.S.
Congress enacted and President Eisenhower signed into
Resources
document to establish the Outdoor Recreation
Review
seven
the
Commission (ORRRC).
Early in the
law
1960s,
twenty-
reports were produced by a staff of 100 persons
ORRRC.
Shortly
thereafter,
Recreation was established
Not
been
only
recognized,
the Bureau
of
of
Outdoor
under President Kennedy.
has the importance of outdoor
recreation
but participation in outdoor recreation
has been increasing rapidly.
been
The major factors have
increased total population, higher real income per capita,
greater leisure time, and more travel (Clawson, 1959).
Indeed, "the outdoors has always been and is still a
great laboratory for learning,
playground
people
other
for wholesome fun and
hike,
enjoyment.
It
affords
a special kind of fulfillment not available in any
setting.
Thus,
deer in the forests,
groves
and a
a museum for study,
in
there must be fish in the
scenery to paint and to
which to camp and picnic,
wilderness to explore,
rivers,
photograph,
trails on which
and pleasant places in
to
our
2
cities,
more
Yes,
them.
we
if
are to retain them we must work
we must
than that,
plan,
for
coordinate,
cooperate, and educate." (Jensen, 1973, pp.v-vi)
Statement of the Problem
The
economists' interest in
an
economic problem has
to
place valuations on it.
arisen
because
resources
volume
of
is
the
valuation has
This need for
for
land
water
and
and
but the area of land
water are essentially fixed.
as
need
largely developed from the
competition
increasing,
outdoor recreation
For the sake
the
of
optimum allocation of scarce resources, all the valuations
analyzed
and choices among various alternatives should be
to compete for the scarce means. Just as Clawson said "...
it
is customary to measure the economic or monetary gains
and costs of each use of land or water. If this process is
and if recreation is
to
considered
in the same manner as alternative uses
of
the resources,
then a value must be put on the amount
of
to be carried to its conclusion,
be
recreation provided." (Clawson, 1959, p.2).
On the other hand,
as resource planners become more
aware of the importance of outdoor recreational activities
and
as resources capable of providing outdoor
opportunities
diminish,
the
concept of
recreation
demand
becomes
increasingly important. Not only the planners and decison-
3
makers
are meeting the challenge by greater
demand
analyses
turning
(such
and
their
and
descriptive
from
as the social characteristics of anglers,
park-goers) to search for the
underlying
on
now
are
but researchers
studies,
attention away
emphasis
studies
hunters,
behavioral
components of such participation.
Moreover,
while the prices of goods or services can
usually be determined through the market mechanism system,
the
value
of
nonmarket goods or services
recreation
cannot
Therefore,
valuation
difficult.
Although
methods
that
be calculated
of
like
outdoor
via the market
system.
nonmarket goods or services
there
are a number
have been proposed for
of
is
measurement
evaluating
outdoor
recreation, only a few of them have been proved correct in
specification and estimation.
"Oregon's
habitat
for
diverse geography provides the
a wide variety of fish
and
necessary
wildlife.
renewable resource is one of the most valuable assets
state
has
millions
and
of individuals each year "
1979-1980, p.188)
are
it provides recreation and jobs
fish
are
Blue
( Oregon
the
many
Book,
As for these resources, anadromous fish
the most valuable segment of
these
to
This
dependent
Oregon's
absolutely
fishery,
upon
and
continuing
satisfactory habitat in which to carry out the fresh-water
phase
chinook
of
their life cycle.
As a
matter
salmon-- a distinctive economic and
of
fact,
the
recreational
asset-- was
declared
the state fish by the
Oregon
1961
legislature
For
the
commercial fishery,
records are
on
kept
landings and the yield is marketed on a per unit basis,
monetary
But
value for these fish can be reliably
for sport fishing,
its
Therefore,
monetary
it is not pOssible
value through
evaluation
an
estimated.
one of the most important outdoor
recreational activities in Oregon,
estimate
a
method
a
to
system.
market
fishing
for sport
is
needed to estimate the value of this important resource.
There are several problems existing in the growth of
this form of recreation.
rise
In particular it has given
to conflicts in resource use. There is growing competition
between
the
the commercial fishery and the sport fishery.
same time there is increasing pressure to use
streams
purposes
for
migration
and
near streams,
which
would
spawning of such fish
Timber
salmon
with
interfere
At
the
harvesting
hydro power development, flood control, and
pollution are seen as potential hazards to the maintenance
of
salmon runs.
One
newspaper reported '1One turbine
Winchester Dam was shut down Wednesday
to
divert
Thu.,
migrating fish to
ladders."
in an attempt
(The
Oregonian,
Aug. 9, 1984). Another concern is the mounting call
for funds to increase the fishery stock.
salmon
has
at
sport anglers have grown,
As the number of
more and more
been placed upon fishery managers to improve
pressure
present
5
migration
and spawning areas and to invest more money
research.
Of course, rational decision-making will not be
in
possible if there are no values available for all kinds of
uses.
Several
Oregon,
early
studies
e.g., Brown,
on
sport
the
fishery
and Castle (1964),
Singh,
of
Stevens
(1966) etc., have enlightened us on this subject. However,
by
estimating
the
valuation
of
fishing
only
without
providing
the value estimates for the end products of the
fishing,
i.e.,
subsequent
the
fish
caught,
these
studies has been somewhat limited
decision-making
generally
can
purposes.
For instance,
and
earlier
public
for
hatchery stocks
withstand far greater harvest
than
rates
natural stocks (Pacific Fishery Management Council, 1982),
and hatchery stocks have become large since,
the
fish
Oregon
Department of Fish and Wildlife
for example,
operates
hatcheries which produce almost 90 million fish
33
per
year (Oregon Blue Book, 1979-1980). However, without value
per fish caught,
enhancement
will
a rational economic analysis of
not be
possible.
In
addition,
fishery
these
earlier
studies
effects,
i.e.,
analysis.
Consequently, the value of the resources or the
benefits
have
not
substitutes
considered
were
the
omitted
cross-price
from
their
to users may have been incorrect and the implied
optimal allocation of resources may have been distorted.
To engage in resarch in any field of social science,
6
information
pertaining
essential.
data,
No
problem
matter what methods are used
through
questionnaire,
research
the
to
documentary
sources,
to
is
collect
observation,
mail
etc., all social science
or interviewing,
data are usually uncontrolled or nonexperimental.
Even in
the
the case of a complete enumeration of the population,
data may be subject to serious errors due to faults in the
methods
measurement or observation
of
(O'Muircheartaigh
and Payne ed., 1978). These response errors may arise from
the questionnaire, from the execution of the fieldwork, or
from
nature
the
of the
collection
data
value
response errors are the difference between the true
and the value recorded on the schedule.
cause
The
process.
These errors will
the
bias in the estimated regression coefficients,
well-known "measurement error" problem (Johnston, 1972).
Early
research
on
estimation
the
outdoor
of
recreational benefits was based upon average participation
rates
and travel costs
Clawson (1959),
(1964).
Some researchers,
demand
in
Brown, Singh, and Castle
Knetsch (1963),
Gum and Martin (1975),
gains
for various distance zones, e.g.,
e.g.,
later suggested that
efficiency in estimating
functions
observations
Brown and Nawas (1973),
outdoor
could be obtained by
instead
of zone
averages.
using
substantial
recreational
individual
However,
in
a
recent study Brown et al. (1983) argued that if individual
observations
are
to
be
used,
each
observation
on
participation
should
just
the traditional zone
as
for
be adjusted to a per capita
average
basis,
cost
travel
model. Nevertheless, several criticisms have been advanced
concerning the preceding argument.
Based
analyze
upon
the above statements,
this study
and discuss these statements in more
will
detail
and
demand,
and
suggest possible solutions.
Objectives
The main objectives of this thesis are:
To
study
specification
the
value
link between
and
and measurement of demand for salmon
sport
fishing in Oregon.
To investigate the sources of error in the salmon sport
fishing
demand
analysis
and
to
use
the
instrumental
variable method to deal with the measurement error.
To
the
demonstrate empirically how different versions
of
travel cost method can affect the amount of estimated
consumer surplus.
To analyze and compute average and
the
marginal values of
primary site and substitute sites by
and hedonic travel cost methods.
using
regional
Methodology
This thesis is concerned with consumer behavior with
regard to the salmon sport fishing activity. A basic model
of
consumer behavior can be formed by including time
travel
dimensions.
Theoretically,
this
involves
and
an
activity model and a derived model (just as the producer's
input
demands are derived from the underlying demand
for
the commodity which he produces, the consumer's demand for
outdoor
recreational
activity
demand for travel to it.);
economic
the
can be
foundation
interpretation
for
of
an
empirical
the parameters of
the
there is only an
practically,
model of the travel demand.
by
measured
This model provides
model
such
permits
and
an
model in the context of an evaluation problem.
empirical
Therefore,
the travel cost demand model will be seen as a key feature
of
this approach,
both because of the importance of
the
spatial
aspect
because
of the relatively easy collection of travel data.
In practice,
at
the
in outdoor
recreational
activities
this approach will be used to observe people
the destination and compute their costs of
site
distance
curve.
measure
and
as a function of the
decay
distance
access
traveled.
function can be translated into a
to
This
demand
Moreover, the rate of distance decay is taken as a
of
the
valuation
recreational activity itself.
placed
on
the
outdoor
Basically,
employed
of
the
consumer
as an evaluation method to measure the
salmon sport fishing.
above,
surplus approach will
Following the
be
benefits
demand
analysis
the demand curves are used to link the willingness
to pay with the estimated value of fishing activity.
Source of Data
A
sample
population
1977.
of
This
licences
anglers
drawn
was
Oregon angling licences
sample
sold,
licences
9,000
of
purchased
was about 1.5 percent
including
in-state
of all categories.
of
and
the
from
during
total
the
out-of-state
A questionnaire was designed
to obtain data from the angler about his expenditures
and
fishing activities on a quarterly basis. The questionnaire
was mailed at the end of each quarter during 1977
first
January
Quarter,
questionnaires
were sent;
April 1 through June 30;
1
through
March
2,700 were sent
For the
1,20,0
31,
out
covering
3,600 questionnaires were mailed
for the period July 1 through September 30; and 1,500 were
mailed for the October 1 through December 31 quarter.
should
be
different
information
the
noted that the questionnaires were sent
sample
of
anglers
for
each
(It
to
quarter.)
a
More
was expected from the survey by concentrating
bulk of sample in the most active fishing quarter
spring and summer.
10
An
resulted
extensive mail and telephone follow-up
a total return of
in
addition
to
all
non-respondents
being
telephone to complete and return the
respondents
suspected
whose
of
telephoned.
consuming,
was
55o6
about
questionnaires
percent.
In
reminded
by
questionnaires,
all
incomplete
or
were
being erroneous in some respect
Although
campaign
were
also
this procedure was costly and time-
the quality of the information from the survey
greatly
improved by the
telephone
follow-up.
detailed information about the survey design,
copies of the questionnaire,
along
More
with
has been reported by Sorhus,
Brown, and Gibbs (1981).
Data
on the number of salmon caught for each
river
or port during 1977 were obtained from the Oregon Fish and
Wildlife
Department.
salmon-steelhead
To estimate the total annual catch,
tag return data were
statistical
port
were
28.44 percent of
about
returned
supplemented
checks and creel sampling
for 1977.
the
with
There
data.
salmon-steelhead
tags
These tag returns have been corrected
for nonresponse bias to get an estimate of 372,174 for the
total salmon catch by sport anglers in Oregon.
Outline for Presentation of Research in this Study
Some
important
theoretical considerations
in
the
specification of demand models for outdoor recreation will
11
be
presented
considerations,
in chapter 2.
Following these
theoretical
site
empirical estimates of single
some
types of travel cost demand models for Oregon salmon sport
fishing
will be presented in chapter 3.
estimates
travel
will
cost
include
demand
several
model
researchers in the past,
specifications
have been
that
Singh,
individual
(1973),
and
the
used
by
Castle
e.g., Clawson (1959),
(1964),
observation approach,
(2)
e.g.,
unadjusted
the
Nawas
Brown and
and Gum and Martin (1975), and (3) the individual
observations, adjusted to a per capita basis,
(1983).
of
namely, (1) the traditional zone
average model which was first used,
Brown,
empirical
These
These
three
different versions of
Brown et a]..
cost
travel
methods, which use aggregated and disaggregated data, will
be
appraised and discussed in chapter 4.
In addition,
discussion of the problem of measurement error in reported
travel
costs
and
a solution to
this
problem
will
be
presented in chapter 4.
In order to include quality and substitute variables
in
the model,
a regional travel cost model of the demand
for fresh-water salmon sport fishing will be estimated and
presented in chapter 5. In this chapter, a modification of
the
travel
characteristics
also
water
cost
method
that
incorporates
site
-- the hedonic travel cost method -- will
be discussed and empirically applied to both
and ocean salmon sport fishing in
Oregon.
fresh-
Summary
12
and conclusions will be presented in chapter 6.
13
II.
SOME THEORETICAL CONSIDERATIONS IN THE SPECIFICATION
OF DEMAND FOR OUTDOOR RECREATION
In
a rational
conventional demand theory,
will strive to maximize his utility
constraint.
various
purpose of the theory is to explain
economics
which
is
concerned
with
for
termed
often
This is
services by consumers.
the
the theory is
i.e.,
to explain and predict the observed demands
and
positive
what
the
Another purpose of the theory has
economic relations are.
been
subject to his income
factors that affect demand,
designed
goods
One
consumer
By way of
applied to normative problems.
contrast,
this is termed normative economics which is concerned with
what
ought
be
to
with
set
a
of
criteria
for
the
measurement of "good1' and "bad". Thus, economic policy can
be
made
through
judgements,
and,
such
criteria
hopefully,
the
which
involve
value
economic well-being of
consumers can be improved.
For outdoor recreation the definition and the factors
determining
demand.
with
for
For
demand are much the same as for
conventional
the consumer's taste is a
factor
regard to outdoor recreation as it is to the
demand
any
instance,
other
commodity;
the
income
of
individuals
similarly has a relation to outdor recreational demands.
However,
outdoor
there
recreational
are
several
demands and
differences
between
conventional
demands.
Many outdoor recreation sites are provided at a zero price
or
only a nominal entry fee
insignificant
The entry fees are
usually
compared to other users' expenses,
such as
transportation cost.
factor
alone
recreation,
would
to
the
be
If the entry fees are used as
estimate
the
proximity
Therefore,
for
price factor is in
most
terms
of
of
demand
outdoor
locational
availability
and
of substitute outdoor recreation sites
may
Similarly,
accessibility
outdoor
for
most important factors affecting
ignored.
recreation
demand
the
price
relative
the
be expected to have an effect on the demand.
During
recreation
the
has
recreational
past two decades,
research
on
outdoor
started to focus upon the measurement
benefits.
Conceptual frameworks
have
of
been
developed to assign monetary values to outdoor recreation.
Therefore,
these
intangible
values.
benefits
There
are
are
no
regarded
longer
a variety
of
methods for measuring the benefits of outdoor
as
estimating
recreation,
but only a few of them are appropriate and valid.
In this
chapter, formulation and estimation considerations will be
discussed,
respectively,
from
the
view of
demand
for
outdoor recreation.
A Model of Demand Analysis for Outdoor Recreation
Demand is a multivarjate relationship. Many factors,
such as price of commodity,
consumers' income, consumers'
15
tastes,
prices of other related
wealth,
population,
policy,
etc., are
the
particular product.
has
income
can
determinants of the demand for
model
other prices,
This simplification of reality
help us to understand the consumers'
alternatives.
way
they
available
among
choose
thus
decision-making
In the same manner, an estimation of such a
planning
demand for outdoor recreation can aid
of
a
But the conventional theory of demand
and tastes.
processes--the
government
distribution,
emphasized the price of the commodity,
income,
consumers'
commodities,
and policy choices by focusing on the important variables.
A
framework
established
thus
is
to
the
investigate
interactions among these important variables.
Theoretically,
individual's
many
decision
participate
to
in
particular
a
outdoor recreation activity.
Variables such as age,
income,
be put in
and
individual
education
can
characteristics;
other
an
affect
can
factors
the
sex,
category
of
such
as
variables,
travel cost, congestion, and resource characteristics, are
in
the
category
of
availability
recreation.
of
Empirically, the number of variables to be included in the
model
depends
upon
the nature of the
phenomenon
being
studied and the purpose of the research.
In
his
original
demand
functions
demand
schedule
for
research,
four of the
Clawson(1959)
national
was measured by plotting
the
derived
parks.
The
estimated
16
cost per visit in relation to number of visits per 100,000
population
indicated
Knetsch (1963)
in a distance zone.
that C1awsons demand function was underestimated
of
He also
the effect of the time constraint.
that
other
Based
variables
upon Clawson's method,
(1964)
the
demographic
should
included.
Castle
and
incorporated income as an independent variable
in
They claimed
demand function for outdoor recreation.
that
suggested
be
Singh,
Brown,
because
"the Clawson approach is a special case of the
general phenomenon of transfer costs"(ibid.,
more
They
p.10).
thus could apply these transfer costs to estimate the
net
economic value of the sport fishery resource.
Clawson and Knetsch (1966) used population,
leisure,
demand
multiple
a
factors
the major
significant
households,
affecting
Tolley
Boyet and
regression model
to
(1966)
analyze
areas.
the
They
population, and distance from the park
explanatory variables.
Ranken
participation
factors
in the use of specific park
found that income,
were
as
for outdoor recreation.
developed
causal
mobility
and
income,
and
Sinden
In a survey
found
(1971)
in various outdoor recreational
on
that
activities
was related to the income of the household, the proportion
of
adults,
education,
average
sex,
and
age
of
the
children,
the
age,
holidays per year of the
household
have
certainly
head.
These
and
other
similar
studies
17
provided
some
important
insights
However, since the
recreational preferences and behavior.
nature
demand
of
different
from
for
explaining
for
recreation
outdoor
the demand for
somewhat
is
some
commodities,
other
possible problems need to be delineated.
The Specification Problem
The
first
problem
is
decide
to
what
constitutes the demand for outdoor recreation,
to
specify
the
model by which
really
relationship
the
how
i.e.,
among
variables will be studied.
Time has usually been ignored in traditional
theory,
which implies that the consumer has instantaneous
access to all markets,
and the consumption is independent
of the the time taken to consume.
consumption
time
demand
aspects
activities
are
too
However, there are some
where the access and
important
to
be
consumption
ignored.
For
instance, an activity of fishing involves outlays of money
and time for traveling and fishing.
and
income
demand
must be taken as budget
Therefore,
constraints
for outdoor recreational activities.
recreational
both time
on. the
In addition,
activities are not the same as the goods
on
which the traditional consumer demand theory is based,
so
the
be
analysis
of demand for outdoor recreation cannot
tackled in the same way.
18
would
It
thus appear that in the case
recreation,
goods,
components,
and
and
time,
these
are
travel
are
components
outdoor
of
main
the
inputs
to
the
Therefore,
production of outdoor recreational activities.
a production theory may offer a moresatisfactory approach
than demand theory. In fact, as long as the production for
outdoor recreation can be established,
various
inputs can be derived.
the demand for the
For
example,
fishing
a
activity
produced and consumed by an angler requires
services
of
necessary
fishing
a site,
for
the angler's
fishing.
and
(An angler can purchase or
rent
the
fishing
transport himself to the site.) Of
course,
equipment,
activity
equipment
and
time,
the
his time
allocate
to
there are some other inputs to the production process that
are not under the angler's control, such as water quality,
fish density, and congestion at the site.
The
above
represents
utility
the
technical
function
preferences)
production
outdoor
to
function
possibilities) can
(which
constitute
represents
Becker's
the
(which
combine
a
consumer's
approach.
In
an
innovative article, he said "Households will be assumed to
combine
time
and
market
goods to
produce
commodities that directly enter their utility
(Becker,
1965,
specified as
(a)
p.495).
:
U = U (Z
,
1
..., Z
in
Thus,
more
basic
functions."
a utility function can be
19
where
the
are called commodities,
Z
and each Z
has
a
i
production function of the form:
(b)
= f
Z
i
where
(x , T
i
X
i
I
time
a vector
is a vector of market goods and T
I
of
i
used in producing
inputs
combination
equations
of
the
be
can
(a) and (b)
The
commodity.
ith
used
to
construct a utility function of the form:
(c) U = U (z
z
) =U(f,
1
X ; T
,
1
f
= U (X
)
m
1
1
..., T
m
Therefore,
consumer's
be
can
choice
made
by
maximizing equation (c) and subject to the income and time
constraints.
In
conventional
theory,
can
demand
be
expressed as a function of those other variables appearing
in the constraints to utility. Thus, a demand function for
outdoor
and
recreation could be a function of
both own and relative prices for
and time.
some
income,
time,
recreational
goods
As mentioned earlier, apart from this approach,
other studies provide additional knowledge about the
factors determining the dependent variable. These factors,
representing
individual socio-economic status and
family
structure, can also be included in the model.
However, the ultimate objective of this study is not
to develop a detailed model of the determinants of outdoor
recreational activities,
particular
purpose
but to emphasize the demand
outdoor recreation.
In other words,
for
the main
is to show that the spatial factor is the key
to
20
understanding
the overall demand for outdoor
recreation,
and the demand for travel is the core of the problem.
The Identification Problem
The identification problem arises because price
quantity
of
are simultaneously determined by the interaction
supply and demand
explained
data.
Working
Decades ago,
had
(1927)
the identification problem by using time-series
He showed that,
period
and
of
time,
the
in a particular market at a
observed price and
given
data
quantity
reflect the simultaneous interaction of supply and demand.
However,
can
function
Working showed that a demand or supply
be
identified if we can assume a
relatively
stable
demand and a widely shifting supply or a relatively stable
supply
and
supply
and demand shift,
function
a widely shifting demand.
some
However,
if
both
in order to identify the demand
variables
other
than
price
should
be
included to explain or account for the shift of the demand
or supply functions.
Basically,
a demand model for outdoor recreation is
mainly related to forecasting use and estimating
of a specific recreational activity.
different
purposes
modeling
the
distinguished:
of
demand
analysis,
for
site-specific
outdoor
However,
three
based upon
approaches
recreation
area models,
benefits
can
to
be
site-specific
21
user models,
cost
and population-specific models.
travel
model of demand is a site-specific area model
assumes
that
each
per feet ly
elastic
services.
In
purchase
unit
The
individual
recreationist
supply curve for the
traditional economics,
faces
specific
Site's
an individual
will
a good until his marginal valuation of the
last
of good exactly equals the price of
behavior
which
of
the
The
good.
this marginal value function thus
underlies
the downward-sloping demand curve.
Now, assume the demand
curve
individuals,
but
curve moved in a
parallel
manner
(because the more
distant
constant
is
horizontal
different
have
to
for
supply
prices
all
the
the
at
individuals
pay higher prices through thehigher travel
and
other related costs to reach the site.). Working's article
thus provides a basis to trace out the statistical
demand
curve for that site.
Therefore,
model
is
the
key
feature of
the
that the individual recreationist
site-specific
confronts
a
horizontal supply curve, the price at which he consumes is
given, and he can consume any quantity at the given price.
Accordingly,
demand
the
quantity demanded is determined by
the
relation of the individual in accordance with
his
given price for participation. As a consequence, price and
quantity
words,
are
with
recreation
not
simultaneously
supply
can
thus
specified,
be
easily
determined.
the demand
estimated.
other
In
for
outdoor
Hence,
the
22
problem
of
simultaneity
and
identifications
are
not
issues, at least in the case of this study.
Evaluation Methods of Demand for Outdoor Recreation
A
series
recreational
validity.
of
evaluation
methods
non-priced
for
resource have been developed and tested
Some
of these methods,
such as the
so-called
indirect and direct approaches to estimating demand,
involved
sites where there is no charge (or
insignificant entry fee).
been
made
that
recreationists
and
outdoor
to
an
As a consequence, attempts have
would pay,
given
the
price
conventional
Other methods, such as the cost method,
the gross expenditures method,
derive
only
to develop proxies which would show the
market mechanism.
method,
have
establishing a hypothetical price for access
recreational
for
the gross national product
the market value method,
do not attempt
to
the demand curve in order to measure the value
of
recreation to the recreationists.
The
following
section will briefly discuss these various methods.
Comparison of Various Evaluation Methods
1.
Cost
Method.
This
method,
National Park Service from 1950 to 1957,
value
employed
by
the
assumes that the
of outdoor recreation resource use is equal to
the
23
costs
involved in developing it.
weaknesses in this method (see,
1962).
There are several basic
for example, Crutchfield,
But the most obvious one is that any
resources
project
regardless
whether
of
alternative
could be justified (by
uses.
So
recreational
this
method),
have
the resources might
this method provides no
better
means
of
ranking projects.
Gross Expenditures Method.
used
by
This method has been
travel
or
agencies.
It
state fish and wildlife departments,
tourism
departments,
attempts
and
other
related
to measure the value of recreation to
recreatjonjsts
and
the
both
the local area in terms of the
total
amount spent on recreation by the recreationists. However,
if
a particular recreational
expenditures
would
still
be
activity
spent on
the
disappeared,
other
goods
or
services,
and
substitute
which would replace the recreational activity.
this
method
tells
nothing
about
the
Furthermore,it does not assess the loss in a move from
an
original pursuit to alternative uses of the expenditures.
Gross
National
Product
Method.
This
method
attempts to measure the contribution of recreation to GNP,
by
assuming that recreation is a factor of production
related to production.
assume
or
Obviously, it is not reasonable to
recreation as a factor of production.
After
all,
recreation is essentially a consumer good, even though its
pursuit
may
eventually
stimulate
increases
in
24
productivity.
Market Value Method. This method attempts to use
the
market
value
of fish caught (in the case
sport
of
fishing) or a schedule of charges to represent the
market
value of the recreation services produced. But in the case
of
sport fishing,
that
may
or
the product is fishing,
may
inappropriate
not
be
caught.
not the
Moreover,
seems
it
to use charges at private areas to
fish
measure
the value of recreation at public areas because the market
for
all outdoor recreation is not a commercial
one,
and
private areas are often affected by the free public areas.
Indirect Approaches to Estimating Demand Method.
In applied welfare economics,
curve
plays
welfare
of
normally
would
1980).
an important role in measuring the
the
pay
pay
consumers.
a
maximum
rather than forego it (Henderson
and
economic
consumer
that
he
Quandt,
In economics, this maximum amount represents gross
for the consumer,
consumer
is
difference
called
price
cost
the actual amount paid by the
or
expenditure,
while
the
between these two amounts is the net benefits.
In other words,
rather
Theoretically,
less for a good than the
benefits
the
the downward-sloping demand
these net benefits measure "the excess of
which (the consumer) would be willing
than go without the thing,
does pay" (Marshall,
consumer 'S surplus.
over what he
to
pay
actually
1961, p. 124), which is known as the
25
While the consumer's willingness to pay for
goods
theoretically
is
revealed
through
the
outdoor recreational activities are nonmarket
for
which
willingness
to pay may not be
private
market,
commodities
from
measured
consumer behavior in the market. Nevertheless, a number of
techniques
have
been
developed and
applied
derive
to
willingness to pay for outdoor recreation through indirect
and direct approaches to estimating demand function.
The
benefit
indirect
estimates
nonmarket
from
situations.
approaches,
cost,
approach
observed
demand
consumer
behavior
in
indirect
are three various
There
derive
to
the household production function, the travel
and the hedonic price,
outdoor
recreational
function
approach
framework
recreation
(see,
1983).
have been used to
values.
used
production
1981,
infers
household
production
(1965)
household
Becker's
to estimate the demand for
for example,
This
The
evaluate
approach
Bockstael and
has
conceptual
providing a sound theoretical framework.
outdoor
McConnell,
merit
However,
for
from a
practical standpoint it would be more difficult and costly
to use for estimation of outdoor recreational demand
the other approaches.
than
(Considering the characteristics of
data sources and objectives of this study, the travel cost
method
will be mainly relied upon,
as discussed in later
sections.)
6.
Direct
Approaches to Estimating Demand
Method.
26
This
approach
direct
derives
questioning
willingness to pay.
how
much
One
is
economic
value
of individuals with regard
to
from
their
It involves asking the recreationists
they would be willing to pay for the
participate
approach
demand and
in the outdoor
recreational
to
right
activity.
suffers from its use of hypothetical
This
questions.
of the weaknesses is the fact that willingness to pay
governed
directly by the recreationists'
ability
to
pay.
Another deficiency is that the bidding game used
in
this
approach
typical
based upon many assumptions
is
recreationists
incorporate
fail to
the
that
into
their
decisions (for example, the bidding game does not consider
such factors as probable substitute activities).
Also,
serious
For
example,
different
answer,
problem
recreationists
depending
be
of
bias
often
give
often
a
occurs.
much
a
upon whether they are asked how much they would
willing to pay to retain their
recreational
activity
versus how much they would need to be paid for loss of the
activity.
Measures of Consumer Welfare
"The definition of a measure of economic welfare for
the
consumer
has
been
one of
the
most
controversial
subjects in economics. Unlike the producer's case, ... the
criterion
of the consumer--utility--is
not
observable."
27
/
(Just,
true
Hueth and Schmjtz, 1982, p.69). This is especially
for nonmarket valuation,
(e.g., Bishop and Heberlein,
value
such as outdoor recreation
where the
1979),
measures cannot usually be
estimated
validated by observable
market data.
Although
often
U.S.
most
welfare
used in empirical work to measure consumer
example,
(for
the term "consumer surplus" has been
Bureau of Outdoor Recreation,
1973;
Dwyer, Kelley, and Bowes, 1977, etc.), it has been plagued
by
a
strict assumption:
should
then
be
the
constant.
the marginal utility
If this assumption is
Marshalljan
demand
curve,
money
of
unrealistic,
which
on
the
computation of consumer surplus is based, does not reflect
the
relevant
valuation,
and
the
concept
consumer
of
surplus becomes imprecise.
Hicks
consumer
has identified and suggested four measures of
welfare-- compensating variation (and
surplus),
equivalent variation (and surplus)-- that differ from
Marshallian
consumer
correct (see Just,
surplus and are more
Hueth and Schmitz,
the
theoretically
Chapter 6,
1982).
The so-called marginal-valuation curve (or Hicksian demand
curve)
is defined by allowing the presence of the
income
effect when price changes. In order to maintain a constant
real income,
the Hicksian demand curve will lie below (or
above)
the Marshallian demand curve for a price fall
rise).
The
relationships
between these
two
curves
(or
is
28
illustrated as figure 2.1.
In
figure
(uncompensated)
constant,
11
curve
and
)
demand
represents the
D(m)
demand
H (U
(compensated)
constant.
2.1,
income
where
H (U
22
utility
0
U
held
is
rectangle
the
(the area x + z) based upon Marshallian curve D(m).
1
Based
upon
variation
compensated
curve
in income of p cep
0
the
to
Hicks.ian
1
consumer surplus may be represented by
p cfp
held
is
to p , the increase
For a fall in price from p
0
in
m
represent
)
where
curves
Marshallian
H (U
11
)
compensating
a
(area x) can be defined
as
1
amount that needs to be reduced after the price
fall
maintain the consumer as well off as he was before the
price reduction.
H (U
22
(area
Similarly,
based upon compensated curve
an equivalent variation in income will
)
be
p dfp
0
x + z + w) which is the amount of income that
1
must
given to the consumer instead of price change to leave the
consumer
Therefore,
consumer
as
well off as he has become with
it
the
change.
is clear from the above that the change in
surplus resulting from a price fall will be
average of the compensated measures.
In other words,
the
the
uncompensated demand curve is a special case which assumes
marginal utility of income is the same at different income
levels. Thus, if a Marshalijan demand curve is established
for measuring economic welfare, its usefulness will depend
on the extend to which income variations alter valuations.
In
fact,
as
long
as the income
effect
is
zero,
the
29
price
*
p
p
0
p
1
q
quantity
q
0
1
Fig. 2.1 The relationships between Marshallian
and Hicksian demand curves when price
changes.
30
Marshalijan
coincide
demand curve and Iiicicsian demand
curve
with each other and the Marshallian measure
will
and
the compensated measures will be the same.
However,
Hicks indicated that "...
So long as
the
proportion of income initially spent upon (commodity) X is
small,
the
the income effect is likely to be quite small.
demand for a single commodity (in the ordinary sense)
by
consumer
whose
consumption
reasonably
is
diversified-- it is fair to expect that the main effect of
a price-change will be the substitution effect,
income
Along
effect
the
defended
curves
will be relatively small."
same
lines,
Willig
(1976)
consumer surplus computed from
while the
(1956,
rigorously
has
ordinary
as a reasonably accurate measure by
p.65).
demand
theoretically
demonstrating that the difference between consumer surplus
and
equivalent
variation (or compensating variation)
insignificant in most applications.
This implies that the
consumer surplus approach is generally robust,
what
demand
compensated
curves
demand
(ordinary demand curve
curve) are used
is
to
no
matter
or
Hicksian
derive
consumer
surplus. Thus, consumer surplus may usually be a very good
approximation to the appropriate welfare measure.
The Travel Cost Method
Among
the indirect recreation valuation techniques,
31
the travel cost method is most representative and has been
used
for
a quarter of century.
suggested
by Hotelling (1949) in a letter to the Director
of the National Park Service.
possible
estimate
to
surplus
distance
zones
essentially
He stated that it should be
demand
based
(1959),
consumers'
upon
concentric
This method
around the parks.
applied
and
functions
national parks
the
for
Clawson
first
was
method
This
to outdoor recreation
Brown,
Singh,
and Castle
then
valuation
(1964),
was
by
and
Knetsch (1963, 1964).
The
spatial aspect is important in the travel
method,
since
origin,
recognize that they must get to the
the individuals,
from different points of
site to use the service of the site.
the
service
proxy
for
capita
Thus,
recreational
the price for
will vary according to the travel
costs of access to the site.
price,
demand
cost
and
time
To use the travel Costs as a
this method involves estimating a
function
per
participation
rates
as
average costs to the site and
other
socio-
capita
demand
on
function
of
economic
factors.
function
for a recreation site,
Based
upon
the
per
a
the consumer surplus for
the site can be computed.
As mentioned in the previous section,
surplus
the
consumer
is defined as the area under the demand curve and
above the price line.
For the travel cost
approach,
the
differential costs associated with the use of a particular
32
recreation
various
site by recreationists,
distance
from
surrogate for price.
live
who
have been
the site,
Therefore,
originally located at
farther
away,
the former
and
as
a
those recreationists who
closely to the recreation site pay less
live
used
those
than
enjoy
ones
a
consumer surplus over the latter. In reality, the consumer
surplus
per capita. is computed by subtracting the
amount
per
distance zone from the
actual
amount
that
the travel
cost
maximum
hypothetically would have been paid.
spite
In
method
of being commonly used,
suffers from several
resulting
weaknesses.
weaknesses
Th
rigorous
from this method involves a number of
assumptions.
One
needed
assumption
is
that
the
recreationists' response to an increase in user fees would
be
the same as their response to an increased travel cost
of
the same amount.
assumed
to
recreation
that
Secondly,
the costs of
be incurred solely for participating
at the particular site.
all
travel
people
in
the
Finally,
population
characteristics and preferences.
have
it
in
are
the
assumes
same
the
To overcome the rigidity
of these assumptions, several attempts have been made, for
example,
(1976),
sites,
to
to
changes
time
by Burt and Brewer (1971),
Cesario and
Knetsch
generalize the travel cost techniques to many
price
incorporate the substitution effects of
into the model,
and to include a
surrogate
costs as well as money cost in the analysis,
for
and so
33
on.
Early
Oregon
studies
have
used
for evaluating the sport fishery
the
travel
with
method
cost
in
some
modifications, e. g., Brown, Singh, and Castle (1964), and
Stevens
(1966).
Oregon
salmon-steelbead
Hotelling-Clawson
In
and
Brown,
Singh,
and Castle's work on the
expanded
fishery
variables.
model to include additional
addition to the price variable they included
on the number of angler days spent on sport
distance
variable
function
in a negative fashion,
has
travel.
theory
experience
Oregon
acted
as
a
shifter
fishing.
expanded
indicating that time
including
the
Hotelling's
quality
of
costs
concentric
the
sport fishin9.
He defined quality
angler success per unit of effort.
of
of
zone
recreational
as an important determinant of the demand
ocean
The
demand
the
of
an effect over and above the money
Stevens
by
distance
They found that income had a positive effect
income.
travel
basic
the
as
for
the
34
III.
EMPIRICAL ESTIMATES OF SINGLE SITE TYPES OF TRAVEL
COST DEMAND FOR OREGON SALMON ANGLING
As indicated in the previous chapter,
demand
for
recreation
is not
sites
estimation of
the
as
same
the
traditional methods of estimating the demand for goods and
services
will
value
adopt
chapter
This
exchanged in an organized market.
the travel cost method to measure demand
recreational
the
for
fishing
in
Both
Oregon.
aggregated and disaggregated models will be used,
comparisons
and
but the
of their results will not be discussed
until
the next chapter
The
travel
main objective of this chapter is
cost
estimates
models
of
the
fishing in Oregon
catch
will
so as to obtain
the
to
estimate
most
accurate
demand for and value of
In addition,
be estimated,
salmon
the value of the
based upon estimates of
from
the
from
he Oregon Department of Fish and Wildlife.
travel cost model and estimates of
fish
sport
salmon
value
catch
Estimated Zone Average Travel Cost Demand
Traditionally,
estimate
the
statistically
per
the
capita
travel cost method is
demand
function
used
by
fitting
the relationship between trips per unit
population by certain distance zone and the average
to
of
costs
of reaching the recreational site from that distance zone
35
Trips
the
per
unit of population can be computed by
number of trips to the Site from the
summing
distance
given
zone and then dividing by the total population of the same
distance
zone.
computed
by
averaging the total amount of
opportunity
cost
recreatjonjst
distance
The average cost per distance zone can be
time
travel
of
monetary
individual
each
incurs to reach the site from the
zone origin.
and
original
Other socio-economic variables are
certainly important for constructing demand functions, but
variables such as income,
age, or education are difficult
to use in an aggregated model. However, average income and
average
salmon
fishing equipment
tested in the various models.
variables
expenditures
In addition,
be
will
several dummy
are also used in the fresh-water salmon fishing
demand model.
In this section, the demand for fresh-water
salmon and ocean salmon will be estimated, respectively.
Fresh-Water Salmon Sport Fishing
Among
the
the various zonal travel cost models
following
semi-log form was judged to
be
fitted,
the
most
appropriate,
based upon statistical considerations,
such
as t values,
goodness of fit,
theoretical
coefficients,
income
considerations,
etc., and upon logical and
such
as expected
reasonableness of projections,
variable
was deleted due to the
signs
etc..
of
(The
insignificant
t
36
value.
Also,
deletion
of
the income variable had
very
little effect upon the crucial travel cost coefficient, as
can be seen from equation (A-i), APPENDIX F.)
ln(TRPSCAP)
(1)
+ 0.0001552
= -1.4250 - 0.05024 RTC
ii
ii
(-9.38)
SSFE
- 1.102 x
(2.47)
- 1.651 X
- 0.9204 X
3
2
1
(-6.33)
(-3.41)
(-3.81)
2
n = 37
In
equation (1),
TRPSCAP
= 0.816.
salmon
denotes average
'3
fishing
trips
per
capita from distance zone
specified river j. RTC
combines
ordinary
operating
time.
(The
third
of the wage rate,
dividing
variable
(the
with the opportunity
average
cost
of
incurred
travel
of
one-
and the wage rate is computed by
yearly income
equipment in zone i.
SSFE
2,000.)
by
the average replacement value of
related
the
cost
opportunity cost is assumed to be worth
the
denotes
cost
a vehicle plus food and lodging costs
travelling)
to
i
denotes revised travel cost which
travel
while
and
R
1J
fishing
salmon
The dummy variable
X
1
takes
one
the value of one if the anglers of zone i
the Portland metropolitan counties of
of
Washington,
X
and X
2
in
Multnomah,
or Clackamas and the value of zero otherwise.
are also dummy variables representing the
Rogue
3
and Coos Rivers,
one,
live
and
parentheses
is
respectively, when the value is equal to
otherwise
represent
equal to zero.
the
t-value.
The
The
numbers
in
thirty-seven
37
distance
zones
were
constructed
from
individual
158
respondents who fished in the nine specified rivers.
Subtracting
distance
would
zone
the
actual
amount of travel
hypothetically
in
angler
the
from the maximum amount that
j.
cost
be willing to pay is equivalent
to
The
computing the consumer surplus per capita for zone i.
total consumer surplus is then computed by multiplying the
per
capita
distance
population
consumer surplus by the
each
in
and then summing the consumer surplus
zone
for
each zone. The net benefits per capita for distance zone i
can be expressed as a mathematical form:
tc
0
(la)
CS
=
:i.
/tc
i
we assume the travel cost demand function has
bx
form as q
= a e i, where q
denotes the
If
semi-log
i
predicted
per
distance
capita
zone and x
i
i
rate
participation
of
denotes the travel cost,
the
ith
while
the
1
constant
is assumed to include the effect of any other
a
i
variables.
tc,
then
q
1
integral
the observed travel cost of zone i by
btc
= a e
i and the consumer surplus is the
Denote
i
i
of the demand function as x
i
ranges from tc
infinity. (For a linear form, the range is from tc
maximum
amount of travel cost,
to
1
which causes q
to the
to
equal
1
zero.)
zone is:
Thus,
the consumer surplus per capita in the
ith
38
bx
(ib)
Cs
i
=
ae idx=
i
(
I
Itc
I
Therefore,
btc
1)
tc
ae
1
btc
i
-b
the
consumer
computed from equation (1),
predicted
-b
surplus
population,
the ith distance zone is
consumer
equal
the
to
the
zone
the
total consumer surplus for each zone
Adding
up the zonal
i
Then, multiplying
surplus for each zone by
consumer
total estimated net economic benefit
the
easily
be
fishing trips to river j per capita for zone
capita
obtained.
can
that is, the consumer surplus
divided by the travel cost coefficient.
per
b
1
b
for
j
tc
(O-e
capita
ibdx =_Le
a e
i
1
per
.bx
bx
surpluses,
is
the
is obtained. This is
traditional approach for evaluating consumer Surplus.
Another way to evaluate consumer surplus is the
Gum-Martin approach (Gum and Martin,
so-called
1975). Following the
same procedure,
except for using actual fishing trips per
capita
of
instead
surplus
total
the predicted
for each river can also
figure,
be
consumer
the
computed.
Estimated
net economic benefits to Oregon fresh-water
salmon
anglers are shown in Table 1 from using equation (1).
The
estimated catch of salmon in each river reported by Oregon
Department of Fish and Wildlife is also included in
Table
1.
Dividing
the traditional and Gum-Martin estimate of
39
Table 1.
River
Estimated Net Economic Benefits and Catch for
Oregon Fresh-Water Salmon Sport Anglers in 1977,
Based Upon Zonal Average Participation Rates Per
Capita
Estimated
Catch of
Salmon
Gum-Martin
Traditional
Estimates of
Estimates of
Consumer Surplus Consumer Surplus
193,800
Alsea
2,290
Clacicamas
2,149
487,900
161,900
13,172
1,316,600
1,480,300
573
45,200
45,200
Deschutes
3,833
71,400
87,400
Rogue
8,864
236,600
247,100
Umpqua
4,570
477,100
708,700
14,222
1,720,400
1,638,100
4,692
161,200
160,700
54,365
4,916,300
4,723,200
Columbia
Coos
Willamette
Wilson
Total
$
399,900
$
40
consumer surplus by the total fresh-water salmon trips
of
230,280, an average consumer surplus per trip of $21.3 and
respectively,
$20.5,
are
obtained.
Although an average
consumer surplus per fish can be computed by dividing
the
total estimate of consumer surplus by the number of salmon
using
caught,
decisions
affecting
justifiably
that
such
"It
For example,
marginal benefits that
decisions
making
marginal
fish abundance and harvest has
questioned.
is
allocation
average values for
and
...
Bishop has
argued
important
are
average
been
for
will
benefits
exaggerate the contribution of recreational fishing at the
margin."
(1980,
p.232)
sport
The relationships between
fishing benefits and fish catch will be discussed in later
sect ions
Ocean Salmon Sport Fishing
The
procedure
used to fit the travel
cost
demand
model for ocean salmon fishing was essentially the same as
for
fresh-water
salmon
except the ports
in
which
anglers went fishing were grouped on a county basis
each
travel
coastal
represents a specific-site
cost demand model.
constructed
salmon
county
from
There were 47
the
Thus
in
the
distance
zones
211 observations that fished for
ocean
The following equation was the most
of several that were fitted:
satisfactory
41
= -2.1516 - 0.01745 RTC
ln(TRPSCAP)
(2)
ii
ii
(-10.86) (-7.38)
2
n47
The
symbols
r
= 0.548.
in equation (2) are the same as
defined
in
equation (1).
The consumer surplus per capita is computed for each
zone, then multiplied by the zone population to obtain the
total
consumer
traditional
zones,
estimates
total
a
approximately
estimate
each
Summing
zone.
consumer surplus
estimated
consumer
An
for
of
$15,548,700
of
$14,491,700.
trip
surplus
net
economic
was obtained.
surplus
was
the
the
for
benefit
47
of
Gum-Martin
The
slightly
lower
at
average Gum-Martin consumer surplus
per
of approximately $57 is estimated by either dividing
the
total estimate of consumer surplus by total trips
252,950
or
by taking the reciprocal of the
travel
of
cost
coefficient.
Theoretical Relationships Between Angler Benefits
and Fish Catch
Although
the travel cost method for estimating
value of sport fishing and hunting activity has long
in
use,
studies
making
value
the
usefulness
of the earlier
have been somewhat limited for
purposes
and
public
because those studies have not
estimates for the fish caught or the bag
the
been
subsequent
decision-
provided
of
game.
42
Consequently,
needed
estimates
of
values
marginal
associated with marginal changes in fish catch or game bag
have not been available.
certainly
total
be
could
Some crude average values
obtained by simply dividing
estimated
the
consumer surplus by the total sport harvest of fish
or game, but the validity of using such average values has
not been justified.
However,
marginal
value
importance
knowing how
of
in fish and game abundance
changes
of
crucial
the
the
affect
sport fishing and hunting can hardly
over-
be
emphasized. Without this knowledge an efficient allocation
of
public funds and natural resources
instance,
salmon
fish
if
sport fishing,
expenditures
enhance
are
catch
is
unlikely.
value
is unrelated to the
then there is no need
for
For
of
public
on fish hatcheries and stream improvement to
salmon runs,
concerned.
at least so far as angler
On the other hand,
benefits
if there is a
positive
relationship between salmon catch
benefits
from salmon sport fishing,
and
then a
strong
economic
considerable
use of public resources to protect and enhance salmon runs
can be justified.
If
consumer
a
linearly
homogeneous
relationship
surplus and fish catch were found to
between
exist,
it
would greatly facilitate evaluation of fishery enhancement
projects.
it
But
before proceeding with such an assumption,
is important to discuss whether this assumed
linearly
43
homogeneous
There
One
relation is consistent with consumer
conditions.
necessary
are two main aspects of the
theory.
aspect concerns the form of the utility function that
would
consumer surplus to vary
cause
fish catch.
to
The second aspect concerns the kind of budget
constraint
function,
proportionally
that would,
result
in combination with
the
utility
in a particular functional form of
the
demand for fishing trips. Suppose a utility function is as
follows:
r
r
2q
U = q
3.
3
2
b
r =bq 1<1.0,
Where,
01
2
denotes
1.
0
catch
fish
1-r ,q
b andb >0, r
by anglers,
2
3
denotes
q
number
of
2
fishing trips, and q
denotes all other consumption goods
3
This
formulation
effort
the
assumes that catch
angler
has good information about
for given rivers
subject
to
approach
might
and
catch-effort
then the.situation
a household
more
be
the
production
appropriate,
of
that
but
(If catch per unit of effort
the angler's control,
complicated,
unit
per
is not subject to the angler's control,
ratio
more
also
is
is
function
Bockstael
and
McConnell (1981).)
The budget constraint facing the angler is
Mpq22+pq
33
Where, M is income, p
is the price (i.e. travel cost) per
2
trip,
and
p
is
3
the
price
vector
for
other
goods.
44
Maximizing
(3)
multiplier
method
subject to (4) and using
for the solution of
Lagrangian
the
constrained
this
maximum, a Marshaj.ljan demand function can be derived as:
b
2
According
for
-1
bq iMp
01
2
q
(5)
to the above demand function,
salmon sport fishing trips is a
function
other
of
increasing
strictly
the fish catch expected by
words,
the demand
the
angler.
In
the demand relation in (5) implies that
no
fishing trips would be taken at all if the angler does riot
consider
that
will
the probability of catching fish
greater than zero.
be
The consumer surplus computed from (5)
can be expressed as:
tc
tc
b
0
b q 1Mtdx = b q
Cs =
(6)
b
01
Ip
X
0
lMlnx
01
p
2
where
tc
is
2
the largest observed travel cost
the
(or
0
price
that reduces quantity demanded to zero) and
p
is
2
the
travel cost incurred by the angler.
implies
that
the
consumer
proportional to fish catch q
surplus
The equation (6)
would
directly
be
if and only if b
= 1.0.
Relation of Estimated Angler Benefits to Salmon Catch
The
previous section has computed consumer
for the various rivers,
shown
in Table 1.
surplus
based upon a single equation,
The traditional estimates of
as
consumer
45
Surplus
for
each of the nine rivers in Table 1 was
regressed as a linear function of fish catch,
procedure
then
following a
similar to that employed by Samples and
Bishop
(1985):
= -58,981 + 100.20 CTCH
CS
j
(-0.32)
Since
the
n = 9
= 0.714.
r
j
(4.18)
constant term in (7) is far
being
from
statistically significant and there are some advantages in
using
term
the linearly homogenous form of (7),
was deleted,
constant
the
and the regression forced through
the
origins, yielding
2
= 94.05 CTCH
CS
j
to
= 0.710.
r
j
(6.84)
According
n = 9
equation (8),
the marginal value
of
salmon catch is about $94 per fish.
However,
since
only
the
fishing
rivers
are
nine
most
important
salmon
represented in Table 1, some adjustments of this value are
needed.
one,
To
the
degree
linear regression model was transformed to
double-log
Thus,
check to see if (8) is homogeneous of
form
the
and fitted to the same data in Table
double-log
equation
was
estimated
as
the
1.
the
following:
2
1nCS
= 5.477 + 0.8594 1nCTCH
j
n = 9
r
= 0.562.
j
(2.05)
(2.69)
In order to test whether the degree of homogenity is
equal
to
one,
the coefficient of 1nCTCH
minus
J
one
is
46
divided by the standard error of this coefficient, and the
t-value
falls
obtained was -0.44.
short
of
Since this small value of
significance
even
at
the
t
percent
50
probability level, the hypothesis that the salmon anglers'
consumer
surplus
is a linearly homogeneous
function
of
is
fish catch cannot be rejected.
that
One
important
aspect of the preceding analysis
the
estimated
fish
completely
consumer
catch
surplus in Table 1.
1
are
estimate
the
Table
in
independent of the data used to
collected
Salmon sport catch data are
each year by the Oregon Department of Fish
Wildlife
and are based upon salmon-steelhead
returns
and
surplus
analysis
other
information.
based
is
used
However,
upon survey
steelhead sport anglers in 1977.
data
data
punch
and
card
consumer
the
salmon
and
The independence of
the
of
thus makes the estimated linearly
homogeneous
relationship more impressive.
Equation (8) is homogeneous of degree one means that
if
the
number
consumer
of fish caught
surplus
characteristic
would
also
were
be
doubled,
then
doubled.
of linear homogeneityhas some
the
This
meaningful
implications. First, as long as the number of salmon catch
can be predicted,
Second,
then
if
the consumer surplus can be
it is decided to increase angler's
estimated.
benefits,
those factors that affect the number of salmon catch
should be improved,
e.g.,the water quality or the
number
47
of
hatcheries.
mentioned
However,
to
be
is that the salmon catch is also influenced
by
biological
and
commercial
catch
accurately
predict
assumed
affect
other
one
factors,
in the
ocean.
needs
that
thing
such as
and
sport
the
cannot
one
TherefOre,
the consumer surplus simply
from
also
salmon catch since many other variables can
the
number
fish
of
caught.
Similarly,
an
merely
doubling the number of salmon caught by sport anglers on a
given
stream would not necessarily double benefits to the
anglers
also
since there are many other variables
influence the consumer
value
per
surplus.
that
could
Nevertheless,
fish from the above analysis should
be
the
quite
useful as an approximation.
The
Gum-Martin
procedure
estimate
to
consumer
surplus, which involves using the observed number of trips
per
capita rather than the predicted number of trips
per
capita, has some advantages over the traditional approach.
The reason is that the Gum-Martin procedure should be less
sensitive
possible
to
specification
that
might
errors
cause fishing
rivers to be over or underestimated.
same
procedure,
surplus
the
Gum-Martin
trips
Thus,
estimate
in Table 1 is regressed as a linear
fish catch:
(10)
GMCS
j
= -148,728+ 111.50 CTCH
(-0.89)
(5.09)
j
model
demand
the
in
n = 9
of
some
following the
of
consumer
function
of
48
Again,
as
for equation (7),
the constant term
(10) is not statistically significant with a t value
than one.
in
less
Since there are some advantages to the linearly
homogeneous
form
again
was
the constant term
of (10),
deleted, yielding:
2
GMCS
= 96.01 CTCH
j
(7.29)
= 9
j
r
= 0.763.
The hypothesis that the degree of homogeneity of the
consumer
surplus-fish catch relationship is not equal
to
one was tested by fitting a double-log function:
2
1nGMCS = 4.0326
j
(1.88)
Computing
hypothesis
linearly
(3.98)
j
n
9
(1.0178 - 1.o)/o.2556
=
t
salmon
that
homogeneous
rejected.
1.0178 1nCTCH
anglers'
=
the
0.07,
are
benefits
net
function of fish
= 0.694.
r
cannot
catch
be
The total consumer surplus from the traditional
method
and
fairly
close.
Gum-Martin method in Table
the
However,
are
1
both
in checking the consumer surplus
for each river, there is a considerable difference between
these two methods.
observed
the
fishing trips to estimate the consumer
consumer
this
method
surplus for each distance zone
may be more accurate
method.
Therefore,
Martin
estimates
performs
Because the Gum-Martin method uses the
equation
of
than
(11),
consumer
the
based
In fact,
upon
traditional
which uses the
surplus,
better than equation (8).
surplus,
Gum-
statiâtically
if
we
use
49
individual
observations (instead of zonal
Gum-Martin
did in their original article (Gum and Martin,
1975),
averages),
then the statistical difference between these
methods
these
will
two
methods based upon
relationship
shown
in
be more prominent.
The comparison
the
linearly
as
two
between
homogeneous
of consumer surplus-fish catch will also
the section that discusses adjusted
be
individual
travel cost demand.
Effect of Other Factors Upon Estimated Benefits Per Fish
Many
factors,
congestion,
It
had
such
as
scenery,
could affect consumer surplus per fish catch.
been
Metropolitan
suggested that proximity
area
might
also
be
an
affecting the level of angler benefits
that
to
the
have
and correspondingly higher estimates of
surplus
per fish catch.
the
factor
The hypothesis is
demands
to
Portland
important
salmon rivers closer to Portland would
measuring
and
access,
higher
consumer
This hypothesis can be tested
the approximate minimum distance of each
Portland Metropolitan area,
assumed to be at least 10 miles.
with
Thus,
all
1y
river
distances
for the rivers in
the same order as presented in Table 1, distances in miles
from Portland are 104,
18, 10, 212, 65, 245, 172, 10, and
38, respectively.
Then,
various
models for the consumer surplus
per
50
river
as a function of two independent variables,
catch
and distance from Portland,
traditional
surplus
river
measure
of consumer
were fitted.
surplus,
salmon
the
For
consumer
the
per
river is regressed against salmon catch
per
(CTCH)
and salmon catch per river
distance
times
from Portland (DP) in miles:
(13) Cs = 112.01 CTCH
j
j
- 0.3224 (CTCH*DP)
(9.21)
From
j
2
R
n = 9
(-2.73)
equation (13) it could be inferred
additional
mile from the
Port'i/n
= 0.860.
each
that
Metropolitan area would
reduce
the
cents.
This estimate of the distance from Portland effect
actually
average value per salmon caught by
seems
too
high since a distance of
about
200
miles
the
would reduce the value per fish to less than one-half
value of a fish caught near Portland.
distance
because
from
Portland
effect may be
32
One reason that the
overestimated
some of the southern Oregon rivers,
such as
is
the
Rogue, almost certainly had a large number of anglers from
California.
travel
It is very difficult to properly estimate the
model when a few recreationists
cost
distance are included in the analysis.
of
state
travel cost equations,
estimation
if
out
of
and no estimate of the out of
anglers' consumer surplus is included in
Therefore,
great
Consequently,
state anglers were not included in the
the
from
Table
1.
there are significantly higher percentages
of out of state anglers fishing in the Rogue and the other
51
Southern Oregon rivers,
equation (13) would overstate the
negative effect of distance from Portland upon the average
value per fish.
For the Gum-Martin estimate of consumer surplus, the
same procedure was used as for (13) yielding:
GMCS
(14)
= 112.55 CTCH
j
- 0.2969 (cTCH*Dp)
j
j
(9.30)
(-2.53)
2
n
R
9
= 0.876.
Result from (14) are similar to those from (13) with
an
implied reduction in value per fish of about 30
for
each
area.
additional mile from the Portland
It
distance
should
statistically
Metropolitan
be noted that the coefficient
from Portland variable,
DP,
cents
for
the
by itself was
not
significant for either the
traditional
the Gum-Martin estimate of consumer surplus,
or
although the
DP coefficient did have the expected negative sign.
The
or
estimate of consumer surplus per fish from (13)
has
(14)
approximation,
for
salmon
relatively
of
to
be
given
considered
as
rough
very
a
the fact that the consumer
surplus
fishing on the southern Oregon stream may
underestimated because of a larger
California
anglers.
Furthermore,
some
be
percentage
anglers
may
prefer chinook salmon over coho, and total salmon catch of
all species cannot reflect such preferences.
although
salmon,
the anglers in this study fished
a
stream
that
offers a higher
In addition,
primarily
for
probability
of
52
catching
both
preferred.
creel
salmon
and
steelhead
have
might
been
In order to investigate some of these factors,
survey data from the Oregon Department of Fish
and
Wildlife will be examined.
Since
of
creel census data are not available for
the rivers in Table 1,
most
two
the analysis will include
rivers only. It is believed that the creel surveys provide
more
Table
accurate
1
steelhead
much
estimates of catch than the catch data
which are based primarily upon
tag returns.
and
salmon
the
These creel surveys also
in
provide
more accurate data on effort than this study used to
estimate consumer surplus as shown in Table 1.
For the Deschutes river,
that
the
1977
creel census data indicate
catch of adult spring
and
salmon was only 1,459 adults and 915 jacks.
catch
chinook
fall
estimated from salmon and steelhead tags was
as shown in Table 1.
the
However,
3,833
In addition, salmon fishing trips on
the Deschutes river were apparently underestimated by
relatively small 1977 survey of Oregon anglers,
the
resulting
in too low estimates of consumer surplus in Table 1. Given
the
seems
per
1977
creel census data for the Deschutes
river,
that a more realistic estimate of consumer
fish
could be computed by
dividing
the
it
surplus
Gum-Martin
estimate of consumer surplus in Table 1 by an adult salmon
equivalent
(Assuming
catch
three
based upon the 1977 creel census
jacks would be equivalent to
one
data.
adult
53
salmon, an adult equivalent catch would be 1,459 + (915/3)
= 1,764
)
Thus, a somewhat more accurate estimate of value per
salmon
catch
1,764
on the Deschutes river would be
= $50 per fish,
underestimate
$87,400
although still too low due to
of salmon fishing trips for
the
/
the
Deschutes
river.
For
catch
the Alsea river,
of
creel census data indicate
283 adult chinook and 785 jack chinook
adult coho and 185 coho jacks.
data
are
far
and
These more accurate
below the 2,290 salmon used
96
catch
Table
in
a
1.
However, it appears that the overestimate of catch used in
Table
is
at
least
overestimate
of
effort
reulting
a
1
in
partially
from
offset
the
corresponding
1977
by
a
similar
angler
survey,
overestimate
consumer
of
surplus for the Alsea river in Table 1.
Although
sources
the
comparison
between
data
different
cannot be scrutinized in more detail,
thing
one
that can be concluded is that most of the variation in the
value
per
error,
catch
both
catch
If
due
to
sampling
in the consumer surplusby river and in
estimates
returns.
the
fish by river in Table 1 is
based
upon
salmon
and
steelhead
the
tag
creel survey data were available for most of
rivers then both the consumer surplus and the
estimates could be corrected to give more
values per fish by river.
Of course,
salmon
accurate
other factors
that
54
affect
the
estimated
investigated.
further
But
value
this
per fish also
need
study does not attempt
to
be
take
to
steps in this direction due to the limitation
of
data sources.
Estimated Adjusted Individual Travel Cost Demand
The
zone
average travel
cost
method
(originally
employed by Clawson (1959) and followed by Knetsch (1963),
Brown,
Singh,
and
Castle
(1964),
and
others)
was
criticized as being inefficient, due to the potential loss
of information from averaging within distance zones (Brown
and
Nawas,
recently,
1973;
Gum and Martin (1975).
Brown et al.
observations
are
(1983) argued that if
to be used,
more
However,
individual
each individual
dependent
variable observation should be divided by its share of the
population
trips
and expressed as trips per capita
only,
expected
not
the
different distant zones
to have quite different
reasoning
are
since
instead
population
can
of
be
The
sizes.
is that if the individuals' participation rates
adjusted to a per capita basis,
then
a
biased
estimate of the travel cost coefficient can result because
the procedure would not properly account for cases where a
lower
percentage of the people in the more distant
participate
in the particular recreational
zones
activity.
In
the next section, the individual observation adjusted to a
55
per
capita
basis
will
be
Following
discussed.
that
section, the individual observation itself, the unadjusted
individual observation, will also be discussed.
With
the
the adjusted individual observation
number
observation
factor,
of salmon fishing trips for
each
is first multiplied by the
sample
then
distance
zone.
individual
divided
For
expanded
example,
there
suppose
from one distance
expansion
are
zone
to represent 500 salmon angling trips,
to
its
five
with
Then, if the first observation were
would be divided by its share of populationi
5,000,
individual
by its share of population in
observations
population of 25,000.
approach,
this 500
25,000 1 5 =
give a per capita participation rate of 500
/
5,000 = 0.1.
Fresh-Water Salmon Sport Fishin9
Following
the
above
procedure,
a
total
of
158
individual observations were used to obtain 158 individual
participation
rates per capita.
(
For'the zonal
average
approach, these 158 observations were used to construct 37
average
participation rates per capita,
as shown in
first
section
model
was one of the better models fitted of the
in this chapter.) The
following
individual travel cost demand functions:
the
semi-log
various
56
(15)
ln(TRPSCAP)ij = -2.693 - 0.02175 RTC1j +
(-4.44)
0.00004939 SSFE
(2.19)
n = 158
equation
less
than
counterpart
model,
(15),
one-half
in
R
= 0.131.
the travel cost coefficient
absolute
magnitude
in the traditional zone average
is
of
its
travel
cost
equation (1). This smaller travel cost coefficient
implies a value per trip of nearly $46, which is more than
twice that estimated from equation (1).
equation
amount
(15)
that there likely was
is
error
of
in the travel
costs
considerable
a
reported
respondents in the 1977 Oregon anglers survey,
when
some
trips
receiving
the
measurement
were made two or
questionnaire.
error,
three
Despite
this
than
the
by
especially
months
before
problem
of
the estimates of consumer surplus for
nine rivers were computed from equation (15),
Table 2.
with
One problem
as shown in
The total consumer surpluses in Table 2 are more
twice
those of Table 1,
which were
less
than
$5
million.
The
consumer
surplus by river in Table 2 was
also
fitted as a linearly homogeneous function of salmon catch.
For
traditional
following
homogeneous
estimates
of
consumer
surplus,
equations (16) and (17) represent the
function
and
double-log
the
linearly
function,
57
Table 2.
Estimated Net Economic Benefits and Catch for
Oregon Fresh-Water Salmon Sport Anglers in 1977,
Based Upon Individual Participation Rates Per
Cap it a
River
Estimated
Catch of
Salmon
Alsea
2,290
Clackamas
Gum-Martin
Traditional
Estimates of
Estimates of
Consumer Surplus Consumer Surplus
498,000
459,800
2,149
1,493,400
553, 300
13,172
3,896,500
3,347,300
573
190,600
78, 900
Deschutes
3,833
111,400
208,900
Rogue
8,864
641,600
557, 200
Umpqua
4,570
710,700
1,511, 500
14,222
3,255,000
3,980,100
Wilson
4,692
123,000
383,000
Total
54,365
10,920,300
11,080,000
Columbia
Coos
Willamette
$
58
respectively.
2
(16)
Cs
= 214.54 CTCH
j
n
9
= 0.674.
r
j
(6.08)
lnCS
= 7.1586 + 0.7387 1nCTCH
(2.10)
Since
-0.64,
the
n= 9
= 0.320.
r
j
j
(1.82)
the t-value is equal to (0.739-1.0) / 0.407 =
Hence, the hypothesis that
it is not significant.
coefficient equals one cannot be
Gum-Martin
rejected.
estimates of consumer surplus,
For
the
following
the
two equations were obtained:
2
GMC5
= 224.905 CTCH
n = 9
= 0.764.
r
j
j
(7. 32)
2
1nGMCS = 4.5849 + 1.0537 CTCH
j
n= 9
= 0.705.
r
j
(2.12)
(4.09)
Again, the t-value for testing whether the degree of
homogeneity
0.209;
is
therefore,
homogeneity
mentioned
is
0.258
equal to one is (1.054 - 1.0) /
=
the null hypothesis that the degree of
equal
to
one
earlier in the third
cannot
section,
be
rejected.
the
As
Gum-Martin
approach for estimating consumer surplus for each distance
zone
Here,
may be more accurate than the traditional
the
equations
(18)
and
(19)
show
approach.
a
better
statistical performance than equations (16) and (17).
59
Ocean Salmon Sport Fishing
There
were
211
individual
observations
used
to
generate 211 individual participation rates per capita, as
compared
capita
to only 47 zone average participation rates
per
Fitting the data to
the
the earlier section.
in
semi-log
model for ocean salmon
the
angling,
following
demand equation is obtained:
ln(TRPSCAP)
ii
= -2.836 -0.01153 RTC
+
ii
(-9.25)
0.00006909 SSFE
ii
(3.62)
2
n = 211
When
fishing
the variable SSFE,
and
related
steelbead fishing,
R
the replacement
equipment
was deleted,
= 0.327.
used
value
salmon
for
of
and
then the demand equation
was the following:
ln(TRPSCAP)
-
ii
= -2.6910 - 0.01169 RTC
(-9.12)
2
211
r
= 0.285.
Equation (21) thus can be compared with equation (2)
that was based upon the zone average approach. Just as for
fresh-water fishing, the absolute value of the travel cost
coefficient in (21) is smaller than the absolute magnitude
of
the travel cost coefficient for the zone average model
of
equation
(2).
This smaller
absolute
value
implies
60
higher
net
Based
economic benefits for ocean
the traditional and Gum-Martin
upon equation (21),
estimates
of
consumer
anglers.
salmon
surplus
were
and
$19,624,900
$21,647,400,
respectively. An average Gum-Martin consumer
surplus
trip of approximately $86
either
the
per
computed
by
dividing the total Gum-Martin consumer surplus
by
total
ocean
was
salmon fishing trips of 252,950
or
by
taking the reciprocal of the travel cost coefficient (i.e.
1
/ 0.01169).
One limitation of benefit estimates
based
the
upon (21) arises because of measurement error bias in
travel cost coefficient,
the
preceding
However,
section
for the same reason mentioned in
for fresh-water
angling.
salmon
a discussion of the pros and cons of the various
estimates will be presented later in the next chapter.
Estimated Unadjusted Individual Travel Cost Demand
With the unadjusted individual observation approach,
each
individual observation is utilized in the regression
without adjusting them to a per capita basis.
for
using
defended
Two reasons
by its advocates.
they think
First,
often
are
unadjusted individual observations
averaging
eliminates much of the natural variation in the data, thus
providing
a
statistical
misleading
precision.
appearance
(It
has
of
improvement
been questioned
as
in
to
2
whether
R
is a satisfactory yardstick
of
performance.
61
See,
for
example,
questioned
1974.)
Vicicerman,
they
Second,
are
the validity of assuming observed anglers
representative
of the entire population from whence
came
dividing
-- i.e.,
of trips
number
by
they
total
the
population of the zone.
Fresh-Water Salmon Sport Fishing
The
unadjusted
observations
procedure
uses
data points and regresses
as
adjusting the dependent variable.
following
each
158
the
of
without
them
Using this method,
the
better
semi-log model was chosen as one of the
models:
(22)
ln(TRPS)
+ 0.00010 SSFE
= 1.17 - 0.011 RTC
j
j
j
(11.68) (-3.23)
(3.09)
2
n = 158
R
= 0.110.
The dependent variable denotes the observed
trips
of
the
independent
jth
individual
variables
are
fishing
the
and
observation,
defined the same as
the
for
earlier sections. It should be noted that in (22) there is
only
one subscript for
each
observation.
TRPS
Hence,
3
indicates
person
the
took
number
of salmon fishing
trips
during the three month period in
person was contacted,
and it is used directly.
concept
zone,
of
traditional
distance
the
jth
which
the
Thus, the
which has been used
travel cost method,
in
has not been adopted
the
by
62
the unadjusted individual approach.
All
the
of
statistically
estimated
coefficients
but
significant,
in
magnitudes
the
coefficients
vary from previous estimates.
surplus
trip is valued at $61 using the
method
per
and
$91 using the Gum-Martin
(22)
are
of
the
consumer
The
traditional
while
the
total estimates of consumer surplus are approximately
$14
million
and $21 million,
method,
respectively.
The net economic
benefits computed from (22) are much higher than from
(1)
and
the
Brown,
(15).
individual's
capita
et
(1983) stated
al.,
that
if
participation rates is not adjusted to a per
then
basis,
coefficient
can
biased estimates of the travel
result because the procedure
would
cost
not
properly account for cases where a lower percentage of the
people
in
the
recreational
the
more distant
activity.
various
However,
approaches
individual
observation
individual
observation)
zones
(zone
per
participate
in
the
detailed discussions of
average
capita,
per
and
capita,
unadjusted
will be delayed until
the
next
chapter.
The
consumer
surplus
dependent
variable
and
Wildlife
as
per river was
Oregon Department
of
as
the
Fish
and
estimates of salmon catch by each river was used
the independent variable to obtain the
equations:
used
following
two
63
Cs
(23)
304.39 CTCH
=
= 9
= 0.774.
r
j
j
(7. 39 )
2
ln(CS)
(24)
= 5.128+ 1.02327 1nCTCH
j
= 0.705.
r
j
(2.44)
To
n= 9
test
(4.09)
he degree of homogeneity for
if
(23)
is
equal to one, (24) was used to compute t = (1.02327 - 1.0)
/
0.2501
0.O93.
=
relationship
Again,
the
However,
average
procedures
as
salmon
the value per fish is
than three tines the value per fish
zone
homogeneous
linearly
traditional consumer surplus and
of
catch cannot be rejected.
more
the
model
in
from
Following
the
same
except that
the
Gum-
(8).
for (23) and (24),
estimated
Martin consumer surplus was used, a marginal value of $469
per fish can be obtained. (The Gum-Martin consumer surplus
also
showed
a
linearly
homogeneous
relationship
with
salmon catch.)
Ocean Salmon Sport Fishing
Following
unadjusted
the
number
explanatory
the
same
procedure as
above,
individual observations were used
of
trjs
variables.
taken as
a
function
the
to
regress
of
various
The following semi-log model
judged to be the most indicative of the data:
211
was
64
ln(TRPS)
(25)
j
=0.7249 - 0.003418 RTC
(-4.42)
(10.23)
j
+
0.00006321 SSFE
(5.33)
2
fl = 211
= 0.193.
R
Based upon (2), an average consumer surplus of $217
and
per trip was calculated using the traditional method,
an
average value o
$293 per trip was computed
using
by
The total estimates of
consumer
surplus using the tiaditiona1 and the Gum-Martin
approach
the
are
Gum-Martin
around
estimates
$55
method.
and
of
million,
These
respectively.
are highr than those estimates using the other
estimating approach.
and
$74
Since the "true" values are
unknown
there are differences of opinion about the evaluation
the
various
benefit estimates,
it
was
decided
to
present an eva1uatin of the various estimates in the next
chapter.
has been recognized that measurement errors
It
an important problem in estimating the travel cost
model.
In
errors,
especially
discussed.
than
the next chapter,
Also,
traditional
discussed.
in
the problem of
reported
travel
are
demand
measurement
cost,
will
be
some modified travel cost methods other
trave1
cost
method
will
be
briefly
65
IV.
DISCUSSION ANDAPPRAISAL OF SEVERAL VERSIONS OF THE
TRAVEL COST METHOD
Before
activity,
estimating
researchers
the
must
demand for
choose
a
recreational
one
appropriate
evaluation method along various evaluation methods to meet
their
requirements.
such as
After an evaluation method,
the travel cost metl!od,
has been chosen, another question
arises. Like most other equivalent economic exercises, the
essential
question is whether to use an aggregated
disaggregated
versions
and
approach
In this chapter,
of the travel cost method,
disaggregate
a
different
based upon aggregate
will
approaches,
the
or
be
and
appraised
discussed.
The travel cost method is an "indirect" method, that
is,
it
does
directly
about
However,
the
problems.
One
not depend upon asking
their
willingness to
the
pay
recreationists
or
to
sell
travel, cost method does suffer from several
problem
encountered
with
the
travel cost method is the long length of time between
the
recreational
trips
of
the
questionnaire,
leading to problems of recall error
This
chapter
sometimes
and
the
completion
will discuss the problem of measurement errors in
reported travel cos1s, and present possible solutions.
66
Individual Oservatjons Versus Zonal Averages
The
estimatin of outdoor recreational benefits has
been traditionally 1ased upon average participation
and
travel
example,
Clawson,
Castle,
one
costs for various distance
reason
laborious
to Prais and Aitchison (1954),
to use grouped observations is to
numerical
observations,
for
(see,
1959, Knetsch, 1963; Brown, Singh, and
According
1964).
zones
rates
treatment
another
reason
keep
to
the
individual
the
of
is
avoid
data
the
confidential. Besides these two reasons given by Prais and
Aitchison,
outdoor
one even more important reason to estimate the
recreation
demand from grouped
observations
is
when it is difficult to obtain accurate measurements.
However,
substantial
some
gains
recreational
researchers
in
efficiency in
estimating
observations instead of zone
and Nawas,
1973;
et
Gum and Martin,
using
(Brown
More recently,
(1983) expressed concern about the use
al.
unadjusted individual observations.
if
averages
1975).
that
outdoor
demand functions could be obtained by
individual
Brown
suggested
have
individual
observations
are
of
They have argued that
to
be
each
used,
observation on participation rates should be adjusted to a
per
capita
variable
biased
is
basis.
They
stated that
if
the
not adjusted to a per capita basis,
estimate
of the travel cost coefficient
dependent
then
will
be
67
obtained because the procedure would not properly
for
account
the lower percentage of the people who come from more
distant
zones to participate in the outdoor
recreational
activity.
Nevertheless,
several criticisms have been advanced
concerning the preceding argument.
One criticism was that
there is no theoretical reason for expecting a decline
percentage
participation
from
the more
distant
in
zones.
Furthermore, no empi!rical analysis was presented to show a
percentage
zones.
participation
Therefore,
investigate
ne
possible
decline from the
distant
more
objective of this section
reasons
for
participation from more distant zones.
expecting
is
declining
A second objective
is to estimate the impact of increasing distance upon
participation
to
the
rates for ocean salmon sport fishing and to
assess its effect uppn consumer surplus estimates. A third
objective
is to show that estimates of demand based
upon
unadjusted individual observations can be used to properly
compute
consumer suz plus if such estimates of demand
corrected
by
relationship.
be
a
a
distance
and
participation
This correction procedure will be shown
reasonable
individual
separate
to
of
the
to a per capita basis or to
the
alternative to the
observations
are
adjustment
traditional zone average travel cost model.
68
Reasons for DeclininH9 Participation Rates
possible
One
percentage
more
reason
participation rates for the population of
distant zones'is the following.
demand
declining
explain
to
individual
the
If
the
functions in all distance zones were symmetrically
distributed
then
demand
about some population mean
only
those
distributed
above
with
individuals
demand
functions
demand
mean
the population
function,
function
would participate fzom those zones that were more than the
average
distance
estimation
demand
of
with
the
Since
from the recreational site.
individual
unadjusted
observations would not reflect the declining percentage of
participants,
an
underestimate
of
cost
travel
the
coefficient will be incurred.
clarify
To
and illustrate the
demand
functions
remarks,
Suppose that the true
consider the following simple case.
individual
preceding
for
a
given
recreational
activity is
(26)
6 - l.O PC
q
i
where
denotes
a
+ a
i
i
a random
"intensity"
variable
which
1
represents the difference in intensity of preference among
the various recreatjonjsts.
If E(a ) = 0,
then the
mean
1
individual
demand function would be E(q ) = 6 - 1.0
i
TC
I
is not an error term, but
(It is important to note that a
1
rather
is
a
varible
that denotes
the
difference
in
69
intensity or strength of demand for recreational
activity
among
discrete
various
individuals.) Suppose
a
is
a
1
variable
takes certain values that are
that
distributed
symmetrically about zero with the following probabilities.
E(a
)
= (1/16) fl(-4)+4(-2)+6(0)+4(2)+].(4)} = 0
i
The variance of a
would then be
2
i
V(a
)
2
i2
2
+4(2) +1(4)
The
2
= (1/16) {l(-4) +4(-2) +6(0)
= E(a -0)
I
2
= (1/16) {64)
}
4
same
implied by (27) is the
distribution of a
1
as the distribution of the sum that could be obtained from
flipping
four
unbiased
coins
where
a
tail
would
be
assigned a value of -1.0 and a head a value of +1.0. Thus,
the
probability
would
equal to a sum of -4,
a sum of +4.
be 1/16 of obtaining
four
tails
and similarly for four heads giving
The probability of obtaining three tails and
one head equal to a sum of -2 would be 4/16, with the same
probability for three heads and one tail,
+2.
Finally,
the
giving a sum of
probability of obtaining
exactly
two
heads and two tails with zero sum is 6/16.
With
(26),
the assumed true individual demand function of
then consider the simplest possible travel cost and
distance
zone data as shown in Table
3,
from
generated
equations (26) and (27). For distance zone 1, the expected
number of trips per recreationist is E(q ) = 6_1.0*1+0
5,
1
but
some
recreatjonjsts
take more and some
take
less,
depending upon their intensity of demand, that is their a
1
70
Table 3.
Observations Generated for Three Distance Zones
Where the True Individual Demand Functions Are
Assumed to Be q =6-1.OTC +a
E(a )(1/16)
ii
i
,
i
{i(-4)4(-2)+6(0)4(2)-i-l(4) }
*
Main
Distance
Zone
Population
Intensity
of
Demand
Average
TC
per
visit
(a)
(q)
i
-4
-2
1,600
2
3,200
6,400
0
2
1
1
3
5
7
4
1
9
1
100
1,200
3,000
2,800
900
-4
-2
0
0
2
0
0
4
8
12
8
4
4
4
4
4
4
6
2
-4
-2
7
7
0
7
7
7
0
0
0
4
16
24
16
4
0
2
4
*
i
1
1
1
2
3
Number Total Zone
Total
Mean
of
Visits
#
per
Visits
Respon- of
visits
per
partic- dents
ipant
capita
$
2
1
3
1
4
6
4
2,400
3,200
1,200
0
0
0
5.0
2.125
0.4375
1,600
1,200
Assuming a random sampling of one percent from the
general population and corresponding expansion factor
of 100.
71
value.
For example,
corresponds to a
the first line of numbers in Table 3
= -4;
per
the number of visits
hence,
1
participant
Note that the
= 6-1+(-4) = 1.
is equal to q
1
obtained based upon the binomial
number of respondents is
Since there is only one respondent for a
distribution.
=
1
total number of visits would be
the
-4,
total
number
of visits are equal to q
(i.e., the
100
number
times
of
1
respondents and then times the sample blow-up factor). For
the second line of numbers in Table 3, corresponding to a
1
-2,
=
The estimated total number
of
be 3 times 4 times the expansion factor
of
= 6-1+(-2) = 3.
q
2
visits
would
100 equals 1,200.
The other numbers were generated in the
same way.
should
It
assigned
q
.
be
noted
that
zero
would
trips
to those respondents who have negative
be
zero
or
For example, the respondents in the first line of zone
1
2 with a
= -4 would have q
i
would
be
indicated
respondents
increase.
= 6-4-4 = -2, and
zero trips
I
will
by
take
(Actually,
such
zero trips as
this
more
Thus,
respondents.
travel
the
is one of the driving
costs
forces
behind the travel cost method.)
Fitting
cost
model
observation
obtained:
the
data in Table 3 to the
based
approach,
upon
the
the
linear
unadjusted
following
OLS
travel
individual
equation
is
72
(29)
n = 58
= 5.5521 - 0.5985 TC
= 0.501.
ii
(14.42)
(-7.50)
Computing the traditional consumer surplus from (29)
an average consumer surplus per participating
for zone 1,
recreatjonjst
$20.50
in
about $20.50 is
of
Multiplying
obtained.
recreationists
by the assumed 1,600 participating
zone 1 yields an estimated total consumer surplus
zone 1 of about $32,800.
for
Following the same procedure for
zone 2 gives $8.33 * 2,200 = $18,326,
and $1.55 * 2,000 =
$3,100 for zone 3. Thus, a total consumer surplus of about
$54,226
from
unadjusted
the
observation
individual
approach is obtained.
= 6-
Based upon the assumed true demand function, q
1
l.OTC
+ a
i
computed.
true
the true individual consumer surplus can be
,
i
For the first line of numbers in Table
demand function is q
= 2 - TC
1
,
3,
the
represents
and it
i
one actual participant. The consumer surplus is then equal
2
to
(1)
1(2
* 1) = 0.5.
(The formula for computing
the
consumer surplus from a linear travel cost demand function
2
can
be
shown
be
to
CS
(q
=
i
)
*
1(2
coefficient
)).
multiplying
the expansion factor of 100,
Expanding
surplus of $50 is obtained.
surplus
computing
of
$1,800
2
for
the
rest
this
consumer
.
cost
Similarly,
surplus
by
a true consumer
a total
for the second line
= 4-TC
from q
travel
I
consumer
obtained
is
Following the same
by
procedure
i
of the lines in
Table
3,
a
total
true
73
consumer
surplus
unadjusted
the
obtained
the
Thus,
overestimates
I
consumer surplus by about 42 percent (54,226
1.42).
Of
that
is
individual observation approach
true
38,200
$38,200
of
course,
if distances and travel costs are
percentage
the
participation rates
the
for
distant zones decline more rapidly than the case in
such
more
Table
3, then an even greater overestimation of consumer surplus
could
result
from the unadjusted individual
observation
approach.
It is interesting to compare the error in estimating
consumer
with
surplus from the unadjusted individual
that from the traditional zone average
Using
model.
the
approach
travel
zone average visits per capita as
cost
the
dependent variable, the following zone average travel cost
estimate of the demand function is obtained:
(30)
=3
= 5.5625 - 0.7604 TC
q
= 0.978.
1
(10.38)
Using
surpluses
$13,376,
(30),
(-6.66)
the traditional estimate
for zone 1,
and $243,
zone 2,
and zone 3,
respectively.
of
consumer
are $24,256,
Thus, a total consumer
surplus
of about $37,875 would be estimated by
the
zone
average
travel
the
true
cost
model,
consumer surplus of $38,200.
fairly close
to
In other words, the error of
estimation is only about one percent, much better than the
42
percent error in the unadjusted individual observation
74
approach.
The
results from Table 3 illustrates the fact
estimates
of
individual
observation
consumer
overestimated,
percentage
surplus
approach
from
can
that
unadjusted
the
substantially
be
when there is a significant decline in the
participation rates of the more distant zones.
It should be noted that if one can assume that there is no
variation
the
in
participants,
i e
,
intensity
demand
of
then the unadjusted
= 0 in (26),
a
the
among
1
observation
function.
approach
However,
will
this
assumption
may
demand
true
approximate, the
very
be
not
realistic since one can always find great variation in the
quantities taken by individuals with similar travel costs.
Although the above example in Table 3 is enlightening,
an
empirical analysis by using actual data seems to be needed
to
obtain a better idea of the actual magnitude
that
could
be
incurred
by
the
unadjusted
bias
of
individual
observation approach.
Effect of Distance UEon Particiation Rate in.
Ocean Salmon Fishing
It
is hypothesized that a larger percentage of
the
population would participate in ocean salmon sport fishing
from
nearby
population
distance
would
zones and a
participate
lower
from more
percentage
distant
of
zones.
75
Thus,
the
would
null hypothesis to be tested is that
have
no
Participation
effect
rate
the
upon
distance
participation
is defined as the proportion
rate.
the
of
population who actually fished for ocean salmon during the
survey year. This participation rate is then fitted by OLS
regression
as a function of measured round-trip
distance
from the zone of origin to the ocean port:
ln(y
(31)
)
= -1.9818 - 0.003806 DIST
ii
(-23.86)
(-12.60)
2
n = 211
The
r
= 0.432.
participation rate is denoted by y
which
is
ii
computed
family
observation
divided
zone.
by multiplying the number of anglers in the ijth
by
by the sample blow
up
its share of the population in
DIST
then
factor,
its
distance
is the measured round-trip distance from the
ii
ith
family
observation's
destination port j.
city
of
In equation (31),
residence
to
the
the large negative
value of t = -12.60 indicates that increasing distance had
an
extremely strong negative effect on the
rate
there
for ocean salmon fishing.
were
no
It should be
other independent variables
participation
noted
that
had
that
significant effect upon participation rate when DIST
was
ii
included in the equation. For example, the income variable
had
an unexpected negative sign with t = -1.09,
salmon-steelhead
variable
had
fishing
t = 0.29.
equipment
No matter
replacement
which
and
the
value
explanatory
76
variables
were
included in (31),
remained
DIST
only
1J
significant
with a stable coefficient and
distance
important
by far the most
is
absolute
Thus, it is clear that
value of t always greater than 12.
measured
with
factor
affecting the participation rate.
One
obvious
decreasing
way
to
with
cope
problem
the
participation rates is to adjust the dependent
variable
by
sample
the
blow
up
shared
and
factor
population of each individual observation. (Brown et
1983).
of
this
problem
from correspondence between Professors
William
However,
developed
al.,
way
another
to
solve
G. Brown and Kenneth E. McConnell. They concluded that the
probability of whether or not to participate must also
be
considered if an unadjusted individual observation type of
model is to be used. To scrutinize this idea, first denote
the expected number of trips per capita, TRPSCAP
,
as
ii
TRPSCAP
(32)
ii
ii
ii
* BLF
= (NA
where y
ii
anglers, NA
)/NA
* TRPS
= (y
)
ii
ij
I
POP
ii
,
denotes the number of
ii
times the blow up factor BLF
ij
by
shared
,
then divided
13
population POP
i
,
.e.,
the
probability
of
ij
participation as defined for equ ation (31); TRPS
denotes
ii
the reported number of trips by the ijth respondent. Since
both
and TRPS
y
ii
are greatly affected by travel
ii
or distance, (32) can be further expressed as:
(33)
TRPSCAP
* TRPS
= (y
ii
)/NA
ii
= f(DIST
)
ii
ii
* g(DIST
).
ii
costs
77
Therefore,
the
computation
of
consumer
cannot validly be obtained by integrating TRPS
y
1]
surplus
only when
is also a function of distance as shown in (33).
13
To
be
see if a valid estimate of consumer surplus
obtained
based upon (32),
can
individual
the unadjusted
data is fitted yielding the following linear equation:
) =0.9288 - 0.001318 DIST
ln(TRPS
13
13
(11.41)
(-4.45)
n = 211
r
2
In
(34),
DIST
= 0.087.
denotes the two-way distance
from
ij
the ith anglers city of residence to the jth port,
while
TRPS
trips
denotes the number of ocean salmon
fishing
ii
reported
valid
by the ith respondent to the jth port.
estimate
integrating
of
the
consumer surplus can be
product
of
equations
Thus,
obtained
and
(31)
by
(34),
divided by the number of anglers:
TRPSCAP
* TRPS
(y
ii
ii
)/NA
ii
ii
-0.005125
= (0.34889e
)/NA
ij
Integrating
trips
per
equation (35) based upon
capita,
corresponding
the
Gum-Martin
the
observed
consumer
surplus
to each of the 211 individual
observations
was obtained. Multiplying each individual consumer surplus
by
its
values
share
summing
all
these
gave a total estimate of consumer surplus of about
$13.56 million.
cents
of the population and
per
mile
(An average reported travel cost of
has
been
used
here,
based
upon
27.5
the
78
following linearly homogeneous function:
RTC
= 0.2747 DIST
ii
211
= 0.817,
r
ii
(30.63)
where RTC
is defined as revised travel costs.)
ii
the
If
effect of distance upon
rates is ignored,
i.e.,
participation
the
term in (32) and (33)
if the y
ii
is
deleted
approach
total
and
the
unadjusted
used to estimate consumer
is
Gum-Martin
observation
individual
surplus,
consumer surplus of $52.71
then
million
is
obtained.
It
is
estimates
average
also interesting to compute and compare
of consumer surplus from the
traditional
the
zone
travel cost model and the individual observations
adjusted
to a per capita approach.
Fitting
the
average
number of trips per capita per distance zone as a function
of measured distance yields
ln(TRPSCAP
)
= -2.0280 - 0.005452 DIST
ij
(-9.71)
(-7.49)
n47
Based
upon
(37),
2
r
an average
=0.555.
Gum-Martin
consumer
surplus of about $52 per trip and a total consumer surplus
of
that
about $13.16 million is obtained.
the
(It should be noted
cost per mile is about 28 cents
for
the
zone
average travel cost model.)
Consumer
adjusted
surplus can also be computed by using
individual
observations approach.
Fitting
the
the
79
individual
trips
per capita as a
function
measured
distance, the following equation is obtained,
1n(TRPSCAP
(38)
)
= -2.2755 - 0.005161 DIST
1)
(-20.01)
(-12.48)
2
n = 211
= 0.427.
r
Based upon (38), a total Gum-Martin consumer surplus
of
$13.46
million
with
is estimated,
corresponding
a
estimate of $53 per trip.
These
four different estimates of consumer
are shown in Table 4.
are
very
surplus
The last three estimates in Table 4
close to each other,
which is
an
interesting
reult considering that different definitions and equations
were used for those three estimates. By contrast, however,
the
unadjusted
estimate
Martin
individual observation approach
gave
of about four times that of the other three Gumconsumer
surplus
comparison
The
estimates.
various estimates of consumer surplus as shown in Table
has
thus
consumer
several
implications.
First,
surplus
based
upon
individual
observations
reliable.
Second,
solely
approach
the
if
participation
valid
consumer
observations
estimates
can
must
lead
to
considered
be
unadjusted
Third,
incorrect
4
unadjusted
the
individual
then the probability
be linked with it to
surplus.
of
the estimate of
cannot
observation approach should be used,
of
an
estimate
using
consumer
a
individual
surplus
unless they are adjusted to a per capita basis,
80
Table 4.
Estimated Consumer Surplus to Ocean Salmon Sport
Anglers of Oregon, Based Upon Four Different
Methods of Estimation
Method
of
Estimation
(1) Estimated
(2) Estimated (3) Estimated
Total GumConsumer
Total TradiMartin Consumer tional ConSurplus Per
Surplus
Trip from(l)
sumer Surplus
(Ulo)
$ millions
$ millions
$
Unadjusted
Individual
Observations
Approach,
Equation(34)
52.71
38.48
208
UlO Approach
with Probability of
Participation
Rates Included,
Equation(35)
13.56
13.52
54
Traditional
Zone Average
Travel Cost
Model,
Equation(37)
13.16
14.50
52
13.46
12.35
53
Individual
Observations
Adjusted to a
Per Capita
Basis,
Equation ( 38)
81
just as for the zone average travel cost
if
model.
However,
all
there are equal percentages of participation from
distance
then
zones,
not
individual observations would
need to be adjusted.
Measurement Errors in Travel Cost Variable
As
mentioned earlier,
estimating
one advantage of
consumer surplus by using individual observations is
there
that
the
is no averaging of the data which would reduce
informational
content of the basic data set.
corresponding
disadvantage
However,
using
of
individual
observations is that if there is appreciable error in
the
reported travel costs, then a bias in the estimated travel
will
coefficient
cost
"measurement
be
error" problem
caused,
(Kmenta,
the
well-known
1971,
pp.3O7-322;
Johnston, 1972, pp.281-291).
On the other hand, the averaging together of several
observations
one
is
method
that can
associated with measurement error.
using
aggregate
averaged
out,
reduced
and
estimate
should
data,
reduce
The reason is that
in which the wide variations
the variance due to measurement
the
the
resulting
travel
cost
error
by
are
is
coefficient
have much less bias than from using
individual observations (Brown,
bias
the
et al., 1983). Therefore,
though the zone average method does not have the advantage
82
of
disaggregated models in being able to investigate
the
actual behavioral patterns of individuals, it does help to
mitigate the bias from measurement errors.
section
This
measurement
empirical
will show the
effects
of
comparing
errors existing in travel costs by
the results based upon different methods of estimation and
from
the use of the instrumental variable method to solve
this problem.
Sources and Consequences of Measurement Errors
There are two possible sources of measurement errors
in
the travel cost demand model:
dependent
variable,
i.e.,
the
the
one source is from
number
of
recreational
trips; the other source is from the explanatory variables,
i.e.,
the
it is well known that a random error term
However,
to
the
travel costs and other socio-economic factors.
dependent variable will not cause a bias
regression
coefficient
estimates.
Therefore,
important to investigate the measurement errors of
costs
affects
only,
the
because
only
the travel
consumer surplus
cost
estimates.
added
the
in
it
is
travel
coefficient
Travel
costs
represent a summation of many smaller costs, some of which
may not be obvious to the recreationists, such as the wear
on tires, and some of these costs are not actually imposed
83
on
the recreatjonjsts at the time when the recreation
consumed.
is
several
Neuburger (1971) stated that there are
reasons why people might fail to correctly consider costs:
1) the costs might be so small that it is not worth taking
account of them, 2) certain variable costs may be regarded
wrongly as fixed costs, 3) the respondent may be unware of
the connection between a particular activity and the costs
to which it gives rise.
addjtjton
In
to the above sources
measurement
of
errors for travel costs, it is believed that a substantial
error
in
reporting trip expenses is very likely
to
list their expenditures spent on fishing
trips
they
which may have been taken two or three months before
received
their
"recall error".
very
questionnaires.
about
especially
when
so-called
the
is
found
(In fact, Hiett and Worrall (1977)
substantial
questioned
This
recall
errors by marine
and
their fish catch
questioned
when
anglers
effort,
fishing
more than two
the
were
because the respondents
1977 Oregon anglers survey,
asked
in
after
months
their fishing trip.)
there
If
travel
the
are errors of measurement in
cost variable, then the true error term in the travel cost
demand
model will not be independent of the
variable.
following.
This
Assume
statement
the
can
be
relationship
travel
proved
between
as
in
the
variables is as equation (39) which retains all the
cost,
the
true
basic
84
assumptions
classical normal
the
of
regression
linear
model:
TRIP =b +b TC +u
(39)
0
i
where
TRIP
1
i
1
denotes
participation
the
rate
of
ith
1
individual,
TC
denotes the true travel cost for the
ith
1
individual. Suppose instead of using true travel cost TC
1
the observed travel cost tc
i
where v
1
=TC +v
tc
(40)
I
is used:
I
is a random variable representing the measurement
1
errors
in tc
The equation with the actual observations
.
1
is
TRIP =b +b tc +w
(41)
0
i
where w
w
= u
1
1
1
a
v . Assume u '-s (O,6), v
- b
ii
ii
6w). Also,
-'(0,
-i_'(O,Gv) and
i
I
assume that the u's, v's, and w's are
1
serially
Independent.
and w
tc
i
(42)
,
between
To check the relationship
their covariance is expressed as
I
Cov(tc ,w
ii
)
= E ((tc -E(tc ))(w -E(w ))}
i
= E((TC +v -TC
i
i
)
I
i
I
1
w } = E{v (u -b v )}
i
i
1
ii
-b óv 4 0
1
This means that the least squares estimator of b
in
(41)
1
is inconsistent.
Moreover,
when
there are measurement errors in the
travel cost, the estimate of the slope b , i.e., the travel
1
cost coefficient, will have a downward bias. It can easily
be shown
(e.g.,
Johnston,
1972,
p.282;
Koutsoyiannis,
1977, p.263) that the probability limit of b
is
1
85
I
A
(43)
plim(b ) =
1
2.
2.
1 + (
2.
where
the variance of
is
measurement
and
errors,
2.
6
is the variance of the true values of travel cost.
2.
Since
(
(5y I t5.) >
2.
0,
which implies pliin(b
< b ,
)
1
b
OLS
the
also
It
measurement
zonal
cost
6
from
by
the
travel
approach used in the traditional
This
model.
to
bias
foLlows from (43) that the
error would be substantially reduced
averaging
equal
consumer
causing a corresponding overestimate of
surplus.
and
1
1
thereby
1
b ,
underestimates the true coefficient
mean
is
Gv in (43) will be reduced
in
is because the variance of a
2.
In,
and hence
2.
the
zonal
average travel cost
essentially unchanged.
model
while 6-ic remains
A
Therefore,
plim(b ) would tend to
1
b
for travel cost model with zonal averages as the number
1
of observations per zone average becomes large.
The Instrumental Variable Approach
From
when
the
that
above discussion it should be clear
there are measurement errors in the observed
travel
OLS estimates of the parameters are no
longer
cost,
the
unbiased
and consistent.
generate
better estimates should be considered.
various
Thus,
using other
methods
to
Although
solutions have been suggested for the problem
of
86
measurement errors (see, for example, Koutsoyiannis, 1977,
pp.
265-274), a more practical procedure for dealing with
this problem is the method of instrumental variables.
use
of
instrumental
Reiersol (1941).
by
developed
first
variables was
The
He found that economic variables subject
to exact relationship were affected by measurement errors.
In
an
article
variables,
discussing
Sargan
findings:
use
the
produce
the OLS method is lilcely to
1)
may
be
obtained if measurement
reduced
somewhat,
variables
method
will produce
coefficients
even
apparent,
the
4)
use
the
3)
when
instrumental
consistent
estimates
errors
measurement
large
use of large numbers
be
can
errors
the
of
large
2) better
biases when there are :Large measurement errors,
results
useful
several
suggested
(1958)
instrumental
of
of
of
are
instrumental
variables may not improve the accuracy of the estimates.
Consider
simple
a
model Y
a+aX+w
=
example,
where w
1
X
and
I
=u -av due to a
I
ii
as
an
i
dependency between
then a procedure to overcome the problem
w ,
of
I
measurement errors
instrumental
regression,
will be as follows:
variable Z
x
values
0
first,
select an
i'4..
then use OLS to
;
+c Z +e
= c
i
estimated
ii
o
1
lii
;
using
finally,
from the previous
estimate
regression,
the
X ,
the
do
OLS
A
again for the regression,
= d +d X +f
Y
i
0
ii
.
Theoretically,
i
the instrumental variable Z should a) be independent of w;
b) have a large variance;
c) be highly correlated with X;
87
d)
have
one-way causality relation
a
used
instrumental variable for the
as
variable (RTc).
most appropriate for use in this study.
used
in
different
from
the above procedure,
previous
the
result were exactly the same.
estimating travel cost,
Although the
was
section
slightly
principle
its
to
and
Here, DIST will be used for
RTC, then RTC will be used in the
travel cost demand function.
a
cost
it is considered
procedure
as
travel
Because DIST possesses all the properties
desired of an instrumental variable,
be
the
In
X.
the measured round-trip distance (DIST)
previous section,
was
with
Fitting the travel cost
function of round-trip distance DIST for the
RTC
ocean
salmon zone average travel cost model
2
= 0 2837 DIST
RTC
n = 47
r
0.942
i
i
(27.28)
Then,
fitting
average trips per capita as a function
of
estimated travel cost RTCS the following semi-log equation
is obtained.
ln(TRPSCAP)
= -2.02803-0.01922 RTC
(-9.71) (-7.49)
2
a = 47
Equation
r
= 0.555.
(45) is to be compared with equation
(2),
the observed travel cost demand equation, for the absolute
value of the travel cost coefficient.
of
The absolute
the travel cost coefficient in (2) is indeed
lower
than
in (45),
value
slightly
showing a downward bias due to
the
88
the
zonal
measurement
because
but the bias is not too large
measurement error,
average
data
error,
as
can alleviate
problem
the
total
The
earlier.
discussed
of
estimates of consumer surplus based upon (2) and (45)
are
shown
two
Table
in
5.
The
difference
Gum-
based upon the
is only about 10 percent,
equations
these
between
Martin consumer surplus.
was
It
observations
that
earlier
deduced
individual
the
bias
larger
is likely to incur a
approach
than the zone averages approach if measurement errors
are
existing in the travel costs. Therefore, it is interesting
,
to fit the estimated travel cost RTC
in
the adjusted
individual observations demand function.
RTC
was
fitted
as
distance
a function of
reported
(Here,
in
earlier
equation (36)):
ln(TRPSCAP)
(46)
-2.2755-0.01879 RTC
ij
ij
(-20.01) (-12.48)
2
n = 211
Equation
(21).
of
A
also
= 0.427.
then can be compared
equation
with
large difference in the travel cost coefficients
two
these
substantial
cost.
(46)
r
equations
measurement
indicates
errors
the
in the
presence
observed
travel
The corresponding estimated consumer surpluses
shown
consumer
in
surplus
Table 5.
between
The
difference
(46) and
(21)
of
are
of
Gum-Martin
is
around
61
percent, much higher than the difference between equations
89
Table
5.
Variable
Used and
Equation
Estimated
Consumer Surplus to Ocean Salmon
Anglers of Oregon, Based Upon Observed Travel
Cost
Variable (TCV) and Its
Instrumental
Variable (IV), unit: $ million
Consumer Surplus
Based upon Zone
Average Approach
Gum-Martin Traditional
TCV
Equation
IV
Equation
Consumer Surplus
Based on Adjusted
Individual Method
Gum-Martin
Traditional
21.65
19.62
(21)
(21)
14.49
15.55
(2)
(2)
13.16
14.50
13.46
12.35
(45)
(45)
(46)
(46)
90
(45) and (2).
In
short,
based upon the results of
observed travel costs are used,
are
ignored,
then
the
i.e.,
Gum-Martin
Table
5,
if
measurement errors
surplus
consumer
estimated from adjusted individual observations were about
50 percent higher than the estimate from the zone averages
But if measurement errors are considered, i.e.,
approach.
then the difference of
the instrumental variable is used,
Gum-Martin
consumer
individual
about
2
percent.
in
observations
can
is
thus clear that
results between
and
adjusted
the
the
was
most
adjusted
of
only
the
individual
the zonal average model is due
to
the
from measurement errors in the travel cost variable
Furthermore,
of
It
between
and the zone averages
observations
difference
bias
surplus
the difference in consumer surplus from
use
individual observations per capita versus zone average
be
variable
essentially
approach,
eliminated
using
reported travel costs.
via
the
instrumental
measured distance in place
of
91
V. INCLUSION OF QUALITY VARIABLES IN THE TRAVEL COST MODEL
While
the traditional single site travel cost model
has been widely applied to outdoor recreation, it does not
provide
the
marginal value of a quality
change
of
the
site. In addition, this traditional travel cost model does
not
include
substitute
sites in the model
theory indicates should be included.
the
Furthermore, without
it is almost
marginal value for quality of the site,
impossible
to
make
critically
economic
as
incremental
important
decisions. And the consequence of omitting substitutes can
result in a biased estimate of the net economic
In
order to solve these two problems,
regional
method
two methods -- the
travel cost method and the hedonic
-- will
benefits.
travel
be discussed and applied to estimate
cost
the
demand for salmon sport fishing in Oregon.
Using Regional Travel Cost Models To Estimate The Benefits
From Fresh-Water Salmon Fishing
The travel cost method has been typically applied to
estimate
the
value of the particular sites
assuming
by
that all participants have the same opportunities to reach
all
substitute sites at the same cost.
important assumption,
and
Based
a single site model can be
substitutes are thus omitted from the
features
of
upon
this
formed,
analysis.
this technique have been criticized by
The
many
92
appplied
this
One of the criticisms is that
economists.
value
the
for
technique
only
site,
does not provide information about the marginal
it
estimates an all-or-none
value of quality changes in that site. The other criticism
is that this technique cannot justify whether to develop a
new
site
or
not.
criticism
another
addition,
In
is
associated with the omission of substitutes which causes a
Therefore, a method
biased estimate of economic benefits.
for predicting the demand curve for and value of a new
changed
recreation
limitations
the
site
presented next.
having
above
the
A construction and discussion
is needed.
so-called
without
travel
regional
cost
method
or
will
of
be
The other method, which uses a multi-site
technique, will be presented in a later section.
Regional Travel Cost Method
Although
related
to
the
regional travel cost
regional
economics,
both
method
is
emphasize
not
the
importance of the effect of spatial factors. However, some
of the underlying logic of the regional travel cost method
coincides
with
economics.
Therefore,
the
driving
it
original spatial theory,
1966)
model of land use,
travel cost method.
force
behind
regional
seems plausible to discuss the
the von ThUnen (see, e.g., Hall,
before presenting the
regional
93
Von
Thlinen considered the pattern of land use as
function of the different prices of agricultural goods and
of their different costs of production,
market
and distance to a
center as a significant determinant
introducing
location
independently
into economic theory,
effect
that were measurable.
there
relevant variables
other
was
By
only
cost
but
real-world
In order to assess the
of distance on systems of production,
assumed
he not
the theory of marginal
invented
also developed an economic model with specific
predictions
cost.
of
constant.
no variability in transport cost
von
He
Thiinen
assumed
except
that
imposed by distance; he assumed prices to be determined in
the
market center by the normal operation of
demand;
supply
and
and he assumed no barriers to trade or production
other than price and cost, and so forth
Under
these
monotonically
conditions,
transport
with distance from the market
rises
cost
center,
and
transportation is the major variable factor of production.
Increasing transport costs have the effect of lowering the
farm gate price of any good produced further away from the
market
center,
extra
(marginal)
inputs
of labor and capital in its production
Therefore,
the
lowering the return to
rational producers will intensify production near the
center and use land less intensively as they live
away from the center
the
travel
cost
further
Similarly, the driving force behind
method
is
that
recreationists
from
94
different
common
origins incur diffeient travel cost to reach
different
can be expected to participate at
site
a
rates.
Based
data
upon the revised travel cost method and
and
the 1977 angler survey and from the Oregon Fish
from
Wildlife
Department,
cost
the following regional travel
model was specified.
TRPSCAP
(47)
= f( DIST
,
FISH /DIST
ii
SSFE
,
TRPSCAP
distance
zone
denotes
ik
k
INC
ii
ii
where,
/DIST
, FISH
ij
j
trips per capita from the
origin to the jth
DIST
river;
ith
the
is
13
measured
of
one way distance from the main concentration
population in the ith distance zone to the nearest part of
the jth river. Quality of the jth river is approximated by
(FISH /DIST
),
where
ii
j
j
The effect of substitute
catch in 1977 for the jth river.
sites
represented
is
salmon
annual
denotes the
FISH
by
),
where
river,
and
(FISH /DIST
k
FISH
k
i]c
denotes
the
annual catch of the kth
denotes
the
measured
portion
of the kth river.
DIST
1k
all
one way distance
with
largest
value
for
and
the
nearest
selecting
(FISH /DIST
k
denotes
the
The kth river was chosen among
of the possible substitute rivers by
river
to
).
that
SSFE
ij
1k
average replacement value of salmon
related equipment in zone i to the jth river.
fishing
INC
13
represents the average income for ith distance zone to the
jth river.
95
The
above
shows distance
function
play
will
an
Just as
important role in the regional travel cost model.
distance triggered the development of von Thunen's thesis,
distance
travel
cost
cost
distance
the key for
constructing
regional
a
travel
Based upon the theory of the
model
distance
method,
negatively
has
also
is
related,
and fishing
implies that
which
demanded
are
increasing
the
trips
from the origin to the recreational fishing site
trips
the effect of lowering the quantity of fishing
taken. The coefficient of the quality variable is expected
to have a positive sign,
expected
fishing
trips
affected
by
replacement
negatively related to
be
to
while the substitute variable is
demanded.
distance.
These two
The
the
quantity
coefficients
both
are
variables
of
average
of
value of fishing equipment and average income
are expected to have a positive sign, according to general
economic
theory.
instrumental
It should be noted that distance is
variable for travel cost,
which
will
an
rise
monotonically with distance.
demand
Equation (47) specifies the trips per capita
function
this
one
for the fishing sites in a region.
equation,
one could
estimate
the
using
Thus,
particular
demand function for any existing recreational fishing site
in
this
region,
opportunities
no
matter whether the
have been changed or
not.
salmon
fishing
Moreover,
this
model is a good substitute for the contingent value method
96
to
estimate the value of a newly
site (or to decide if a new site is worthwhile to
fishing
develop).
fishing
opportunities,
and
and
newly
proposed
although a contingent
value
it is often
too
time-consuming.) By including quality
and
study could be conducted in such a case,
expensive
travel
that the traditional single site
(Note
method cannot estimate the value of
cost
recreational
developed
the
substitute variables in a regional travel cost model,
value
will
of fish will vary with site quality and
be
travel cost model.
to
the
predicted
too,
trips
simply
of
salmon
because
Therefore,
trip
be
the
quality of
the
then
hatcheries,
and economic benef.ts will be
improved.
can
is increased due
For example, if FISH
enhancement
model
traditional
the
theoretically sound than
more
the
fishing
increased
sites
is
the marginal value per fish or
per
course,
the
derived from this
model.
Of
counteracting effect from an increase of substitute
FISH
k
also can be estimated from this model.
Estimation of Regional Travel Cost Demand Model
Although several functional forms of regional travel
cost
models were fitted to the fresh-water salmon fishing
data
from the 1977 Oregon anglers survey,
equation
is
one
of
the
better
results,
statistical performance and prediction:
the
following
based
upon
97
1n(TRPSCAP)
(48)
-4.6081-0.02603
=
DIST
ii
(-1.92) (-3.19)
0.075
+1.912 (FIsH /DIST
-0.0007109 (FISH /DIST
)
ii
i
(1.32)
(-2. 78)
2
R
n = 38
In
because
= 0.448.
were
the INC and SSFE variables
equation (48),
included
not
being
both t values' were far from
statistically significant
Also, the quality variable with
of 0.075 had a better t value than with a power
power
There
1.0.
using
several other advantanges by
are
that a smaller sum
of
the
ii
j
is
of
. One
power of 0.075 for the quality variable, FISH /DIST
advantange
)
ik
Ic
squared
residuals
and
another
advantange is that a decreasing marginal consumer
surplus
about
the
regression
can
be
obtained,
per
fish results.
1.0
will have an increasing marginal consumer surplus per
fish,
which
However,
the
it
fishing
(The quality variable with a power
violates
the law
of
diminishing
return.)
should be noted that the power of 0.075
quality
variable is somewhat
of
for
than
smaller
originally expected.
Based upon (48), the consumer surplus for each river
computed
was
total
and is presented in Table 6.
Dividing
the
of
consumer
surplus by the total fresh-water salmon trips Of
230,280,
an
traditional
and Gum-Martin estimates
average consumer surplus per trip of $23.8 and
respectively,
was
obtained.
$23.7,
A marginal consumer surplus
98
Table 6. Estimated Net Economic Benefits for Oregon FreshWater Salmon Sport Anglers in 1977, Based upon
Regional Travel Cost Model
River
Traditional estimates
of consumer surplus
Gum-Martin estimates
of consumer surplus
Alsea
129, 300
236,600
Clackamas
529, 300
197, 000
1,701,430
1,637,810
135, 200
54,900
80, 070
107,470
Rogue
431, 320
304, 560
Umpqua
559, 940
790,470
1,856,160
1,929,150
61,900
191, 200
5,484, 620
5,449,160
Co lumbi a
Coos
Deschutes
Willamette
Wilson
Total
99
per
catch
fish of $30.9 for a projected increase in fish
of 100 in the Columbia river was obtained by assuming that
estimates
marginal consumer surplus per
(e.g.,
fish
in
for a projected increase of 3,000in fish catch
$27.6
the
of
Smaller
unchanged.
catch in other rivers remaining
fish
larger
Columbia river) were obtained for
projected
increase in fish catch.
Using exactly the same variables as in (48) but with
a different functional form, the following linear equation
was fitted,
(49)
TRPSCAP
0.007841-0.002433
=
DIST
ij
(-2.53)
(0 028)
0.075
+0.1423 (FISH /DIST
-0.00009138 (FISH /DIST
)
ij
j
)
k
ik
fell
far
(-3.02)
(0.831)
2
coefficient
The
of
= 0.342.
R
= 38
the constant term in (49)
of statistical significance with a t value of
short
0.028;
thus,
constant
the
term
was
only
and
deleted
the
following equation was obtained,
(50)
TRPSCAP
=
-0.002415
DIST
(-3.47)
0.075
+0.147 (FISH /DIST
j
- 0.00009149 (FISH /DIST
)
k
ij
(-3.10)
(6.87)
n38
Although
)
ik
2
R
=0.342.
the magnitude of the coefficients for
the
100
explanatory
variables
in
similar
are
(50)
the
to
coefficients for the corresponding variables in (49),
values in (50) are larger.
t
equal,
equation
(49).
Both
consumer
being
things
other
Thus,
all
(50) statistically performed better than
and
(49)
per
surplus
(50)
lower
total
regional
travel
slightly
but
fish
marginal
diminishing
have
estimates of consumer surplus than from (48).
Other
specifications of the above
cost
model were also fitted by OLS.
gave
good
example,
version
results
t
from
values
for
Those equations also
viewpoint.
statistical
a
the
(Bowes and Loomis,
Squares
Least
Generalized
given
1980) of the model
For
in
equation (50) were all significant with absolute values of
at least 4.0. Another specification tried was to use total
trips,
TTRPS
,
as
the dependent variable,
rather than
ii
(49), and (50), with the
trips per capita as used in (48),
explanatory
POP
,
variables multiplied by the zone
population,
following
The
corresponding to that observation.
1J
equation for this kind of model was fit by OLS:
(51)
TTRPS
= -0.001443 (DIST*POP)
ii
(-4.56)
0.075
+ 0.09122
(FISH /DIST
)
*pp
ii
j
(6.38)
- 0.00005637
)*POP
(FISH /DIST
ik
k
(-4.71)
n38
2
R
=0.132.
101
The Gum-Martin estimate of consumer surplus computed
from
(51) is about $6 9 million which is somewhat
than
computed
from
absolute
value
equation
(51) tends to be too small.
the
value
of
observations
and
(Pop)
of
coefficient
the
negative values for TTRPS.
observations,
large
that
those
for
population
of
coefficient
forcing the
predicting
of
large
For example, one of the actual
but the
had actual total trips at 9,998,
value of total trips was only about
coefficient
absolute
in
with large shared population at 295,800 and
distance at 63,
the
(DIST*POP)
The reason is
be quite small to avoid
to
predicted
the
with unusually larger values
distance (DIST),
(DIST*P0P)
of
becomes too
(DIsT*pop)
that
It should be noted
(48).
larger
value,
of (DIST*P0P) was 10 percent
then
predicted total
the
2,654.
If
larger
in
would
trips
become negative.
Furthermore,
distributed
since
around
heteroskedasticity
population
the
the
probably
exists
problem
the
site,
unevenly
is
(Bowes
and
of
Loomis,
1980). If the square root of the population is used as the
weighting
squares
equivalent
(Ibid,
of
factor,
then
estimates
of
resulting
"the
such
weighted
ordinary
least
observations
to generalized least square (GLS)
are
estimates."
p.468). But population rather than the square root
population was used in (51),
this
population
factor
thus resulted in another kind of heteroskedasticity. Since
102
none
of
cost
the above specifications of the regional
travel
all
other
model
clearly
seemed
specifications,
superior
to
based upon statistical considerations and
reasonableness of estimated net economic benefits, the Box
and Cox transformation procedure (Zarembka,
useful
be
1974) may
for the choice between different functional forms.
However, the procedure of choice of a functional form will
not be presented in this study.
One
noteworthy
from
interesting result
and
this
study was that the fishing quality variable, FISH /DIST
ii
always had more explanatory power when assigned a power of
0 075.
This
unexpectedly low
value
may
data.
In specifying the model,
has
be caused primarily by poor specification
been
included
explanatory
related
avoided,
then
is
only one quality variable
not
a
appropriate
very
If fish density and other quality-
variable
information
available,
may
which
and
for
each
fishing
specification
this
or at least mitigated.
stream
problem
This poor
could
were
be
specification
also explain why the marginal value per fish was only
about
case
25
percent of the average value per fish
of the Columbia
River)
(Similarly,
the
(in
the
marginal
values per fish were only about 25, 20, 40, and 20 percent
of the average values per fish for the Willamette, Utnpqua,
Rogue,
and
Deschutes rivers,
data used in this model,
respectively.) As for
the
recall errors by the respondents
103
in
the
1977
returned
Oregon angler survey and the
salmon-steelhead
are
tags
rate
low
probably
promising
cost
fairly
results were obtained from the regional
analysis.
values
possible
by
travel
more accurate estimates
of
per fish for specified streams might
be
Furthermore,
marginal
main
the
causes of inaccuracies in the data. Nevertheless,
of
combining the steelhead data from
the
1977
angler
survey
angling
data
(since
there were almost twice as many observations
from
with the fresh-water salmon
the steelhead anglers). similarly, it might be possible to
include the ocean salmon angling data with the fresh-water
salmon
an
in
extended regional
travel
cost
analysis.
However, such an extended analysis would require resources
beyond
those
available
for
the
completion
this
of
dissertation.
Use
of
the Hedonic Travel Cost Model
to
Vaule of Site Characteristics
Estimate
Since Hotelling-Clawson's travel cost method
the
yields
only the value of a given site in its current state, it is
not
helpful
in choosing between options that change
the
sites' recreational characteristics. Although the regional
travel cost method resolved this problem in a
usefulness
limited.
model,
and
The
completeness are
somewhat
sense,
its
theoretically
reason is that in the regional travel
cost
it is doubtful that changes in characteristics can
104
be related clearly to anglers' utility and welfare.
In
cost
the next section,
a modification of the
travel
method incorporates site characteristics to yield
hedonic
travel cost method,
which will be discussed
a
and.
empirically
applied to Oregon salmon sport fishing.
This
method
a
based
upon
has
sound
theoretical
framework
techniques used by Lancaster (1966), Griliches (1971), and
others
to
estimate the value of
qualitative
individual
characteristics.
Hedonic Travel Cost Method
The
direct
traditional approach states that goods are
objects of utility,
while Lancaster
hypothesized
that it is the properties or characteristics of the
from
which utility is derived.
consumption
is an activity in which goods are inputs
orderings are assumed to rank
characteristics
indirectly
For
only
to rank
a dinner party,
social setting,
intellectual
all
and
and
Utility or
collections
collection
f
of
goods
through the characteristics that they possess.
example,
hedonic)
goods
He thus could assume that
the output is a collection of characterisrics.
preference
the
a combination of meal
may possess nutritional,
characteristics.
This
approach has two fundamental
and
aesthetic,
and
characteristics
(or
propositions:
(1)
goods possess objective characteristics
relevant
to
105
the
choices which people make among different collections
of
(2) individuals differ in their
goods,
reactions
to
different characteristics, rather than in their assessment
of
the
characteristics
collections.
view
the
least
a
content
of
Using these two basic propositions,
relationship between people and
two-stage affair,
relationship
one can
things
it is composed
i.e.
goods
various
as
at
the
of
between things and their characteristics and
the relationship between characteristics and people.
This
approach can be illustrated by the
consumer's
choice problem under a regular budget constraint
Max U
(52)
v (Z)
s.t. Z = Bq
pq
where
the
problem
the
objective
function
v(Z)
of
the
optimizing
in the characteristics approach is a function
vector
constraint
q,
M,
of
characteristics
Z
The
regular
pq = M is a constraint on the vector of
of
budget
goods
on which p is the vector of prices facing the consumer
and M is his income
Z
and q are linked through the goods-
characteristics relationship Z = Bq, where B is the matrix
ef coefficients relating goods and characteristics
The
dual
problem of the above
will be as the following:
optimizing
problem
106
M = pq
Mm
s.t. v(Z) = U
Z = Bq.
A
cost
function
therefore
be
can
derived
this
from
problem as:
M = C (z, p)
also known
The derivative property of this cost function,
as
Shephard's
approach.
functions,
demand
price derivatives are the Hicksian
Its
this
to
is of central importance
Lemma,
p), while the derivative with respect to
h(Z,
J
b
C (Z, p)/
=
is
= b
Z
j
(z, p)
j
j
characteristic.
the shadow (or implicit) price of jth
This
price measures the marginal cost of a
small
public goods which have been valued by
using
shadow
increase in Z
3
Among
the
hedonic approach are the
(Anderson
1978),
and
Crocker,
climate (Hoch,
1971;
Harrison
section,
with
the
and
etc..
1981),
the hedonic approach will be
cost method and applied to
travel
Rubinfeld,
1974), noise level (Nelson, 1979),
and outdoor recreation activity (Morey,
this
pollution
air
followings:
In
incorporated
the
Oregon
salmon sport fishing activity.
Based upon Lancaster's version,
each
recreational
characteristics.
The
site
should
one can assume that
have
a
bundle
added expenditures for an
of
enhanced
107
bundle
extra
the
the
characteristics could reveal the value of
of
characteristics.
behind
This is the driving force
hedonic technique.
Therefore,
at
recreationists
a
given origin, by spending more travel costs and travelling
a
little further,
can possibly obtain a better bundle of
characteristics. In other words, individuals from the same
travelling different distance to
origin
sites
will
incur different travel costs
reach
different
with
different
objectively measured set of characteristics,
density,
is
water quality,
thus
possible,
such as fish
species variety and so forth. It
at least in theory,
the
to estimate
marginal cost (or implicit price) of added characteristics
for recreationists from a given origin.
To estimate the marginal cost of increasing a
amount
first
characteristic
of
to the recreationists
step of the hedonic travel cost
approach.
small
is
But
the
it
should be noted that the estimating procedure of this step
is
exactly
opposite
with the
traditional
travel
cost
method. The traditional travel cost technique uses a sitespecific
from
model
which
approach
which features one site and many
recreatjonjsts
come.
However,
the
origins
hedonic
holds one origin constant and computes the
cost
origin.
The
derivative of the cost function with respect to each
site
of
each
of
reaching
characteristic
all different sites from
thus
yields
that
the implicit price
characteristic for that origin.
108
Therefore, each origin will yield a different set of
implicit
prices for site
characteristics.
In
practice,
this step is done by running a set of regressions, one for
each origin,
costs
on characteristics,
i.e., regressing travel
for a given origin on characteristics of
sites.
Then,
imputed
coefficients of the regressors are the
the
of the characteristics for
prices
different
that
origin.
This step can be expressed in mathematical terms:
TC
=b0 +b Z
s
(56)
1
ls
+b Z
2
2s
+...+b jZ jS
denotes the travel cost from a given origin to a
where TC
S
given
site s,
is the level of the jth characteristic
Z
is
at
given
site
b
s,
is the imputed price
of
the
jth
J
The constant term b
characteristic for the given origin
0
may
represent
mean
the
value
omitted
the
of
characteristics
The
each
next
step is to derive the marginal
characteristic.
quantity
the
Regress
value
of
of
characteristics each recreationist enjoys on ths prices of
the characteristics obtained from the first step and other
factors
which
are
characteristics
characteristics.
estimated
This
determinants
is
the
of
demand
demand
for
function
for
A demand function for trips can also
be
by regressing the number of trips on the prices
of characteristics,
and other factors
expressed by two demand
functions:
This step can
be
109
= f (B
z
,
k
j]c
TRIPS
= g (B
,
k
Ic
where
R )
k
R )
k
is the vector of imputed prices faced by the kth
B
k
individual,
and
R
a vector
denotes
demand
other
of
Ic
determinants
denotes
TRIPS
for the kth individual.
the
k
number of trips for the kth individual.
The
compute
estimated
demand
the value of the site.
The consumer surplus
each
characteristic
level can be obtained
each
characteristic
demand equation,
implicit
price
each
consumer
taken
surplus
computing
by
the
Summing
up
the
consumer surplus
the value for the site is
per trip times total
for that site.
for
at
consumer surplus of each characteristic,
Then,
to
evaluated
individual faces.
per trip can be derived.
used
be
may
equations
In addition,
number
of
trips
the value of changing
travel costs or a characteristic at a particular site also
can be estimated.
Estimation of the Hedonic Travel Cost Demand Model
and
ocean
sport fishing data are combined together to
apply
with
site
Fresh-water
salmon
to
salmon
sport fishing
data
travel
cost
method
characteristics.
This
data set represents 158 individual
.the
incorporating
observations from fresh-water and 211 from ocean. However,
this
sample of 369 was further reduced to 290 because
of
110
the necessity of having a minimum number of responses from
a
given origin to run the
which
the
obtained.
from
be
can
characteristics
prices for
implicit
regression,
first-stage
a minimum number of 5 was arbitrarily
In fact,
assigned for a county (which represents the origin) to run
regression.
least
It turned out that only 14 counties had at
observations
5
traveled
that
sport
salmon
for
fishing.
Respondents
effort
their
the 1977 Oregon angler
in
success
reported
rate
fishing
This
survey.
is the only variable that
and
success
fishing
site
represents
quality in the model (other quality variables are riot easy
to
appropriately define,
sources).
fishing
Therefore,
distance
salmon
of
data
14 different implicit prices of the
success rate were obtained for 14
regression
first-stage
site
due to the limitation
used
the
The
counties.
reported
round
trip
from a given county to the given salmon
fishing
as the dependent variable and used reported
average
catch
per hour for the site
as
the
independent
variable. Thus, the implicit price, measured in miles, was
simply
the
linear
regression.
different
coefficient of the fishing success rate in
linear
These
regression
statistically satisfactory.
price
14
implicit
equations
prices
were
from
not
14
all
Among them, 5 of the implicit
coefficients had negative signs which violated
the
basic assumption that the quality characteristic increases
111
linearly
with
substituted
distance.
However,
negative implicit prices in
for
were
zero
values of
second
the
stage regression.
individual demand function for fishing
success
could then be estimated by regressing the rate of
fishing
The
Success
consumed by the individual on the implicit price,
reported
income,
One
trips
and reported number of
of
linear demand model fitted by OLS was:
= 0.1484
SE
(59)
0.002314 NT - 0.00002104 IP
k
k
k
(20.18)
(-2.10)
n = 290
R
(-2.67)
2
equation (59),
= 0.036.
success
denotes the fishing
SE
k
rate,
denotes
catch per hour, for the kth individual, NT
k
the
and
IP
the
kth
should be noted that the income variable
was
number of salmon trips during that quarter,
k
denotes
the
angler.
It
included
originally
However,
"in
discarding
is
implicit price of site quality for
the
and a t value of 0.8
classical
linear
interested
than
the
value
standard
theoretical
of its estimate (from given data) will decrease
1971,
making,
model,
regression
the mean square error of all the least squares
(Rao,
obtained.
an independent variable whose parameter
smaller (in magnitude) than the
deviation
was
he
p 38)
Besides,
"when
a
estimates"
researcher
in using the regression estimates in
wants the mean square error estimates
best linear unbiased estimates"
(Ibid,
is
decision
rather
p.39).
112
Therefore, the income variable was deleted from the model.
This demand for fishing success can be converted
to
demand for catch per trip by using a sample average of 6.8
hours
per
which
is
measured in miles,
(59).
If
this consumer surplus is evaluated at $0.1
mile,
then
upon
trip.
the
traditional
and
$197
per
based
method,
of
Applying the sample mean catch per trip
to the values per trip,
about
from
$103,
estimate
Gum-Martin
and
trip,
computed
thus can be
the values per trip are $77 and
respectively.
0.39
The average consumer surplus per
$264
average values per fish are
Gum-Martin
and
traditional
for
estimates.
The
corresponding
demand
function for
trips
was
estimated as follows,
NT
(60)
=
SE -0.004949
5.5094- 4.8713
k
PSAL
Ic
Ic
(9.54)
(-2.21)
(-1.56)
- 0.03433 PCON
Ic
(-2.73)
where
PSAL
n = 290
is the marginal price of success in
terms of
Ic
money for lcth person,
denotes the marginal price of
PCON
Ic
other
quality
variables in terms of money (the
constant
term in each of the first-stage regression represents
mean value of the omitted characteristics).
in
(60)
are defined the same as for
the
Other symbols
equation
(59).
It
seems reasonable that trips should vary inversely with the
price of success and other variables, but it is not at all
113
why
clear
rate
trips should fall as the fishing success
increases.
and (60) are two simultaneous demand equations
(59)
derived from the same utility function, and they represent
the
angler's
these
fishing
choice of salmon
two simultaneous equations were fitted
Simultaneous
Since
activity.
equation bias was suspected
by
OLS,
(Koutsoyiannis,
1977). Thus, other estimation methods should be applied to
obtain
unbjasdd and consistent
linear
models
estimates.
by
estimated
(59) and (60) were
of
Therefore,the
the
method of two-stage least squares (2SLS) and yielded,
= 0.2115 - 0.01845 NT - 0.00003172 IP
SE
k
Ic
(6.72)
NT
5.1991
=
n = 290.
(-2.74)
(-2.36)
- 2.2417
Ic
SE - 0.004758
(1.42)
(-0.73)
PSAL
Ic
Ic
(-1.51)
- O.03627PC0N
Ic
n = 290.
(-1.41)
Equation
surplus.
(61)
Based
can be used to measure the
upon the Gum-Martin method,
the
consumer
average
consumer surplus per trip is $68, and $175 per fish. These
results indicate that the estimated net economic
benefits
from the OLS equation may be overstated, at least compared
to 2SLS.
In summary,
the application of the hedonic approach
to Oregon salmon sport fishing was not very successful, at
least
for this study.
There are several possible reasons
114
that
application.
may explain the gap between theory and
First,
1977
the survey data
collected from the
used here was
which was primarily
Oregon angler survey,
designed
method
for the application of the traditional travel cost
rather
than
for
characteristics.
the hedonic method
site
incorporating
Thus, for example, the quality variables
the
based upon
for the various site were hard to define,
available data.
Second,
travel
some
method
cost
example,
it
linearly
with
is
not
because
from
some
the
unit
the
externalities
(e.g.
cost
of
a
But this is not a reasonable
richer
individuals may
enjoy
nearer
Besides,
sites.
of a characteristic can be
cost
For
increase
characteristics
that
so
hedonic
the
logical.
completely
that
is constant.
characteristics
constant
assumed
distance
characteristic
assumption,
are
of
assumptions
basic
true
congestion at the site,
only
the
if
and traffic
jams on the road) do not exist.
Third,
the data
for ocean fishing
and fresh-water
fishing were combined together for the hedonic travel cost
demand
but these two types of sport
model,
fishing
are
probably not homogeneous goods.
Last,
was noted
it
in chapter 4
likely for an indirect method,
cost
the
method,
process
that it is
such as the hedonic travel
to incur serious measurement errors
of
very
data gathering.
In
fact,
the
during
fishing
115
success rate,
may
have
data
fishing success divided by fishing
Using
been underestimated by the anglers.
from
the Oregon Department of
Fish
effort,
and
the
Wildlife,
average catch per trip would be about 0.7, which is almost
twice as much as the sample mean catch per trip. This fact
shows
that
data,
or both,
study
of testing three major data
about
marine
(1977)
be
the fishing success data,
effort
or fishing
may have serious measurement errors. In a
recreational
approaches
collection
fishing,
Hiett
and
Worrall
found that total effort and total catch should not
taken
from
considerable
a
household
tendency
survey
because
of
the
is
very
toward
bias.
This bias
likely from the recall errors.
Thus,
"such estimates (of
effort
and catch) should be obtained from
study ...'
(Ibid, p.22).
the
intercept
116
SUMMARY AND CONCLUSIONS
VI.
The
analysis
upon
this study has focused
of
estimates of demand for and economic benefits from
salmon
sport
Oregon
consumer
of
estimates
Various
fishing.
the
surplus per trip and per fish were obtained from different
estimation
methods.
analysis
time
The
is based upon the
the travel cost method
cost
salmon
the traditional single site type of
from
method
presented in Table
are
fishing
approach
zonal
7
average
The values from the adjusted
individual
from
the
from
the
approach are even higher than
for
approach,
individual
travel
fresh-water
for
over twice as high as the values
are
unadjusted
estimated
The
and money costs of travel to a site.
results
demand
for
technique
primary
while
the
values
the adjusted individual observations
The
high
individual
resulted
is
surplus
from
the
to
have
travel
cost
estimates
observations in Table 7 are believed
in
measurement
are
consumer
part
from the bias caused
error
by
Since most of the measurement
averaged out in the zone average method,
believed
to
be more
reliable
than
the
errors
this method
individual
observation approach
In addition to the bias from measurement
is
thought
estimated
error,
that another reason for the consumer
from
the
unadjusted
individual
it
surplus
observations
117
Table
7.
A Comparison of Consumer Surplus Values for
Fresh-water Salmon Sport Fishing, Estimated by
Various Models Using Reported Travel Costs
Traditional
Consumer Surplus
Gum-martin
Consumer Surplus
average
per
trip
average
per
trip
Model
Zonal Average
21
21
Adjusted Individual
47
48
Unadjusted Individual
61
91
Table
8.
$
A Comparison of Consumer Surplus Values for
Ocean
by
Salmon Sport Fishing, Estimated
Various Models Using Reported Travel Costs
Model
Average Traditional
Consumer Surplus
Per Trip
Zonal Average
Adjusted Individual
Unadjusted Individual
$
62
Average Gum-Martin
Consumer Surplus
Per Trip
$
57
78
85
217
293
118
being so high is because this procerdure does not properly
account
As explained in some
from the more distant zones.
in
come
the lower percentage of the people who
for
chapter
individual
4,
detail
by
observations generated
linear demand function and a specified random distribution
of
demand
estimation
approach,
percent
intensity resulted in a 42
percent
error
of
by the unadjusted individual observation (Ulo)
while the error of estimation was only about
These
method.
with the traditional zone average
1
results illustrate that estimates of consumer surplus from
the UlO approach can be seriously overestimated when there
is
participation
a significant decline in the percentage
rates of the more distant zoneS.
A
summary
approach,
(ulo
participation
basis)
all
UlO
approach
rates included,
estimation
of
probability
with
average
zone
traditional
and individual observations adjuted to per capita
method,
Table
of four different methods of
applied
9.
but
in
The estimates of consumer surplus obtained from
the UlO approach were very close to each
UlO approach gave an estimate
while
the
times
that of any one of the other three,
Gum-Martin
measure
emphasized
that
measured
presented
to ocean salmon fishing is
of consumer
these
surplus.
results were
of
other,
four
about
based upon the
It
obtained
should
by
be
using
distance instead of reported travel costs in the
travel cost demand models. The advantage of using measured
119
Table
9.
A
Comparison of Consumer Surplus Values for
Ocean Salmon Sport Fishing, Estimated by
Various Models Using Measured Distance
Model
Average Traditional
Consumer Surplus
Per Trip
Zonal Average
Ad3usted Individual
Unadjusted Individual
UlO with Probability
of Participation Rates
$
57
Average Gum-Martin
Consumer Surplus
Per Trip
$
52
49
53
152
208
54
54
120
distance
that
is
reported
travel
comparison
the bias from
costs
can
be
measurement
errors
avoided
that
so
in
the
among the various results is concentrated only
upon other causes for the difference, such as the decrease
in participation rates as distance increases.
The
comparison
of
various estimates
consumer
of
surplus, discussed in chapter 4 and summarized in Table 9
has several implications.
First of all,
the estimate
of
consumer surplus based solely upon the UlO approach cannot
be
considered
observations
reliable.
using
Second,
individual
the
by themselves can lead to incorrect consumer
surplus estimates unless they are adjusted to a per capita
basis,
just
Third,
if the UlO approach is used,
of
participation
approach
(The
of
rates
should
then the probability
linked
be
to
order to estimate a valid consumer
in
reasoning and procedure for linking the
participation
unadjusted
as
a function
individual
model.
cost
as for the zone average travel
of
observations
distance
was
the
UlO
surplus.
probability
with
the
presented
in
chapter 4, and the results are partially summarized in the
last
line
of
Table 9.) However,
if there is
an
percentage of participation from all distance zones,
the
individual observations can be used alone
and
equal
then
would
not need to be adjusted.
The problem of measurement error in travel costs was
discussed and analyzed empirically,
and measured distance
121
to
used as an instrumental variable for travel costs
was
solve the measurement error problem. The results for ocean
salmon
fishing
showed
that
the
Gum-Martin
individual
surplus estimated from the adjusted per capita
observations
zone
was
average
the
from
about 50 percent higher than
approach,
consumer
were
when reported travel costs
as shown in Table 8. However, the difference in the
used,
Gum-Martin consumer surplus between these two methods
was
2 percent when the instrumental variable
was
about
only
of
This result implies that most
as shown in Table 9.
used,
per
adjusted
the
difference in results between
the
capita individual observations and the zonal average model
was
due to the bias from measurement errors in the travel
cost
variable.
surplus
Moreover,
between
these
the
two
difference
in
essentially
was
methods
consumer
eliminated by using the instrumental variable approach.
The
benefits
tested
relationship
and
between
fresh-water
net
estimated
salmon catch
was
as a linearly homogeneous equation in
Marginal values per fish,
economic
empirically
chapter
3.
equal to the average values per
could thus be obtained. It should be noted that the
fish,
values per fish were made by a two stage procedure. In the
first stage,
the
consumer surplus per river was computed from
traditional travel cost demand model.
stage,
consumer
surplus
salmon catch per river.
per river
was
In the
regressed
second
upon
The fish catch was not a variable
122
in
the demand equation of the first stage.
value
marginal
The
of a fish was simply computed from the increase
comsumer
surplus
associated
with the
the
in
increase
in
number of fish caught. Thus, the number of fish caught was
not
to the demand function in the
related
Therefore,
values
this
derived
value
from
the
from
may be quite different
demand functions in
stage.
first
fishing
which
success was included as a variable.
per
reliable estimates of the marginal
value
based upon the traditional zone average
model
most
The
fish,
and the two stage estimating procedure noted above, ranged
between $90 and $100 per fresh-water salmon.
However, the
values per fish estimated from the individual observations
were again
much higher than those estimated from the zone
averages,
but are not thought to be accurate for
already outlined.
that
The homogeneous equation
reasons
of degree one
was used implies that if the catch is doubled,
the consumer surplus would also be doubled.
then
This approach
implies that as long as the salmon catch can be predicted,
the
consumer surplus can be estimated from
homogeneous
equation.
In addition,
the
linearly
if it is decided
to
increase anglers' benefits, then those factors that affect
the salmon catch should be improved.
If
the
variable of catch per river times
distance
from Portland, measured in miles, was also included in the
above
linearly homogeneous model,
then each
additional
123
from the Portland Metropolitan area was estimated to
mile
reduce the value per fish by about 32 cents. This estimate
of the distance from Portland effect,
high
because
southern
fished
of anglers from California that
Oregon rivers but who were not included
analysis.
fishing
however, may be too
in
the
in
In other words, the consumer surplus for salmon
on
been
have
may
southern Oregon streams
the
relatively underestimated.
From
one
analysis of value per fish in chapter
the
value
can conclude that most of the variation in the
per fish by river was due to sampling errors,
3,
both in the
consumer surplus by river and in the catch estimates based
upon
salmon and steelhead tag returns.
data
were available for all the nine rivers,
If
survey
creel
then
both
the consumer surplus and the salmon catch estimates
could
be
corrected
give more accurate values per
to
fish.
In chapter 5, quality and substitute site variables,
were
directly into a regional
incorporated
model.
derived
regional
Marginal
from
value
this
type
per
of
travel cost method,
fish thus
demand
can
cost
travel
be
equation.
directly
For
the average value per
the
trip
was around $24. The marginal value per salmon caught for a
certain
river
can be estimated from the regional
travel
cost model as follows: 1) hypothetically increase the fish
catch in that river,
2) keep the other rivers' fish catch
unchanged, 3) use the regional travel cost demand equation
124
and
new level of fish catch in that river to compute
new consumer surplus,
is
4) the incremental consumer surplus
divided by the incremental
then
the
increase
salmon
in
catch in that river.
The
regional
estimates
fishing
travel cost method results show
marginal
about
value
However,
percent of the
underestimate
specification,
important
to
of
or
average
being only
marginal
value
poor data,
This
value.
be
may
or both.
cost
travel
presented in chapter 5 seemed too low,
25
computed
the
fish from the regional
per
data
as long as catch and distance
the new sites are available.
models
future
or
sites can be obtained from present models without
need for new surveys,
for
new
net economic benefits from
of
that
due
possible
poor
to
it
However,
is
from
note that the average values per fish
the regional travel cost models were surprisingly close to
the
average
values from the earlier
traditional
single
site type of models that were fitted to the same data
presented
can
in chapter 3,
even though these earlier models
be criticized from a specification point of view
not including substitute and quality
variables.
further
other
research
with
activities is needed,
was
that
total
little
data
for
with
for
Although
recreational
one important finding of this study
the traditional travel cost model estimates
and
and
average consumer surpluses were
the addition of the substitute
changed
and
of
very
quality
125
variables in the more completely specified regional travel
cost
models.
travel
cost
This finding indicates that the traditional
model may be rather
robust
total and average consumer surplus.
estimated
(The stability of the
cost coefficient and the
travel
estimating
for
corresponding
consumer surplus estimate is illustrated in Appendix F.)
A hedonic
Hedonic
travel cost model
cost
travel
models
was
usually
characteristics as quality variables.
estimated.
also
site
include
However,
only
the
quality variable that was used in this study was a fishing
success
catch
computed by dividing the salmon
variable,
reported by the angler by his reported hours of fishing on
that trip. Based upon this hedonic travel cost model which
was first estimated by OLS in this study, the average GumMartin
consumer
which
fish,
value.
seems
However,
success
least
surplus was $103 per trip and
to be an unusually high
when
per
$264
estimate
of
fishing
the demand functions for
and for fishing trips were estimated by two stage
squres
simultaneous
(2SLS),
equations,
i.e.,
they
were
considered
the average Gum-Martin
as
consumer
surplus was reduced to $68 per trip and $175 per fish.
One
thing that needs to be noted is that the
value
per fish in the hedonic travel cost method is derived from
the demand for the fish catch rate (reported salmon
divided
the
by reported hours of salmon fishing) rather
demand
for fishing trips.
Therefore,
the
catch
than
marginal
126
value
per
catch
rate.
But for the traditional single site type
of
the marginal value per fish cannot
be
travel cost model,
Despite this
obtained by simply increasing fishing trips.
advantage,
fish
the
fish can be estimated by increasing
be
to
hedonic travel cost method seemed
the
much more sensitive to problems with specification and the
Therefore,
data.
estimates
travel
it needs to be noted that the numerical
value
of
model
cost
of trips and fish from
and
were rather unstable
hedonic
the
be
should
considered to be rather questionable for this study
Despite problem of estimation,
regional
and
directly
related
these
the
hedonic travel
the valuation by the
methods
cost
catch,
(because
to recreation site management
such
demand functions involve variables,
be
can
as
fish
over which management may have some control). This
feature is especially important for resource managers.
As noted earlier, one cause of the problems with the
hedonic
very
approach was that this approach is thought to
demanding of good data.
pertaining
data
It needs not only the
needs
travel
not
characteristics
Also,
sites.
it
trips
and
but objective data that would quantify
the
Therefore,
the
only data pertaining to number
cost,
data
but also the
to anglers from various origins,
concerning their trips to various
be
of
the
various
sites.
of
expense
of gathering an appropriate set of data
hedonic
travel
cost model could be quite large.
for
the
On
the
127
other
hand,
fitted
to a rather rough set of data,
be
empirical
and the
of this study indicate that this model was rather
results
robust
can
model
traditional travel cost
the
relable for estmat1ng
and
consumer
total
the
surplus and average consumer surplus per trip or per fish.
Considering
predictive
the
analytical
the
power,
usefulness,
and the need for data, the traditional travel
cost
may be more reliable than the hedonic
model
travel
cost model for most studies of recreational fishing.
The regional and hedonic travel cost methods with
quality
variable
approaches
for
were
studying
shown to be
the
to
make future research more
improvements
behavior,
recreationists'
although the success in this study was quite
order
promising
possibly
limited.
successful,
in methodology along with
In
further
appropriate
data
are required.
For
price
example,
approach
may
the utility function for the
be simultaneously
traditional and Lancaster's consumer
commodities
factors
travel
hedonic
constructed
theory,
i.e.,
of the utility function.
cost method,
quality
Therefore,
method
both
and characteristics can be joined together as
Also,
in
the
hedonic
it is important that sufficient data
should be avalable for the various origins and sites,
the
from
data
characteristics
must
be
and
quantifiable.
suitable for the traditional travel cost
are often not appropriate for application
of
the
128
hedonic
first
travel
stage
function
is
cost method.
The reason is that
of the hedonic travel cost
method,
constructed for an origin so that
in
the
a
cost
the
data
must cluster around the origin. But the traditional travel
cost method is based upon site-specific area studies,
the
data
the
are
always acquired from different otigins
specific
site.
quantify
some
In addition,
the
of
site
to
it seems very difficult
to
such
as
characteristics,
scenery, and congestion. However, dummy variables might be
used to approximate some of these quality variables.
In
travel
short,
cost
the
more complex regional
models seem to require a better
and
hedonic
quality
data to accurately estimate the value of quality
of
changes
Therefore, the approach to collect data should be designed
appropriately,
and
must be minimized
the recall errors of the
respondents
129
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APPENDI CES
135
are 38 zonal average observations for
There
fresh-
water salmon analysis in Oregon shown in APPENDIX A. These
zonal
38
data
were
158
from
constructed
individual
observations and were used to estimate the regional travel
However, the 158 individual observations from
cost model.
fresh-water salmon anglers were originally divided into 37
with most of zones having four or five
zones
respondents
who had actually fished during the period of survey. Those
37 zonal data were mainly used to estimate the traditional
zone
average
became
(Xl);
into two zones.
average
37
zones
then
average
The variables in APPENDIX A
travel cost from ith zone
replacement
related equipment (x2);
ith
Those
38 zones as shown in APPENDIX A after one zone was
partitioned
denote
travel cost demand.
to
value of salmon
jth
fishing
river
and
average reported family income of
zone fishing in jth river (X3);
average measured one
way distance from ith zone to jth river (X4); total salmon
catch in jth river in 1977 (X5);
average measured one way
distance from ith zone to kth substitute river (X6); total
salmon catch in kth substitute river in 1977 (x7); average
trips
per
population
capita
for
from
ith
to
zone
ith zone to jth
river
variable for ith zone to jth river (xlO),
1,
jth
(X9);
river
(X8);
and
dummy
which equals to
if X9 > 95,000, and 0, otherwise.
APPENDIX
fresh-water
B includes 158 individual observations for
salmon sport fishing
in Oregon .
Those
158
136
individual
data
adjusted
were used to estimate the
and
unadjusted individual observation travel cost model. There
are
variables included in
six
APPENDIX
B,
Xl
denotes
number
of salmon fishing trips for ith individual to
river;
X2 denotes reported travel cost for ith individual
to
and
fishing
salmon
X3 represents replacement value of
jth river;
jth
related equipment for ith individual to
jth
river; X4 represents family income for ith invidual to jth
river; X5 is the share of distance zone population for ith
individual
X6 is the trips per capita
to jth river;
for
ith individual to jth river.
APPENDIX
observations
has
C
ocean
47
which were used for zone average travel cost
Those 47 zonal data
models in chapter 3 and in chapter 4.
were
constructed from 211
variables
observations.
individual
The
in APPENDIX C can be expressed as population of
ith distance zone to jth port (Xl);
way
average
zonal
salmon
distance
from ith zone to
jth
average measured twO
port
(X2);
average
number of trips per capita from ith zone to jth port (X3);
average
(X4);
reported travel costs from ith zone
average
opportunity
to jth
cost of travel time from
port
ith
zone to jth port (X5).
APPENDIX
observations
Those
211
unadjusted
D
for
is
composed
of
211
ocean salmon sport fishing
individual
data were used
for
individual
in
Oregon.
adjusted
individual observation travel cost methods
and
in
137
chapter
can
3 and in chapter 4.
The variables in APPENDIX
be denoted as followings:
number of
D
fishing
salmon
trips for ith individual to jth port (Xl); reported travel
costs
for
value
of
ith individual to jth port
salmon fishing and related
individual
to
individual
to jth port (X4);
jth
port
(X3);
replacement
(X2);
equipment
family
income
for
ith
for
ith
the share of distance
zone
number of
population for ith individual to jth port (X5);
anglers
who went together on that trip for ith individual
to
port
jth
individual
(X6);
measured two way
jth port (X7);
to
blow-up
distance
for
ith
factors
for
ith
individual to jth port (X8).
APPENDIX
fished
Those
E contains 290 individual observations who
for salmon in Oregon during the period of
survey.
290 individual data were used for the second
regression
variables
the
in
in
hedonic
APPENDIX
individual (Xl),
travel
cost
E are success per
stage
The
method.
hour
kth
for
based upon the reported success from the
questionnaire; average success per hour for kth individual
(X2),
family
based
upon
all
reported successes at
income for kth individual (X3);
fishing trips for kth individual (X4);
kth individual (X5),
by
automobile
travel
number of
site;
salmon
rate of travel for
which is 40 miles per hour if travel
or pickup,
by camper;
the
and is 35 miles
per
hour
if
cost per mile for kth individual (X6),
which is $0.0975 if auto or pickup was used, and is $0.116
138
if
camper was used;
hour
miles;
implicit price of salmon
for kth individual in jth county (x7),
mean
catch
measured
per
in
value of the omitted characteristics for kth
individual in jth county (X8), measured in miles.
6E1
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140
APPENDIX B
Xl
1
1
X2
X3
72
78
2000
20 6500
2113 10000
4 132
8
73
1
1
9
7
1
26
1
1
20
8
3
2
10
12
1
2
13
1
3
4
9
1
1
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16
12
6
3
3
6
3
9
20
1
4
15
7
1
8
1
2
7
2
0
X4
179
3823 10000
3512 13500
37 10000
5
11000
106 21500
34 4000
4275 10000
125 13500
82 13500
57 16500
158 16500
1035 16500
368 16500
1064 21500
1027 21500
1428 21500
170 21500
1554 21500
7836 21500
130 21500
6700 21500
5443 30000
3431 30000
1372 30000
3843 30000
20
1
14
9
13
4
5 11000 42500
1
6293 75000
2
3
1
43
Il
2
2
12
8
5
1
2
11
5
6
12
8
11
10
10
2000
4000
145 6500
1540 10000
75
5
563 10000
2236 13500
1156 13500
203 13500
1198 13500
115111 13500
X5
X6
16325 .0.0081
7565 0.020 1
6990 0.0708
12988 0.0475
12988 0.0089
12987 0.0361
12987 0.0114
5875 0.0220
1586 0.3 165
1586 1.4395
1586 0.4918
1586 0.1847
1581 0.0776
1586 0.039 1
1586 0.5536
1586 0.039 1
1586 0.1166
1586 0.2333
1586 0.1847
1586 0.3695
1586 0.1166
1586 1.5372
1586 0.0618
1586 0.2459
1586 0.9224
29950 0.0807
1586 1.2295
1586 0.8607
1586 0.7995
1586 0. 1557
32412 0.0334
7388 0.0586
32412 0.0667
32412 0.0 190
321112 0.0334
7388 0.2064
32412 0.1334
32412 0.08314
32412 0.0167
20700 0.0054
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142
APPENDIX B (cont.)
2
6
1
8
1
1
1
3
73
40
2
3
8
12
12
7
1
20
1
4
14
10
10
1
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1
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2
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1
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7
12
18
3
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19
12
15
6
0
24
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6
6
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1
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1
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18
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1
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8
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2
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1
110
20
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2
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2
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7
6500
613 6500
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1895 10000
20567 0.025 1
17711 16500
28550 0.02111
105 16500
208 16500
5 16500
889 21500
990 21500
822 30000
14844 0.0322
14844 0.0511
107
1481111 0.0148
1118114 0.0376
28550 0.0063
148411 0.136i4
111844 0.0148
148411 0.0170
148144 0.0589
420 30000 254150 0.0085
1432
119
1114
4000
6500
6500
890 10000
1421 10000
25 10000
3112 13500
21 16500
22 16500
125 16500
1565 21500
130 21500
4500 30000
40
6500
563 10000
1750 10000
2435 10000
70 13500
1373 13500
268 13500
1070 13500
1591 16500
1564 16500
1890 16500
230 16500
37 16500
65 16500
5072 21500
8365 0.11359
8365 0.5234
8365 0.0436
20567 0.0208
20567 0.0070
8365 0.0873
8365 0.0873
8365 1.0355
20567 0.0125
8365 0.6538
8365 0.0436
8365 0.4186
8365 0.2433
34338 0.0157
34438 0.0157
34438 0.2825
34438 0. 1256
34438 0.0628
311438 0.0179
34438 0.0537
34438 0.0157
34438 0.1791
34438 0.0628
311438 0.0089
34438 0.0089
34438 0.1075
34438 0.0353
311438 0.0089
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144
APPENDIX C
Xl
X2
X4
X5
160360 232 .021450 89
36
79
X3
160360 251 .01623 59
160360 253 .08205 26 136
14
2
29950 20 .14762
33300 128 .14028 28 32
205500 186 .03364 21 140
111540 650 .00721 160 162
137750 190 .13215 27 25
137750 190 .07517 41 45
137750 190 .09283 39 50
137750 190 .03389 56 139
96360 97 .02050 12 20
205520 134 .02214 46 37
438960 211 .01674 36 74
551000 148 .00393 34 36
193680 626 .00364 175 197
110200 118 .12231 14 26
29650 20 .149239
858140 1148 .06226
4
6
18
42
551000 202 .00785 63 69
212800 228 .02958 35 52
254150 210 .021402 23
171480 140 .07667 44
60
35
65
214350 158 .02903 33
76520 386 .01616 85 71
125720 588 .00973 107 87
131600 293 .00596 39 148
225400 399 .00652 84 154
79900 172 .07671 17 16
79900 152 .03798 25 31
79900 1147 .05075 20
39
79900 159 .054014
614
79900 165 .10252 23 33
17
111560 784 .00265 131 237
8
1
16235 20 .11400
14
16235 20 .10589
3
20 .321486
10
6
20 .16115
168900 207 .02860
168900 182 .03496
168320 329 .03229
156720 566 .00656
15150 20 .80918
60100 255 .05905
9
40
75
5
22
45
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3
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35
65
60
2
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52
96
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60100 266 .02413
96680 416 .02321
16
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156
APPENDIX F
= -1.1900 - 0.05044 RTC
ln(TRPSCAP)
(F-i)
ii
ii
(-9.56)
(-4.89)
+ 0.0002406 SSFE
- 0.00002058 INC
(-1.41)
(2.83)
-1.07184 X
- 0.8876 X
1
-1.7594 X
3
2
(-6.23)
(-3.65)
(-3.72)
2
n
R
37
(F-i) included one more variable,
Equation
family income (INC),
page 36.
However,
should
average
and can be compared to equation (1),
the t value of the income variable was
significant at the 10 percent probability
not
of
= 0.826.
level.
It
be noted that the difference in the absolute value
travel
the
cost coefficient
in
equation
(1)
and
equation (F-i) is only about 0.4 percent. The stability of
the
travel
other
observed
variables in the single site travel cost model
when
are
When all the other variables, except the revised
deleted.
travel
coefficient can also be
cost
by
one,
the
of the travel cost coefficient along
with
the
cost
estimates
variable,
are
deleted
one
corresponding estimates of the Gum-Martin consumer surplus
and the coefficient of determination for each equation are
shown in Table F-i.
Even
from
0.816
though the coefficient of determination
to
0.446 in Table F-i as the
variables
drops
are
157
deleted,
estimated
the
travel
cost
coefficients
consumer surplus remain relatively
corresponding
and
stable.
This stability indicates that the simple travel cost model
may
be
rather
robust
for
estimating
total
consumer
surplus.
Table
F-i.
Some Regression Results and the Estiamtes of
Oregon
Consumer Surplus for
Gum-Martin
Fresh-Water Salmon Angling in 1977
2
Gum-Martin
Consumer
Surplus
Variables
Deleted
from (F-i)
Estimated
Travel Cost
Coefficient
None
-0.05044
(_9.56)*
0.826
$ 4,704,500
INC
-0.05024
(_9.38)*
0.816
4,723,200
INC, SSFE
-0.04986
(_8.6l)*
0.778
4, 759, 200
INC, SSFE,
X3
-0.04751
(_7.32)*
0.707
4,994,600
INC, SSFE,
X2, X3
-0.04900
(_6.59)*
0.603
4,842, 700
INC, SSFE,
Xi, X2, X3
-0.04562
(_5.31)*
0.446
5, 201, 500
*
R
Values of t are given in parentheses
estimated travel cost coefficients.
below
the
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