The Net economic value of recreation on the national forests : twelve types of primary activity trips across nine Forest Service regions

Historic, Archive Document

Do not assume content reflects current
scientific knowledge, policies, or practices.

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^\ United States
JLJj) Department of
Agriculture

Forest Service

Rocky Mountain
Forest and Range
Experiment Station

Fort Collins,
Colorado 80526

Research Paper
RM-289

The Net Economic Value of
Recreation on the National Forests:
Twelve Types of Primary Activity

Trips Across Nine Forest
Service Regions

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Daniel W. McCollum

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George L. Peterson

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J. Ross Arnold

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Donald C. Markstrom

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Daniel M. Hellerstein

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Abstract

The Public Area Recreation Visitors Survey (PARVS) was used to
estimate demand models, from the point of view of a site operator,
for recreation on Forest Service lands for twelve types of primary ac-
tivity trips in all nine Forest Service regions. The models were esti-
mated using the travel cost method with a "reverse multinomial logit
gravity model." At the first stage, they are share models estimating
the probability that a trip observed at a given recreation site originated
in a particular county. This probability is equivalent to the expected
proportion of total trips to a site coming from a particular origin. A
second staging process, identical to that used in traditional travel cost
models, was used to derive site demand functions from the point of
view of a site operator. These functions were used to estimate aver-
age consumer surplus. The relative values for different primary ac-
tivity trips across different regions of the country are examined, as
are relative values for different primary activity trips within the
regions.

Research Paper RM-289 February 1990

/
J*

I The Net Economic Value of
Recreation on the National forests:

Twelve Types of Primary Activity Trips
Across Nine Forest Service Regions,

Daniel W. McCollum, Economist
[Rocky Mountain Forest and Range Experiment Station]}

George L. Peterson, Project Leader
Rocky Mountain Forest and Range Experiment Station1

J. Ross Arnold, Research Associate
Colorado State University

Donald C. Markstrom, Research Wood Technologist
Rocky Mountain Forest and Range Experiment Station1

Daniel M. Hellerstein, Research Associate
Rocky Mountain Forest and Range Experiment Station1

1 Headquarters is injFort Collins}} in cooperation with Colorado State University.

Preface

The information in this report is the product of one of several special
studies intended to provide technical advice on the economic value
of recreation for use in the 1990 RPA Program Analysis. The mone-
tary values reported herein were estimated using the travel cost
method with data collected by the Public Area Recreation Visitors
Survey (PARVS) at Forest Service sites only. The estimated values
are advisory and do not constitute official Forest Service policy.

The research and computer assistance of Michelle Haefele contrib-
uted immeasurably to the completion of this work. Her contribution
is gratefully acknowledged. Glen Brink and Norman Merritt provided
valuable programming support for this project. Ken Cordell, at the
Southeastern Forest Experiment Station, provided helpful comments
and feedback on several sections of this report. Gary Eisner, Richard
Guldin, John Loomis, Greg Super, and Richard Walsh also reviewed
earlier drafts and provided comments and criticisms, which we have
endeavored to incorporate. An early report of this work was presented
at the joint meetings of Western Regional Research Project W-133,
Benefits and Costs in Natural Resource Planning, and the Western
Regional Science Association, in San Diego, CA, February 20-22,
1989. Useful comments and discussion were contributed by several
participants. The authors, however, are responsible for any errors.

Contents

Page

Introduction 1

What Question Does the 1990 RPA Program Analysis Pose? 2

Some Background on PARVS 3

The Reverse Gravity Model 4

The Applied Trip Distribution Model 5

The Alaska Model 6

Levels of Modelling and Aggregation 6

The Data and Associated Methods 7

The Public Area Recreation Visitors Survey 8

Refining the Raw Data 9

Origins, Destinations, and Market Areas 11

Characteristics of Recreation Trips 12

Results 12

Model Estimation 12

Consumer Surplus Estimates 14

Discussion 22

Conclusions 25

Literature Cited 25

Appendix 1: More on the Trip Generation Model 27

Appendix 2: The Estimated (First-Stage) Trip Distribution Models ... 28

The Net Economic Value of
Recreation on the National Forests:
Twelve Types of Primary Activity Trips
Across Nine Forest Service Regions

Daniel W. McCollum, George L. Peterson, J. Ross Arnold,
Donald C. Markstrom, Daniel M. Hellerstein

Introduction

The Forest and Rangeland Renewable Resources Plan-
ning Act of 1974 (RPA), as amended by the National
Forest Management Act of 1976 (NFMA), was passed to
make natural resource planning more rational and ac-
countable. The RPA calls for planning at two levels: the
national level and the forest level.

Two key documents produced at the national level are
the Assessment and the Program. The Assessment
describes the current forest and rangeland situation, and
analyzes the environmental, social, and economic trends
(and their consequences) that will likely affect the
resource situation over the next 50 years. Opportunities
for change, and obstacles to making changes, in current
and future resource situations are described for both pub-
lic and private lands. Based on the findings of the Assess-
ment, the Secretary of Agriculture recommends to the
Congress a 50-year RPA Program for the Forest Service.
The Recommended Program is a strategic plan that estab-
lishes long-term resource management goals. In the plan-
ning process, alternative national plans are developed to
reflect different emphases on the various resource manage-
ment goals — different strategies for meeting societal needs
over the next 50 years. Each alternative includes elements
for all three branches of the Forest Service — the National
Forest System, Research, and State and Private Forestry.
Each strategy consists of many intermediate objectives that
measure performance in attaining the goals.

In choosing which strategy or plan to recommend, the
Secretary of Agriculture considers the environmental,
social, and economic consequences of each alternative.
To analyze the economic consequences of each plan, it
is helpful for different levels and timing of resource out-
puts to be reduced to a common metric and period in
time. Dollars have been selected as the metric and the
present time as the period of comparison. Demand-side
unit values must be estimated for each resource output
or category of outputs to compute the value of benefits
generated by each alternative plan. These unit values
have been casually referred to as "RPA values." When
supply costs are subtracted from the demand-side value
of total resource outputs in any single year, the remain-
der is net value. Discounting net value to the present
yields net present value (NPV). NPV is used to rank al-
ternatives in decreasing order of economic value. The
NPV by resource output and the overall ranking are im-
portant decision criteria. The guidelines, and some of

the conceptual framework, for resource pricing and valu-
ation for the RPA Program are discussed in USDA Forest
Service (1989).

RPA values are also used in the forest planning proc-
ess established under the NFMA. Again, these values
are used to analyze economic consequences of differ-
ences in the level and mix of resource outputs, and to
rank alternatives.

The effort reported here represents the first time a con-
sistent method has been applied across regions and ac-
tivities to estimate the economic value of recreation on
Forest Service lands. Indeed, it is the first time RPA
values have been estimated from primary data. The back-
ground work for the 1985 RPA values was a review of
the economic literature on recreation demand values by
Sorg and Loomis. Such information is useful but, as Sorg
and Loomis state, "Surveys of the literature are not sub-
stitutes for region-specific estimates of the value of recre-
ation" (Sorg and Loomis 1984:1).

The economic literature is replete with valuation
studies of particular recreation areas under particular
conditions for particular activities (see Sorg and Loomis
(1984) and the updating of that work by Walsh et al.
(1988)). Those studies used a variety of data sources from
a variety of subsets of the general population, and a var-
iety of modelling frameworks with a variety of independ-
ent variables and functional forms. They applied a
variety of assumptions and came up with a variety of
results. None of the studies is universally applicable, but
all have something to say about the value of recreation.
The study presented here is an attempt to employ the
same source of data from the same time period, and the
same model with uniform assumptions for several cate-
gories of recreation activities across several regions of
the country. The Public Area Recreation Visitors Sur-
vey (PARVS) data used in this study were collected ex-
pressly for the purpose of providing information about
the recreation uses and users of public lands. Some valu-
ation work conducted for the 1990 RPA Assessment also
used the PARVS data, but the context of that work was
household markets, and the objective was to estimate
resource scarcities and price variations (Cordell and
Bergstrom 1989).

The advantage of using the same data source and the
same model is the comparability it provides across ac-
tivities and regions of the country. This study is unique
in the insight it can provide to the relative values across
activities within a region and between regions of the
country.

1

What Question Does the
1990 RPA Program Analysis Pose?

The RPA Program Analysis is intended to contribute
toward a strategic plan that establishes long-term
resource management goals. One component of the
Analysis involves consideration of the economic conse-
quences of alternative strategies and a ranking of alter-
natives. Such consideration requires that resource
outputs be expressed in a common metric for compari-
son. The chosen metric is dollars. Many forest outputs,
particularly recreation outputs, do not move through for-
mal markets and, hence, are not priced by the market
in the same way outputs like timber are priced. Thus,
the need arises for a valuation exercise like the one
reported here.

A critical prerequisite to interpreting and applying the
results of this study is to clearly specify the question be-
ing asked. Two possibilities are: (1) What is the value
of the marginal unit of forest recreation output? What
is the value the last person appearing at the site places
on his recreation experience? (2) What would be the eco-
nomic benefit lost if the site was closed to recreation?
Another way to phrase the latter question is: What is the
value of the recreation experience averaged over all users
of the site?

The answers to these two questions are very different.
The first question is usually answered by the price, the
same concept of price as that for a loaf of bread. Price
is termed a marginal value. This value is found at the
intersection of the supply and demand functions. The
critical caveat to this concept of value is that it depends
on the good being price rationed.

The answer to the second question is the average con-
sumer surplus. Consumer surplus is the difference be-
tween the maximum amount an individual is willing to
pay to obtain a bundle of goods and the amount he
actually pays. Graphically, it is the area under the de-
mand function and above the price paid for the bundle
of goods. Consumer surplus is a dollar measure of the
excess value (or benefit) an individual receives from con-
suming a good, over and above what he pays to obtain
the good. It represents the net benefit received by peo-
ple recreating at a site.2 Consumer surplus is generally
a nonmarginal value. It is our view that the second ques-
tion is the one being posed in the RPA Program Analy-
sis. Consumer surplus is the valuation concept that
correctly answers this question.

Some further distinction needs to be made between
marginal and nonmarginal values. A nonmarginal value
is the sum of the values of consumption units excluded
(or included) by a nonmarginal change in the demand
or supply of a good. A nonmarginal change in demand
or supply is generally taken to result from a large change

2ln order to capture that value in a market, the producer of the good
would have to perfectly price discriminate. In that case, each individual
would pay his maximum willingness to pay and consumer surplus would
be zero. But whether the producer price discriminates (i.e., whether the
surplus can be extracted) or not, the consumer surplus represents real
economic value.

in quantity (or price) or condition of the good. A margi-
nal value is the value of the unit of use excluded (or in-
cluded) by a marginal change in the demand or supply
of the good. A marginal demand or supply change is
generally taken to result from a small change in quanti-
ty or condition of the good, for example, a change such
that one less unit of the good is available. A key factor
in this discussion is whether the good is price rationed.

Price rationing means that a fee, or price, is charged
to use the good. All users who value the good at less
than the fee are excluded from use. When goods are price
rationed and price is increased, the nonmarginal value
is the sum of the values of all those users who can no
longer use the good because their value is less than the
new (higher) fee or price. In the case of a price decrease,
the nonmarginal value is the sum of the values for those
users who can now use the good because their value is
greater than the new (lower) price. In both cases, those
users have the lowest values of all who consume the
good. The marginal value for a price rationed good is
the lowest valued unit consumed. When the price is
raised, the user with the lowest value is excluded. When
price is lowered, the user with the next lowest value is
included.

The situation changes, however, when the good is not
price rationed. When price is not used as a rationing
device, the marginal value is not necessarily the lowest
value. In this case, and recreation on public lands is a
prime example, it is equally probable that any user of
the good will be excluded (or included) when the de-
mand or supply changes. Hence, the marginal value (as
well as the nonmarginal value) can be anywhere in the
range of values — from lowest to highest. In such a case,
price, as the marginal value is frequently referred to, is
not a useful concept of value. What is needed is the
mathematical expectation of the value any randomly
chosen user would place on the good. This expected
value is the average consumer surplus.

This view is supported by the economic literature. In
a widely accepted paper, Mumy and Hanke (1975) ad-
dress exactly this issue. The first case they examine is
one where the price of a publicly provided good is zero.
This is the case at many Forest Service sites for many
activities when no access fee is charged to recreate on
Forest Service land. The second case is that of under-
pricing, when a price is charged but no pretense is made
that it is related to economic efficiency or that it covers
the cost of providing the good. This case is also relevant
for some Forest Service sites and activities. In both these
cases, where price is not used as a rationing mechan-
ism, the theoretically correct concept of value is the aver-
age consumer surplus. The basis of this conclusion is
that all demand units have an equal probability of be-
ing satisfied, as discussed above. Hence, it is not cor-
rect to assign the value that one individual (the last or
marginal user) places on the good as the value of the
recreation experience at the site. The correct value to as-
sign is the mathematical expectation of the values
received by all satisfied units of demand. This expected
value corresponds to the average consumer surplus.

2

Some Background on PARVS

The 1985-1986 Public Area Recreation Visitor Survey
(PARVS) was (according to the PARVS Training Manu-
al and Codebook) "a nationwide project developed by
the USDA Forest Service, the National Park Service, the
U.S. Army Corps of Engineers, the Tennessee Valley
Authority, and several state agencies to provide highly
credible and broadly comparable estimates of the eco-
nomic importance of providing recreation opportunities
on public lands." PARVS had three primary objectives:

1 . ' 'To describe the activity patterns of recreators on-
site on public recreation lands."

2 . ' 'To obtain a description of the people visiting pub-
lic recreation areas for recreation."

3. "To provide visitor expenditure data that would
result in estimates of the income and employment
growth resulting from publicly provided recreation
opportunities."

PARVS consisted of an onsite questionnaire, ad-
ministered to randomly selected recreation site users,
and a detailed mail-back questionnaire. The mail-back
questionnaire was administered to the people inter-
viewed onsite who agreed to complete the more detailed
questionnaire. The onsite portion of the survey was ap-
proved by the Office of Management and Budget (OMB)

for use at all sites nationwide. The mail-back question-
naire was approved only for use in the Southern Region
(Forest Service Region 8; fig. 1). The survey was ad-
ministered at a variety of sites including national forests,
national parks and monuments, U.S. Army Corps of En-
gineers reservoir sites, TVA recreation areas, state parks,
state forests, and other state recreation areas. The only
portion of the PARVS data accessible for this study was
that collected at Forest Service sites.

Three distinct samples were used in this study. All
are subsets of the PARVS Forest Service data set. The
first subsample is the recreation sample. The intent with
this subsample was to represent recreation at typical
Forest Service ranger districts in the "lower 48" states.
This sample was partitioned into primary activity trips
to attempt to capture differences between different types
of recreation activities. The second subsample was the
Alaska recreation sample. This subsample was intended
to represent recreation at typical Forest Service ranger
districts in Alaska. Again, partitions were made in the
data to look at different types of recreation activities. The
wilderness subsample was intended to represent recre-
ation use at Forest Service sites specifically designated
as wilderness areas. At wilderness sites, no attempt was
made to distinguish between different types of activi-
ties. The wilderness subsample contains sites both in the
lower 48 states and in Alaska.

ALASKA REGION
10

PACIFIC NORTHWEST REGION

6

Figure 1.— Regions of the National Forest System.

3

The Reverse Gravity Model

The model used to estimate demand functions for this
study was a variation of the gravity model. The gravity
model has been used for modelling recreation demand
in several studies (Cesario and Knetsch 1976, Ewing
1980, Sutherland 1982). The standard gravity model, as
applied to recreation demand, considers the individu-
al's choice of a recreation site, weighting alternative sites
in inverse proportion to the cost of visiting them. The
"reverse gravity model" used here considers the likeli-
hood that a recreation visit observed at a particular site
originated in one of a number of origins. In this varia-
tion of the gravity model, trip origins are weighted in
inverse proportion to the cost to the users of reaching
the recreation site.3 This type of model was necessi-
tated by the sampling strategy used in PARVS. PARVS
used a choice-based sample of group trips at the recrea-
tion sites rather than a sample of the general population.
Such choice-based samples are very common in recrea-
tion demand studies.

The PARVS sampling plan defined the Forest Serv-
ice ranger district as the study site for sampling recrea-
tion users. Our data were a sample of recreation users
interviewed at selected ranger districts. Because only a
small number of sites were selected, it was not possible
to model the variety and diversity of recreation sites
available to people at a given origin location. We had
to model the variety of origins providing trips to a given
site. Additionally, an aggregate zonal model was re-
quired because recreationists were surveyed during one
visit to a site. All observations represent one trip to the
site. With no variation in the dependent variable (trips
per individual or household), an individual model could
not be estimated. The units of the dependent variable
must be aggregated to trips per capita based on some
larger population group. The units of aggregation were
defined as counties, and independent variables were the
relevant county averages. No information was available
on the sampling rates at the sites from which to estimate
total use of the sites during the sampling period. In short,
the data limited the choice of models. The limitation is
that the model must be theoretically appropriate for the
type of choice-based sample PARVS represents. As long
as the model is theoretically appropriate for the data, the
results should be unbiased. The limited choice of models
does not necessarily imply an adverse effect on the
results.

The model consists of two independent components:
the trip generation component and the trip distribution
component.

Trip Generation Component:

Nj = g(h(Aj), Mj) [1]

3The "reverse gravity model" will be discussed in detail by: Hellerstein,
D. M.; McCollum, D. W.; Peterson, G. L. 1989, in preparation. A reverse
gravity specification for the travel cost model. Draft manuscript, Rocky
Mountain Forest and Range Experiment Station, Forest Service, USDA,
Fort Collins, CO.

Trip Distribution Component:

Pr(i|j) = f(Kis TC^, Si) [2]

where

N: = the total number of recreation trips to site j;
h(Aj) = a function of site characteristics or site attrac-
tiveness;

Mj = an index of accessibility of site j to the mar-
ket area from which it attracts trips (market
areas will be discussed in the data section);
Pr(i|j) = the probability that a trip observed at site j
came from origin i;
Kj = a vector of characteristics of origin i;
TC4j = the cost of a round trip to site j from origin i;
St = a vector of the prices of substitutes for a trip
to site j from origin i.

The trip generation model estimates the total number of
recreation trips that will arrive at a given site. The trip
distribution model estimates the relative proportions of
those total trips coming from each origin within the rele-
vant market area. The total demand for trips to site j from
origin i, then, is the product of the trip generation com-
ponent and the trip distribution component:

Njj = Nj Pr(i|j) [3]

where is the number of trips from origin i to recrea-
tion site ).

Equation [3] is a trip demand function from the point
of view of the site operator. It represents the number of
trips the site operator can expect to appear at the gate
as a function of user cost, site characteristics, and mar-
ket area characteristics. The site operator can induce
changes in demand by manipulating site characteristics.
For example,, he could increase the capacity of a camp-
ground or open a new nature trail. These effects would
enter the model through the trip generation component.
The site operator can also experience exogenous (to the
site) changes in the distribution of demanded trips from
changes in the relationship between the site and its sur-
rounding market area. For example, a new housing de-
velopment could be built close to the site, or a new road
could be built that dramatically reduced the time and
expense of getting to the site. These effects would enter
the model through the trip distribution component.

In the short run, site characteristics are fixed. With
constant levels of site characteristics, consumer surplus
per trip can be derived using only the trip distribution
component of the model. Hence, we can abstract from
the total model and focus on the distribution model, with
the total trips to a site taken as given. Abstracting from
the trip generation component of the model actually im-
plies a trip generation model. This implied model, and
the trip generation model in general, are discussed in
appendix 1.

The behavioral process implied by the model used
here has been explored from the point of view of the ori-
gins, and found to be plausible. The behavioral process
is based on a fixed effects Poisson distribution, and is
similar to that discussed by Hausman, Hall, and
Griliches (1984).

4

Because we are able to abstract from the trip genera-
tion component of the model, it becomes nothing more
than a scaling factor. Total trips can be taken as given.
This, combined with the problems of not knowing the
PARVS sampling rate or total trips to the sites, led us
to standardize the number of trips. Current (at the time
PARVS was conducted) levels of trips to each site were
set to 100, and all further work was done in the units
"proportion of current trips." Hence, the dependent
variable in the estimated equation was the number of
trips (out of a total of 100 trips to the site) arriving at
a site from a particular origin.

The Applied Trip Distribution Model

The trip distribution component of the model was
specified as a multinomial logit model:

Pr(i|j) =

exp(f(Ki, TCjj, S^)

m

E exp(f(Kh, TChj, Sh))
h= 1

[4]

where f(Kj, TC^, Sj) was of the form:

bk ln(Ki) + bc ln(TCij) + bs ln(Sj)

and there are m origins that deliver trips to site j. Be-
cause the model was estimated as an aggregate model
with the aggregation units defined as counties, the in-
dependent variables in the model were defined as
follows:

Kj = origin characteristics; these were:
POP = county population

INC = per capita personal income in the county
EDUC = proportion of the county population with a
college education
URBAN = proportion of the county population living
in an urban area as defined by the Census
Bureau

WHITE = proportion of the county population classi-
fied by the Census Bureau as white.

TCij = 2 DIST. CPM + GRPj 2 DIST ;j 0.3 INC j; where

40 2080

DIST = one-way distance from origin i to site j

CPM = vehicle operating cost per mile

GRP = group size

DIST = estimated one-way travel time from i to j
40

0.3 INC = value of travel time = 30% of the estimated
2080 hourly wage rate

Sj, S, = travel cost from origin i lb the two closest
Forest Service districts other than j.

The origin characteristics were taken from the 1980
Census of Population (U.S. Bureau of the Census 1983).
Those data were 6 years old at the time the PARVS data
were collected. Nevertheless, it was considered to be the
best data available on a consistent basis across origin
zones. Because group trips were used in the dependent

variable, per capita income was selected over personal
or household measures of income. Travel cost was based
on round-trip distance from the center of the origin
county to a point on the Forest Service ranger district
identified by the district as the most heavily used area
or access point. Vehicle operating cost was 13 cents per
mile; it included costs for gasoline, oil, and maintenance
items. This represents the marginal cost of operating a
vehicle. Cost was determined using data from the U.S.
Department of Transportation (1984) inflated to 1986
dollars using the consumer price index for gasoline.
Higher mileage charges, such as those allowed by the
Internal Revenue Service, include more than the mar-
ginal cost of operating a vehicle and are not appropri-
ate for this study. Group size was the average number
of people travelling together in the same vehicle, re-
ported on the PARVS questionnaire. Travel time was es-
timated by dividing the distance by an average speed
of 40 miles per hour. Travel time was valued at 30% of
the wage rate estimated by dividing per capita income
by 2080 hours. Valuing travel time at 30% of the wage
rate is consistent with recent entries in the economic
literature (Bishop et al. 1988, Kealy and Bishop 1986)
and with the guidelines set forth by the Water Resources
Council.

Substitutes were defined to be the two closest Forest
Service ranger districts other than the one on which the
PARVS respondent was contacted. This was done for
pragmatic reasons because the only data on substitutes
consistently available for all origins were for Forest Serv-
ice ranger districts. A broader range of substitute sites,
including national parks and forests, state and county
parks, forests, and recreation areas would have been
more desirable. Likewise, in the wilderness models, sub-
stitutes were defined as the two closest Forest Service
designated wilderness areas other than the one at which
the respondent was contacted. The travel cost to the sub-
stitute sites was calculated the same way as for the site
to which the recreation trip was taken. We are working
with group trips in the dependent variable and group
cost for the travel cost and substitute variables.

This model specification reduces to a multiplicative
power function:

Pr(i|

POP!"1 TC^2 sfc S2b;< EDUC^5 URBAN^" WHITE^7 INC^9

E POPh1 TCh^ S,hJ S2h4 EDUC^ URBANE WHITE^7 INC^"

h = 1

[5]

The parameters ba through b8 were estimated using
maximum likelihood techniques.

The estimated trip distribution model is analogous to
the first-stage demand function (visitation rate equation)
in the traditional travel cost model. A standard second-
stage travel cost process was used to produce a site
demand function. The travel cost variable (TCjj) in the
numerator of the trip distribution model was increased
incrementally up to a maximum travel cost, and a
second-stage demand function was traced out. The
denominator in the trip distribution model was held
constant as TCj: was increased in the numerator. Be-
cause TC^ appears in only one component of the sum-

mation, the difference between the summed
denominator when TCjj is increased and when it is not
should be relatively small. The result of holding the
denominator constant during the integration is part of
the implied trip generation model discussed in appen-
dix 1. It is the second-stage demand function that is ac-
tually observed by the site operator. Hence, this is the
function from which the measures of consumer surplus
were derived.

The Alaska Model

There were some differences in the way the trip distri-
bution model was applied to Alaska (Forest Service
Region 10) relative to the preceding discussion of the
recreation and wilderness models in the lower 48 states.
First, it was considered unrealistic to think that a per-
son from the lower 48 states would go to Alaska to visit
a single Forest Service ranger district. As a result, the
"site" was considered to be the whole of Alaska. Peo-
ple taking multiple destination trips to Alaska, when all
their destinations were in Alaska, were considered to be
taking a single destination trip to Alaska. Therefore, the
values reported for Alaska are to be interpreted as the
value of a trip to Alaska and not for any particular site
within Alaska. Second, the origin zones were defined
to be states rather than counties. This was done because
of the relatively small number of counties that were
represented in the PARVS data. If counties had been
used as the aggregation units there would have been
much less variation in the dependent variable (trips from
an origin) and a huge number of origins delivering zero
trips. Admittedly, the higher level of aggregation could
lead to other problems, such as assuming away differ-
ences that may exist in subgroups of the aggregation.
In view of the alternative, the higher level of aggrega-
tion appears reasonable. In addition, for the Alaska
wilderness model, the size of the sample made it neces-
sary to aggregate some neighboring origin states. Third,
substitute sites were left out of the Alaska models be-
cause of our consideration of the whole of Alaska as the
recreation site as well as the problem of defining what
would be a consistent substitute for a trip to Alaska. This
means we are implicitly assuming Alaska to be a unique
recreation site — not a totally unreasonable assumption.
Finally, the aggregation of activities was somewhat
different for the Alaska recreation models than for those
in the lower 48 states.

The cost of travel to Alaska was calculated by sum-
ming two separate travel cost components. The first com-
ponent used road miles between the origin state and
Seattle. It was assumed that people making the trip to
Seattle would travel on main highways rather than the
primarily local roads used in visiting sites in the lower
48 states. Hence, travel time was estimated by dividing
the distance by an average speed of 50 miles per hour,
rather than the 40 miles per hour used in the lower 48
states. The second component of travel cost assumed that
people would take a ferry from Seattle to Alaska; it used
the great circle distance times a factor of 18 cents per

person per mile and a speed of 20 miles per hour. The
cost per mile and average speed estimates came from the
Alaska Department of Fish and Game.

Levels of Modelling and Aggregation

Two levels of modelling were used in this study. The
first was the general recreation level. For the general
recreation models, all trips were aggregated, regardless
of primary activity, and a separate model estimated for
each Forest Service region. An important distinction to
be made is that the regional models discussed here are
not truly regional, in the sense of capturing the diversi-
ty contained in a Forest Service region. An example of
a regional model in that sense is found in Sutherland
(1982). Rather, the models presented here are intended
to model a "typical Forest Service recreation site" in that
region. The term "regional models," as used in this
report, denotes that the model was estimated using only
sites in the given region.

It was assumed that the same underlying demand
process was present at all sites within a region. This al-
lowed observations from each site in the region to be
stacked. Hence, the models were estimated as if all ob-
servations from all sites in a region were from a single
site. This process homogenizes sites and behavior in a
region, and ignores differences between sites. To the ex-
tent that one is interested in looking at the value of a
trip to a typical Forest Service site in a region, such
homogenization is acceptable.

The second level of modelling was by primary activ-
ity. For these models, trips were partitioned based on
the reported primary activity of the trip. While recrea-
tionists did not necessarily participate exclusively in
their reported primary activity, it was assumed that other
activities were secondary to the declared primary activ-
ity. Hence, the value of the trip could be attributed to
that primary activity. This involves a double layer of
weak complementarity4 assumptions. First, weak com-
plementarity is invoked to allow the value of the trip to
be attributed to the recreation site. Another weak
complementarity-like assumption is invoked to allow the
value of the trip to be attributed to a primary activity.5
A preferable course might be to admit that recreation
trips are inherently multiple activity trips. The value
would be interpreted as the value of a trip whose primary
purpose is X, rather than as the value of activity X. It

*Weak complementarity is a technical condition that, if it holds, allows
demand functions for nonmarket (or public) goods to be revealed by de-
mand functions for market (or private) goods. A public good and a priv-
ate good are weakly complementary if, when consumption of the private
good is zero, the demand, or marginal willingness to pay, for the public
good is also zero. In the case at hand, we are assuming the demand
for recreation at Forest Service sites and trips to the sites are weakly com-
plementary. If no trips are taken to the site, then the demand for recrea-
tion at the site is zero. Weak complementarity is discussed by Ma\er (1 974)
and by Freeman (1979).

5This second layer of weak complementarity assumes that if the primary
activity were not available at the recreation site, the trip would not have
been made. If the primary activity were available but other activities were
not, the trip would still be made. Hence, the value of the trip can be at-
tributed to the primary activity.

6

is a subtle but important distinction. As with the gener-
al recreation level models, these models are intended to
model participation in the primary activities on typical
Forest Service districts in the region.

It was not possible to estimate a regional model for
each primary activity trip type and region. Sparseness
of data in some activity partitions caused us to aggregate
regions. When aggregation was necessary, we aggre-
gated as little as possible. Table 1 shows the aggrega-
tion level that was used for each primary activity and
region. The Alaska models (Region 10) do not appear

in table 1 because of the aforementioned differences in
activity aggregations. All of the Alaska models were es-
timated exclusively for Alaska. They were all regional
models.

The Data and Associated Methods

This section provides more detail about the Public
Area Recreation Visitors Survey (PARVS). It also
describes the data transformations and manipulations
that were applied to the raw PARVS data.

Table 1 . — Levels of aggregation for first-stage activity demand models.

Activity

Rpnion

L pvpI of annrpnation'
ucvci ui ay y i cyauui i

1

Regions 1,2,4

2

Regions 1,2,4

3

Regional

4

Regions 1 ,2,4

5

Pacific Coast

6

Pacific Coast

8

Rpninnal

g

Regional

1

Rocky Mountain

o
e.

Rocky Mountain

3

Rorkv Mountain

I i i_i o r\ y iviuui Hull I

4

Rnpkv Mountain

5

Pacific Coast

6

Regional

8

Eastern

9

Eastern

1

Regional

2

Regional

3

Regions 1,3,4

4

Regional

5

No Model

6

Regional

8

Regional

9

Eastern

1

Regional

2

Regional

3

Regions 3,4

4

Regional

5

Pacific Coast

6

Pacific Coast

8

Eastern

9

Regional

1 - 6

No models

8

Eastern

9

Eastern

1

Rocky Mountain

2

Rocky Mountain

3

Rocky Mountain

4

Rocky Mountain

5

Pacific Coast

6

Pacific Coast

8

Eastern

9

Regional

Activity

Region

Level of aggregation1

1

Ropkv Mni intain

nUl/ r\ y IVIUUIILulll

2

Rorkv Mountain

i lUo r\y iviuui iiciii i

3

Rorkv/ Mountain

4

Rorkv Moi intain
nuurvy iviuui iiciii i

5

Pacific* f"^oa^t

6

Pacific Coast

8

Eastern

9

Regional

Rorkv Mountain

1 lvwrxy IVIUUI Hull 1

2

Rorkv Mountain

■ iuur\y iviuui 1 1011 i

3

Rorkv Mountain
nuLr\y iviuui hciiii

4

Rorkv Moi intain

nuurxy IVIUUI HCIIII

5

Parifir f^oa^t

6

Pacific Coast

8

Eastern

9

Regional

1 - 4

No models

5

Regional

6

Pacific Coast

a

o

Ron inn p 1
ncy ii_M leal

9

Eastern

1

Western

2

Western

3

Western

4

Western

5

Western

6

Western

8,9

No models

1

Rocky Mountain

2

Rocky Mountain

3

Rocky Mountain

4

Rocky Mountain

5

Western

6

Western

8

No model

9

Nationwide

1

Regions 1,3,4

2

Regional

3

Regions 1,3,4

4

Regions 1,3,4

5

Regional

6

Pacific Coast

8

Regional

9

Eastern

10

Regional

Developed camping

Primitive camping

Big game hunting

Cold water fishing

Warm water fishing

Sightseeing

Day hiking

Picnicking

Swimming

Wildlife observation

Gathering forest products

Wilderness recreation

"Regional indicates that the model was estimated with data exclusively from that region. Other levels of aggregation are:
Rocky Mountain— Regions 1,2,3,4

Pacific Coast — Regions 5,6
Eastern— Regions 8,9
Western— Regions 1,2,3,4,5,6
Nationwide— All regions except Alaska.

7

The Public Area Recreation Visitors Survey

The basic sampling unit for PARVS was a Forest Serv-
ice ranger district. From the 786 ranger districts on all
national forests, 57 were selected for PARVS recreation
site interviewing (table 2). Districts were selected to en-
sure representation of recreation use at the regional lev-
el based on three main criteria: (1) total recreation use

■ Table 2.— PARVS Forest

in a district — heavy versus light use districts; (2) type
of use — developed versus dispersed recreation use dis-
tricts; and (3) downhill skiing — within heavy use dis-
tricts, the districts with the lightest downhill skiing use
were selected. Districts were also selected across regions
to reflect major physiographic types (mountains, coastal
areas, lakes, piedmont, etc.). An effort was made to
gather data at a representative sample of Forest Service

Service recreation sites.

Ranger District

Forest

State

FS Region

Interviews

Elk City

Nezperce

ID

1

40

Salmon

Nezperce

ID

1

42

Priest Lake

Idaho Panhandle

ID

1

69

Ashland

Custer

MT

1

15

Beartooth

Custer

MT

102

Hungry Horse

Flathead

MT

1

43

Dillon

White River

CO

2

91

Blanco

White River

CO

2

64

Pine

San Juan

CO

2

27

South Platte

Pike-San Isabel

CO

2

108

Tensleep

Bighorn

WY

2

68

Wapiti

Shoshone

WY

2

30

Springerville

Apache-Sitgreaves

AZ

3

63

Payson

Tonto

AZ

3

71

Espanola

Santa Fe

NM

3

24

Mimbres

Gila

NM

3

44

Glenwood

Gila

NM

3

62

New Meadows

Payette

ID

4

70

Teton

Targhee

ID

4

11

Flaming Gorge

Ashley

UT

4

47

Cedar City

Dixie

UT

4

57

Logan

Wasatch-Cache

UT

4

134

Big Piney

Bridger-Teton

WY

4

29

Valyermo

Angeles

CA

5

153

Monterey

Los Padres

CA

5

28

Minarets

Sierra

CA

5

34

El Dorado

Lake Tahoe Basin M.U.

CA

5

37

Mammoth

Inyo

CA

5

30

Goosenest

Klamath

CA

5

9

Oak Ridge

Willamette

OR

6

35

McKenzie

Willamette

OR

6

15

Crooked River

Ochoco

OR

6

53

Klamath

Winema

OR

6

26

Big Summit

Ochoco

OR

6

110

Unity

Wallowa-Whitman

OR

6

28

Ashland

Rogue River

OR

6

58

Cle Elum

Wenatchee

WA

6

124

White River

Mt. Baker-Snoqualmie

WA

6

175

Boston Mnt

Ozark-St. Francis

AR

8

19

Seminole

NFS in Florida

FL

8

87

Oconee

Chattahoochee-Oconee

GA

8

47

Chickasawhay

NFS in Mississippi

MS

8

62

Cheoha

NFS in North Carolina

NC

8

42

Croatan

NFS in North Carolina

NC

8

18

Wambau

Francis Marion & Sumter

SC

8

25

Tellico

Cherokee

TN

8

90

Unaka

Cherokee

TN

8

55

Tell City

Wayne-Hoosier

IN

9

100

Mio

Huron-Manistee

Ml

9

59

Androscoggin

White Mountain

NH

9

68

Ironton

Wayne-Hoosier

OH

9

67

Eagle River

Nicolet

Wl

9

99

Greenbriar

Monongahela

WV

9

8

Juneau

Tongass

AK

10

167

Ketchikan

Tongass

AK

10

27

Anchorage, Seward3

Chugach

AK

10

103

aCombines data from the two selected districts on the Chugach National Forest.

8

ranger districts within each region. Overall recreation
use was the criterion, with consideration given to deve-
loped versus dispersed recreation, not use or quality of
the experience for any particular recreation activity. Be-
sides the 57 ranger districts selected for recreation in-
terviewing, 17 wilderness area sites (of the 158
designated wilderness areas nationwide) were selected
(table 3). The targets were to conduct 200 interviews on
each ranger district: 100 during the summer and 50 each
during the fall/winter and winter/spring periods.

Local Forest Service managers were consulted in selec-
tion of interview locations on each district. Roadside
traffic stops were set up at each interview location with
the intent to interview people in their vehicles as they
exited the Forest Service district at the end of their recre-
ation trip. Bad weather and safety considerations forced
some interviewing indoors to visitor centers, museums,
interpretive sites, and other such areas in the middle of
the respondents' trip. Interviewers were also to keep
track of the number of vehicles leaving the area between
and during the interviews in order to estimate a sam-
pling rate. This procedure was difficult to administer,
particularly at the indoor locations, so the number of in-
tervening vehicles was not recorded. Hence, no data are
available from which a sampling rate could be estimated.

Once the roadside interview location was set up, the
flag person stopped the first vehicle to come by. If that
vehicle was from the targeted group, namely recrea-
tionists exiting the site, an interview was conducted,
contingent on willingness of the respondent to partici-
pate. Upon completion of the interview, the next vehi-
cle that could be directed into the interview station
without disrupting or confusing the flow of traffic was
pulled over and the cycle begun again. This process con-
stituted a random selection of groups using the recrea-
tion site. Within each vehicle, the person to be
interviewed was selected randomly. Only persons aged
12 or older were eligible to be interviewed. Random
selection of groups, and respondents within a group, was
also done for nonroadside interviews.

The interviews conducted on Forest Service lands
were conducted at specific times, not periodically
throughout the season. In accordance with the PARVS
training manual and codebook, 7 days were spent on
each ranger district.

Refining the Raw Data

The total Forest Service component of the lower 48
state PARVS interviews numbered 7,172, of which 976
came from designated wilderness areas. Of the remain-
ing 6,196, 448 refused the interview, and 171 had no
recreation site identified on the survey form, leaving a
sample of 5,577 interviews from the 57 PARVS sites,
90% of the original nonwilderness sample.

Missing responses in the data limited the usefulness
of some parts of the PARVS questionnaire, including
reported miles to the site, respondents' identification of
substitute sites and activities, reported distances to sub-
stitute sites, reported hours spent participating in specific
recreation activities, and amount of time spent at other
recreation sites on multiple destination trips. Missing
data for other variables (origin of the recreation trip,
whether the trip was single or multiple destination,
primary activity/purpose of the trip, etc.) limited the sam-
ple sizes. To the extent possible, statistical procedures
were used to classify missing observations into useful
codes. The following procedures were used to minimize
the impact of missing data on key variables in our
analysis.

Travel cost models require identification of an origin
and destination for each observation in the data set.
Counties were selected as the basic unit of analysis for
this study. County origins were not listed for 400 respon-
dents (about 6% of the potential PARVS recreation inter-
views). Where possible, the respondent's zip code was
used to identify an origin county. One hundred seventy-
eight respondents were assigned county codes in this
manner. The county used was always the county of ori-

Table 3.— PARVS Forest Service wilderness sites.

Wilderness areas

Forest

District

State

Region

Great Bear

Flathead

Hungry Horse

MT

1

La Garita

Gunnison-Rio Grande

Cebolla

CO

2

Indian Peaks

Arapaho/Roosevelt

Boulder

CO

2

Pusch Ridge

Coronado

Santa Catalina

AZ

3

Kachina Peaks

Coconino

Flagstaff

AZ

3

Dome

Santa Fe

Jemez

NM

3

Jedediah Smith

Targhee

Teton Basin

ID

4

Mt. Shasta

Shasta-Trinity

Mt. Shasta

CA

5

San Gorgonio

San Bernardino

San Gorgonio

CA

5

Wenaha-Tucannon

Umatilla

Pomery

OR

6

Mt. Jefferson

Willamette

Detroit

OR

6

Colonel Bob

Olympic

Quinault

WA

6

Juniper Prairie

Ocala

Lake George

FL

8

Joyce Kilmer/Slickrock

Nantahala

Cheoha

NC

8

Hercules Glades

Mark Twain

Ava

MO

9

Blackjack Springs

Nicolet

Eagle River

Wl

9

Misty Fjord

Tongass

Misty Fiords

AK

10

9

gin for the trip, even if that was not the home county of
the respondent. The PARVS questionnaire contained
questions to make that distinction.

An assumption made in traditional travel cost analy-
sis is that the site being studied is the sole destination
and purpose of the trip. A question on PARVS asked
respondents to classify their trip as single or multiple
destination. Six hundred ninety-five respondents listed
their trip as multiple destination. In the absence of in-
formation on the proportion of their trip spent at the site
in question, there was no way to allocate joint costs or
trip value among all the destinations visited on the trip.
(A PARVS question that would have allowed an alloca-
tion of joint costs and trip value was one of the questions
with missing data problems.) Those respondents (the
695) were dropped from the analysis. Another 1,803
respondents did not respond to that particular question.
In an attempt to recover as many of those 1,803 observa-
tions as possible, a two-step procedure was developed
to classify the nonrespondents as single destination trips
or indeterminate. If 80% of the respondents to the
single/multiple destination trip question at a given site
(each site was analyzed separately) indicated the trip was
single destination, that site was classified as a "primarily
single destination trip site.' ' Those sites were eligible for
step two of the procedure. The missing observation
respondents from sites not meeting the 80% criterion
were dropped from the analysis. Forty-five sites qualified
for step two.

In the second step, a nonparametric chi-square analy-
sis was used to compare those not answering the single/
multiple destination trip question with the respondents

who classified their trip as single destination. The re-
ported number of hours spent travelling to the site was
used as the nonparametric variable for the analysis. This
variable was converted to a categorical variable for the
test. The chi-square analysis compared the observed fre-
quencies (from the missing response group) with the ex-
pected frequencies (from the single destination trip
group). A significant difference between the two rejected
the hypothesis that the two groups came from the same
population. Again, separate analyses were carried out for
each site. At 18 of the 45 sites eligible for this second step,
this hypothesis could not be rejected. For those sites, the
missing data group was combined with the single desti-
nation trip group. At the remaining 27 sites, the missing
data group was dropped from the analysis. This two-step
procedure resulted in 546 of the 1,803 respondents whose
single/multiple destination trip response was missing be-
ing successfully classified as single destination trips and
recovered for the analysis.

The RPA program analysis calls for recreation values
to be reported by specific recreation activities. The PARVS
questionnaire responses to the activity participation
questions indicated that the recreation trips observed by
PARVS were undeniably multiple activity trips. A ques-
tion on the survey did, however, ask respondents to name
the activity that was the main reason for their trip to the
site. On this basis the sample was partitioned into
primary activity trip types. Table 4 shows the PARVS ac-
tivities that were combined to make up the primary
activity groups used in this study. Using the weak com-
plementarity assumption discussed earlier, the value of
the trip was attributed to the primary activity.

Table 4. — PARVS activities included in primary activity groups.

Developed camping
Camping in developed campgrounds

Primitive camping
Backpacking

Camping in primitive campgrounds

Swimming
Outdoor pool swimming
Other outdoor swimming
Sunbathing
Surfing

Unclassified swimming

Wildlife observation
Wildlife observation and photography
Other nature study
Photography

Day hiking
Day hiking
Walking for pleasure
Running or jogging
Bicycling

Cold water fishing
Cold freshwater fishing
Anadramous fishing

Warm water fishing
Warm freshwater fishing

Big game hunting
Big game hunting

Picnicking
Picnicking
Family gathering
Enjoying outdoors
Going to parks
Other places of enjoyment
Relaxing

Sightseeing
Sightseeing
Driving for pleasure
Travelling

Gathering forest products
Gathering firewood
Collecting berries

All other activities
Canoeing or kayaking
Horseback riding
Small game hunting
Using self-guided trails
Reading roadside markers
Visiting museums
All other PARVS activities

10

Discriminant analysis was used to assign primary
activities to respondents not answering the primary ac-
tivity question. Within each primary activity group (com-
posed of those who did answer the primary activity
question), the proportion of total activity time spent in
each activity was calculated. These time-in-activity pro-
files were used in the discriminant analysis to derive clas-
sification functions. The classification functions were
then used to predict the primary activity for those per-
sons who left the primary activity question blank. This
analysis did not affect the overall sample size (used for
the general recreation level models) but did increase the
sample size in each of the primary activity partitions
(used for the primary activity trip level models).

The final sample size of PARVS general recreation
interviews was 3,072. If the classification procedures dis-
cussed above had not been used, the sample size would
have been 2,348. The classification procedures increased
our sample by 31%.

The PARVS recreation sample of 3,072 was used to es-
timate models for the "lower 48" states. It includes
neither Alaska nor the designated wilderness areas. The
final sample used to estimate the Alaska models consist-
ed of 297 interviews with out-of-state visitors. These data,
too, were partitioned into primary activity groups. The
final usable wilderness area sample consisted of 615 in-
terviews (576 in the lower 48 states and 39 in Alaska).
In both cases, Alaska and wilderness, the procedures
described above for the lower 48 states were used to re-
cover interviews where missing data presented a problem.

Table 5 shows the final sample sizes (in terms of the
number of interviews completed) in each of the primary
activity partitions and in wilderness recreation for each
Forest Service region in the lower 48 states. Table 6 gives
comparable information for Alaska. The column totals
in tables 5 and 6 give the number of interviews making
up the general recreation model sample in each region.
In addition, table 6 shows the activity aggregations used
in the Alaska models — different than those used in the
lower 48 states.

Table 6.— Numbers of PARVS recreation interviews by primary activity
in Forest Service Region 10 (Alaska).

Primary activity

Interviews

Developed site activities
Camping, picnicking, swimming

37

Sightseeing
Mechanized travel and viewing scenery

135

Wildlife related activities
Hunting
Fishing

Nonconsumptive wildlife

1
18
12

31

Other activities

94

Total (General recreation)

297

Wilderness recreation

39

Origins, Destinations, and Market Areas

The number of trips observed to each of the recreation
sites is equal to the number of interviews completed at
each site. As discussed previously, the reverse gravity
model used in this study is essentially a share model.
The dependent variable used in the model was the num-
ber of trips to a site from a particular origin. Some ori-
gins delivered more than one trip and other origins
within a site's market area delivered zero trips. Hence,
the number of observations (or data points) used in the
estimation procedure was the number of origins in a site's
market area rather than the number of trips to the site.

Counties were the basic unit of origin in this study.
The sites were Forest Service ranger districts. Distances
between origins and sites were estimated by using cir-
cuity factors to adjust the great circle distances between
latitude and longitude points to highway miles. The great
circle distance is essentially the air miles between two
points. Circuity factors are state-specific adjustment fac-
tors to convert, on average, great circle distance to high-
way miles — both on an intrastate and interstate basis (U.S.

Table 5. — Numbers of PARVS recreation interviews by primary activity and Forest Service Region.

Forest Service Region

Primary activity

1

2

3

4

5

6

8

9

Total

Developed camping

48

37

71

32

54

109

35

52

438

Primitive camping

10

19

11

8

8

74

27

24

181

Swimming

7

1

1

2

42

16

120

85

274

Wildlife observation

3

4

4

2

7

17

2

5

44

Day hiking

7

27

17

12

28

8

4

23

126

Cold water fishing

45

81

43

53

41

69

23

27

382

Warm water fishing

0

0

1

2

5

8

12

26

54

Big game hunting

37

60

17

109

4

77

63

22

389

Picnicking

15

24

17

15

44

22

41

40

218

Sightseeing

43

34

25

27

25

58

27

30

269

Gathering forest products

16

1

12

11

9

21

0

6

76

Other activities

80

100

45

75

24

145

91

61

621

Total (General recreation)

311

388

264

348

291

624

445

401

3,072

Wilderness recreation

7

91

72

23

104

86

165

28

576

11

Department of Commerce 1978). The estimations were
done using a precursor to the ZIPFIP software package.6
Distances were calculated from the geographic center of
the origin county to a representative point on the ranger
district. These representative points were determined in
conjunction with district recreation staffs. The points
were defined as the single recreation site or area that at-
tracts the most trips (visits) by recreationists or a site near
the center of the most heavily used geographic area of
the district, excluding downhill ski areas.

There would have been some advantages to using the
reported distances from the PARVS data. Two factors
prevented this, however. On many of the surveys the dis-
tance question was left blank. Second, there were coun-
ties used in the estimation that delivered zero trips to
the site. There were no survey responses at all for those
origins. As a result, calculated distances between origins
and sites were used.

Market areas are the geographic areas from which the
recreation sites attract visits. To define market areas, a
graphics/mapping program was used to display the dis-
tribution and frequency of recreation trips coming from
the counties around each PARVS site. Market areas were
delineated on a site by site basis with consideration given
to both the distribution and frequency of visits to the site.
This is consistent with the arguments presented by Smith
and Kopp (1980). In order to estimate the models, con-
sideration also had to be given to the number of zero visit
counties included in a site's market area. This amounted
primarily to eliminating very distant origins delivering
one trip. At one site in Colorado, for example, the bulk
of the visits came from a relatively local band of coun-
ties around the site. There were, however, visits observed
from three or four counties in Texas. It was decided to
drop those counties from the market area on the assumed
basis that trips to the site from that distance involved a
different underlying demand process. It was also con-
sidered probable that those were misclassified multiple
destination trips. Origins dropped from the market area
were not used to estimate the first-stage share models.
Determination of market areas was done at the general
recreation level — based on all trips to the site — and not
for each individual primary activity trip type. About six
trips per PARVS site, for a total of 331 trips across all sites,
were eliminated because they came from outside a de-
fined market area.

The distances to substitute sites, identified for each ori-
gin in a market area, were calculated as great circle
distances adjusted by circuity factors, the same as the dis-
tances to the sites at which the interview occurred. The
demographic variables, describing characteristics of each
origin county, came from the 1980 Census of Population.
Demographic variables presented the same problem as
the distance variable; namely, there were missing
responses in the PARVS data, and no survey data at all
for zero-visit counties.

*Hellerstein, D.M.; McCollum, D.W.; Donnelly, D.M. 1989. "ZIPFIP: A
Zip and FIPS Database Package. " Draft manuscript, USDA, Forest Serv-
ice, Rocky Mountain Forest and Range Experiment Station, Fort Collins,
CO.

Characteristics of Recreation Trips

Tables 7, 8, and 9 show the average group size and aver-
age number of days onsite for each region and primary
activity trip type, across the recreation, Alaska, and
wilderness samples. These simple averages of the re-
sponses to questions on the PARVS were used as the con-
version factors for moving between the units reported in
the Results section. Group size is the reported number
of people travelling together in the same vehicle. Aver-
age days onsite per person per trip was derived by divid-
ing the average total hours onsite per person per trip by
24. Average total hours onsite is the difference, in hours,
between the time the respondent reported arriving onsite
and the time Jie reported leaving the site, both recorded
in the PARVS data. The accuracy of these numbers de-
pends on the accuracy of the respondent's recall of when
the group arrived onsite and the projected time they
would be leaving the site in the case of a nonexit inter-
view. In the case of an exit interview, the time of the in-
terview is the departure time. Average days onsite per
person per trip represents the number of calendar days
the person spent onsite. This corresponds to the num-
ber of activity occasions per person per trip. An activity
occasion is defined as a person participating in an ac-
tivity on a calendar day. This is the unit agreed to by the
RPA staff to be reported in place of the more traditional,
but widely controversial, recreation visitor day (RVD).

The conversion factors are presented for each region
and for each type of primary activity trip. They are also
presented on a nationwide basis (all regions combined)
for each primary activity trip type, and on a general recre-
ation basis (all trip types combined) for each region. In
calculating these conversions, the mean was substituted
for regions and activities having small sample sizes.
When the sample size dropped below five for either the
group size or onsite time variable, the national mean (by
primary activity trip type) for that variable was substi-
tuted. In addition, the Region 4 warm water fishing trips
were excluded from the national averages because both
the group size and the length of time onsite greatly ex-
ceeded the averages from all other regions and were
judged to be outliers.

Results

Model Estimation

The estimated trip distribution models are summarized
in appendix 2. The coefficients from the final models,
their t-statistics, and goodness-of-fit measures, along with
sample size information, are presented en masse. The de-
pendent variable was the number of trips arriving at the
site from a particular origin. For the general recreation
models, the coefficients on the travel cost variables are
uniformly negative and very significant. The coefficients
on population are positive, ranging from 0.453 to 0.974,
and very significant. The two measures of substitute sites
were highly correlated, so one of the measures was
dropped from the model. In all regions, the coefficient

12

Table 7— Conversion factors for recreation site consumer surplus values.

Primary Activity Trip Type

Devel. Prim. Wildlife Day Cld wat Wrm wat Big game Sight- For. Gen. rec.

Region Units camp. camp. Swim. obsv. hiking fishing fishing hunting Picnic seeing prod, (all trps)

1

Ava

Group

Size3

3.20

2.96c

3.33

2.64c

2.29

3.09

2.61c

2.42

3.40

2.64

2.36c

2.97

Avg.

Days°

3.90

3.17

0.63c

2.94c

1.24c

1.15

1.44c

5.18c

2.56

0.90

2.42c

2.81

2

Avg.

Group

Size

2.89

2.56

3.39c

2.64c

2.42

2.80

2.61c

2.19

3.15

2.48

2.36c

2.52

Avg.

Days

2.14

2.06

0.63c

2.94c

0.76

3.25

1.44c

3.25

1.91

0.45

2.42c

2.09

3

Avg.

Group

Size

2.91

2.50

3.39c

2.64c

2.46

2.65

2.61c

2.60

3.83

2.90

2.45

2.77

Avg.

Days

3.72

2.73c

0.63c

2.94c

1.39

3.24

1.44c

2.65

1.82

0.88

2.42c

2.80

A
■f

Avg.

Group

Qi -*o

RQ

Q QQC

o.oy

1 01

0 pr

O OR
C..C.Z)

O.OO

^ 1 ft

O. I D

c. . 00

C..O I

Avg.

Days

3.26

3.17

0.63c

2.94c

1.24c

3.40

1.44c

7.31

2.47c

0.63

2.42c

3.98d

5

Avg.

Group

Size

3.08

2.75

2.90

2.33

2.29

2.49

2.61c

2.33c

3.53

2.83

2.36c

2.81

Avg.

Days

3.73

2.99

1.26

2.94c

2.93

1.31

1.44c

5.18c

2.61

0.90°

2.42c

2.28

6

Avg.

Group

Size

2.63

2.66

2.88

3.12

2.28c

2.58

2.61c

2.44

3.25

2.28

2.10

2.58

Avg.

Days

4.39

2.68

0.45

1.80

1.24c

1.09

1.44c

7.73

1.14

0.84

3.84

3.06

8

Avg.

Group

Size

2.34

3.15

3.55

2.64c

2.28c

2.45

2.61c

2.42

2.79

1.92

2.36c

2.91

Avg.

Days

5.42

2.21

0.44

2.94c

1.24c

1.86

1.44c

3.43

3.22

1.73

2.42c

1.85

9

Avg.

Group

Size

3.20

3.26

3.51

2.64c

2.45

2.65

2.42

2.14

2.88

2.44

2.36c

2.88

Avg.

Days

5.04

4.24

0.45

2.94c

0.83

2.73

1.80

4.73

3.44

0.98

2.42c

2.45

All

Avg.

Group

Size

2.93

2.96

3.39

2.64

2.28

2.69

2.61d

2.33

3.22

2.54

2.36

2.76

Reg.

Avg.

Days

4.06

2.73

0.63

2.94

1.24

2.26

1.44d

5.18

2.47

0.90

2.42

2.66

a Average number of people travelling in a vehicle to Forest Service district.
b Average days onsite per person per trip.

c The mean value across all regions was substituted due to a small sample size.

d Region 4, warm water fishing, was excluded from calculation of the mean due to an excessively large conversion factor, judged to be an outlier.

Table 8.— Conversion factors for recreation site consumer surplus values Table 9.— Conversion factors for wilderness recreation consumer sur-
in Forest Service Region 10 (Alaska). plus values.

Primary activity3

Average
group sizeb

Average
days per trip0

General recreation

2.64

18.40

Developed

3.03

18.59

Sightseeing

2.61

16.61

Wildlife

2.83

26.16

a These activities are not strictly comparable to those used in the "low-
er 48" models. The activities listed here for Alaska are aggregations of
primary activities used in the lower 48. These activity aggregations are:

Developed. — Developed site activities, including camping, picnick-
ing, and swimming.

Sightseeing. — Mechanized travel and viewing scenery.

Wildlife. — All wildlife related activities, including hunting, fishing, and
nonconsumptive.

General recreation. — All primary activities.

b Average number of people travelling together to Alaska.

0 Average days in Alaska per person per trip. Note that this differs from
the onsite time used to calculate average days per trip in the lower 48
states models. Because Alaska was defined to be a single site, the time
on site is the total time in Alaska. This was calculated as total trip time
minus round-trip travel time as reported in the PARVS survey.

on the remaining substitute site measure was positive and
significant. It is not clear exactly what effects were be-
ing captured by the variables representing origin charac-
teristics. Income was dropped as a separate explanatory
variable because it already appeared in the model as part

Average

Average

Region

group size

days per trip

1

2.28

1.973

2

2.23

1.00

3

2.64

1.40

4

3.29

2.35

5

3.03

2.68

6

3.00

3.44

8

2.97

1.48

9

2.65

3.74

10

1.73

18.40b

a All of the respondents in Region 1 (all 7 of them) had missing infor-
mation in one or more of the responses used to calculate days on site.
The days per trip for Region 1 is an average of those observed in Regions
1, 3, and 4 since Region 1 was included in a Region 1,3,4 demand model.

b All of the respondents in Region 10 had missing information in one
or more of the responses used to calculate days per trip. The days per
trip reported here is the overall average days per trip from the Alaska
recreation sites.

of the travel cost. In almost all cases, the income coeffi-
cient was not significantly different from zero and had
a negligible effect on the fit of the model. The remain-
ing three origin characteristic variables did not appear
to be consistently significant nor did they consistently
have the same sign.

Turning to the primary activity trip models, the ob-
servations are much the same as they were in the gener-
al recreation models. In almost all cases, the coefficients

13

on travel cost were negative and significant, and those
on population were positive and significant. In a little
over one-third of the region and activity pairs, the coeffi-
cient on the substitute measure was not significantly
different from zero. In six of the pairs (out of a total of
74 region and primary activity pairs) the coefficient on
the substitute measure was negative. In none of those six,
however, was the coefficient significantly different from
zero. It is not inconceivable to get negative coefficients
on the substitute measure, though we expect them to be
positive. This could be due to our measurement of sub-
stitute opportunities as the two closest Forest Service
ranger districts other than the one at which the recrea-
tionist was contacted. A negative coefficient indicates
that the other sites are complements to the chosen site
rather than substitutes. Such a finding would not be to-
tally unreasonable. People may choose locations where
there are more recreation opportunities available so if
one area is congested they can easily move to another.
It could also indicate that multiple destination trips are
present, even though the data were filtered for such trips
using one of the PARVS questions.

In general, the workings of substitution between recre-
ation goods is not well understood and could vary be-
tween sites, times, activities, or individuals. In some
sense, it is surprising that our very rough measure of sub-
stitute opportunities worked as well as it apparently did.

As in the general recreation models, the coefficients
on the origin characteristic variables were not consis-
tently significant nor did they consistently have the same
sign across regions and activities. Individual origin char-
acteristic variables were taken out of the final models
when they were insignificant. The substitute variable
and the population variable were always included in the
final model for theoretical reasons.

The travel cost coefficients in the Alaska models were
larger in absolute magnitude (more negative) than those
for the lower 48 states, indicating that trips to Alaska
are more price sensitive than trips in the lower 48
states — not surprising given the expense of a trip to Alas-
ka. This could well be true for any recreation trip that
involved great expense. The model for wildlife-related
activities in Alaska was the only model in which per cap-
ita income appeared as an independent variable. The ef-
fect of income in this particular model was so strong that
it could not be excluded.

The wilderness models in the lower 48 states were
similar to the general recreation models. The travel cost
coefficients were negative and significantly different
from zero. Population coefficients were positive and sig-
nificantly different from zero. The substitute term coeffi-
cients were positive and generally significant. The
magnitudes of individual coefficients vary somewhat,
but the range is generally consistent with that seen in
the general recreation models.

The travel cost coefficient in the Alaska (Region 10)
wilderness model was smaller in absolute value than
those in the Alaska recreation models. This difference
indicates that trips to Alaska for wilderness recreation
are less price sensitive than trips for general recreation
purposes. Whether this difference is real or merely a con-

sequence of the particular sample of data cannot be de-
termined without further empirical work. As in the
Alaska recreation models, the travel cost variable as-
sumed travel to Alaska from Seattle by ferry.

Consumer Surplus Estimates

Table 10 shows the average consumer surplus values
for the general recreation models, for each of the regional
activity models, and for the wilderness models; table 11
shows these values for the Alaska models. The values
were derived by calculating the area under the second-
stage demand function, discussed earlier, for each
sampled site in each region. Hence, for most region and
activity pairs there were several values estimated — one
for each site. The high, low, and average values for each
region and activity pair are shown in table 10. For the
lower 48 states recreation sites, the integration was car-
ried out to a maximum travel cost of $195. For Alaska
(table 11), the integration was carried out to $3,020 for
the recreation sites and $1,700 for the wilderness site.
The discrepancy in maximum travel costs between the
Alaska recreation sites and the Alaska wilderness site
was due to the difference in average group size observed
between these sites (we are dealing with group trips and
group costs). Alaskan recreation sites had a higher max-
imum travel cost because the cost was for a larger group.
In addition, the slopes of the demand functions were
different, implying a different cutoff price. The lower
48 states wilderness sites were integrated out to a maxi-
mum travel cost of $225. All of these maximum travel
cost values were calculated using the maximum round-
trip distance observed in each of the three data subsam-
ples be/ore market areas were determined.

Sites within the PARVS sample were included in a
particular regional activity value calculation only if they
delivered primary activity trips of that type. An in-
dividual site that delivered no big game hunting trips
was excluded from the big game hunting model. The
values are presented for three units of aggregation —
group trips, person trips, and person days. The conver-
sions were given in tables 7,8, and 9. The unit of obser-
vation in the PARVS data, which was the unit used to
estimate the models, was the group trip. As a result, the
values in terms of group trips represent our best esti-
mates of consumer surplus. These are to be interpreted
as the value of the trip for the entire group. The values
were converted to person trips (group trips divided by
group size) and person days (group trips divided by
group size and average days onsite) using the conver-
sion factors derived from the PARVS data. The values
in the converted units are only as accurate as those con-
version factors.

Also shown in tables 10 and 11 are the estimated fee
increases that would cut recreation use of the site to 50%
of its current level. The assumption is that if these fee
increases were imposed on recreation at the sites, use
of the sites would drop to 50% of current use levels.
These are fee increases above and beyond any existing
fees (which were assumed to be zero). The fee increases

14

Table 10. — Consumer surplus values (in dollars) for primary activity trips by Forest Service Region.

Average Average price (fee increase)

consumer surplus at 50% current use 3

Region Units High Low Average High Low Average

General Recreation Models

1

Group trips'3

72.10

21.15

60.99

88.78

3.70

49.48

Person trips0

24.28

7.12

20.53

29.89

1.25

16.66

Person daysd

8.63

2.53

7.30

10.63

0.44

5.93

2

Group trips

61.68

42.99

50.00

54.68

18.44

29.20

Person trips

24.48

17.06

19.84

21.70

7.32

11.59

Person days

11.70

8.16

9.49

10.38

3.50

5.54

3

Group trips

60.39

33.10

53.56

61.16

12.54

43.04

Person trips

21.80

11.95

19.34

22.08

4.53

15.54

Person days

7.78

4.27

6.90

7.88

1.62

5.55

4

Group trips

98.67

33.58

53.98

79.13

4.79

33.11

Person trips

35.11

11.95

19.21

28.16

1.70

11.78

Person days

8.83

3.00

4.83

7.08

0.43

2.96

c
o

r/"M i trir^e

oruup inpb

56.15

32.28

47.11

1 1 O'X

ou.uo

Person trips

19.98

11.49

16.77

16.04

4.00

10.69

Person days

8.76

5.04

7.35

7.03

1.75

4.69

b

Group trips

33.02

18.48

25.23

1 7.5o

"7 OC

7.<£b

H 4 OO

1 1 .2o

Person trips

12.80

7.16

9.78

6.81

2.81

4.37

Person days

4.19

2.34

3.20

2.23

0.92

1.43

Q

o

Group trips

35.03

12.66

23.31

1 0.01

o.oo

Person trips

12.04

4.35

8.01

5.16

1.32

2.90

Person days

6.51

2.35

4.33

2.79

0.72

1.57

y

Group trips

54.98

13.47

38.63

AC A1

4b. 4o

O. IV

dA.Kj l

Person trips

19.09

4.68

13.41

16.12

1.28

8.34

Person days

7.79

1.91

5.47

6.58

0.52

3.40

Developed Camping

1

Group trips

96.73

55.22

86.57

133.84

16.95

97.60

Person trips

30.23

17.26

27.05

41.82

5.30

30.50

Person days

7.75

4.42

6.94

10.72

1.36

7.82

2

Group trips

97.58

80.52

90.58

137.04

87.52

109.37

Person trips

33.76

27.86

31.34

47.42

30.28

37.85

Person days

15.79

13.03

14.66

22.17

14.16

17.70

3

Group trips

50.67

31.56

46.15

48.78

13.48

33.81

Person trips

17.41

10.85

15.86

16.76

4.63

11.62

Person days

4.68

2.91

4.26

4.50

1.24

3.12

4

Group trips

147.99

85.28

104.07

159.36

80.31

117.78

Person trips

41.34

23.82

29.07

44.51

22.43

32.90

Person days

12.68

7.31

8.92

13.66

6.88

10.09

5

Group trips

42.11

25.47

36.40

35.39

9.00

20.47

Person trips

13.67

8.27

11.82

11.49

2.92

6.65

Person days

3.66

2.22

3.17

3.08

0.78

1.78

6

Group trips

39.54

24.88

33.28

19.93

9.85

15.24

Person trips

15.03

9.46

12.65

7.58

3.75

5.79

Person days

3.42

2.15

2.88

1.73

0.85

1.32

8

Group trips

53.69

23.25

38.93

27.44

6.53

15.40

Person trips

22.94

9.94

16.64

11.73

2.79

6.58

Person days

4.23

1.83

3.07

2.16

0.51

1.21

9

Group trips

77.09

40.59

66.28

100.40

12.01

58.95

Person trips

24.09

12.68

20.71

31.38

3.75

18.42

Person days

4.78

2.52

4.11

6.22

0.74

3.65

15

Table 10.— Continued.

Average Average price (fee increase)

consumer surplus at 50% current use a

Region Units High Low Average High Low Average

Primitive Camping

1

Group trips
Person trips
Person days

102.94
34.78
10.97

80.21
27.10
8.55

94.03
31.77
10.02

132.77
44.85
14.15

73.26
24.75
7.81

103.49
34.96
11.03

2

Group trips
Person trips
Person days

103.66
40.49
19.67

79.53
31.07
15.09

97.47
38.08
18.50

142.23
55.56
26.99

72.21
28.21
13.70

117.06
45.73
22.21

3

Group trips
Person trips
Person days

103.30
41.32
15.12

83.28
33.31
12.19

93.12
37.25
13.63

129.43
51.77
18.95

48.12
19.25
7.05

92.48
36.99
13.54

4

Group trips
Person trips
Person days

101.54
34.30
10.83

98.71
33.35
10.52

99.94
33.7b
10.65

135.63

AC OO

4b. od.
14.46

128.65

A n ACL

43.4b

13.72

131.53
44.44
14.02

5

Group trips
Person trips
Person days

50.06
18.20
6.09

44.75
16.27
5.44

47.41
17.24
5.77

35.65
12.96
4.34

28.69
10.43
3.49

32.17
11.70
3.91

6

Group trips
Person trips
Person days

35.38
13.30
4.96

25.89
9.73
3.63

32.44
12.19
4.55

16.18
6.08
2.27

9.97
3.75
1.40

14.55
5.47
2.04

8

Group trips
Person trips
Person days

27.44
8.71
3.94

7.87
2.50
1.13

16.21
5.15
2.33

12.62
4.01
1.81

3.22
1.02
0.46

6.81
2.16
0.98

9

Group trips
Person trips
Person days

43.10
13.22
3.12

18.95
5.81
1.37

32.35
9.92
2.34

34.76
10.66
2.52

7.77
2.38
0.56

21.82
6.69
1.58

Swimming

5

Group trips
Person trips
Person days

45.42
15.66
12.44

28.12
9.70
7.70

39.13
13.49
10.72

25.06
8.64
6.87

9.95
3.43
2.73

19.75
6.81
5.41

6

Group trips
Person trips
Person days

71.60
24.86
24.86e

61.25
21.27
21.27s

65.18
22.63
22.63e

53.76
18.67
18.67e

33.67
11.69
1 1 .69e

41.25
14.32
14.326

8

Group trips
Person trips
Person days

42.72
12.03
12.03e

17.21
4.85
4.85e

29.58
8.33
8.33e

19.04
5.36
5.36e

4.89
1.38
1.38e

10.73
3.02
3.02e

9

Group trips
Person trips
Person days

52.79
15.04
15.04e

16.68
4.75
4.75e

35.45
10.10
10.10e

38.65
11.01
11.01e

4.31
1.23
1.23e

18.50
5.27
5.27e

Wildlife Observation

1

Group trips
Person trips
Person days

82.71
31.33
10.66

69.52
26.33
8.96

76.12
28.83
9.81

89.77
34.00
11.57

40.24
15.24
5.19

65.01
24.62
8.38

2

Group trips
Person trips
Person days

78.42
29.70
10.11

71.88
27.23
9.26

75.15
28.47
9.68

77.99
29.54
10.05

63.54
24.07
8.19

70.77
26.80
9.12

3

Group trips
Person trips
Person days

84.31
31.94
10.86

68.08
25.79
8.77

77.66
29.42
10.01

110.81
41.97
14.28

66.94
25.36
8.63

95.07
36.01
12.25

4

Group trips
Person trips
Person days

67.33
25.50
8.68

67.33
25.50
8.68

67.33
25.50
8.68

50.67
19.19
6.53

50.67
19.19
6.53

50.67
19.19
6.53

5

Group trips
Person trips
Person days

79.80
34.25
11.65

38.63
16.58
5.64

64.90
27.85
9.47

84.51
36.27
12.34

32.92
14.13
4.81

58.39
25.06
8.52

6

Group trips
Person trips
Person days

81.86
26.24
14.57

77.83
24.95
13.85

79.80
25.58
14.20

100.06
32.07
17.80

61.42
19.69
10.93

77.87
24.96
13.86

16

Table 10.— Continued.

Average Average price (fee increase)

consumer surplus at 50% current use a

gion

Units

High

Low

Average

High

Low

Average

Cold Water Fishing

1

Group trips
Person trips
Person days

89.34
28.91
25.17

73.42
23.76
20.68

85.49
27.67
24.08

118.12
38.23
33.27

62.62
20.27
17.64

96.02
31.07
27.05

2

Group trips
Person trips
Person days

99.41
35.50
10.92

90.60
32.36
9.96

94.97
33.92
10.44

132.86
47.45
14.60

95.84
34.23
10.53

106.38
37.99
11.69

3

Group trips
Person trips
Person days

106.59
40.22
12.41

81.90
30.91
9.53

96.02
36.24
11.18

131.89
49.77
15.35

82.60
31.17
9.62

107.72
40.65
12.54

4

Group trips
Person trips
Person days

90.51
34.15
10.05

56.25
21.23
6.24

67.28
25.39
7.47

87.37
32.97
9.70

27.52
10.38
3.05

44.31
16.72
4.92

5

Group trips
Person trips
Person days

70.98
28.51
21.77

55.48
22.28
17.02

61.82
24.83
18.96

60.35
24.24
18.51

27.41
11.01
8.41

43.79
17.59
13.43

6

Group trips
Person trips
Person days

70.78
27.43
25.19

59.85
23.20
21.30

66.94
25.95
23.82

61.77
23.94
21.98

31.50
12.21
11.21

46.54
18.04
16.56

8

Group trips
Person trips
Person days

52.44
21.40
11.50

51.00
20.82
11.18

51.54
21.04
11.30

22.47
9.17
4.93

21.25
8.67
4.66

21.69
8.85
4.76

9

Group trips
Person trips
Person days

70.49
26.60
9.75

44.94
16.96
6.22

60.40
22.79
8.35

69.67
26.29
9.64

17.06
6.44
2.36

46.24
17.45
6.40

Warm Water Fishing

8

Group trips
Person trips
Person days

45.60
17.47
12.13

32.79
12.56
8.72

41.11
15.75
10.93

19.43
7.44
5.17

10.98
4.21
2.92

16.31
6.25
4.34

9

Group trips
Person trips
Person days

65.59
27.10
15.04

21.28
8.79
4.88

45.88
18.96
10.52

63.33
26.17
14.53

5.23
2.16
1.20

34.49
14.25
7.91

Day Hiking

1

Group trips
Person trips
Person days

79.89
34.89
28.13

44.97
19.64
15.83

67.72
29.57
23.85

78.93
34.47
27.79

10.90
4.76
3.84

50.15
21.90
17.66

2

Group trips
Person trips
Person days

81.03
33.48
33.48e

70.48
29.12
29.12e

74.46
30.77
30.77e

93.10
38.47
38.47s

42.73
17.66
17.66s

63.08
26.07
26.07e

3

Group trips
Person trips
Person days

86.17
35.03
25.20

67.35
27.38
19.69

77.90
31.67
22.78

107.47
43.69
31.42

35.32
14.36
10.33

79.05
32.13
23.11

4

Group trips
Person trips
Person days

65.74
34.42
27.74

62.01
32.47
26.16

63.76
33.38
26.90

43.77
22.92
18.47

28.72
15.04
12.12

34.16
17.89
14.41

5

Group trips
Person trips
Person days

98.91
43.19
14.74

77.44
33.82
11.54

92.35
40.33
13.76

118.58
51.78
17.67

80.66
35.22
12.02

102.25
44.65
15.24

6

Group trips
Person trips
Person days

103.27
45.29
36.49

99.58
43.68
35.19

101.30
44.43
35.80

141.34
61.99
49.94

123.63
54.22
43.69

131.69
57.76
46.53

8

Group trips
Person trips
Person days

74.43
32.64
26.30

38.86
17.04
13.73

55.89
24.51
19.75

52.45
23.00
18.53

10.48
4.60
3.70

28.10
12.32
9.93

9

Group trips
Person trips
Person days

86.17
35.17
35. 17s

58.47
23.87
23.87s

17

74.49
30.40
30.40s

103.79
42.36
42.36s

21.15
8.63
8.63s

64.24
26.22
26.22s

Table 10.— Continued.

Average Average price (fee increase)

consumer surplus at 50% current use a

Region Units High Low Average High Low Average

Big Game Hunting

1

Group trips

70.64

30.59

57.81

66.59

5.83

38.08

Person trips

29.19

12.64

23.89

27.52

2.41

15.73

Person days

5.63

2.44

4.61

5.31

0.46

3.04

2

Group trips

45.27

19.59

29.75

30.45

6.48

14.09

Person trips

20.67

8.95

13.59

13.90

2.96

6.43

Person days

6.36

2.75

4.18

4.28

0.91

1 .98

3

Group trips

85.57

63.32

75.52

114.51

29.67

77.91

Person trips

32.91

24.35

29.04

44.04

11.41

29.96

12.42

9.19

10.96

16.62

4.31

1 1 .31

4

Group trips

120.03

50.09

71.56

116.62

15.09

56.99

Person trips

53.35

22.26

31.81

51.83

6.71

25.33

Person days

7.30

3.04

4.35

7.09

0.92

3.46

6

Group trips

115.42

88.85

104.94

152.99

84.34

120.97

Person trips

47.30

36.41

43.01

62.70

34.57

49.58

Person days

6.12

4.71

5.56

8.11

4.47

6.41

8

Group trips

78.91

47.06

62.76

64.69

15.09

35.01

Person trips

32.61

19.45

25.94

26.73

6.24

14.47

Person days

9.51

5.67

7.56

7.79

1.82

4.22

9

Group trips

94.85

69.38

84.25

117.84

29.41

74.16

Person trips

44.32

32.42

39.37

55.07

13.74

34.65

Person days

9.37

6.86

8.33

11.64

2.91

7.33

Picnicking

1

Group trips

85.64

60.82

76.21

94.13

42.53

71.30

Person trips

25.19

17.89

22.41

27.69

12.51

20.97

Person days

9.84

6.99

8.76

-1 f\ on

A QQ

d on

2

Group trips

85.02

75.73

80.38

110.51

60.73

86.00

Person trips

26.99

24.04

25.52

35.08

19.28

27.30

Person days

14.12

12.58

13.35

1 o.ob

i u.uy

1 A OQ

3

Group trips

85.33

77.94

82.07

109.16

77.65

90.31

Person trips

22.28

20.35

21.43

28.50

20.27

23.58

Person days

12.24

11.18

11.77

15.66

11.14

12.96

4

Group trips

79.49

70.36

74.93

100.99

44.63

72.81

Person trips

20.65

18.28

19.46

26.23

11.59

18.91

Person days

8.36

7.40

7.88

10.62

4.69

7.66

5

Group trips

55.82

37.43

45.31

40.31

15.52

25.33

Person trips

15.81

10.60

12.84

11.42

4.40

7.17

Person days

6.06

4.06

4.92

4.38

1.69

2.75

6

Group trips

47.93

32.05

41.52

26.61

10.17

20.17

Person trips

14.75

9.86

12.77

8.19

3.13

6.21

Person days

12.95

8.66

11.22

7.19

2.75

5.45

8

Group trips

50.39

21.80

37.01

24.51

6.09

14.36

Person trips

18.06

7.81

13.27

8.78

2.18

5.15

Person days

5.61

2.43

4.12

2.73

0.68

1.60

9

Group trips

69.67

26.63

54.07

75.29

7.04

45.81

Person trips

24.19

9.25

18.77

26.14

2.44

15.91

Person days

7.03

2.69

5.46

7.60

0.71

4.62

18

Table 10.— Continued.

Average Average price (fee increase)

consumer surplus at 50% current use a

Region Units High Low Average High Low Average

Sightseeing

1

Group trips

54.89

6.77

35.85

46.57

1.98

20.74

Person trips

20.79

2.56

13.58

17.64

0.75

7.86

Person days

20.79s

2.56e

13.586

17.646

0.75e

7.86e

2

Group trips

49.28

28.38

38.55

30.36

9.80

19.15

Person trips

19.87

11.44

15.55

12.24

3.95

7.72

Person days

19.876

1 1 .44s

15.55e

12.246

3.95e

7.72e

3

Group trips

51.25

29.64

44.35

35.83

11.87

27.06

Person trips

17.67

10.22

15.29

12.36

4.09

9.33

Person days

17.676

10.22e

15.29e

12.366

4.09e

9.33e

4

Group trips

38.98

11.88

27.92

21.98

1.77

10.96

Person trips

12.34

3.76

8.84

6.96

0.56

3.47

Person days

12.346

3.76e

8.84e

6.96e

0.56e

3.47e

c
0

Group trips

51.12

38.59

AG. ~7r\
40. / U

41 19

I D . / c.

97 7A

Person trips

18.06

13.64

16.15

14.53

5.91

9.80

Person days

18.06®

13.646

16.156

14.53e

5.91e

9.80e

D

Group trips

45.73

34.97

AC\ 7Q

OQ OO

1 r on

00 OP,

Person trips

20.06

15.34

17.89

12.38

6.67

8.89

Person days

20.06e

15.346

17.896

12.386

6.67e

8.89e

Q

o

Group trips

25.01

10.39

\ o.oy

o.oy

Q AA

D.f D

Person trips

13.03

5.41

9.84

4.53

1.79

3.36

Person days

7.53

3.13

5.69

2.62

1.04

1.95

y

Group trips

66.88

22.32

77 C\0

Of . 1 o

Person trips

27.41

9.15

20.19

31.57

2.48

15.22

Person days

27.41e

9.15e

20.196

31.57e

2.48e

15.226

Gathering Forest

Products

1

Group trips

80.71

52.81

72.85

83.28

18.72

62.21

Person trips

34.20

22.38

30.87

35.29

7.93

26.36

Person days

14.13

9.25

12.76

14.58

3.28

10.89

2

Group trips

80.76

80.76

80.76

82.16

82.16

82.16

Person trips

34.22

34.22

34.22

34.81

34.81

34.81

Person days

14.14

14.14

14.14

14.39

14.39

14.39

3

Group trips

84.90

60.99

74.39

92.46

25.52

69.99

Person trips

34.65

24.89

30.36

37.74

10.42

28.57

Person days

14.32

10.28

12.54

15.59

4.30

11.80

4

Group trips

76.13

49.68

63.78

74.10

14.26

41.52

Person trips

32.26

21.05

27.03

31.40

6.04

17.59

Person days

13.33

8.70

11.17

12.98

2.50

7.27

5

Group trips

67.13

67.13

67.13

43.30

43.30

43.30

Person trips

28.44

28.44

28.44

18.35

18.35

18.35

Person days

11.76

11.76

11.76

7.58

7.58

7.58

6

Group trips

76.76

74.02

75.49

67.63

51.94

59.31

Person trips

36.55

35.25

35.95

32.20

24.73

28.24

Person days

9.52

9.18

9.37

8.39

6.44

7.36

9

Group trips

77.45

68.90

73.18

64.75

43.99

54.37

Person trips

32.82

29.19

31.01

27.44

18.64

23.04

Person days

13.56

12.07

12.82

11.34

7.70

9.52

19

Table 10.— Continued.

Average Average price (fee increase)

consumer surplus at 50% current use a

Region Units High Low Average High Low Average

Wilderness Recreation

1

Group trips

16.26

16.26

16.26

5.77

5.77

5.77

Person trips

7.13

7.13

7.13

2.53

2.53

2.53

Person days

3.62

3.62

3.62

1.28

1.28

1.28

2

Group trips

43.82

16.26

30.04

21.23

4.48

12.86

Person trips

19.65

7.29

13.47

9.52

2.01

5.76

Person days

19.65e

7.29e

13.47e

9.32e

2.01e

5.76e

3

Group trips

36.89

15.50

26.20

15.35

4.67

10.01

Person trips

13.97

5.87

9.92

5.81

1.77

3.79

Person days

9.98

4.19

7.09

4.15

1.26

2.71

4

Group trips

37.18

37.18

37.18

15.66

15.66

15.66

Person trips

11.30

11.30

11.30

4.76

4.76

4.76

Person days

4.81

4.81

4.81

2.03

2.03

2.03

5

Group trips

31.26

18.85

25.06

13.49

8.55

11.02

Person trips

10.32

6.22

8.27

4.45

2.82

3.64

Person days

3.85

2.32

3.09

1.66

1.05

1.36

6

Group trips

27.69

21.42

24.66

10.75

6.72

9.13

Person trips

9.23

7.14

8.22

3.58

2.24

3.04

Person days

2.68

2.08

2.39

1.04

0.65

0.88

8

Group trips

34.91

30.15

32.53

12.89

10.59

11.74

Person trips

11.75

10.15

10.95

4.34

3.57

3.95

Person days

7.94

6.86

7.40

2.93

2.41

2.67

9

Group trips

47.89

12.29

30.09

22.38

3.25

12.82

Person trips

18.07

4.64

11.35

8.45

1.23

4.84

Person days

4.83

1.24

3.04

2.26

0.33

1.29

10

Group trips

302.71

302.71

302.71

252.75

252.75

252.75

Person trips

1 74.98

174.98

174.98

146.10

146.10

146.10

Person days

9.51

9.51

9.51

7.94

7.94

7.94

a The average fee increase (price) necessary to reduce recreation use to 50% of the current use level.
b Average net value per trip of a visit to Forest Service district.

c Average net value per person per trip of a visit to Forest Service district (group trip value divided
by average group size).

d Average net value per person per day of a visit to FS district (person trip value divided by average
calendar days per trip). This corresponds to value per activity occasion.

e Denotes that average days per trip is less than one. Hence, the value per activity occasion (per-
son day) is the same as the value per person per trip.

are presented as a high value, low value, and average
value for each region and activity pair, as were the con-
sumer surplus values. The same conversion factors were
used to convert the fee increases to units of person trips
and person days that were used to convert the consumer
surplus values. These fee increases do not warrant a lot
of discussion. Their meaning is questionable because
cutting use of the recreation sites to 50% of current lev-
els would involve shifts in the demand functions, not
just movement along the functions. They are useful,
however, as an indication of the slopes of the demand
functions. Those regions and primary activity trip types
requiring a high fee increase to cut use to 50% of their
current levels have a relatively steeper demand function
than those requiring a small fee increase.

It appears, from table 10, that the consumer surplus
values vary among regions. It also appears that, within
each region, consumer surplus values vary among

primary activity trips. It is instructive to look at each
region and see the types of activity trips having the
highest and lowest values. The weakest conversion data
is the length of trip, because of missing data. Hence, we
focus on the results in terms of group trips (which we
regard as our most reliable results) and person trips
(which we perceive to be most comparable with other
entries in the economic literature).

Table 12 is a summary of the consumer surplus values
for each primary activity trip type and region. The two
highest primary activity trip values in each region (com-
pare columns within a row) for group trips and person
trips are highlighted with a double underline. The two
lowest values are single underlined. Overall, primitive
camping, day hiking, and big game hunting are most
likely to be the highest valued primary activity trip types
in a region. Sightseeing, developed camping, and primi-
tive camping are most likely to be the lowest valued

20

Table 1 1 . — Consumer surplus values (in dollars) for Alaska Recreation.

Average price

tUi loU nit? r

dl DU70

Primary activity3

surplus

current useb

U6H t?i dl I t;Oi fcJdUUI 1

oroup u i[Jb

OH l ,H\J

Person tripsd

166.80

131.81

Person dayse

9.06

7.16

/ a \ /~t n a ri

uevciupcu

Group trips

00 I .uo

0U0. 1 /

Person trips

125.83

100.10

Person days

6.77

5.38

Sightseeing

Group trips

419.35

319.10

Person trips

160.57

122.19

Person days

9.67

7.36

Wildlife

Group trips

482.92

360.79

Person trips

170.79

127.60

Person days

6.53

4.88

3 These activities are not strictly comparable to those used in the "low-
er 48" models. The activities listed here for Alaska are aggregations of
primary activities used in the lower 48. These activity aggregations are:

Developed. — Developed site activities, including camping, picnick-
ing, and swimming.

Sightseeing.— Mechanized travel and viewing scenery.

Wildlife. — All wildlife related activities, including hunting, fishing, and

nonconsumptive.

General recreation.— All primary activities.

b The average fee increase (price) necessary to reduce recreation use

to 50% of the current use level.
0 Average net value per trip of a group visit to Alaska.
6 Average net value per person per trip of a visit to Alaska (group trip

value divided by average group size).
e Average net value per person per day of a visit to Alaska (person

trip value divided by average calendar days per trip).

primary activity trip types. Primitive camping is partic-
ularly interesting. It is one of the two highest valued trip
types in Regions 1,2,3, and 4, and one of the two lowest
valued trip types in Regions 6,8, and 9. Big game hunt-
ing is similarly interesting. It is one of the two lowest
valued trip types in Regions 1 and 2, and one of the two
highest valued trip types in Regions 6, 8, and 9. Sight-
seeing is uniformly one of the two lowest valued trip
types in Regions 1, 2, 3, and 4 — what might be called
the Rocky Mountain region. Developed camping is uni-
formly one of the two lowest valued trip types in Regions
5 and 6 — the Pacific coast, and in Region 3 — the South-
west. Day hiking trips are among the highest valued in
Regions 5,6,8, and 9. In Region 4, day hiking trips are
among the lowest valued in terms of group trips and
among the highest valued in terms of person trips. This
latter observation illustrates the possible impact of the
conversion factors. Depending on which unit of aggre-
gation is considered, a trip type is either the highest or
lowest valued in the region. Forest product gathering
trips — a major element of which is collecting firewood —
is highly valued in Regions 1, 2, 5, and 9. Cold water
fishing trips are highly valued in Regions 2 and 3.

Several reasons exist as to why any particular activ-
ity might show different consumer surplus values in
different regions. One is the presence or absence of sub-
stitute sites at which to participate in the activity. The
more available substitutes, the lower the value of any
particular site. These values are tied to the sites at which
the data were gathered. Forest Service sites in some
regions might not be the places where certain activities
are engaged in, though for most of the activities consid-
ered here, that is probably not the case. A particular sub-
set of the data for some region-activity pair might be less
than perfectly representative, causing the values to be
either too high or too low. There is always some prob-
ability, though usually small, of a given sample or sub-
sample being unrepresentative when statistical sampling
techniques are used.

Table 13 is the same summary of values presented in
table 12, except the comparisons in table 13 are between
rows within a column. The two regional values that are
the highest for a given trip type (compare rows within
a column) in group trips and person trips are highlighted
by double underlining; the two lowest regional values
are single underlined. The focus of table 12 is on par-
ticular regions, across activities, whereas the focus of
table 13 is on particular activities, across regions. The
highest values for a given activity are most frequently
found in Regions 2 and 6. The lowest values are most
frequently found in Regions 8 and 4.

In many cases the most consistent values across
regions come from models aggregated across regions.
This can be seen by putting together the information in
table 1, in the model section, with the information in
table 13. The model appearing to be best as far as con-
sistency of values across regions may not be the best in
terms of explaining the behavior in a particular region.
The consistency of values between regions may, in some
cases, be the result of using a model aggregated over
more than one region, rather than consistency of eco-
nomic behavior in the regions.

Alaska (Forest Service Region 10) does not appear in
either table 12 or 13 because the activity aggregations
used in Alaska were somewhat different from those used
in the lower 48 states. The general recreation level values
for Alaska, however, are comparable with those from the
lower 48 states because all trips are included, regard-
less of primary activity. The values from Alaska are also
comparable with those from the lower 48 states for trips
whose primary activity is sightseeing. The only differ-
ence, in both models, is that in Alaska the whole state
was considered to be the site. Multiple destination trips
were included as long as all destinations were in Alaska.
In the case of general recreation, the values are the aver-
age value for any trip in the region, i.e., any primary
activity trip to Alaska. In the lower 48 states, the values
are the average value for a trip to a typical site in the
region. The general recreation values for Alaska were
$439.64 per group trip and $166.80 per person trip, com-
pared with ranges of $23 to $61 and $8 to $21, respec-
tively, in the lower 48 states. The primary activity trip
values for sightseeing in Alaska were $419.35 per group
trip and $160.57 per person trip, compared with ranges

21

Table 12.— Average consumer surplus (in dollars) for primary activity trips by region.
(Values highlighted within regions3)

Devel. Prim. Wildlife Day Cld wat. Wrm wat. Big game Sight- For.

Region Units camp. camp. Swim, observ. hiking fishing fishing hunting Picnic seeing prod.

4
1

Group trips'3

OC C"7

c\a no

NM

76.12

67.72

85.49

NM

57.81

76.21

35.85

72.85

Porcnn trinc^
r tr 1 oUI 1 11 Ipo

97 rm

9,1 77

9P. P.7

OO R7

97 £7
d.1 .Of

MM
NM

no. on

OO A 1

^ o co
1 O.OO

30.87

Person days1^

6.94

10.02

NM

9.81

23.85

24.08

NM

4 R1

t.U 1

R 7fi

I O.OO

1 9 7fi

o

Group trips

90.58

97.47

NM

75.15

74.46

94.97

NM

29.75

80.38

38.55

80.76

Porcnn trine
r tsi oui l III

oo.uo

MM

INIVI

9P. 47

on 77
ou. / /

77 no

oo. y^i

MM

1 7 CO

i o.oy

OK CO

1 O.OO

Person days

14.66

18.50

NM

9.68

30.77*

10.44

NM

4.18

13.35

1^

1 J.JJ

14. 14

O
O

Group trips

46.15

93.12

NM

77.66

77.90

96.02

NM

75.52

82.07

44.35

74.39

Porcnn trine

I J.OO

77 OR

MM

OO AO
^y .4<1

71 P.7
Ol .Of

7fi OA

MM
NM

on n^

O-t ylO
d \ .40

l o.^y

on oc

Person days

4.26

13.63

NM

10.01

22.78

11.18

NM

10.96

1 1 .77

I •J e—ZP

19 ^4

4

Group trips

104.07

99.94

NM

67.33

63.76

67.28

NM

71 .56

74.93

27.92

63.78

Porcnn trine
i GloUN liipo

on r\-7

77 7fi
oo. / D

MM
NM

or rh

77 7P.

OR 7Q

MM
INM

01 .01

4Q AC

i y .4d

Q Qyl

B.04

0"7 AO
<i/.UO

Person days

8.92

10.65

NM

8.68

26.90

7.47

NM

4.35

7.88

8.84f

11.17

c

o

Group trips

36.40

47.41

39.13

64.90

92.35

61 .82

NM

NM

45.31

45.70

67.13

Person trips

1 i DO

1 7 o>i

■* o /in

0"7 OC

lit .OO

Af\ OO

O A OO

NM

NM

12.84

16.15

28.44

Person days

3.17

5.77

10.72

9.47

13.76

18.96

NM

NM

4.92

16.15'

11.76

6

Group trips

33.28

32.44

65.18

79.80

101.30

66.94

NM

104.94

41.52

40.78

75.49

Person trips

12.65

12.19

22.63

25.58

44.43

25.95

NM

43.01

12.77

17.89

35.95

Person days

2.88

4.55

22.63f

14.20

35.80

23.82

NM

5.56

11.22

17.89f

9.37

8

Group trips

38.93

16.21

29.58

NM

55.89

51.54

41.11

62.76

37.01

18.89

NM

Person trips

16.64

5.15

8.33

NM

24.51

21.04

15.75

25.94

13.27

9.84

NM

Person days

3.07

2.33

8.33*

NM

19.75

11.30

10.93

7.56

4.12

5.69

NM

9

Group trips

66.28

32.35

35.45

NM

74.49

60.40

45.88

84.25

54.07

49.25

73.18

Person trips

20.71

9.92

10.10

NM

30.40

22.79

18.96

39.37

18.77

20.19

31.01

Person days

4.11

2.34

10.10'

NM

30.40f

8.35

10.52

8.33

5.46

20.19'

12.82

a Across a row, a double underline identifies the two highest valued primary activity trips within a region; a single underline identifies the two
lowest valued.

b Average net value per trip of a group visit to Forest Service district (all participants included).

0 Average net value per person per trip of a visit to Forest Service district (group trip value divided by average group size).

d Average net value per person per day of a visit to Forest Service district (person trip value divided by average calendar days per trip). This
corresponds to value per activity occasion.

e Values of NM indicate that no model was estimated for that region and primary activity trip pair. This occurred when there were no trips in
a region that could be classified as being of that primary activity.

' Denotes that average days per trip is less than one. Hence, the value per activity occasion (person day) is the same as the value per person
per trip.

of $19 to $49 and $9 to $20, respectively, in the lower
48 states. The Alaska trip values are significantly higher
than trip values in the lower 48 states. One reason for
this difference might be the length of the trips. In the
lower 48 states, trips were between 2 and 4 days in
length; in Alaska, trips averaged 18 days.

The average consumer surplus values (in terms of
person trips) appear generally lower for wilderness recre-
ation than for recreation at nonwilderness sites (as in-
dicated by the general recreation values). Only in
Regions 6 and 8 are the values so close as to be virtually
the same. Only in Regions 8 and 10 are the wilderness
values higher than the general recreation values.

In Region 10 (Alaska) all of the wilderness respondents
had missing information in one or all of the survey ques-
tions used to calculate trip length. Because of that, the
average days per trip for wilderness users was taken to
be the same as the average days per trip for all Alaska
recreation users (18.4 days). To the extent that this is
an overestimate (underestimate) of the true days per trip

for wilderness users in Alaska, the person day values
will be underestimated (overestimated).

Discussion

The values reported here are conservative estimates,
primarily because the limits of integration used in the
calculation of consumer surplus (the maximum travel
cost values) were set to correspond to the maximum dis-
tance observed in the relevant sample. In effect, we are
assuming people who travel from the furthest distances
have zero consumer surplus. In the same way, we are
putting an upper limit on the surplus of people travel-
ling shorter distances. This is likely to be unrealistic,
but we agree with those who feel uncomfortable in ex-
tending the analysis substantially beyond the range of
the data. We feel it is more useful to have an estimate
known to be a lower bound (consumer surplus is at least
$X) than to have one that may be an underestimate or

22

Table 13. — Average consumer surplus (in dollars) for primary activity trips by region.
(Values highlighted within trip types3)

Devel. Prim. Wildlife Day Cld wat. Wrm wat. Big game Sight- For. Gen. rec.

Region Units camp. camp. Swim, observ. hiking fishing fishing hunting Picnic seeing prod, (all trips)

1

Group trips"

86.57

94.03

NMe

76.12

67.72

Person trips0

27.05

31.77

NM

28.83

29.57

Person daysd

6.94

10.02

NM

9.81

23.85

2

Group trips

90.58

97.47

NM

75.15

74.46

Person trips

31.34

38.08

NM

28.47

30.77

Person days

14.66

18.50

NM

9.68

30.77'

3

Group trips

46.15

93.12

NM

77.66

77.90

Person trips

15.86

37.25

NM

29.42

31.67

Person days

4.26

13.63

NM

10.01

22.78

4

Group trips

104.07

99.94

NM

67.33

63.76

Person trips

29.07

33.76

NM

25.50

33.38

Person days

8.92

10.65

NM

8.68

26.90

5

Group trips

36.40

47.41

39.13

64.90

92.35

Person trips

11.82

17.24

13.49

27.85

40.33

Person days

3.17

5.77

10.72

9.47

13.76

6

Group trips

33.28

32.44

65.18

79.80

101.30

Person trips

12.65

12.19

22.63

25.58

44.43

Person days

2.88

4.55

22.63'

14.20

35.80

8

Group trips

38.93

16.21

29.58

NM

55.89

Person trips

16.64

5.15

8.33

NM

24.51

Person days

3.07

2.33

8.33'

NM

19.75

9

Group trips

66.28

32.35

35.45

NM

74.49

Person trips

20.71

9.92

10.10

NM

30.40

Person days

4.11

2.34

10.10'

NM

30.40'

85.49

NM

57.81

76.21

35.85

72.85

60.99

27.67

NM

23.89

22.41

13.58

30.87

20.53

24.08

NM

4.61

8.76

13.58'

12.76

7.30

94.97

NM

29.75

80.38

38.55

80.76

50.00

33.92

NM

13.59

25.52

15.55

34.22

19.84

10.44

NM

4.18

13.35

15.55'

14.14

9.49

96.02

NM

75.52

82.07

44.35

74.39

53.56

36.24

NM

29.04

21.43

15.29

30.36

19.34

11.1.8

NM

10.96

11.77

15.29'

12.54

6.90

67.28

NM

71.56

74.93

27.92

63.78

53.98

25.39

NM

31.81

19.46

8.84

27.03

19.21

7.47

NM

4.35

7.88

8.84'

11.17

4.83

61 .82

NM

NM

45.31

7f)

Of . Iw

47 1 1

24.83

NM

NM

12.84

16.15

28.44

16.77

18.96

NM

NM

4.92

16.15'

11.76

7.35

66.94

NM

104.94

41.52

40.78

75.49

25.23

25.95

NM

43.01

12.77

17.89

35.95

9.78

23.82

NM

5.56

11.22

17.89'

9.37

3.20

51.54

41.11

62.76

37.01

18.89

NM

23.31

21.04

15.75

25.94

13.27

9.84

NM

8.01

11.30

10.93

7.56

4.12

5.69

NM

4.33

60.40

45.88

84.25

54.07

49.25

73.18

38.63

22.79

18.96

39.37

18.77

20.19

31.01

13.41

8.35

10.52

8.33

5.46

20.19'

12.82

5.47

a Within a column, a double underline identifies the regions with the two highest values for that primary activity trip type; a single underline iden-
tifies the regions with the two lowest values.
b Average net value per trip of a group visit to Forest Service district (all participants included).

c Average net value per person per trip of a visit to Forest Service district (group trip value divided by average group size).

d Average net value per person per day of a visit to Forest Service district (person trip value divided by average calendar days per trip). This
corresponds to value per activity occasion.

6 Values of NM indicate that no model was estimated for that region and primary activity trip pair. This occurred when there were no trips in
a region that could be classified as being of that primary activity.

' Denotes that average days per trip is less than one. Hence, the value per activity occasion (person day) is the same as the value per person
per trip.

may be an overestimate and not know which it is (con-
sumer surplus may be more or less than $X but we do
not know which).

The data section discussed ways in which the raw data
were filtered for single or multiple destination trips.
Only single destination trips were used in the analysis.
It is often difficult to separate single from multiple des-
tination trips. The PARVS data allowed that distinction
to be made. It is important because the presence of mul-
tiple destination trips in the data would bias the valua-
tion results upward. When a multiple destination trip
is taken, the total value of the trip must be allocated
among all destinations on the trip. If such trips are in-
cluded in the analysis of a single site (without some way
of attributing partial trip values to the particular site),
the total value of the multiple destination trip will be
assigned to that site when, in fact, only a portion of the
trip value belongs with that site.

At the same time, there is the possibility of a bias be-
ing created by leaving multiple destination trips out of

the specification of substitutes in the model. To the ex-
tent that multiple destination trips substitute for single
destination trips, this would be a concern. The whole
area of multiple destination trips is one of continuing
debate in the economic literature, and the extent of any
bias, if it exists, created by not including multiple des-
tination trips in the model as a substitute for single des-
tination trips is unknown.

The careful reader might notice that there is not a per-
fect correspondence between the regions that most fre-
quently exhibit the highest or lowest primary activity
trip values and the regions exhibiting the highest or
lowest general recreation values. In particular, Region
6 most frequently exhibits one of the two highest primary
activity trip values, yet it shows one of the two lowest
general recreation values. Region 4 most frequently ex-
hibits one of the two lowest primary activity trip values,
yet it has one of the two highest general recreation
values. Region 1 exhibits the highest general recreation
values, but is infrequently highest or lowest in primary

23

activity trip values. Several factors are involved in these
curious observations. One is that the general recreation
values include all trips and not just those that could be
classified as any particular primary activity. In each
region there was a sizable number of trips that could not
be classified as any primary activity. These trips pull the
general recreation value up or down without affecting
the primary activity trip values. A second factor is that
all general recreation level models were estimated using
regional models. The general recreation values came ex-
clusively from sites within the region. As the data were
partitioned into primary activity trip types, it became
necessary to aggregate regions in many cases. Hence, the
models from which regional primary activity trip values
were derived were sometimes estimated using observa-
tions from other regions. While the models were second-
staged on each individual site, and regional values were
taken only from sites in the region, the effect of other
regions on the first-stage parameter estimates cannot be
filtered out.

Values reported here must be taken in the context of
the data with which they were estimated. It was point-
ed out earlier that these models were estimated using
only the Forest Service component of the PARVS data.
In designing the sampling frame for that component, ef-
forts were made to ensure a representative sample of
Forest Service ranger districts. Therefore, values esti-
mated from these data can only be extended to "typical
Forest Service sites." They are not for premium sites,
nor are they for substandard or degraded sites. They are
for average Forest Service sites.

In terms of absolute numbers, some of the primary ac-
tivity trip values reported here are different from values
reported in existing studies in the economic literature.
Sorg and Loomis (1984) and Walsh et al. (1988) present
relatively exhaustive reviews of the literature on valua-
tion of outdoor recreation. Several factors must be con-
sidered before coming to a conclusion on whether a
particular set of values are right or wrong, good or bad.
First, of course, is the quality of the study. Sorg and Loo-
mis, and Walsh et al. adjusted the values from the studies
they found to "approach more uniformity of method."
Travel cost values were increased by 30% when the
study omitted travel time, and 15% when the study
truncated out-of-state users. Travel cost values were
decreased 15% when an individual travel cost model
was used rather than an aggregated or zonal model. Our
intent is not to argue with those adjustments, but to point
out that final values are sensitive to the specification of
the model and the independent variables it includes.
Values may also be sensitive to the theoretical appropri-
ateness of the model used in the study.

One important factor not considered by Sorg and Loo-
mis or Walsh et al. was whether the model considered
the effect of substitute sites. Unless one is dealing with
a unique resource, for which there are no good substi-
tutes, economic theory indicates that substitutes belong
in the demand model. In general, leaving substitutes out
of the model leads to inflated estimates of consumer sur-
plus. Finally, we would reiterate that our reported values
are conservative. The studies cited by Sorg and Loomis

and Walsh et al. likely cover a wide range of assump-
tions regarding how far the integration was carried out
in calculating consumer surplus.

One must also realize that values for recreation are site-
specific. Because of that, site quality enters in. One
would expect differences in value between a premium
hunting or fishing site and an average site. To some ex-
tent, values for recreation are individual-specific. One
would expect different values for a site used primarily
by local people and one to which people travel from all
over the country. In this regard, values are very depend-
ent on the sample of users from which the model is esti-
mated. Great care must be taken to ensure a
representative sample. Results and values can only be
attributed back to and interpreted vis-a-vis the popula-
tion that the sample represents. All too often values are
estimated using a very specific subpopulation and at-
tributed blindly back to a much broader group. Care
must be taken to avoid such careless application of
results.

Concern was expressed by some reviewers of these
values that the wildlife values — fishing, and particular-
ly big game hunting — were markedly lower than values
reported in previous studies. Concern was also expressed
over low values in some regions for developed camp-
ing and primitive camping. We share some of those con-
cerns. The values reported here for some regions and
primary activity trip types are low compared to those
reported elsewhere. For some other regions and primary
activity trip types the values may appear high based on
intuition.

The PARVS sites were chosen to be representative of
the range of sites available on Forest Service lands. The
goal was to model recreation behavior on a typical Forest
Service ranger district. Districts were chosen to represent
all levels of use — high, moderate, and low. That implies
the values reported here apply to the typical Forest Serv-
ice district. The operative words in the preceding sen-
tence are typical district. Districts were chosen for
inclusion in PARVS based on overall recreation use, not
use in any particular activity. The big game hunting
values, therefore, represent big game hunting on a typi-
cal Forest Service district, not big game hunting on a
typical Forest Service big game hunting district. The dis-
tinction is subtle but critical. A typical Forest Service
district may or may not be a typical Forest Service big
game hunting district. To some extent, one might ex-
pect an inverse relationship between hunting use at a
site and other recreation use at the same site. The point
is that values must be interpreted in light of the sample.

Another critical element is the timing of the sample.
To the extent that different activities occur at different
times of the year, participants in a particular activity may
be underrepresented, or missed entirely, by sampling at
any given time. Again, take big game hunting as an ex-
ample. Fall sampling for PARVS was done in October.
This is prime time for people going out to the forest to
view the fall colors, but may be too early for the primary
hunting season in some parts of the country. For exam-
ple, the various gun deer and elk seasons in Colorado
run from mid-October to mid-December. In Wisconsin,

24

gun deer hunting season runs from mid to late Novem-
ber. Depending on exactly when sampling was done in
a particular area, the bulk of big game hunters may have
been missed.

Region 2 big game hunting was looked at in particu-
lar detail because of the lower than expected values that
came out of that model. Based on goodness of fit, the
Region 2 big game hunting model was one of our better
models in terms of explaining the behavior reflected by
the data. One thing we did to further explore that model
was to raise the truncation level in the calculation of con-
sumer surplus. Because of the particular coefficients in
that model, raising the truncation level to over $1000
(originally the maximum travel cost was $195) had very
little effect on the consumer surplus values. The charac-
ter of the sample in Region 2 (and in others) was over-
whelmingly local. The character of the region is that
there are a lot of sites that are similar in terrain, habitat,
etc. This means there are a lot of available substitutes,
particularly in Colorado and Wyoming where the Region
2 PARVS sites were. The consumer surplus, or willing-
ness to pay, may genuinely be low for those particular
sites. How much would a hunter be willing to pay to
hunt at site A when he can go ten miles down the road
and hunt under virtually the same conditions for a low-
er cost or at no cost? Probably not very much. It was
pointed out, by a reviewer, that a survey done by the
State of Colorado showed annual hunter expenditures
averaged hundreds of dollars to hunt big game in Colora-
do. That may be true, but it is irrelevant when the cor-
rect measure of value is consumer surplus — willingness
to pay above and beyond existing costs and fees. Indeed,
those high expenditure levels may be taking up so much
of the total value that the remaining consumer surplus
is small.

Big game hunting is illustrative of many of the primary
activity values reported here. The sample was by and
large relatively local. The character of Forest Service
sites is such that, in many areas of the country, there
are substitutes readily available. This does not imply that
recreation on Forest Service lands is of low value. It does
imply that the value of recreation on Forest Service lands
that can be picked up by a recreation demand model is
relatively low. The values captured by the travel cost
method are strictly use values. Nonuse values, such as
existence value and option value, are ignored. (See
Bishop et al. (1987), Peterson and Sorg (1987), and
Randall (1987) for discussions of nonuse values.) For
resources such as National Forests, nonuse values may
be quite large. By nature, the travel cost method provides
more of a lower bound value than a maximum value.
Conservative estimates of value are prudent, but they
should be recognized as such.

The real value of this study might be not so much the
absolute magnitudes of the values but the relative values
between regions and primary activity trip types. It is a
big advantage, in making such comparisons, to use the
same modelling framework estimated with data collected
using the same survey instrument for all regions and
primary activity trips. Another advantage of this study

is that the focus, for all types of primary activity trips,
is exclusively on Forest Service sites.

Conclusions

Having presented the results and discussed the issue
of directly comparing those results to results of other
studies, let us address the question: "What do these
values represent?" The values presented here are esti-
mates of average consumer surplus for recreation trips
whose primary purpose is a particular category of ac-
tivity. They are not the same as prices in the sense that
one pays a price for a loaf of bread. In economics jar-
gon, they are the average of the excess prices a dis-
criminating monopolist would charge, over and above
existing prices, if he could charge a separate price for
each trip. If the Forest Service were to establish an in-
dividualized access fee to its lands that would be exact-
ly the difference between the maximum amount an
individual would pay to recreate on Forest Service land,
rather than forgo recreating on Forest Service land, and
the sum of the costs and fees he already pays, the aver-
age of all those access fees would be the values reported
here. They do not represent the cost of providing the
recreation opportunity and they do not represent the in-
tersection of a supply and a demand function. They are
a measure of the average individual net benefit received
from recreating on Forest Service lands. These values
answer the question, identified in an earlier section as
being the question posed by the 1990 RPA Program
Analysis: "What is the net value of the recreation ex-
perience at a typical Forest Service site averaged over
all users of the site?"

Literature Cited

Bishop, R. C.j Boyle, K. J.; Welsh, M. P. 1987. Toward
total economic valuation of great lakes fishery
resources. Transactions of the American Fisheries So-
ciety. 116: 339-345.

Bishop, R. C; Heberlein, T. A.; McCollum, D. W.;
Welsh, M. P. 1988. A validation experiment for valu-
ation techniques. Madison, WI: University of
Wisconsin-Madison, College of Agricultural and Life
Sciences, Center for Resource Policy Studies.

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niques for assessing the demand and supply of out-
door recreation in the United States. Paper SE-275.
Asheville, NC: U.S. Department of Agriculture, Forest
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Ewing, G. O. 1980. Progress and problems in the devel-
opment of recreation trip generation and trip distri-
bution models. Leisure Sciences. 3: 1-24.

Freeman, A. M., III. 1979. The benefits of environmen-
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25

Hausman, J.; Hall, B. H.; Griliches, Z. 1984. Economet-
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909-938.

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Smith, V. K.; Kopp, R. J. 1980. The spatial limits of the
travel cost recreational demand model. Land Econom-
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229-247.

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Institute.

26

Appendix 1. More on the Trip Generation Model

We originally intended to estimate the trip generation
component of the reverse gravity model as well as the
trip distribution component. For the immediate purpose
of estimating recreation values for the 1990 RPA Program
Analysis, we realized that the trip generation component
of the model was unnecessary. The lack of data on the
total numbers of trips to the sites reinforced our deci-
sion not to estimate the trip generation component of
the model.

In a more general and complete analysis it would be
desirable to estimate the trip generation component of
the model. The trip generation component was speci-
fied above to be a function of site characteristics or at-
tractiveness and an index measuring the accessibility of
a site to the market area from which it attracts trips. To
move toward a measure of site characteristics or attrac-
tiveness, a factor analysis was performed using a vector
of site characteristics to explain variation in annual recre-
ation visitor days (RVD's) on Forest Service ranger dis-
tricts. The RVD's and site characteristics came from the
Recreation Information Management (RIM) System data
base maintained by the Forest Service.1

The factor analyses showed that different site charac-
teristics are important for different activities. There were,
however, several common characteristics or similar
characteristics important to several activities. Proximi-
ty (within 10 miles) to a lake or river was important in
about two-thirds of the activities considered. Proximity
to camping sites was important in several activities.
Proximity to picnic areas, hiking trails, and potable
water were important in more than one activity. Acres
of particular Recreation Opportunity Spectrum (ROS)
class lands were important to particular activities. For
example, acres of land classified as primitive were im-
portant to primitive camping and backpacking, gather-
ing forest products, hiking, and big game hunting. These
factor analyses indicate that there are certain quantifia-
ble site characteristics that can be used to predict recre-
ation participation at a site. The remaining task is to put
these factors into an index or other form that can be used
in a regression-type analysis.

One possibility for the measure of market access to the
site would be to use the denominator from the trip dis-
tribution component of the model. That, in fact, is the
usual practice in the traditional gravity model, where

1 The RIM base is compiled from information supplied by Forest Serv-
ice ranger districts. It includes various site characteristics such as: acres
of land in different ROS (Recreation Opportunity Spectrum) classes (primi-
tive, roaded natural, semi-primitive motorized, etc.), numbers of camp
units and other facilities such as picnic areas and boat launch areas on
the district, capacities of some facilities, proximity to lakes and rivers,
site elevation, proximity to gas stations and grocery stores, availability
of potable water, miles of hiking trails, among many others. It also in-
cludes annual RVD's in 53 activity groups. A debate has gone on for a
long time regarding the appropriateness and usefulness of RFD's as a
measure of recreation participation. The reliability of the numbers and
the methods by which they are estimated have been called into ques-
tion. Without getting involved in that debate let us assert that RIM RVD's
are useful for determining what site characteristics affect total participa-
tion in a given activity. Because of the way RVD's are defined and esti-
mated, however, RIM RVD's are not a usable quantity from which to derive
the number of trips to a site.

recreation opportunities are modelled from the point of
view of origins rather than destinations. This term, re-
ferred to as the ' ' inclusive value , ' ' would provide a rela-
tive measure of the accessibility of each site to its
respective market area. There are, no doubt, other meas-
ures that could be used as well.

The major roadblock to estimating the complete
reverse gravity model is data on the total numbers of trips
to the sites. If such data were available for some set of
sites, it would enable researchers to estimate the effects
of site quality, different levels of site facilities, conges-
tion, and the like on recreation visitation.

We recognize that by abstracting from the trip gener-
ation component of the model we have, in fact, implied
a trip generation component. Recall the complete model
(in equation [3]):

N- eUi

NirNj P(i|j)= -1 =A0eu'

' ' m

Eeu>=

k = l

where A0 is the quantity Nj , assumed to be constant,

and Uj and u^ are functions of travel cost and origin
characteristics. The denominator of the trip distribution
model is part of the constant A0 because travel cost at
a particular site, TCj;, in the denominator was held con-
stant while TCjj in the numerator was increased incre-
mentally to trace out the second-stage demand function.
The implied trip generation model resulting from the as-
sumption of a constant A0 is

where N0 is some initial level of trips to the recreation
site, EeUk is the constant denominator (when Uj is in-
cremented only in the numerator when the function is
integrated), and Ee h is the true denominator (when Uj
is incremented both in the numerator and the denom-
inator during the integration). The complete model is

N0Eeu* e»>

As long as EeUh and EeUk are approximately equal as Uj
changes when the function is integrated, the assump-
tion of a constant A0 has a negligible effect on the
model. When the function is integrated, only one ele-
ment in Ee h changes (the travel cost at one site in the
summation of sites) so the effect on the sum should be
relatively small. To the extent that Ee h is greater (less)
than Ee k over time, additional trips to the site are be-
ing generated (lost). One implication of this implied trip
generation model is that changes in total trips to a site
are induced by changes in the market area that delivers
trips to the site. Another implication is that site charac-
teristics do not affect the number of trips to a site. In the
short run, such conditions may be believable.

27

Appendix 2. The Estimated (First-Stage) Trip Distribution Models

The four goodness of fit measures shown here are
based on Peterson and Stynes (1986). "Eta squared"
measures the actual magnitude agreement between the
observed and predicted number of visits. "Corr" is the
correlation coefficient between the observed and predict-
ed number of visits. "MAE" and "MAPE" are the mean
absolute value absolute error and the mean absolute
value proportional error, respectively. They reflect the
(absolute value) average error in prediction in absolute
and proportional terms, "n" refers to the sample size,

the number of origin counties used as data points in the
estimation of the model.

Regional indicates that the model was estimated with
data exclusively from that region. Other levels of aggre-
gation are:

Rocky Mountain — Regions 1,2,3,4

Pacific Coast — Regions 5,6

Eastern — Regions 8,9

Western— Regions 1,2,3,4,5,6

Nationwide — All regions except Alaska.

General Recreation Models

Region 1 Model = Region 1

Independent
Variable

Travel Cost
Population
Substitute Site
% Urban
% White
Education

Coefficient

-0.876
0.866
0.989

-0.130
3.045
0.660

Eta Squared = 0.858 MAE = 4.471

Corr = 0.870 MAPE = 0.813
n = 82 origins containing 311 trips

Region 2 Model = Region 2

Independent

Variable Coefficient

Travel Cost -1.102

Population 0.453

Substitute Site 0.720

% Urban 0.155

% White 1.422

Eta Squared = 0.694 MAE = 4.030

Corr = 0.703 MAPE = 0.809
n = 107 origins containing 388 trips

Region 3 Model

Independent
Variable

Travel Cost
Population
Substitute Site
% Urban
% White

Region 3

Coefficient

-1.233
0.794
1.573

-0.282
0.766

Eta Squared = 0.859 MAE = 3.860
Corr = 0.859 MAPE = 0.634
n = 60 origins containing 264 trips

t-statistic

-16.974
12.866
8.755
-3.317
2.295
2.725

t-statistic

-15.704
10.365
8.123
4.042
2.880

t-statistic

-9.728
15.217

7.315
-4.644

2.771

Region 4 Model = Region 4

Independent

Variable Coefficient

Travel Cost -1.060

Population 0.644

Substitute Site 0.807

Education 1.653

Eta Squared = 0.733 MAE = 4.345
Corr = 0.736 MAPE = 0.885
n = 90 origins containing 348 trips

Region 5

Independent
Variable

Model = Region 5

Coefficient

Travel Cost
Population
Substitute Site
% White
Education

-1.192
0.974
0.259
5.190

-1.365

Eta Squared = 0.751 MAE = 4.478
Corr = 0.766 MAPE = 0.666
n = 93 origins containing 291 trips

Region 6

Independent
Variable

Model = Region 6

Coefficient

Travel Cost
Population
Substitute Site
% Urban
% White

-1.933
0.538
0.751
0.293

-3.121

Eta Squared = 0.767 MAE = 4.228
Corr = 0.782 MAPE = 0.102
n = 180 origins containing 624 trips

Region 8 Model = Region 8

Independent
Variable

Travel Cost
Population

Coefficient

-1.352
0.665

t-statistic

-19.399
15.089
6.397
9.012

t-statistic

-14.284
13.632
3.249
6.012
-4.793

t-statistic

-24.012
11.271
5.561
4.929
-2.450

t-statistic

-18.927
9.441

28

Substitute Site
% White
Education

0.199
1.784
-0.627

Eta Squared = 0.547 MAE = 3.988
Corr = 0.552 MAPE = 0.870
n = 149 origins containing 445 trips

Region 9 Model = Region 9

Independent
Variable

Travel Cost
Population
Substitute Site
% Urban
% White

Eta Squared = 0.823
Corr = 0.882

Coefficient

-1.327

0.836

1.066
-0.063

1.832

MAE = 2.607
MAPE = 0.589

n = 190 origins containing 401 trips
Developed Camping

Region 1 Model = Regions 1,2,4

Independent
Variable

Travel Cost
Population
Substitute Site
Education
% White

Eta Squared = 0.777
Corr = 0.828

n

Coefficient

-0.476
0.923
1.000
-0.669
6.115

MAE = 1.685
MAPE = 0.576

110 origins containing 107 trips

Region 2 Model = Regions 1,2,4
[Same as Region 1 values.]

Region 3 Model = Region 3

Independent
Variable

Travel Cost
Population
Substitute Site
Education

Eta Squared = 0.847
Corr = 0.848

Coefficient

-1.555
0.893
1.124
-0.651

MAE = 2.257
MAPE = 0.504

n = 45 origins containing 70 trips

Region 4 Model = Regions 1,2,4
[Same as Region 1 values.]

Region 5 Model = Pacific Coast

Independent
Variable

Travel Cost

Coefficient
-1.561

2.436
4.868
-3.545

t-statistic

-26.337
11.966
8.168
-1.615
2.308

t-statistic

-3.991
8.947
5.733

-1.685
2.983

t-statistic

-5.546
7.386
3.165

-1.317

t-statistic
-8.299

Population
Substitute Site
% White
Education

0.772
0.326
6.337
-1.037

Eta Squared = 0.826 MAE = 1.856
Corr = 0.838 MAPE = 0.469
n = 71 origins containing 142 trips

Region 6 Model = Pacific Coast
[Same as Region 5 values.]

Region 8 Model = Region 8

Independent
Variable

Travel Cost
Population
Substitute Site
% White

Coefficient

-0.991
0.678

-0.126
1.784

Eta Squared = 0.619 MAE = 1.677
Corr = 0.620 MAPE = 0.484
n = 40 origins containing 31 trips

Region 9 Model = Region 9

Independent

Variable Coefficient

Travel Cost -0.740
Population 0.710
Substitute Site 0.848

Eta Squared = 0.516 MAE = 1.366
Corr = 0.517 MAPE = 0.540
n = 117 origins containing 47 trips

Region 1

Primitive Camping

Model = Rocky Mountain

Independent
Variable

Travel Cost
Population
Substitute Site

Coefficient

-0.039
0.601
0.645

Eta Squared = 0.676 MAE = 1.379
Corr = 0.717 MAPE = 0.470
n = 54 origins containing 33 trips

Region 2 Model = Rocky Mountain
[Same as Region 1 values.]

Region 3 Model = Rocky Mountain
[Same as Region 1 values.]

Region 4 Model = Rocky Mountain
[Same as Region 1 values.]

7.002
2.103
5.089
-2.412

t-statistic

-3.462
2.546

-0.273
0.839

t-statistic

-4.470
5.217
2.075

t-statistic

-1.406
4.820
1.960

29

Region 5 Model = Pacific Coast

Independent
Variable

Travel Cost
Population
Substitute Site

Eta Squared = 0.876
Corr = 0.878

Population
Substitute Site

0.358
-0.143

5.373
-0.773

Coefficient

-1.543
0.545
1.081

MAE = 1.503
MAPE = 0.476

n = 37 origins containing 65 trips

Region 6 Model = Region 6

Independent
Variable

Travel Cost
Population
Substitute Site
% Urban

Eta Squared = 0.846
Corr = 0.848

Coefficient

-1.662
0.418
1.135
0.423

MAE = 1.718
MAPE = 0.495

n = 36 origins containing 62 trips

Region 8 Model = Eastern

Independent
Variable

Travel Cost
Population
Substitute Site
% Urban

Eta Squared = 0.753
Corr = 0.771

Coefficient

-1.964
2.068
0.283
-0.391

MAE = 1.054
MAPE = 0.497

n = 36 origins containing 25 trips

Region 9 Model = Eastern
[Same as Region 8 values.]

Swimming

Regions 1-4 No models estimated

Region 5 Model = Region 5

Independent
Variable

Travel Cost
Population
Substitute Site
% White

Eta Squared = 0.779
Corr = 0.779
n = 37 origins containing 39 trips

Region 6 Model = Pacific Coast

Coefficient

-1.398
0.685
0.159
5.845

MAE = 2.003
MAPE = 0.769

Independent
Variable

t-statistic

-6.784
7.011
2.892

t-statistic

-5.358
3.374
2.721
1.029

t-statistic

-4.576
4.618
0.619

-1.917

t-statistic

-3.376
4.539
0.579
2.408

Eta Squared = 0.666 MAE = 2.260
Corr = 0.666 MAPE = 0.573
= 45 origins containing 53 trips

Region 8 Model = Region 8

Independent
Variable

Travel Cost
Population
Substitute Site
% Urban
Education

Eta Squared = 0.277
Corr = 0.282

Coefficient

-1.153

0.479

0.544
-0.173
-1.021

MAE = 3.317
MAPE = 0.477

n = 52 origins containing 120 trips

Region 9 Model = Eastern

Independent
Variable

Travel Cost
Population
Substitute Site
% Urban
% White
Education

Eta Squared = 0.700
Corr = 0.726
n = 76 origins containing 202 trips

Coefficient

-1.216
0.551
0.357
-0.078
-1.447
-1.279

MAE = 3.201
MAPE = 0.498

Wildlife Observation

Region 1 Model = Western

Independent
Variable

Travel Cost
Population
Substitute Site
% White
Education

Eta Squared = 0.388
Corr = 0.389

Coefficient

-0.681
1.038
0.816
13.783
-2.104

MAE = 1.088
MAPE = 0.396

Travel Cost

Coefficient
-0.825

t-statistic
-3.435

n = 41 origins containing 21 trips

Region 2 Model = Western
[Same as Region 1 values.]

Region 3 Model = Western
[Same as Region 1 values.]

Region 4 Model = Western
[Same as Region 1 values.]

t-statistic

-7.234
3.174
2.877
-3.337
-2.713

t-statistic

-12.721
4.709
2.800
-1.852
-2.600
-4.293

t-statistic

-2.117
3.385
1.633
2.477

-1.808

30

Region 5 Model = Western
[Same as Region 1 values.]

Region 6 Model = Western
[Same as Region 1 values.]

Regions 8,9 No models estimated

Region 1

Day Hiking

Model = Rocky Mountain

Independent
Variable

Travel Cost
Population
Substitute Site
Education

Coefficient

-0.646
0.376
0.561
1.036

Eta Squared = 0.800 MAE = 0.926
Corr = 0.805 MAPE = 0.327
n = 62 origins containing 55 trips

Region 2 Model = Rocky Mountain
[Same as Region 1 values.]

Region 3 Model = Rocky Mountain
[Same as Region 1 values.]

Region 4 Model = Rocky Mountain
[Same as Region 1 values.]

Region 5 Model = Pacific Coast

Independent
Variable

Travel Cost
Population
Substitute Site

Eta Squared = 0.373
Corr = 0.373

Coefficient

-0.394
0.278
-0.207

MAE = 1.358
MAPE = 0.404

n = 39 origins containing 31 trips

Region 6 Model = Pacific Coast
[Same as Region 5 values.]

Region 8 Model = Eastern

Independent
Variable Coefficient

Travel Cost -0.686
Population 0.229
Substitute Site 0.545

Eta Squared = 0.504 MAE = 1.131
Corr = 0.519 MAPE = 0.437
n = 28 origins containing 15 trips

t-statistic

-4.253
3.407
2.013
2.660

t-statistic

-1.795
2.935
-1.020

t-statistic

-2.260
0.621
0.999

Region 9 Model = Region 9

Independent
Variable

Travel Cost
Population
Substitute Site
% Urban
Education

Eta Squared = 0.533
Corr = 0.536

Coefficient

-0.552
1.236
-0.032
-0.320
-1.737

MAE = 1.096
MAPE = 0.483

n = 55 origins containing 20 trips
Cold Water Fishing

Region 1 Model = Region 1

Coefficient

Independent
Variable

Travel Cost
Population
Substitute Site
Education
% Urban

-0.536
0.751
1.907
1.035

-0.210

Eta Squared = 0.812 MAE = 1.886
Corr = 0.842 MAPE = 0.672
n = 42 origins containing 45 trips

Region 2 Model

Independent
Variable

Travel Cost
Population
Substitute Site
% Urban

Region 2

Coefficient

-0.426
0.246
0.911
0.169

Eta Squared = 0.542 MAE = 1.994
Corr = 0.542 MAPE = 0.494
n = 60 origins containing 74 trips

Region 3

Independent
Variable

Model = Regions 3,4

Coefficient

Travel Cost
Population
Substitute Site
Education
% Urban

-0.348
0.640
0.530
1.119

-0.288

Eta Squared = 0.725 MAE = 2.054
Corr = 0.726 MAPE = 0.564
n = 53 origins containing 80 trips

Region 4 Model = Region 4

Independent
Variable

Travel Cost

Coefficient
-0.739

t-statistic

-1.682
3.443
-0.049
-1.681
-1.809

t-statistic

-3.105
3.669
4.549
2.076

-1.999

t-statistic

-2.413
2.721
4.441
1.791

t-statistic

-2.471
5.971
1.329
2.830

-3.839

t-statistic
-4.928

31

Population
Substitute Site
Education
% Urban

1.128
0.991
2.565
-0.464

Eta Squared = 0.660 MAE = 2.135
Corr = 0.672 MAPE = 0.750
n = 49 origins containing 49 trips

Region 5 Model = Pacific Coast

Independent
Variable Coefficient

Travel Cost -0.832

Population 0.309

Substitute Site 0.224

% Urban 0.221

Eta Squared = 0.447 MAE = 2.619
Corr = 0.452 MAPE = 0.411
n = 79 origins containing 107 trips

Region 6 Model = Pacific Coast
[Same as Region 5 values.]

Region 8 Model = Eastern

Independent
Variable

Travel Cost
Population
Substitute Site

Eta Squared = 0.449
Corr = 0.449

Coefficient

-0.815
0.813
0.329

MAE = 1.410
MAPE = 0.498

n = 77 origins containing 43 trips

Region 9 Model = Region 9

Independent
Variable

Travel Cost
Population
Substitute Site
% Urban

Eta Squared = 0.578
Corr = 0.579

Coefficient

-0.906
0.940
0.804
-0.212

MAE = 1.348
MAPE = 0.523

n = 46 origins containing 22 trips

Warm Water Fishing

Regions 1-6 No models estimated

Region 8 Model = Eastern

Independent
Variable

Travel Cost
Population
Substitute Site

Coefficient

-1.008
1.019
0.591

5.845
2.742
3.290
-3.473

Education

-1.407

-1.373

t-statistic

-5.734
4.752
0.968
1.809

t-statistic

-4.714
5.018
1.393

t-statistic

-4.363
3.613
1.700

-1.186

t-statistic

-3.935
3.214
1.300

Eta Squared = 0.707 MAE = 1.591
Corr = 0.724 MAPE = 0.655
n = 44 origins containing 23 trips

Region 9 Model = Eastern

[Same as Region 8 values.]

Big Game Hunting

Region 1 Model = Region 1

Independent
Variable

Travel Cost
Population
Substitute Site

Coefficient

-0.932
0.435
1.431

Eta Squared = 0.500 MAE = 2.651
Corr = 0.502 MAPE = 0.731
n = 34 origins containing 36 trips

Region 2 Model = Region 2

Independent

Variable Coefficient

Travel Cost -1.716

Population 0.460

Substitute Site 0.827

Education -1.109

% Urban 0.225

Eta Squared = 0.873 MAE = 1.935
Corr = 0.876 MAPE = 0.597
n = 39 origins containing 56 trips

Region 3 Model = Regions 1,3,4

Independent

Variable Coefficient

Travel Cost -0.645

Population 0.329

Substitute Site 0.501

Education 1.552

Eta Squared = 0.430 MAE = 2.980
Corr = 0.437 MAPE = 0.623
n = 136 origins containing 161 trips

Region 4

Independent
Variable

Model = Region 4

Coefficient

Travel Cost
Population
Substitute Site
Education

-0.787
0.414
0.599
1.364

Eta Squared = 0.447 MAE = 3.547
Corr = 0.453 MAPE = 0.642
n = 69 origins containing 108 trips

t-statistic

-4.966
3.572
4.084

t-statistic

-8.026
3.012
2.507

-1.955
2.350

t-statistic

-9.002
5.883
4.165
6.034

t-statistic

-8.764
6.072
3.772
4.280

32

Region 5 No Model Estimated

[Same as Region 1 values.]

Region 6 Model = Region 6

Independent

Variable Coefficient

Travel Cost -0.289

Population 0.797

Substitute Site 0.616

% White -9.523

Eta Squared = 0.762 MAE = 2.895

Corr = 0.782 MAPE = 0.630
n = 40 origins containing 74 trips

Region 8 Model = Region 8

Independent

Variable Coefficient

Travel Cost -0.663

Population 0.813

Substitute Site 0.794

% Urban -0.126

% White 4.800

Eta Squared = 0.520 MAE = 1.699

Corr = 0.521 MAPE = 0.630
n = 59 origins containing 60 trips

Region 9 Model = Eastern

Independent
Variable

Travel Cost
Population
Substitute Site
% White

Coefficient

-0.457
0.678
0.330
2.389

Eta Squared = 0.459 MAE = 1.804
Corr = 0.462 MAPE = 0.550
n = 85 origins containing 72 trips

Region 1

Picnicking

Model = Rocky Mountain

Independent
Variable

Travel Cost
Population
Substitute Site
% Urban

Coefficient

-0.627
0.148
1.195
0.284

Eta Squared = 0.703 MAE = 1.451
Corr = 0.718 MAPE = 0.379
n = 65 origins containing 65 trips

Region 2 Model = Rocky Mountain
[Same as Region 1 values.]

Region 3 Model = Rocky Mountain

t-statistic

-1.253
7.689
2.382

-3.556

t-statistic

-3.372
3.939
3.902

-1.311
4.338

t-statistic

-3.012
5.696
1.738
2.727

t-statistic

-4.043
1.545
4.604
2.276

Region 4 Model = Rocky Mountain

[Same as Region 1 values.]

Region 5 Model = Pacific Coast

Independent
Variable

Travel Cost
Population
Substitute Site
% Urban
Education

Eta Squared = 0.878
Corr = 0.882

Coefficient

-1.324
0.868
1.730
-0.269
-1.886

MAE = 1.702
MAPE = 0.597

n = 38 origins containing 56 trips

Region 6 Model = Pacific Coast

[Same as Region 5 values.]

Region 8 Model = Eastern

Independent
Variable

Travel Cost
Population
Substitute Site

Eta Squared = 0.633
Corr = 0.654

Coefficient

-1.025
0.523
0.223

MAE = 1.870
MAPE = 0.589

n = 87 origins containing 67 trips

Region 9 Model = Region 9

Independent
Variable

Travel Cost
Population
Substitute Site
% Urban

Eta Squared = 0.671
Corr = 0.696

Coefficient

-0.959
0.490
0.745
0.734

MAE = 1.629
MAPE = 0.579

n = 56 origins containing 29 trips

Sightseeing

Region 1 Model = Rocky Mountain

Independent
Variable

Travel Cost
Population
Substitute Site
% Urban
% White

Coefficient

-0.772
0.634
1.704

-0.152
4.473

Eta Squared = 0.676 MAE = 1.826
Corr = 0.687 MAPE = 0.589
n = 138 origins containing 127 trips

t-statistic

-3.199
6.748
3.284
-1.892
-2.828

t-statistic

-8.324
3.702
1.075

t-statistic

-5.706
1.442
1.558
0.947

t-statistic

-7.665
8.161
6.889

-2.941
3.232

33

Region 2 Model = Rocky Mountain
[Same as Region 1 values.]

Region 3 Model = Rocky Mountain
[Same as Region 1 values.]

Region 4 Model = Rocky Mountain
[Same as Region 1 values.]

Region 5 Model = Pacific Coast

Independent

Variable Coefficient

Travel Cost -1.368

Population 0.636

Substitute Site 0.850

% White 7.861

Education -1.475

Eta Squared = 0.695 MAE = 1.745
Corr = 0.702 MAPE = 0.577
n = 37 origins containing 70 trips

Region 6 Model = Pacific Coast
[Same as Region 5 values.]

Region 8 Model = Eastern

Independent
Variable

Travel Cost
Population
Substitute Site
Education

Eta Squared = 0.928
Corr = 0.928

Coefficient

-1.462

0.458
-0.359

0.620

MAE = 0.924
MAPE = 0.497

n = 57 origins containing 43 trips

Region 9 Model = Region 9

Independent
Variable

Travel Cost
Population
Substitute Site
% Urban

Eta Squared = 0.729
Corr = 0.730

Coefficient

-1.065
1.731
0.953
-0.436

MAE = 0.841
MAPE = 0.441

n = 39 origins containing 18 trips

Region 1

Gathering Forest Products

Model = Rocky Mountain

Independent
Variable

Travel Cost

Coefficient
-0.665

t-statistic

-4.693
4.796
2.919
4.303

-2.480

t-statistic

-6.535
2.117

-1.507
0.987

t-statistic

-3.661
3.458
1.178

-1.668

t-statistic
-4.885

Population
Substitute Site
% Urban
Education

0.237
0.728
-0.151
1.652

Eta Squared = 0.771 MAE = 1.310
Corr = 0.771 MAPE = 0.369
n = 46 origins containing 32 trips

Region 2 Model = Rocky Mountain
[Same as Region 1 values.]

Region 3 Model = Rocky Mountain
[Same as Region 1 values.]

Region 4 Model = Rocky Mountain
[Same as Region 1 values.]

Region 5 Model = Western

Independent
Variable

Travel Cost
Population
Substitute Site

Eta Squared = 0.524
Corr = 0.526

Coefficient

-0.699
0.195
0.201

MAE = 2.573
MAPE = 0.600

n = 64 origins containing 62 trips

Region 6 Model = Western
[Same as Region 5 values.]

Region 8 No model estimated

Region 9 Model = Nationwide

Independent
Variable

Travel Cost
Population
Substitute Site
Education

Eta Squared = 0.514
Corr = 0.515

Coefficient

-0.678
0.144
0.126
0.419

MAE = 2.412
MAPE = 0.632

n = 68 origins containing 71 trips

Wilderness Recreation

Region 1 Model = Regions 1,3,4
pendent

Coefficient

Independent
Variable

Travel Cost
Substitute Site
Population

Eta Squared = 0.781
Corr = 0.784

-1.499535
0.687326
0.911484

MAE = 1.701
MAPE = 0.491

0.906
2.015
-1.406
2.621

t-statistic

-6.678
3.375
1.079

t-statistic

-6.560
2.049
0.691
1.036

t-statistic

-9.422410
2.601425
11.485727

n = 49 origins containing 100 visits^

34

Region 2 Model = Region 2
pendent

Coefficient

Independent
Variable

Travel Cost
Substitute Site
Population
Education

Eta Squared = 0.981
Corr = 0.983

-1.506165
0.684342
0.716298
2.633297

MAE = 1.738
MAPE = 0.466

t-statistic

-4.458333
2.420209
4.426121
3.654250

n = 24 origins containing 91 visits

Region 3 Model = Regions 1,3,4
[Same as Region 1 values.]

Region 4 Model = Regions 1,3,4
[Same as Region 1 values.]

Region 5 Model = Region 5

Independent
Variable

Travel Cost
Substitute Site
Population
% White

Eta Squared = 0.957
Corr = 0.963

Coefficient

-2.201687
1.503417
0.975647
2.486736

MAE = 1.723
MAPE = 0.542

t-statistic

■10.246808
6.581052
9.341115
1.715977

n = 51 origins containing 102 visits
Region 6 Model = Pacific Coast

Independent
Variable

Travel Cost
Substitute Site
Population
% Urban
% White

Eta Squared = 0.651
Corr = 0.651

Coefficient

-1.532289
0.222800
0.815725
1.520557
4.594286

t-statistic

-10.458061
1.447362
6.507590
2.864825
3.741577

MAE = 2.731
MAPE = 0.623

n = 92 origins containing 188 visits

Region 8 Model = Region 8

Independent
Variable

Travel Cost
Substitute Site
Population
Education

Eta Squared = 0.550
Corr = 0.550

Coefficient

-1.377112
0.242063
0.712243
0.724473

MAE = 1.742
MAPE = 0.468

t-statistic

-8.499027
1.718959
8.159330
2.835057

n = 83 origins containing 165 visits

Region 9 Model = Eastern

Independent
Variable

Travel Cost
Substitute Site
Population
Education

Eta Squared = 0.533
Corr = 0.533

Coefficient

-1.340642
0.117296
0.756736
0.604390

MAE = 1.801
MAPE = 0.525

n = 120 origins containing 192 visits
Region 10 Model = Region 10

Independent
Variable

Travel Cost
Population
% Urban

Eta Squared = 0.914
Corr = 0.915

Coefficient

-1.964434
1.414905
3.739754

MAE = 1.222
MAPE = 0.321

n = 28 origins containing 39 visits

Summary of Alaska Models

General Recreation

Independent
Variable

Travel Cost
Population
Education

Eta Squared = 0.930
Corr = 0.935

Coefficient

-3.721468
0.987641
1.700653

MAE = 2.850
MAPE = 0.659

n = 49 origins containing 296 visits

Developed Site Recreation

Independent

Variable Coefficient

Travel Cost -4.079057
Population 0.949929
Education 3.248104

Eta Squared = 0.759 MAE = 1.552
Corr = 0.764 MAPE = 0.505
n = 49 origins containing 36 visits

Sightseeing

Independent
Variable

Travel Cost
Population
% White

Coefficient

-3.659092
1.451694
2.345404

Eta Squared = 0.936 MAE = 2.092
Corr = 0.938 MAPE = 0.722
n = 49 origins containing 135 visits

t-statistic

-9.494486
0.938132

10.060440
2.475480

t-statistic

-2.745348
4.376974
2.204041

t-statistic

-12.671220
15.799839
3.911669

t-statistic

-5.290486
5.034120
2.733365

t-statistic

-10.394194
10.293691
1.611265

35

Wildlife Activities

Independent
Variable

Travel Cost
Population
% White

Per Capita Income

Eta Squared = 0.824
Corr = 0.826

Coefficient

-3.725684
0.702114
9.550927

10.008452

MAE
MAPE

1.330
0.485

t-statistic

-4.408718
2.429812
2.560744
3.796937

Wilderness Recreation (repeated to keep all Alaska
models together)

Independent
Variable

Coefficient

-1.964434
1.414905
3.739754

n = 49 origins containing 31 visits

Travel Cost
Population
% Urban

Eta Squared = 0.914
Corr = 0.915
n = 28 origins containing 39 visits

MAE = 1.222
MAPE = 0.321

t-statistic

-2.745348
4.376974
2.204041

36

McCollum, Daniel W.; Peterson, George L.; Arnold, J. Ross; Mark-
strom, Donald C; Hellerstein, Daniel M. 1990. The net economic
value of recreation on the national forests: twelve types of primary
activity trips across nine Forest Service regions. Res. Pap. RM-289.
Fort Collins, CO: U.S. Department of Agriculture, Forest Service,
Rocky Mountain Forest and Range Experiment Station. 36 p.

The Public Area Recreation Visitors Survey (PARVS) was used to
estimate demand models and values for recreation on Forest Service
lands for 12 types of primary activity trips in all nine Forest Service
regions. Models were estimated using the travel cost method with a
"reverse multinomial logit gravity model."

Keywords: Logit model, recreation values, user benefits, consumer
surplus, gravity model, travel cost model

Great
Plains

U.S. Department of Agriculture
Forest Service

Rocky Mountain Forest and
Range Experiment Station

The Rocky Mountain Station is one of eight
regional experiment stations, plus the Forest
Products Laboratory and the Washington Office
Staff, that make up the Forest Service research
organization.

RESEARCH FOCUS

Research programs at the Rocky Mountain
Station are coordinated with area universities and
with other institutions. Many studies are
conducted on a cooperative basis to accelerate
solutions to problems involving range, water,
wildlife and fish habitat, human and community
development, timber, recreation, protection, and
multiresource evaluation.

RESEARCH LOCATIONS

Research Work Units of the Rocky Mountain
Station are operated in cooperation with
universities in the following cities:

Albuquerque, New Mexico

Flagstaff, Arizona

Fort Collins, Colorado*

Laramie, Wyoming

Lincoln, Nebraska

Rapid City, South Dakota

Tempe, Arizona

'Station Headquarters: 240 W. Prospect Rd., Fort Collins, CO 80526