Valuation of National Park System Visitation: The Efficient Use of Count Data Models, Meta-Analysis, and Secondary Visitor Survey Data
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- Neher, C., Duffield, J. & Patterson, D. Environmental Management (2013) 52: 683. doi:10.1007/s00267-013-0080-2
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The National Park Service (NPS) currently manages a large and diverse system of park units nationwide which received an estimated 279 million recreational visits in 2011. This article uses park visitor data collected by the NPS Visitor Services Project to estimate a consistent set of count data travel cost models of park visitor willingness to pay (WTP). Models were estimated using 58 different park unit survey datasets. WTP estimates for these 58 park surveys were used within a meta-regression analysis model to predict average and total WTP for NPS recreational visitation system-wide. Estimated WTP per NPS visit in 2011 averaged $102 system-wide, and ranged across park units from $67 to $288. Total 2011 visitor WTP for the NPS system is estimated at $28.5 billion with a 95% confidence interval of $19.7–$43.1 billion. The estimation of a meta-regression model using consistently collected data and identical specification of visitor WTP models greatly reduces problems common to meta-regression models, including sample selection bias, primary data heterogeneity, and heteroskedasticity, as well as some aspects of panel effects. The article provides the first estimate of total annual NPS visitor WTP within the literature directly based on NPS visitor survey data.
KeywordsCount data modelTravel costNational park serviceBenefits transferMeta-regression ModelValuationWillingness to payRecreational visitation
The National Park Service (NPS) utilizes value estimates for ecosystem services, including recreational use, for policy, management, planning, and natural resource damage assessment. The National Park System protects a diverse set of nationally significant ecosystems and cultural and historical resources. The areas set aside for their natural values include forest, grassland, tundra, desert, estuary, or river system and may contain impressive landforms such as mountains, mesas, thermal areas, and caverns and provide habitat for a diversity of wildlife and plant life. These ecosystems provide a variety of ecosystem regulation, habitat, production and information functions including climate regulation, water regulation, water supply, nutrient recycling, refugium, and genetic resources. The founding legislation for the national parks in 1916 defined the dual mandate under which these parks are managed: “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” (U.S. Department of the Interior 1995).
The contributions of this article are to (1) provide new estimates of park visitor WTP based on visitor data from park surveys previously collected by the NPS for different purposes; (2) estimate a set of park-level WTP estimates for a diverse set of NPS units that are all based on consistent survey protocols, question design, and estimation methodology; (3) estimate a meta-regression model of park visitor WTP that is largely free of challenges which commonly complicate meta-regression models, including study heterogeneity (Smith and Kaoru 1990; Christensen 2003), heteroskedasticity of estimate variances (Nelson and Kennedy 2008; Stapler and Johnston 2009), and some aspects of non-independence of multiple observations from primary studies (Stanley and Jarrell 1989); and (4) derive the first system-wide estimate of total annual WTP for recreational visitation to the NPS system directly and solely estimated from NPS visitor data.
The meta-regression analysis model employed is intended to be a tool for use in benefit transfer of park visitor WTP to the majority of NPS park units lacking visitor survey data. The motivation for estimation of system-wide NPS WTP values is that regulatory and land management agencies are often required to assess the full economic benefits and costs of management and policy decisions. Given time and resource constraints, it is not feasible to conduct original research for every regulatory issue that arises.
The strategy for development and application of nonmarket values for ecosystem services varies across agencies. The U.S. Forest Service began publishing Resource Planning Act (RPA) values for recreation in 1980, and sponsored a series of literature reviews to inform the selection of these values, beginning with Sorg and Loomis (1984), and including later reviews by Walsh and others (1988, 1992), McNair (1993), and Loomis (2005). The U.S. Fish and Wildlife Service sponsored a similar literature review and synthesis for fishing (Markowski and others 1997). However, the U.S. Fish and Wildlife Service has taken a different strategy of additionally conducting original valuation research. Since 1980, WTP questions for fishing and hunting activities are included in the National Survey of Fishing, Hunting and Wildlife-Associated Recreation, with results reported at the state level (Aiken and LaRouche 2003).
To date, valuation of recreational visits to NPS park units has been largely unsystematic and fragmented. In a 2009 review of the valuation literature for the NPS, Duffield and others (2009) identified 27 different studies of NPS visitor WTP which included 128 different estimates of WTP. These estimates ranged from valuation of a trip floating the whitewater of the Grand Canyon of the Colorado (Bishop and others 1989) to valuing the impact of climate change on recreational benefits in Rocky Mountain NP (Richardson and Loomis 2005). Hardner and McKenney (2006) developed a generalized estimate of total NPS system visitor WTP based on benefits transfer from existing studies of park unit net economic value (Kaval and Loomis 2003; Leggett and others 2003). They noted the limitations of their analysis, and argued that their system-wide estimate of visitor WTP was conservative due to data limitations (p. 12).
Count Data Trip Valuation Modeling Methods
The method used in this analysis for estimating the value of a trip to specific NPS units is a variant of the individual observation travel cost (TC) model, the count data model. This model explains the number of trips an individual has taken to a specific park unit during a defined previous time period (usually 12 months) as a function of the cost (and by proxy, the distance) associated with making the trips to the park from their home. A unique feature of the count data model is that the dependent variable is an integer, which is appropriate for trip frequency data. At its base, the TC model can be estimated using these minimal data.
While the VSP survey questions have evolved over the years of the survey’s existence, there are a number of key questions that are included in many of the park surveys which are necessary for estimation of the TC models. A subset of the VSP park questionnaires included questions on the number of trips taken to the park in the past 12 months. This number of trips is always a nonnegative, non-zero integer. We follow the standard approach for estimating the individual travel cost model as used by Shaw (1988), Englin and Shonkwiler (1995a), Hellerstein and Mendelsohn (1993), and Cameron and Trivedi (1998). Recent examples of studies utilizing count data to estimate visitor net economic value include those by Heberling and Templeton (2009), as mentioned earlier, who examined Great Sand Dunes National Park VSP data, and Bowker and others (2009) who used National Forest Service visitor data to estimate a wide range of values for visitor trips to national forest lands. Donovan and Champ (2009) estimated recreational values associated with elk viewing in Oregon’s Jewel Meadows Wildlife Area.
In this application, standard errors for the estimated park unit WTP measures were estimated through standard non-parametric bootstrapping using the method of Kling and Sexton (1990) with 1,000 bootstrap replicates for each of the 58 park sample models (Martínez-Espiñeira and Amoako-Tuffour 2008).
Meta-Regression Analysis Modeling Methods
Meta-regression analysis modeling studies have seen a dramatic increase in the literature in recent years. First described by Glass (1976), the method is currently applied across a wide spectrum of disciplines, including the social and health sciences, business, and education. Early applications of meta-analysis within the field of resource economics include Smith and Kaoru (1990) and Walsh, Johnson and McKean (1988). Nelson and Kennedy (2008) identified 140 meta-analysis studies, of which one-half focused on environmental issues. In a recent paper, Moeltner and Woodward (2009) introduced the use of Bayesian estimation techniques to address small sample size issues in traditional meta-regression analysis.
Many meta-analyses within the literature have recognized and dealt with a set of common challenges related to estimating meta-regression models from a set of diverse primary studies. These challenges have been discussed by several investigators (Stanley and Jarrell 1989; Smith and Kaoru 1990) and include: (1) data heterogeneity arising from different survey populations, survey protocols, question formats, and value estimation methods; (2) non-independence, when multiple WTP estimates are derived from one study; and (3) heteroskedasticity, arising from different standard errors of estimates from different studies. These issues are addressed in this study by (1) using data from surveys with a consistent protocol and format, and using a standard model to estimate WTP, (2) calculating only one WTP estimate from each survey, and (3) using weighted least-squares with weights inversely proportional to the estimated variances of the WTP estimates. It should be noted that while some aspects of non-independence are avoided by use of only one WTP measure from each park dataset, these data were still collected across parks using a consistent survey protocol and survey question design. Therefore, some aspects of non-independence based on these consistencies across surveys remain uncorrected.
The use of a relatively simple fixed-effects meta-regression model is made possible by the nature of the underlying primary WTP estimates. This consistency of the estimates greatly reduces problems of unexplained heterogeneity.
Count Modeling Data Sources
In 1982, the NPS started the Visitor Services Project (VSP) at the University of Idaho Cooperative Park Studies Unit (VSP 2007). The VSP has conducted over 250 park-specific surveys since the project began. The project conducts a wide spectrum of visitor studies for units of the NPS across the country. While the surveys designed and administered over the years by the VSP have evolved to a degree, many similar, or identical, questions have been administered. The VSP utilizes a survey design and administration protocol consistent with or based on Dillman (2000, 2007).
Historically, not all VSP surveys included the questions and associated data necessary to estimate an individual observation travel cost model. At its base, this type of model requires data on the number of trips taken to the park unit during a certain period, and the cost of traveling (or a proxy thereof) from the visitors’ home to the park. Additional data, on trip purpose, trip characteristics, and visitor characteristics improve the theoretical structure of the estimated model. An examination of the VSP database in March of 2010 found 58 park unit surveys administered during the core visitor season for the park with data necessary to undertake count data modeling.
Distribution of NPS unit survey data by NPS region and park unit type
NPS park unit type
National battlefield park
National historic site
National historical park
National military park
National recreation area
National wild and scenic R
Sample parks as a percent of parks in region
Meta-Regression Analysis Data Sources
The nature of the WTP estimates and primary studies upon which the meta-regression analysis model was built, greatly simplified the construction of meta-regression data. The dependent variable in the model is park-level WTP per visitor trip, estimated though application of the previously discussed count data TC model.
Explanatory variables for the meta-regression analysis included readily available identifiers for park location, park type, and a measure of complementarity (the percent of Federal land in the state surrounding the park unit). Explanatory variables were collected for the 58 park units in the meta-regression analysis, as well as for the remainder of park units in the NPS system (for the subsequent out-of-sample prediction of WTP values).
Count Data Model
The NPS surveys were not originally specifically designed to collect data needed for estimation of count data models of visitor WTP. The original structure of the survey questions and resulting data made it necessary to transform and augment the survey data prior to estimating the models.
The dependent variable in the estimated TC models is defined as person-trips taken to the NPS unit (including the current trip) for a defined previous period of time (usually 12 months). A common issue found in individual TC models is lack of variability in this dependent variable. For many high profile sites (such as national parks) most visitors may only take one or two trips to the park in a year or more (Ward and Loomis 1986). Bowker and others (1996) suggested avoiding this issue by construction of a dependent variable defined as trips times the visitors’ group size. This construct assumes, for example, that four people traveling to a park together is equivalent to one person traveling to the park four times. In this construction travel costs are appropriately scaled to a per-person-trip basis, and the implicit assumption is made that group size and all other trip characteristics for an individual are the same for all trips made in the period (Martínez-Espiñeira and Amoako-Tuffour 2008). Preliminary model specification showed that 18% of the park unit datasets estimated had insufficient variability in the dependent variable to estimate statistically significant travel cost parameters. With only 58 data points to work with in the meta-regression, we chose to preserve model degrees of freedom by utilizing an alternative construction of the dependent variable. Using this construction, estimated TC parameters for all 58 park models were statistically significant. This construction was also adopted by Bhat (2003) and Heberling and Templeton (2009). Following this convention, our dependent variable is defined as the number of trips reported by an individual times the number of people in the visitor’s personal travel group.
The 58 surveys used in this analysis asked respondents for their home zip code. We utilized a SAS program with a call-up function interfacing with Google Maps to calculate the actual driving distance in miles between park and visitor home zip codes. The distance generated was multiplied by two to represent a round-trip distance. The theoretically correct measure of travel cost in TC models is variable cost per mile. Some researchers have used the IRS charity rate per mile as a proxy for variable cost per mile (for example, Bowker and others (2009) in their models of national forest trip values). The use of the charity rate is supported by estimated variable driving costs calculated by AAA for average vehicle operation (AAA 2012). In the current study round-trip distance was multiplied by the corresponding US private vehicle reimbursement rate for charity purposes set by the Internal Revenue Service (IRS) for the specific survey year. This rate was 14 cents per mile in most years and 12 cents per mile in 1994–1996. It should be noted that the variable cost per mile used is significantly more conservative than use of the full IRS private vehicle mileage deduction rate used in some recent studies (Donovan and Champ 2009; Heberling and Templeton 2009). The estimated parameter for the travel cost variable and by extension the estimated WTP per visitor trip is linear in relation to the travel cost per mile utilized. The fit of the model is unaffected by the choice of per-mile travel cost.
No information is available in the VSP data on how the visitor traveled to the park. In these calculations, we assume that everyone travels by vehicle and that all travelers face the same cost per mile. A final component of travel cost is the addition of the specific park entry fee to the estimated distance-based travel cost.
Variables utilized in VSP count data modeling and estimation
National park zip code
Visitor’s home zip code
1999 census median income by home zip code
IRS reimbursement rate per mile (specific to survey year)
(Round-trip road miles × mileage rate)/group size + entrance fee
No. of visits within 1 year × group size
No. of individuals in visitor’s group
=1 if personal group was family
=1 if visitor spent 1 or more days on-site
In order to not bias estimated welfare measures, variables related to the price and qualities of substitute sites should be included in the models. While no individual-specific substitute data were collected in the VSP surveys, early model development for this study explored inclusion of general measures of availability of substitute sites within the respondents’ home state. These models, based on assumed generalized substitute definitions, did not estimate statistically significant parameters for the substitute variables. Further discussion of the sensitivity of estimated welfare measures to modeling choices is included in the “Discussion” section.
Meta-Regression Analysis Model
Explanatory variables used for meta-regression analysis
Estimated WTP per trip in 2011 dollars
If site is a national park NP = 1, else NP = 0
If site is a historic unit = 1, else = 0
If located in Pacific West Region = 1, else = 0
Federally owned land in state
Percent of land in state that is federally owned
If designated by NPS as a remote site = 1, else = 0
Meta-regression analysis models regressing estimated 2011 WTP per trip on the included explanatory variables were estimated. In preliminary analysis models with both linear and log specifications of the dependent variable were estimated. Pairwise interactions of the explanatory variables were also examined. The models were weighted using the inverse of the bootstrapped variance estimates for the 2011 WTP dependent variable as weights.
Analysis and Results
Count Data Model Results
The analysis of data from 58 different surveys conducted over 15 years presented significant challenges with regards to model specification. Estimation of models for each park individually, with the associated examination of fit, and adjustment of model specification and variables included would provide the richest, yet a somewhat overwhelming picture of the data and associated modeling process. This individual specification method for each park, however, would lead to some compromise in comparison of parameter estimates and associated WTP estimates between park units with differing model specifications. A second approach would be to estimate models using only variables available for the largest number of park surveys. This second approach was adopted in this analysis using a reduced model specification to derive WTP estimates for the largest set of park units which have consistently specified explanatory models.
One of the park units modeled in our analysis (Great Sand Dunes NP&Pres) was the focus of an in-depth analysis by Heberling and Templeton (2009). These authors found that the three estimated model specifications (truncated Poisson, and two negative binomial specifications) “have fairly similar results” (p. 624). Their analysis further suggested overdispersion in the truncated Poisson model based on inflated covariate t-statistics, and on the optimal regression-based test suggested by Cameron and Trivedi (1998). They argued for the appropriateness of the negative binomial specification over the truncated Poisson, and reported WTP estimates for only negative binomial specifications.
In the current analysis of 58 different park models using the endogenous stratification negative binomial model we found that the additional dispersion parameter in the model (α), which captures the unobserved heterogeneity that the truncated Poisson fails to capture, was statistically significant in a large number of the models. Specifically, the dispersion parameter was significant at the 99% level in 43 of 58 models, at the 95% level in 4 models, at the 90% level in 2 models, and not significant in the remaining 9 models. These results indicate that the truncated Poisson specification is overly restrictive in 85% of the park models (Englin and Shonkwiler 1995a; Martínez-Espiñeira and Amoako-Tuffour 2008). In order to maintain consistency in functional form across all park models, the endogenous stratification negative binomial model was employed based on evidence from prior studies, statistical evidence from the current analysis, and to conservatively estimate the significance of explanatory variables.
Sensitivity analysis of count model specification to inclusion of covariates: illustration using Great Sand Dunes NP and Preserve
WTP/person/trip (study year $)
Park survey-specific count data travel cost parameter results and estimated net economic value per visit
Travel cost parameter
WTP/person/trip (study year $)
Standard error of WTP
Big Cypress N Pres.
Bryce Canyon NP
Catoctin Mountain NP
Chattahoochee River NRA
C & O Canal NHP
Colonial NHP (Jamestown)
Crater Lake NP
Craters of the Moon NM&Pres.
Cumberland Island NS
Cuyahoga Valley NP
Dry Tortugas NP
Dry Tortugas NP
Effigy Mounds NM
Fire Island NS
Fort Donelson NB
Fort Larned NHS
Fort Stanwix NM
Fort Sumter NM
George Washington Birthplace NM
Golden Spike NHS
Great Sand Dunes NM&Pres.
Great Smoky Mountains NP
Hopewell Furnace NHS
Homestead NM of America
Indiana Dunes NL
Jean Lafitte NHP & Pres.
Johnstown Flood NM
Kings Mountain NMP
Knife River Indian Village NHS
Lincoln Boyhood Home NM
Lincoln Home NHS
Mount Rainier NP
Mount Rushmore NMEM
New River Gorge NR
Pictured Rocks NL
Rainbow Bridge NM
San Antonio Missions NHP
San Francisco Maritime NHP
San Francisco Maritime NHP
Sequoia & Kings Canyon NP
Sleeping Bear Dunes NL
Stones River NB
The table details the key TC parameter estimates and associated t-statistics, the model degrees of freedom, the corresponding estimated WTP per visitor trip (in study year and 2011 dollars), and the standard errors of the estimated 2011 WTP. The estimated coefficients for travel cost are generally highly significant and of the expected (−) sign. In preliminary full model results for the 58 park units (not shown), however, the estimated coefficients on income were generally inconsistent and not significant across the parks studied. This may be a result of the previously noted limitation of the data which necessitated the use of a weak proxy income variable rather than actual visitor-reported income. However, other researchers have also found a weak or non-significant influence for income in TC models (for example, Loomis 2003).
Meta-Regression Analysis Model Results
Estimated meta-regression model of park visitor WTP
T-statistic (P value)
Percent public land in state
Table 6 shows the meta-regression model of NPS visitor WTP (R2 = 0.65). As a point of comparison to other meta-regression models in the literature, in their examination of 140 different meta-analysis studies, Nelson and Kennedy (2008) found a median reported R2 of 0.44. Overall, the estimated coefficients for the explanatory variables had the expected signs (where there was an a priori expectation). Units designated as “National Parks” or “Historic Sites” had higher estimated WTPs than those not in these classifications, other variables being equal. Parks located in the Pacific West NPS region were valued more highly. Higher levels of Federal land ownership in the states that the park units are located in is associated with higher WTP for park visitation. Finally, park units located in remote areas (as designated by the NPS) are associated with higher WTP per trip estimates. Analysis of the weighted residuals showed no additional heteroskedasticity (White 1980), or excessive non-normality, and an examination of variance inflation factors for the explanatory variables showed no significant multicolinearity (Freund and Littell 1986). While several pairwise interaction terms were found to be marginally significant when included in the model, none improved the model adjusted R2, nor substantially changed the model predictions.
Ideally the number of observations used in the meta-regression would be large enough to allow for splitting the sample in order to explore robustness through out-of-sample verification. With only 58 observations in the predictive meta-regression model, we had insufficient sample to successfully explore split-sample verification. As an alternative to split-sample verification, a leave-one-out regression analysis (LOO) was done. This analysis predicts the out-of-sample WTP for each park unit individually based on the model being estimated using the other remaining 57 observations. The LOO analysis found that predicted out-of-sample WTP (LOO) was within 3% of predicted within-sample WTP for 50 of 58 park units. Further predicted LOO WTP was within 10% of predicted within-sample WTP for fully 57 of 58 parks. Only one park unit had an out-of-sample prediction that was more than 10% different from the in-sample prediction ($87 LOO v. $108 in-sample). These results indicate that the model is fairly robust to small changes in the dataset.
Valuation of NPS Visitor WTP System-Wide
The final step in developing a system-wide estimate of total NPS visitor WTP associated with recreational visitation to park units is to apply the estimated meta-model parameters from Table 6 to the remainder of park units in the NPS system. As noted, explanatory variables were chosen for the meta-model of WTP based on their availability not only for the 58 parks included in the final meta-regression model, but also for the majority of the remaining park units not included in the model. Predictions were not made for park units in the U.S. Virgin Islands, Puerto Rico, and Guam.
Average predicted NPS visit willingness to pay by NPS region and park unit type (2011$)
Park unit type
National park service region
National battlefield park
National historic site
National historical park
National military park
National recreation area
National wild and scenic R
The final step in estimating NPS WTP system-wide involves multiplying per-visit WTP predictions times the number of NPS-reported 2011 visits to each park unit. Across the entire NPS system for 2011, it is predicted that aggregate WTP across all NPS park units was $28.5 billion. The 95% confidence interval for this estimate is between $19.7 and $41.3 billion. For the small number of parks for which predictions were not generated due to lack of appropriate covariate information, the average WTP per visit for the entire sample was used.
Hardner and McKenney (2006) estimated total NPS system-wide visitor WTP to be $12.03 billion (2011 $). Their analysis was based on benefits transfer using average values from a wide spectrum of studies on visitation to both NPS and non-NPS locations. Hardner and McKenney noted the large degree of uncertainty in their estimate arising from the limitations of their data, and argue that their estimate is conservative (pp. 11–12). The current study, through the use of original NPS survey data and meta-regression modeling, addresses many of the limitations acknowledged by Hardner and McKenney.
Limitations of Count Data TC Models and Sensitivity Analysis of Modeling Choices
For a large-scale previously existing data source that was not originally designed to collect information for a count data model, the VSP database provides a rich source of generally consistently collected data. Several limitations of the data and modeling should be noted, however. The first is the general lack of information on household/individual income. The use of indexed average census income from 1999 for the visitor’s home zip code provides a relatively weak proxy for individual income data. This proxy income variable was only marginally successful (in terms of statistical significance) as an explanatory variable. A number of researchers have found income as an explanatory variable in travel cost studies to have a negative or non-significant influence (Loomis 2003; Liston-Heyes and Heyes 1999; Martínez-Espiñeira and Amoako-Tuffour 2008). Nevertheless, the availability of respondent-specific income data, rather than that of the respondents’ zip code cohort, would represent a significant improvement in data quality for the modeling effort.
A second limitation associated with using survey data not specifically tailored for travel cost modeling is the lack of information on individual mode of travel and travel costs. The working assumption in this analysis (as well as other recent similar studies (Bowker and others 2009; Donovan and Champ 2009)) is that all visitors travel by private automobile at an equal per-mile cost. This assumption greatly simplifies the construction of the travel cost variable, but glosses over what may be very real differences in travel costs faced by visitors. While the assumption of generalized travel costs per mile obscures visitor-specific differences in costs (Hagerty and Moeltner 2005), some researchers have found that welfare measures generated from average vs. individual travel costs per mile may not differ substantially (Ovaskainen and others 2012; Hagerty and Moeltner 2005).
A third limitation specific to using VSP data is that the data are collected as a “grab sample” usually over a 1–2-week period during the year (generally during the summer months). As such, visitor responses may not reflect those of average visitors across the entire year.
Three additional modeling choices in our analysis were omitting explanatory variables related to the value of travel time, the price and qualities of substitute sites, and multi-destination trips (MDT). Inclusion of the value of travel time within TC modeling is an unsettled area of research (Amoako-Tuffour and Martínez-Espiñeira 2012). A number of researchers have suggested support for valuing time spent traveling at one-third the wage rate (for example, Englin and Shonkwiler 1995b). Inclusion of time value in TC models unambiguously increases estimated welfare measures. For instance, Bowker and others (2009) found that consumer surplus per trip in their national model of general national forest recreation roughly doubled when travel time valued at 1/3 the average national wage rate was included with a 12 cent IRS charity rate for variable travel costs.
A second modeling choice involved excluding substitute site information from the WTP model specification. Economic theory and many researchers (for example, Rosenthal 1987) note that inclusion of a variable for the price and/or quality of substitutes is important in model specification to avoid overstating WTP. Preliminary count data models of WTP estimated in this analysis explored including generalized substitute variables based on the number of NPS units within the individual visitors’ home state. This specification was not successful in estimating statistically significant substitute parameters of the theoretically expected sign. Therefore, final WTP TC models were specified without variables included for substitute prices or qualities. The difficulty in identifying and constructing a working substitute variable is not unique to this study. Heberling and Templeton (2009) as well as Bowker and others (2009) both excluded substitute variables from their model specification for practical purposes. Kling (1989) notes that “[o]ften these omissions are unavoidable, as the necessary data is unavailable or is too highly correlated to include in the estimating equations” (p. 296).
The standard TC model also assumes that travel costs are always incurred for a single-purpose trip (visiting a recreational site) (Haspel and Johnson 1982). Treating multi-site trips as though they were single-destination trips will systematically bias consumer surplus estimates upwards (Martínez-Espiñeira and Amoako-Tuffour 2009). The VSP data we modeled contained a small number of park units with survey responses on whether the trip taken was a single or multiple destination one. However, this information was missing in the large majority of park datasets. Therefore, the WTP models were estimated without distinctions made for single v. multiple destination trips.
These three issues/modeling choices include two that theoretically lead to overstatement of WTP (exclusion of consideration of substitutes and MDT from the models), and one that leads to understatement of WTP (exclusion of the value of travel time from model specification). While the VSP data as analyzed could be re-specified including the value of travel time, without also modeling the impact of substitute sites and MDT this specification would be expected to lead to overstated WTP estimates. In order to assess the likely combined impact of all three of these modeling choices we have employed a sensitivity analysis using a Monte Carlo simulation based on evidence of the magnitude of WTP biases from our data and from the literature. Monte Carlo simulation is an extension of sensitivity analysis in which a computational algorithm is employed to evaluate the uncertainty of model inputs (Vose 2002). Use of Monte Carlo simulation provides an assessment tool of the combined effects of multiple sources of error or uncertainty (in this case, omitted factor or variable bias) (Almansa and Martinez-Paz 2011). In the Monte Carlo analysis, a single value is randomly drawn from each defined distribution of one or more potential sources of error or bias and a single combined error or bias is calculated (Phillips 2003). Monte Carlo simulations have been used in risk assessment in the fields of engineering, business, and finance for decades (Vose 2002).
Inclusion of individual value of travel time valued at one-third the average national wage rate (BLS 2013) as a component of total travel costs for the approximately 30,000 individual survey responses in the 58 park datasets leads to an increase in average estimated WTP across all park units of 267%. This is greater than that found by some researchers (Englin and Shonkwiler 1995b), but within the general range of that found by Bowker and others (2009). This ratio (2.67) was assumed constant in the Monte Carlo simulation.
Information on the likely size and distribution of WTP bias associated with exclusion of consideration of MDT came from a subset of the VSP data. Eight of the 58 park units in our sample had sufficient data to estimate the ratio of WTP for single-destination trips to WTP for all trips in the sample. These ratios ranged from 0.38 to 0.95, with a mean value for the eight parks of 0.607 and a standard deviation of 0.2041.
For simulating the potential bias associated with excluding substitute site information from the park WTP models, an example from the literature was used (Rosenthal 1987). Rosenthal reported estimates of consumer surplus per trip for eleven reservoirs. He compared the CS for zonal TC models specified without substitute site information to two specifications with substitute site information (a traditional TC model and a gravity/logit model). The ratios of CS per trip for the “without substitutes” model compared to “with substitutes” (traditional specification) for the 11 reservoirs had a mean of 0.386 and a standard deviation of 0.092. The ratios of CS for the “without substitutes” compared to “with substitutes” (gravity/logit specification) for the 11 reservoirs had a mean of 0.607 and a standard deviation of 0.267. Based on the constant factor used in correcting for cost of travel time and assumed truncated normal distributions truncated at minimum and maximum observed values for the ratios associated with correcting for MDT and substitute sites (for example, Almansa and Martinez-Paz 2011), 10,000 sets of three-ratio combinations were randomly generated with the assumption of independence among sources of uncertainty. The mean product of these three factors across the 10,000 iterations had a value of 0.66 for the simulation using the traditional TC model specifications by Rosenthal, and 1.12, using the Rosenthal gravity/logit results in the simulation. The simulation results imply that correction for all three factors would lead to estimated average WTP values ranging from 67 to 112% of those estimated by models excluding all three factors, depending on the Rosenthal assumptions used. The simulation results make clear that including the value of travel time in the estimated WTP models without also accounting for the offsetting influence of MDT and substitute sites would lead to a significant overstatement of estimated values. In the case of this data, it appears that, while certainly not ideal, the exclusion of all three factors (travel time value, MDT, and substitutes) provides generally offsetting biases.
Having acknowledged the limitations of the count data TC models estimated, it should be noted that the functional form used and estimation methodology in this study addressed several common problematic issues associated with the analysis of on-site visitor survey data: zero truncation, overdispersion, and endogenous stratification.
Limitations and Strengths of Meta-Regression Analysis Model
The meta-regression analysis model and data used to predict system-wide NPS visitor WTP has a number of appealing qualities. Nelson and Kennedy (2008) outline four key problems endemic to many meta-regression analyses: sample selection bias, primary data heterogeneity, heteroskedasticity, and non-independence of multiple observations from primary studies. By beginning this analysis with the estimation of the primary study values, this analysis was able to largely avoid all four of these potential problems.
With respect to sample selection bias, beginning from a predefined set of studies conducted by the NPS under identical survey protocols obviated the problem of making decisions on which primary study estimates to include in the analysis. Further, use of consistently collected data to estimate identically specified count data models eliminated the large majority of heterogeneity commonly found in meta-analyses. Since the analysis included original estimation of the primary data values used in the meta-regression, variance estimates for the estimated WTP values were generated in order to allow for weighted least-squares regression in the meta-model. Use of weighted least-squares regression using the inverse of the variance of the primary data WTP value as a weight addressed issues of heteroskedasticity in the estimates. Finally, the primary studies (and WTP value estimates) that form the basis of the meta-regression model are all based on independent surveys, with only one value estimate per survey. This characteristic eliminates some, but not all, potential problems associated with non-independent observation and panel effects. Panel effects associated with using the same survey design and administration protocol remain unaddressed.
Utilizing an existing dataset to estimate models not entirely consistent with the original purpose of the data collection is a double-edged sword. On the one hand, compromises must be made in the specification of the models, and assumptions related to visitor behavior. However, successful use of the data represents a tremendous efficiency in terms of survey dollars and time by engaging in a value-added analysis of data that has already served its originally designed purpose. In the case of the large store of VSP data, we were able to estimate 58 new models (including one previously estimated) of visitor WTP associated with recreational use of a wide spectrum of NPS units nationwide. Furthermore, we were able to use these value estimates within a meta-regression analysis framework to predict mean WTP visitor values for the remaining NPS units with no survey data sufficient for WTP model estimation.
One parameter used in this study that has a strong impact on final WTP estimates is the choice of a travel cost value per mile. There is currently little consensus in the literature on the most appropriate construction of the travel cost variable. In their study of national forest visitation values (Bowker and others 2009) used the IRS charity rate for private vehicle use of 12 cents per mile in constructing their travel cost variable. This rate is roughly comparable to the variable costs of operating an automobile reported by the American Automobile Association (AAA 2012). Both Donovan and Champ (2009), and Heberling and Templeton (2009) used the full (non-charity) IRS rate in their analyses. This rate was between three and four times the charity rate. Given the specifications of their models, the impacts of the choice of a mileage rate is nearly directly proportional to the resulting estimated consumer surplus per trip. Within the context of the sensitivity of WTP results to modeling choices, the choices made in constructing the travel cost variable are highly influential. A logical extension of the work reported in this article, which would strengthen and further inform our results, is an examination of data from a subset of NPS visitor surveys which include detailed questions on visitor travel in order to identify the most appropriate mileage cost parameter to utilize in construction of travel cost variables.
While the current analysis is largely successful in developing a system-wide estimate of the value of NPS visitor WTP, there is still much room for improvement in the models employed, and the underlying data used. An important area for future research would be incorporating measures of substitute availability. Another extension of the work presented here would be to estimate individual park-level TC models of WTP focusing on the fullest model specification possible given the variables available for an individual park survey, rather than the more limited specification presented here based on variables available for all parks. The NPS is currently investigating tailoring future VSP park surveys to consistently gather data designed to facilitate revealed preference trip valuation, including information on substitute sites, primary purpose trips, and income levels. Based on the generally robust and promising results of this analysis, such modifications to the VSP survey program hold great promise for future development of NPS-related estimates of general recreation trip WTP. Additionally, the VSP administers surveys in 12–15 park units each year, each survey representing a potential addition to the 58 surveys used in the current meta-analysis. Re-estimation of the meta-regression model with the addition of new survey data collected in just the last 2 years could potentially increase the number of park-specific estimates in the meta-regression model by 40% or more.
Primary funding for this study was a research grant from the National Park Service Social Science Program. The study benefited substantially from comments on a draft report by Dr. Bruce Peacock. Assistance in data collection and organization and editing was given by Joel Dalenberg and Amy Harvey. Butch Street of the NPS provided data on the NPS system. The authors wish to thank Daniel Hellerstein and Jeffery Englin as well as two other anonymous reviewers for many helpful comments and suggestions. Of course, any errors or omissions are solely the responsibility of the authors.