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Who Visits a National Park and What do They Get Out of It?:
A Joint Visitor Cluster Analysis and Travel Cost Model
for Yellowstone National Park
Charles Benson
•
Philip Watson
•
Garth Taylor
•
Philip Cook
•
Steve Hollenhorst
Received: 24 May 2012 / Accepted: 2 August 2013 / Published online: 22 August 2013
Ó Springer Science+Business Media New York 2013
Abstract Yellowstone National Park visitor data were
obtained from a survey collected for the National Park
Service by the Park Studies Unit at the University of Idaho.
Travel cost models have been conducted for national parks
in the United States; however, this study builds on these
studies and investigates how benefits vary by types of
visitors who participate in different activities while at the
park. Visitor clusters were developed based on activities in
which a visitor participated while at the park. The clusters
were analyzed and then incorporated into a travel cost
model to determine the economic value (consumer surplus)
that the different visitor groups received from visiting the
park. The model was estimated using a zero-truncated
negative binomial regression corrected for endogenous
stratification. The travel cost price variable was estimated
using both 1/3 and 1/4 the wage rate to test for sensitivity
to opportunity cost specification. The average benefit
across all visitor cluster groups was estimated at between
$235 and $276 per person per trip. However, per trip
benefits varied substantially across clusters; from $90 to
$103 for the ‘‘value picnickers,’’ to $185–$263 for the
‘‘backcountry enthusiasts,’’ $189–$278 for the ‘‘do it all
adventurists,’’ $204–$303 for the ‘‘windshield tourists,’’
and $323–$714 for the ‘‘creature comfort’’ cluster group.
Keywords National park Travel cost model
Cluster analysis Economic benefit
Introduction
Natural resource managers in the National Park Service
(NPS) and other federal resource management agencies are
tasked with estimating economic benefits to evaluate policy
and management alternatives (Loomis 2002). The NPS has
a specific mandate to manage more than 397 NPS units
across 84 million acres for the benefit of the American
people and to preserve the resource for future generations
(National Park Service 2011a). The NPS’s Organic Act of
1916 (16 U.S.C. §§ 1-18f, 39 Stat. 535) establishes the
purpose of the parks system to ‘‘conserve the scenery and
the natural and historic objects and the wild life therein and
to provide for the enjoyment of the same in such manner
and by such means as will leave them unimpaired for the
enjoyment of future generations.’’
Yellowstone National Park (NP), the first national park,
was established by the Yellowstone Act of 1872 (16 U.S.C.
§§ 1-18f, 39 Stat. 535); an act which includes mandates to
manage the park so as to provide for ‘‘the benefit and
enjoyment of the people’’ and to preserve the park for
future generations. However, competing uses and changing
population demographics make fulfilling the dual mandate
of managing for preservation and public enjoyment a dif-
ficult, shifting target. As the U.S. population changes,
managers of the park must work to understand how people
currently use and enjoy the park and what factors influence
this use and enjoyment. Although visitation to Yellowstone
NP has increased by more than 16 % over the past decade,
visitation to the NP system as a whole has been largely
C. Benson P. Watson (&) G. Taylor
Agricultural Economics and Rural Sociology, University of
Idaho, PO Box 442334, Moscow, ID 83844, USA
e-mail: pwatson@uidaho.edu
P. Cook
Park Studies Unit, University of Idaho, Moscow, ID, USA
S. Hollenhorst
Huxley College of the Environment, Western Washington
University, Bellingham, WA, USA
123
Environmental Management (2013) 52:917–928
DOI 10.1007/s00267-013-0143-4
stable (Table 1) and has not kept pace with overall national
population growth (Pergams and Zaradic 2006). Since
inception, tourism, and public enjoyment of the national
parks have provided the political support for the park
system’s creation, maintenance, and protection (Crompton
2010). There is growing concern among park officials,
however, that changes in the nation’s demographics, poli-
tics, and culture are creating an uncertain future for the NP
system (Floyd 1999, 2001; Solop and others 2003; Tweed
2010; National Park Service 2011b; Taylor and others
2010). NPS’s second century strategic plan (National Park
Service 2011b) recognizes economic importance of the
park system; stating the need to ‘‘develop awareness
among the American public of the many ways national
parks contribute to the economic vitality of our nation. To
do so we will complete a study on the economic value of
the full range of NPS activities and programs (visitor
spending, ecosystem services, community assistance, tax
benefits, etc.) and promote the results.’’
There are two principal reasons to quantify the demand for
a national park: (1) to quantify the benefits of visitation for
the purpose of conducting benefit/cost analysis of expansion,
upgrades, or maintenance, and (2) determine the visitor
characteristics and parameters which significantly affect
park demand. These visitor characteristic variables are
composed of visitor demographics and preferences. Regio-
nal economic impact models, which are commonly calcu-
lated for individual national parks (Stynes and others 2000),
cannot estimate the benefit that visitors receive from visiting
and recreating at the park. To calculate the benefits that the
park operations provide to visitors, an economic model that
calculates a demand curve for visits to the park must be used.
To effectively fulfill their mandate and manage resour-
ces, park managers need to quantify the benefits that parks
provide to visitors. For example, when managers quantify
benefits that visitors gain from NPs, they are able to per-
form benefit/cost analysis of new facility expenditure and/
or expansion. In economics terms, benefits are measured as
the difference between demand for a good and the cost of
that good. The benefits of the national parks include use
values such as recreation and non-use values such as
existence and bequest values. Non-use benefits generated
by the national parks accrue to most Americans regardless
of visitation; however, a large component of the value that
the NPs generate is composed of recreational use values
that accrue to park visitors.
In addition to estimating park benefits, park managers
need to understand the demographics, activities, and social
profiles of NP visitors in relation to how these groups value
the park. For example, a recent USA Today article (Keen
and Dorell 2012) reported that a ‘‘big concern’’ of the
National Park Service is maintaining twenty-first century
relevance, when aging park visitors are not being replaced
by a younger demographic. To address the need to under-
stand visitor characteristics, cluster groups are developed
for summer visitors to Yellowstone NP based on the
activities that they engaged in while in the park. This
allows analysis of the visitor characteristics that determine
demand and benefits of park visitation.
Travel Cost Model
Because national park visits are not bought and sold in a
free marketplace, a non-market valuation technique is
needed to estimate park demand. Travel Cost Models
(TCM) are used to estimate the non-market demand for
recreational sites, such as Yellowstone NP. The concept of
a TCM was first proposed by Hotelling (1949), who sug-
gested estimating the value of parks by examining the
distance people traveled and the number of trips that people
from an area took to a park. Lacking a market price, the
implicit price paid by a visitor to a recreational site is the
travel cost to the site. Trip demand to a site is estimated by
observing that the quantity of visitation to a recreation site
is inversely related to travel cost. The individual TCM
takes survey data from visitors to an area and uses char-
acteristic questions such as age, income, gender, and
driving time to a site to model the number of visits that
each individual makes to that recreational site (Loomis and
others 2009). The history and techniques of the TCMs are
detailed in (Freeman 2003; Ward and Beal 2000; Ward and
Loomis 1986). Travel cost models have been conducted for
national parks in the United States (e.g., Heberling and
Templeton 2009); however, this study builds on these
studies and investigates how benefits vary by types of
visitors who participate in different activities while at the
park.
Table 1 Recreational visitation for Yellowstone National Park and
the National Park System as a whole
Yellowstone System wide
2010 3,640,185 281,303,769
2009 3,295,187 285,579,941
2008 3,066,580 274,852,949
2007 3,151,343 275,581,547
2006 2,870,295 272,623,980
2005 2,835,651 273,488,751
2004 2,868,317 276,908,337
2003 3,019,375 266,099,641
2002 2,973,677 277,299,880
2001 2,758,526 279,873,926
2000 2,838,233 285,891,275
1999 3,131,381 287,130,879
918 Environmental Management (2013) 52:917–928
123
Other TCMs have examined the economic value to
recreational visitors of Yellowstone NP including Kerkvliet
and Nowell (1999) and Neher and others (2013). Neher and
others (2013) also employ VSP data to estimate recrea-
tional benefits to visitors to Yellowstone NP as well as to
many other national parks using a more standardized model
across the parks. Kerkvliet and Nowell (1999) estimated
recreational benefits specifically to trout fishermen in the
Greater Yellowstone Ecosystem, and they also discuss the
problem of heterogeneity of visitors and how this hetero-
geneity will likely influence the benefit that they receive
from their recreational trip. In Kerkvliet and Nowell
(1999), the heterogeneity they focused on was travel itin-
erary and were concerned with the multi-destination
problem in TCMs. Our study focuses on heterogeneity of
visitor activities through the use of a cluster analysis of
visitor activities and deals with the multi-destination
problem by excluding respondents for whom Yellowstone
NP was not their primary destination. There have been a
limited number of previous studies that employed a cluster
analysis to investigate the differences in visitor benefit
across different visitor segments (Coupal and others 2001;
Oh and others 2005). Coupal and others (2001) provided
the most similar use of a combined cluster analysis and
travel cost model in their investigation of snowmobilers in
Wyoming. Their clusters, however, were based on
respondents stated reasons for making their recreational
trip while the clusters used in this study are based on
respondents’ reported behaviors and activity participation
while visiting Yellowstone NP. To the authors knowledge
this is the first study to link a cluster analysis of visitor
activity participation with a travel cost model for the pur-
pose of estimating different willingness to pay measures
for different visitor groups in a national park.
Model Estimation
The dependent variable in a TCM is the number of trips to
a recreation site taken over the last year. Because on-site
surveys exclude people who do not recreate at a study site,
i.e., take zero trips, the data are truncated at zero. In
addition, numbers of trips are integers. Therefore, an esti-
mation method is required for a dependent variable that is
an integer truncated from below. Both truncated Poisson
and truncated negative binomial regression are appropriate
(Grogger and Carson 1991; Hellerstein and Mendelsohn
1993). Significance of the coefficients in a Poisson
regression is overstated if the variance of the dependent
variable (recreation trips per year) is not equal to its mean.
The negative binomial regression does not have this limi-
tation. Recreationists that participate frequently are more
likely to be surveyed and thus, estimates are adjusted for
endogenous stratification. Therefore, zero-truncated nega-
tive binomial (ZTNB) regression is used in this TCM. To
test if the Poisson model or the ZTNB regression is more
appropriate in this application, both models were esti-
mated. However, the parameter of dispersion, alpha, in the
ZTNB model was positive and significant indicating that
over dispersion is present in our data. Therefore, the ZTNB
model is preferred to the Poisson in this instance. Fur-
thermore, the log likelihood value was maximized in the
ZTNB model relative to the Poisson, further indicating that
it is the appropriate model. Therefore, the discussion of the
results will be limited to the ZTNB model.
A TCM trip demand curve is imputed indirectly from
behavior, making the demand coefficients sensitive to
estimation and specification. Once estimated, the trip
demand curve can be used to estimate visitors’ demand for
the site and their consumer surplus; benefit net of travel
costs (Loomis and others 2001). The behavioral under-
pinning of the TCM model is a utility function of a vector
time-consuming good that is maximized subject to income
and time constraints (see Freeman 2003 for a detailed
discussion). For each individual i, the probability of taking
x
i
trips to Yellowstone is estimated using the zero-trun-
cated negative binomial form and is corrected for endog-
enous stratification. The model is given by Eq. 1:
pr x
i
jx
i
[ 0ðÞ¼x
i
C x
i
þ a
1
ðÞ
C x
i
þ 1ðÞC a
1
ðÞ
a
x
i
k
x
i
1
i
1 þak
i
ðÞ
a
1
ðÞ
; x
i
¼ 1; 2... ð1Þ
where U is a gamma distribution, a is the measure of
dispersion (where a large a indicates observations are over-
dispersed relative to the Poisson model). The travel cost
estimator value for k
i
is the expected number of trips taken
by individual i in the past year and is given in Eq. 2:
k
i
¼ Ex
i
ðÞ¼expðb
tc
tc
i
þ b
xp
xp
i
þ b
v
v
i
þ b
d
d
i
þ b
dtc
dtc
i
Þ
ð2Þ
where E(x
i
) is the number of trips each individual
respondent, i, took in the past year; tc
i
is the own price of
travel costs for individual i,xp
i
are the cross prices of
closely related goods (proxied in this study by spending
within the region) which can be either complements or
substitutes, v
i
are the shift variables (see Table 2 for
descriptive statistics of these variables), and d
i
are dummy
variables for the visitor activity cluster groups.
Travel Cost Price Specification
The per person trip travel cost price (own price) has two
components; the out-of-pocket expenditures such as gas
and the opportunity cost of travel time. The time cost of
Environmental Management (2013) 52:917–928 919
123
travel is the hours spent traveling valued at some fraction
of the wage rate, i.e., kW. The wage rate (W) is adjusted to
measure the opportunity cost of time for each individual. In
the traditional TCM model, k is a fraction and thus greater
work hours are desired at the individual’s current wage
rate. The common practice is to value travel time at a
researcher-assigned fraction of the exogenous wage rate
based on outside time value studies (Phaneuf and Smith
2005).
Ward (1984) calculated the expenditure portion of price
as the minimum expenditure required to travel from home
to the recreation site and return. Expenditures made while
making a trip that are in excess of the minimum are
assumed to be for other discretionary goods for which the
traveler received additional benefit. For example, restau-
rant and hotel expenditures are excluded from the travel
cost price calculation as travelers derive benefit from these
expenditures and attributing these costs would overstate the
benefit the visitor receives from the park alone. Ward’s
accounting stance eliminates non-fuel expenditures. Travel
distance was computed in road miles and time taken to get
to and from the park. Distances to Yellowstone NP were
computed to the center of the park from the center of the
respondent’s zip code (Google Maps 2011). Mileage costs
used in this study are operating costs only, such as gasoline
and marginal ‘‘wear and tear.’’ Other costs of car owner-
ship are omitted from the travel costs because insurance
and depreciation will be incurred regardless of the trip. The
cross prices of closely related goods are categorized as (1)
expenditures related to the trip (e.g., a visit to a fine res-
taurant may complement a trip to Yellowstone), and (2)
substitute or complementary sites in a multi-destination trip
or the location value of a site in relationship to another site.
More time on site may substitute for more trips to the site.
Omission of the closely related goods will bias estimated
benefits. For example, if the price of visiting a comple-
mentary site is omitted, then the value of the trip is imputed
to the single site instead of two sites. The closely related
goods are proxied by spending inside the park and spend-
ing outside the park. The expenditures can either be com-
plements or substitutes for the number of trips. For
example, a person may visit a site because of the proximity
of a great restaurant (a complement), or they may spend
more of their recreation budget at the great restaurant and
not visit the site as often (a substitute).
Minimum travel cost in this study is calculated by
adding the per-mile cost of driving multiplied by the dis-
tance to and from the park to an estimate of forgone wages.
The estimate of foregone wages is calculated by using
reported annual income to determine an hourly wage,
estimating amount of time it would take to drive to and
from the park and then dividing by three, the fraction
(k) commonly used to value travel time (Beesley 1965;
Cesario and Knetch 1970; Cesario 1976; Wardman 1998;
Abrantes and Wardman 2011). This study uses $0.14 per-
mile as the per-mile cost of driving, which is the IRS
charity deduction mileage rate (Bowker and others 2009).
Forgone income was calculated using annual income
and dividing by 50 weeks to estimate a weekly salary and
then dividing by 40 h to arrive at an hourly wage. Only the
survey respondent was assumed to forego income for the
trip and was compensated by the other visitors in the
vehicle. To measure the sensitivity of the results to the
calculation of foregone income, the hourly wage was
multiplied by both one-third which has been the most
orthodox approach (Feather and Hellerstein 1997) and by
one quarter to represent a more conservative calculation
which reduces the opportunity cost of leisure time. The
opportunity cost of time component of trip price is based
on the product of trip travel time and the wage rate adjusted
Table 2 Summary statistics of survey respondent demographic variables used in travel cost model
Variable Obs. Mean Std. dev. Min Max
Number of trips (visit in past year) 580 1.49 1.92 1.00 30
Travel cost per person per trip ($) 580 $268 $252 $4.21 $2,017
Spending while in region per group per trip ($) 580 $1,937 $1,387 $49 $12,214
Area resident (1 = yes, 0 = no) 580 0.07 0.25 0 1
Age (years) 580 47.70 12.47 16.00 82.00
Age squared 580 2,430 1,201 256 6,724
Income ($) 580 $80,302 $32,503 $15,000 $135,000
Hispanic (1 = yes, 0 = no) 580 0.04 0.18 0 1
Caucasian (1 = yes, 0 = no) 580 0.96 0.19 0 1
Household size (persons) 580 3.15 1.46 1 9
Visiting alone (1 = yes, 0 = no) 580 0.08 0.27 0 1
Visiting in group larger than 7 (1 = yes, 0 = no) 580 0.14 0.35 0 1
Days in park 580 5.75 6.67 1 91
920 Environmental Management (2013) 52:917–928
123
for taxes. Because time value is based on the wage rate, the
traditional models implicitly assume that recreationists
who have no wage income have no time value. The tra-
ditional models also assume that there is only one wage
earner in a group and thus the average opportunity cost of
time for a trip is inversely proportional to group size
(Freeman 2003).
Data
The data for this study come from the NPS-funded Visitor
Services Project (VSP). The VSP has been collecting vis-
itor expenditure data from individual units of the National
Park System for over 20 years. Analysis of these data has
largely been limited to estimating regional economic
impacts of visitor spending. NPS and the VSP staff at the
University of Idaho collaborate in the administration of an
intercept survey of national park visitors. Park managers
can choose to include an optional section of the survey with
questions about the expenditures of visitors to the park.
Systematic randomly sampled visitor groups receive a
questionnaire to be completed by one person in the visitor
group and returned via the internet or by mail after the park
visit. Respondents are asked the amount the visitor group
spent on various categories of goods and services inside the
park and in the local region. The local region is usually
defined by a mileage or driving time radius around the
park. For Yellowstone NP, respondents reported visitor
group expenditures within 150 miles of the park. The
categories of expenditures for Yellowstone NP included:
lodging, camping fees, guide fees, restaurant and bars,
groceries, and takeout food, gas and oil, fishing and boat-
ing, other transportation expenses, admission, recreation
and entertainment fees, other miscellaneous purchases, and
donations. Respondents who refused to provide their home
zip code or were visitors from outside the United States
were deleted from the sample for the cluster and TCM
analyses.
A summary of the data for this study of Yellowstone NP
is presented below. Complete methods for the 2006 VSP
Yellowstone NP survey are available in (Manni and others
2007). The Yellowstone NP questionnaire was developed
at a workshop held with park staff to design and prioritize
the questions. The survey was administered at Yellowstone
NP July 23–29, 2006. This is during the height of the
summer season, and these visitors are assumed to be typical
of those who visit during the summer. Sample size was
determined based on park visitation statistics from previous
years. Brief interviews were conducted with a systematic,
random sample of 1,376 visitor groups arriving at the park.
Of those groups, 1,302 accepted questionnaires (94 %).
Questionnaires were distributed at five sites within the
park. The sampling locations were selected based on park
visitation statistics and advice from park staff. Visitor
groups were greeted, briefly introduced to the purpose of
the study, and asked to participate. If visitors agreed, they
were asked which member (at least 16 years of age) had
the next birthday. The individual with the next birthday
was selected to complete the questionnaire for the group.
An interview, lasting approximately 2 min, was conducted
with that person to determine group size, group type, and
the age of the member completing the questionnaire. These
individuals were asked for names, addresses, and telephone
numbers or email addresses to mail them a reminder/thank
you postcard and follow-ups.
Of the 1,302 visitor groups that accepted questionnaires,
1,059 were given the option to complete the questionnaire
either online or on paper to be returned by mail. Both the
online and mail-in participants received a printed ques-
tionnaire, with the online-option participants receiving a
questionnaire that contained a postcard with a unique user
ID and password, the internet address, and directions for
completing the survey online. All participants were asked
to complete the survey after their visit. Two weeks fol-
lowing the survey, a reminder/thank you postcard was
mailed to all participants. Replacement questionnaires
were mailed to participants who had not returned their
questionnaires 4 weeks after the survey. Seven weeks after
the survey, a second round of replacement questionnaires
was mailed to visitors who had not returned their ques-
tionnaires. Follow-up letters contained another unique
password that differentiated between mailing waves and
eliminated duplicate submissions. Questionnaires were
completed and returned by 903 visitor groups, resulting in a
69 % response rate for this study. Of the 903 question-
naires completed and returned, 806 (89 %) were completed
on paper and 97 (11 %) were completed online. Respon-
dents were dropped from this study if they did not reside in
the United States (80 respondents; 9 %), had missing data
needed for this analysis (64 respondents; 7 %), or if visit-
ing Yellowstone NP was not the primary purpose for their
trip (179 respondents; 20 %). Including respondents on
non-primary purpose trips would result in overestimation
of benefits using TCM (Haspel and Johnson 1982; Loomis
and others 2000). This left 580 respondents (64 %) who
were included in the TCM and cluster analyses.
The VSP uses three variables to check non-response
bias: group type, group size, and age of the group member
who completed the questionnaire (Manni and others 2007).
This information is collected during the initial visitor
interview on site and again on the questionnaire. Visitor
group type and group size were not significantly different
between respondents and non-respondents (Group type:
v
2
= 7.51, df = 4, P = 0.11. Group size: mean = 4.4 for
Environmental Management (2013) 52:917–928 921
123
respondents (n = 882), 4.2 for non-respondents ( n = 382),
P = 0.553). Respondents, however, were slightly older than
non-respondents (mean = 48 vs. 43, n = 867 and 378,
P \ 0.01), which is not uncommon in public opinion sur-
veys (Dillman and Carley-Baxter 2000). Overall non-
response bias was judged by the VSP to be insignificant
(Manni and others 2007). However, because the week-long
sampling timeframe may not be representative of the entire
year, park managers are cautioned in the VSP report (Manni
and others 2007):
‘‘The data reflect visitor use patterns to the selected
sites during the study period of July 23–29, 2006. The
results present a ‘snapshot-in-time’ and do not nec-
essarily apply to visitors during other times of the
year.’’ (Limitations, p. 5).
The timeframe in which the surveys were conducted for
this dataset represent the height of the peak season of
visitation and, therefore, are likely only representative of
visitors during the summer season. The results of this study
should not be extrapolated to the less common, but still
important, winter visitors to Yellowstone NP.
Heberling and Templeton (2009) were the first to pub-
lish a TCM using VSP data and provided quite a bit of
insight into using VSP data as a promising source for
estimating benefits to visitors from national park visitation.
The focus of their paper was exploring functional forms of
the TCM. This paper further describes the use of VSP data
in TCMs, and expands on Heberling and Templeton’s
(2009) efforts by focusing on the activities of visitors at the
park as demand shifters. This paper begins to address the
shortcomings identified by Tuner (2002) of estimating the
value park visitors place on different activities.
Visitor Activity Clusters and Other Demand Shift
Variables
To characterize visitors into similar groups based on the
activities in which they participated and to estimate the
benefits that different groups of visitors received from their
trips to Yellowstone NP, visitors were assigned to a cluster
using a K-means cluster analysis based on similarity of
activities (Wilson and Thilmany 2006). The clusters are
specified as interaction dummy variables with own price,
thus allowing unique benefits and marginal effects to be
calculated.
Cluster analysis organizes individuals into clusters so
that the similarity of characteristics within each cluster is
maximized, while maximizing differences between clusters
(Xu and Wunsch 2009; Aldenderfer and Blashfield 1984).
Cluster analysis uses multiple variables to determine the
number of clusters and characteristics that differentiate
those clusters. In K-means algorithm cluster analysis, the
similarity or dissimilarity of sets of data is determined by
Euclidean distance from the cluster centroid (Xu and
Wunsch 2009). A Silhouette index, which compares the
Euclidean distance each data point falls relative to other
clusters, was used to determine the appropriate number of
clusters (Rousseeuw 1987). The Silhouette index had a
positive value of 0.188 at five clusters with a standard
deviation of 0.12 confirming that five clusters is an
appropriate number of clusters for this data set. The mean
value of each of the binary variables used to generate the
visitor activity clusters is presented in Table 3 and the
percentage from the total mean provided in Table 4. The
number of respondents in each cluster is provided in
Table 5.
Cluster 1 characterized as the ‘‘do it all adventurists’’
group, is distinct in that participation in all activities are
greater than the mean. Visitors in this cluster experienced
everything Yellowstone NP had to offer and had higher than
average participation in all activities including day hiking,
ranger programs, nature viewing, camping and overnight
hiking. Cluster 2, the ‘‘windshield tourists,’’ had higher than
average participation in viewing roadside exhibits, pho-
tography and painting, and seeing geysers while in Yel-
lowstone NP. Cluster 3, the ‘‘value picnickers,’’ were the
most likely of any group to picnic within the park and were
among the least likely to eat at restaurants and stay in a
lodge while in the park. Cluster 4, the ‘‘creature comfort
seekers,’’ group were the most likely to eat at restaurants
and stay at lodges. This group was the least likely to picnic
while in the park. Cluster 5, the ‘‘backcountry enthusiasts,’’
did not participate in a wide range of activities, but rather
focused on just backpacking and other activities which
included, most notably, rock climbing. This cluster was the
least likely to visit geysers, shop, or eat out.
In addition to the clusters, four categories of taste and
preference variables were included in the TCM: (1) indi-
vidual demographics such as age, race, ethnicity, disability,
and education, (2) the size of the respondent’s visitor
group, (3) closely related goods, as proxied by spending
inside the region on other goods, and (4) income. The
statistical and economic significances of the visitor profile
variables are evaluated to determine which variables affect
demand and benefit received from visiting Yellowstone
NP. Specifying these independent variables in the trip
demand function serves two purposes: (1) providing park
managers with an understanding of the demographics and
qualities that shift demand for visitation to Yellowstone
NP, and (2) serving as control variables for estimates of the
benefit (consumer surplus) provided to the visitor’s
respective cluster group.
The cross price (spending while in the region) included:
lodging, camping fees, guide fees, restaurant and bars,
922 Environmental Management (2013) 52:917–928
123
groceries and takeout food, fishing and boating expenses,
other transportation expenses, recreation and entertainment
fees, other miscellaneous purchases, and donations.
The means of the binary variables used to generate the
visitor activity clusters are presented in Table 3 and
descriptive statistics of the other demand shift variables are
presented in Table 6.
Results and Discussion
The travel cost regression results are presented in Table 7
and the estimates of per person per trip consumer surplus
across the 5 cluster groups can be found in Table 8.
Using the travel cost calculation of 1/3 the wage rate, the
average per trip benefit across all clusters received by
Table 3 Mean values for binary activity variables used in cluster analysis
Activities engaged in while visiting the park Cluster mean
Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5 Sample mean
Sightseeing 1.00 1.00 0.99 0.98 0.86 0.97
Nature viewing 0.96 0.96 0.91 0.82 0.69 0.88
Photography/painting 0.80 0.76 0.66 0.37 0.14 0.57
Road side exhibits 0.87 0.99 0.18 0.35 0.21 0.59
Hiking 0.72 0.24 0.16 0.19 0.17 0.34
Ranger programs 0.52 0.05 0.01 0.06 0.04 0.18
Visiting museums 0.90 0.55 0.24 0.44 0.14 0.52
Visiting geysers 0.95 0.97 0.43 0.88 0.40 0.78
Shopping books 0.84 0.13 0.21 0.34 0.06 0.37
Shopping gifts 0.96 0.71 0.89 0.96 0.04 0.73
Eating 0.82 0.40 0.14 0.99 0.14 0.55
Picnicking 0.63 0.45 0.62 0.12 0.13 0.40
Camping 0.31 0.13 0.18 0.13 0.15 0.19
Staying at the lodge 0.28 0.05 0.03 0.28 0.05 0.15
Overnight hiking 0.03 0.01 0.00 0.01 0.03 0.02
Other activities (i.e., rock climbing) 0.14 0.06 0.03 0.08 0.25 0.12
1 engaged in respective activity, 0 did not engage in respective activity
Table 4 Yellowstone travel
cost cluster percentage of total
mean of the variable (100 %
would indicate visitors in the
cluster engaged in this activity
in the same frequency as the
sample as a whole)
Percentage from total variable mean visitor activity questions
Cluster 1 (%) Cluster 2 (%) Cluster 3 (%) Cluster 4 (%) Cluster 5 (%)
Sightseeing 103 103 102 101 89
Nature viewing 109 109 103 94 78
Photography/painting 138 132 115 65 24
Road side exhibits 147 167 31 59 35
Hiking 209 71 46 54 49
Ranger programs 292 26 7 31 22
Visiting museums 174 107 46 86 27
Visiting geysers 122 125 56 113 52
Shopping books 226 36 57 92 16
Shopping gifts 130 97 122 131 5
Eating 149 72 26 180 25
Picnicking 155 110 153 30 32
Camping 162 69 95 67 76
Staying at the lodge 181 31 17 181 32
Overnight hiking 175 45 0 54 171
Other activities
(i.e. rock climbing)
118 53 22 71 217
Environmental Management (2013) 52:917–928 923
123
summer visitors to Yellowstone NP was $276.
1
When 1/4
the wage rate is used, the per person per trip consumer
surplus is expectedly reduced and is estimated at $235.
These are considerably higher than the benefit of $89 per
person per trip that Heberling and Templeton (2009) esti-
mated for Great Sand Dunes National Park in 2002. This,
however, is to be expected as Yellowstone NP is the
flagship national park and draws many visitors from around
the nation, while Great Sand Dunes is a regional draw for
the Intermountain West.
Although visitors were assigned to their respective
clusters based only on the activities in which they engaged
while visiting Yellowstone NP, the cluster groups also
differed greatly in their demographic and preference vari-
ables and in the specific benefit they received from their
trip. A summary of the consumer surplus for each cluster
group using both travel cost specifications is presented in
Table 8. Across both models, the travel cost variable was
significant at the 1 % level for all cluster groups. The travel
cost coefficients price (calculated by adding the interaction
coefficient to the omitted cluster coefficient for each cluster
group) were, as expected, negative for all groups meaning
that as the cost of visiting the park increased the number of
trips decreased.
Cluster 4, ‘‘creature comfort seekers,’’ received the
highest per person per trip benefit. This cluster received a
consumer surplus of $323–$714 per trip which was over
twice the benefit of the next highest cluster. This cluster,
however, was not greatly differentiated by, nor extreme in,
any of their non-activity related variables. This cluster
stayed in the park fewer days than all but cluster 3. Cluster
4 had the second highest spending while in the region,
which is understandable because of this group’s high par-
ticipation in eating out and staying at the park’s lodges.
They were more likely to be visiting in larger groups;
however, respondents in cluster 2 were even more likely to
be part of a group of more than seven people.
Cluster 2, the ‘‘windshield tourists,’’ received the second
highest benefit at $204–$303. Respondents in this cluster
were the most likely to be part of a group of over seven
people and were the least likely to be a resident of the area.
Respondents in cluster 2 were also the most likely to be
Hispanic, although even for this cluster, the percentage of
Hispanics was only 5 %.
Cluster 5, the ‘‘backcountry enthusiasts,’’ received the
third highest benefit with a consumer surplus of $185–$263
per person per trip. Respondents in this cluster were much
more likely to be a resident of the area and to visit the park
by themselves, and least likely to visit the park in a large
group. Although no cluster group was more than 5 %
Hispanic, visitors in cluster 5 were by far the least likely to
be Hispanic. Not surprisingly, since this group was the
most likely to be area residents, they also spent the least
amount of money while in the region. Cluster 5 had the
highest mean age of any of the groups (50.5 years), but
they also had the highest standard deviation on their ages
(14.5 years). This would indicate that both older and
younger people are classified into this cluster.
Cluster 1, the ‘‘do it all adventurists,’’ received the
second lowest benefit with a consumer surplus of $189–
$278. Respondents in this group spent the most money
while in the region and had the highest travel cost to get to
the park. This cluster had the highest mean annual house-
hold income of over $89,000 and spent the most days in the
park. Respondents in this cluster were much less likely than
average to be an area resident. This was also the cluster that
engaged in the most activities while at the park.
Initially, the finding that cluster 5 would have receive
more benefit from the park than cluster 1 was not intuitive
because cluster 1 included the visitors that participated in
everything at the park and cluster 5 participated in the least
amount of activities while visiting. One explanation may
be that cluster 5 visitors place a high benefit on the few
activities they do at Yellowstone NP, but are more than
happy to return and experience more on a later visit,
whereas cluster 1 visitors attempt to do everything they can
while at the park to maximize their perceived benefit
because they are less likely to visit again.
Cluster 3, the ‘‘value picnickers,’’ received the least
benefit with a consumer surplus of $90–$103 per visit.
Visitors in this cluster were the least likely to go to the park
alone and more likely than average to be part of a large
group. Cluster 3 also spent the least number of days visiting
Yellowstone NP on their trip.
Table 5 Yellowstone number of respondents in each cluster
Cluster
number
Cluster name Number of
respondents
1 ‘‘Do It All Adventurists’’ 166
2 ‘‘Windshield Tourists’’ 128
3 ‘‘Value Picnickers’’ 76
4 ‘‘Creature Comfort Seekers’’ 108
5 ‘‘Backcountry Enthusiasts’’ 102
1
The negative binomial regression is equivalent to a semilog
functional form. Adamowicz and others (1989) show that the annual
consumer surplus estimate for semilog demand with continuous
variables is: E(Q
r
)/(-ß) where ß is the estimated slope on price and
E(Q
r
) is annual visits. Thus, consumer surplus per trip is 1/(-ß). The
estimate of consumer surplus is invariant to the distribution of trips
along the demand curve when surplus is a linear function of Q
r.
The
estimate of consumer surplus is invariant to the distribution of trips
along the demand curve when surplus is a linear function of Q. Thus,
it is not necessary to numerically calculate surplus for each data point
and sum as is the case if the surplus function is nonlinear.
924 Environmental Management (2013) 52:917–928
123
Table 6 Variable means by cluster group
Variable Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5
Number of trips (visit in past year) 1.20 1.23 1.57 1.35 2.36
Travel cost per person per trip ($) $324 $257 $234 $262 $224
Spending while in region per group per trip ($) $2,417 $1,769 $1,679 $2,216 $1,265
Area resident (1 = yes, 0 = no) 0.02 0.02 0.07 0.07 0.21
Age (years) 46.66 45.53 49.71 47.83 50.46
Age squared 2,321 2,216 2,626 2,408 2,755
Income ($) $89,277 $77,461 $77,566 $80,833 $70,735
Hispanic (1 = yes, 0 = no) 0.03 0.05 0.04 0.04 0.02
Caucasian (1 = yes, 0 = no) 0.97 0.96 0.97 0.94 0.96
Household size (persons) 3.34 3.35 2.98 3.24 2.65
Visiting alone (1 = yes, 0 = no) 0.07 0.07 0.04 0.08 0.14
Visiting in group larger than 7 (1 = yes, 0 = no) 0.13 0.18 0.16 0.18 0.09
Days in park 8.21 4.96 4.39 4.94 4.60
Table 7 Results of the zero-truncated negative binomial regression with endogenous stratification correction using both 1/3 the respondent’s
wage rate and 1/4 the respondent’s wage rate for the travel cost calculation
Travel cost 1
Results with travel cost calculated
using 1/3 the wage rate
Travel cost 2
Results with travel cost calculated
using 1/4 the wage rate
Coeff. P [ |z| 95 % Confidence
interval
Coeff. P [ |z| 95 % confidence
Interval
Travel cost ($; cluster 3 is omitted dummy) -0.0097 0.000 -0.0132 -0.0061 -0.0111 0.000 -0.0149 -0.0072
Spending while in region per group per trip ($1 k) -0.070 0.373 -0.0002 0.0001 -0.0737 0. 352 -0.0002 0.0001
Area resident (1 = yes, 0 = no) 1.0002 0.000 0.6319 1.3686 0.9936 0.000 0.6205 1.3667
Age (years) 0.0318 0.000 0.0198 0.0438 -0.0565 0.000 0.0202 0.0445
Income ($1 k) 0.0116 0.000 0.0000 0.0000 0.0110 0.000 0.0000 0.0000
Hispanic (1 = yes, 0 = no) -0.7705 0.366 -2.4396 0.8986 -0.7786 0.362 -2.4518 0.8945
Caucasian (1 = yes, 0 = no) 0.9234 0.067 -0.0656 1.9125 0.9190 0.069 -0.0730 1.9110
Household size -0.3416 0.000 -0.4500 -0.2331 -0.3402 0.000 -0.4485 -0.2319
Visiting alone (1 = yes, 0 = no) 0.5555 0.149 -0.1998 1.3107 0.5481 0.160 -0.2162 1.3125
Days spent in region 0.0093 0.042 0.0003 0.0183 0.0106 0.021 0.0016 0.0197
Group size [7(1=
yes, 0 = no) -1.1575 0.000 -1.7126 -0.6023 -1.1477 0.000 -1.7076 -0.5877
Cluster 1 intercept dummy -1.4184 0.000 -2.1275 -0.7094 -1.3743 0.000 -2.0703 -0.6782
Cluster 2 intercept dummy -1.2220 0.002 -1.9766 -0.4673 -1.1948 0.001 -1.9169 -0.4726
Cluster 4 intercept dummy -1.4637 0.000 -2.1589 -0.7685 -1.4085 0.000 -2.1263 -0.6907
Cluster 5 intercept dummy -0.6060 0.071 -1.2634 0.0514 -0.5738 0.086 -1.2289 0.0813
Cluster 1 slope dummy 0.0061 0.001 0.0025 0.0097 0.0058 0.001 0.0025 0.0091
Cluster 2 slope dummy 0.0064 0.025 0.0008 0.0120 0.0062 0.018 0.0011 0.0114
Cluster 4 slope dummy 0.0083 0.000 0.0060 0.0105 0.0080 0.000 0.0057 0.0102
Cluster 5 slope dummy 0.0059 0.018 0.0010 0.0108 0.0057 0.015 0.0011 0.0103
ln(alpha) 16.49 0.000 15.63 0.000
Wald v
2
791.53 0.000 804.71 0.000
Log pseudolikelihood -390.87 N/A -390.89 N/A
AIC Statistic 1.417 N/A 1.417 N/A
Environmental Management (2013) 52:917–928 925
123
Average household income of cluster 4, which received
the highest benefit, was only 4 % higher than cluster 3,
which received the least benefit. Neither cluster 3 nor
cluster 4 was extreme in their average income relative to
the other clusters.
Demographic variables from the survey respondent had
significant effects on the benefits of travel. Income was
significant and positive; as income increased visitors came
to the park more often. Yellowstone NP visitation is a
luxury good, with an income elasticity of 1.2. Area resi-
dents were, predictable, more likely to visit the park than
were visitors from outside the region. Household size was
significant and negative as was group size. A larger
household or traveling group may make planning a vaca-
tion to a national park more complicated.
Ethnicity and race were not significant in the model, but
this may be due to the low number of Hispanic and non-
white respondents. Ninety-six percent of the visitors were
Caucasian and 4 % were Hispanic.
2
This low number is
consistent with other research showing that minorities do
not visit national parks in large numbers, particularly parks
with many outdoor activities (Solop and others 2003;
Taylor and others 2011).
Conclusion
People who engage in different portfolios of activities while
visiting Yellowstone NP derive different benefits from the
park. Summer visitors who receive the highest benefit also
seem to enjoy built environment features and cultural ame-
nities. This again demonstrates the management difficulties
of fulfilling the National Park Service’s mission of protecting
resources and providing for visitor enjoyment (Sax 1980).
The overall demographic picture of summer visitors to
Yellowstone NP in this study is consistent with previous
studies of national park visitors (Floyd 1999). The visitors
to Yellowstone NP during the summer are, on average,
higher income (survey median household income of
$75,000 versus national median household of $50,233) and
are older (survey median age of 47 versus national median
age of 37) than the nation as a whole. Summer visitors to
Yellowstone NP in this sample were 96 % Caucasian and
96 % non-Hispanic. The low number of minority respon-
dents makes it difficult to say anything definitive about the
relative differences between them and the survey popula-
tion as a whole. However, the results can be interpreted as
preliminary suggestive indications of differences in visitor
characteristics between ethnic groups. The small sample of
both Hispanic respondents (20 of the total 580 respondents)
and non-Caucasian respondents (22 of the total 580
respondents) had higher than the survey average household
incomes ($93,750 for Hispanic respondents and $80,302
for non-Caucasians). No minority respondent engaged in
overnight hiking, and both Hispanic respondents and non-
Caucasian respondents had lower than average participa-
tion in hiking and camping. For the most part, however,
minority respondents were not significantly different from
survey respondents as a whole.
Future Research
The current study demonstrates that VSP survey data can
be used to develop individual visitor estimates of benefits
using travel cost modeling, and that visitor activities act as
demand shifters. However, the usefulness of the study is
limited for several reasons and can be improved with
modifications to the VSP survey and further research.
Little can be said definitively about aggregate benefits to
visitors of Yellowstone NP. Visitors were sampled during
only one week in July, and their characteristics may be
different from visitors during other times of the year.
Benefit per visitor found in this study cannot simply be
multiplied by the annual number of visitors to obtain an
accurate estimate of aggregate benefits. Unfortunately, few
Table 8 Per person per trip benefit (as measured by consumer surplus) received by each cluster group and for the pooled sample
Cluster number Cluster name Per person per trip consumer
surplus with travel cost calculated
using 1/3 the wage rate
Per person per trip consumer
surplus with travel cost calculated
using 1/4 the wage rate
1 ‘‘Do It All Adventurists’’ $278 $189
2 ‘‘Windshield Tourists’’ $303 $204
3 ‘‘Value Picnickers’’ $103 $90
4 ‘‘Creature Comfort Seekers’’ $714 $323
5 ‘‘Backcountry Enthusiasts’’ $263 $185
N/A Pooled Sample $276 $235
All values are in 2,006 dollars
2
Hispanic was considered an ethnicity and not a race on the survey,
therefore people were separately asked for their race and whether or
not they are Hispanic. For example, respondents who indicated they
are Caucasian may have also indicated that they are Hispanic.
926 Environmental Management (2013) 52:917–928
123
national park units have the resources to conduct multiple
VSP surveys throughout the year. Yellowstone NP is one
of the few national parks to conduct a VSP survey in both
summer and winter (Kulesza and others 2012a, b). Future
research could examine differences in visitor benefits based
on seasonal differences, but this would still require
assuming that visitors during the sample week were rep-
resentative of visitors throughout a season.
In addition, future research could focus on accounting
for benefits received by foreign visitors and by domestic
visitors on trips where visiting Yellowstone NP was not the
primary trip purpose. International visitation, multiple-
destination, and multiple-purpose trips have been addres-
sed in other TCM studies (e.g., Parsons and Wilson 1997;
Loomis and others 2000; Carr and Mendelsohn 2003), and
could be done for Yellowstone NP.
VSP surveys collect information that serves multiple
purposes and needs of NPS managers. Only recently, and
subsequent to the current study, has the NPS begun to look
at systematic additions to VSP survey questions which
directly address shortcomings related to travel cost mod-
eling found in this and other studies using VSP data.
For example, a recent development in TCM is the
specification of a two-stage model to specify non-monetary
travel costs (Taylor and others 2010). If visitors did forego
income to make the trip, the full value of foregone income
could be used instead of the standard one-third the total
wage rate that is used now. If visitors did not forgo income
then the costs of transportation to the site would be only the
costs associated with the trip. A question on foregone
income was not asked in the survey for this study so the
issue could not be addressed herein. However, in 2011 and
2012 questions were added to some VSP surveys that
address income foregone to make the trip to the park. TCM
analysis of these recent survey results is ongoing.
Because VSP surveys serve multiple purposes for park
managers, and they pay the costs of implementing the sur-
veys, the inclusion of TCM questions in VSP surveys is left
up to park managers. Requiring that economic valuation
questions be included in all VSP surveys will allow further
cross-park studies, as well as defining a set of questions that
each park could be clustered around and that have an impact
on visits per year. The results found in this study would
benefit from being repeated in the future with park surveys
including additional economic valuation questions.
Acknowledgments Funding for this research primarily came from
the National Park Service Social Science Program, the Idaho Agri-
cultural Experiment Station, and the USDA NIFA. The Park Studies
Unit at the University of Idaho provided much of the data for the
project. The authors would also like to thank Bruce Peacock, John
Loomis, and the anonymous reviews for their helpful comments and
suggestions.
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