Effects of Ad-hoc Data Truncation and Homogeneous Preferences on Recreational Demand and Values: An Application to the George Washington and Jefferson National Forests

Abstract

We estimate a travel cost model for the George Washington & Jefferson National Forests using an On-Site Latent Class Poisson Model. We show that the constraints of ad-hoc truncation and homogenous preferences significantly impact consumer surplus estimates derived from the on-site travel cost model. By relaxing the constraints, we show that more than one class of visitors with unique preferences exists in the population. The resulting demand functions, price responsive behaviors, and consumer surplus estimates reflect differences across these classes of visitors. With heterogeneous preferences, a group of ‘local residents’ exists with a probability of 8% and, on average take 113 visits.

1. Introduction

In previous studies of recreation demand, researchers have dropped visitor observations with very high-frequency trips to recreational sites who may be considered outliers. For example, Englin and Shonkwiler (1995) drop observations with annual trips greater than 12, allowing one trip per month. Egan and Herriges (2006), Bowker et al. (2009), and Sardana, Bergstrom, and Bowker (2016) drop observations with annual trips greater than 52, allowing one trip per weekend. By dropping these observations, researchers truncate the distribution of visitors to the site, and the truncation is somewhat ad-hoc, that is, the truncation rule or threshold does not originate from theory.

These visitors with higher annual trips may represent local residents who report many trips due to close proximity of the recreation site to their place of residence (e.g., home). These local residents who take frequent short-duration trips may, for instance, engage in activities as a regular part of their exercise routine (e.g., jogging, taking a walk) and incur a lower travel cost. They derive higher consumer surplus per visit and due to more frequent visits, their aggregate consumer surplus per individual is un-proportionally higher.

However, to create one homogeneous class of visitors, previous recreation demand studies including those mentioned above model the visitor population as one recreation visitor group with homogeneous preferences. The distribution of trips taken to recreational site by this homogenous group is left-side truncated at zero, and perhaps also right-side truncated by the researcher at some rather ad-hoc cut-off or threshold number of trips. There are at least two issues involved with modeling recreation demand imposing homogeneous visitor preferences and ad-hoc, right-side truncation to the distribution of trips. First, ad-hoc truncation imposes a constraint on the estimated model which is likely different from the actual, underlying conceptual model. Second, homogenous preferences impose another constraint on the estimated model which could result in incorrect estimation of consumer surplus. The latter issue has been treated by Parsons (1991) using an instrumental variable approach and Baerenklau (2010) using a latent variable approach.

Ad-hoc truncation can be addressed by allowing the visitor population to be heterogeneous. Baerenklau (2010) estimates a zonal travel cost model with heterogeneous preferences using a Poisson specification for backcountry hikers for a Southern California study site. They found that the welfare estimates under the constraint of homogeneous preferences were substantially higher as compared to the unconstrained model. Hynes and Greene (2013) combined revealed and contingent travel data to model heterogeneous preferences using an on-site Negative Binomial specification for beach visitors in Ireland. Martinez-Cruz and Sainz-Santamaria (2015) estimated an on-site travel cost model with heterogeneous preferences for peri-urban forests in Mexico City. In both of these papers, it was found that three classes of visitors exist with unique preferences and welfare estimates.

In this paper, we show how ad-hoc truncation constrains the estimated model under homogeneous preferences and how these constraints can be handled using a latent variable approach which allows for heterogeneous preferences. Whether or not the assumption of homogenous preferences leads to underestimation or overestimation of welfare effects (e.g., consumer surplus) is an empirical question that we seek to answer in the paper using the latent variable approach for modeling recreational trips to the George Washington and Jefferson National Forests in the U.S. southeastern region.

2. Theoretical Considerations

2.1. Ad-Hoc Truncation, Homogenous Preferences, and Heterogeneous Preferences

As discussed above, we argue that high-frequency visitors may not be engaging in day visits to the site in question as conventionally thought of in recreational demand modeling, but rather are engaging simply in, say, a daily jog or walk which is part of a broader activity, such as a “daily exercise routine”. This broader “daily exercise routine” is not necessarily dependent on developed recreational facilities. Dropping these individuals or modeling these individuals using a recreation demand framework with homogeneous preferences would be incorrect from a theoretical perspective as explained below. In addition, classifying visitors into a homogeneous class of visitors who mostly engage in developed activities is incorrect from a policy perspective because resource managers who manage decisions control multiple recreational settings such as developed, wilderness, and general undeveloped forest areas ¹ (e.g., see Sardana, Bergstrom, and Bowker, 2016).

The effects of homogenous preferences, heterogeneous preferences, and ad-hoc truncation on consumer surplus estimates are illustrated in Figure 1. First, consider the effects of homogenous preferences vs. heterogeneous preferences. In Figure 1, Panel A, the demand curve under homogenous preferences is given by PC for both Consumers A and B.

Figure 1. Consumer surplus (CS) under constrained and unconstrained models (assumptions).

Given the demand curve under homogenous preferences in Panel A, Consumer A consumes Q_a trips at a price of P_a with consumer surplus equal to area I, and Consumer B consumes Q_b trips at a price of P_b with consumer surplus equal to area I + II + III + IV.

In Panel A, under the assumption of heterogeneous preferences, the demand curve for Consumer A is given by P’D and the demand curve for Consumer B is given by P”Q_c. Given these demand curves, Consumer A again consumes Q_a trips at a price of P_a with consumer surplus equal to area I + V. Consumer B consumes Q_b trips with consumer surplus equal to area I + II + III + IV + V + VI.

For Consumer A, the difference in consumer surplus under homogenous preferences and consumer surplus under heterogeneous preferences is equal to (I) − (I + V) = −V. For Consumer B, the difference in consumer surplus under homogenous preferences and consumer surplus under heterogeneous preferences is equal to (I + II + III + IV) − (I + II + III + IV + V + VI) =−(V + VI). Thus, for both Consumer A and Consumer B, given the demand curves in Panel A, we expect that consumer surplus under heterogeneous preferences will exceed consumer surplus under homogenous preferences, leading to the following hypothesis:

Hypothesis 1: The assumption of homogenous preferences will lead to an underestimation of consumer surplus as compared to the assumption of heterogeneous preferences.

Panel B illustrates the consumer surplus per individual with ad-hoc truncation. The forms of truncation illustrated in Figure 1, in general, appear in previous studies using on-site survey samples when truncation limits are treated as exogenous or pre-determined. For on-site samples, the left-truncation limit is set at zero (Haab and McConnell, 2002, pp. 174–181). For right-truncation, the limit is somewhat ad-hoc and is dependent on a researcher’s subjective definition of the cut-off point for the maximum number of trips for high-frequency visitors.

For example, in Figure 1, Panel B, the point of ad-hoc truncation is given by Point B. In Panel B, under ad-hoc truncation, the demand curve for both Consumers A and B is given by PBQ_b. Given this demand curve, Consumer A consumes Q_a trips at a price of P_a with consumer surplus equal to area I + II and Consumer B who consumes Q_b’ trips has consumer surplus equal to 0, as consumer B’s demand gets cut-off due to ad-hoc truncation.

In Panel B, the demand curve without ad-hoc truncation is given by P’B’C. Given this demand curve, Consumer A consumes Q_a trips at a price of P_a with consumer surplus equal to area II. Consumer B consumes Q_b’ trips at a price of P_b’ with consumer surplus equal to area II + III + IV. The difference in consumer surplus between the demand curve without ad-hoc truncation and the demand curve for this consumer assuming ad-hoc truncation equals to (2II + III + IV) − (I + II) = (II + III + IV-I). Thus, imposing the constraint of ad-hoc truncation, the net change in consumer surplus depends on the relative size of area I as compared to area (II + III + IV), leading to the following hypothesis:

Hypothesis 2: The assumption of ad-hoc truncation will overestimate/underestimate the consumer surplus depending on the relative size of consumer surplus in the unconstrained model for the individual whose demand gets cuts-off due to imposition of the constraint of ad-hoc truncation.

2.2. Travel Cost Method Demand Modeling with Heterogeneous Preferences

In order to account for the more realistic assumption of heterogeneous visitor-type preferences, we employed the Latent Variable approach that identifies distinct groups of individuals, but each group is assumed to be taking visits solely for recreation. This model is a type of latent class model with distinct groups. Latent class models are in the class of finite mixture models where heterogeneous individual preferences are modeled as a mixture of distinct but unobservable groups (Wedel et al., 1993). Modeling heterogeneous preferences is essential if the researcher believes that in the population, there exist at least two types of people who are heterogeneous in the sense that their marginal effects are different. Assigning everyone a priori into one class or another based on household socio-economic demographics is incorrect since these household characteristics are imperfectly observed.

Single-site-based recreation trip demand and the value of recreation site access were estimated using the travel cost method (TCM). The TCM is a revealed preference nonmarket valuation technique that uses costs incurred by an individual or group traveling from their origin (e.g., primary residence) to the destination as a proxy for trip price. Price (travel cost) and quantity (number of trips) data can be used to estimate a demand function that is applied to estimate trip demand and welfare effects in the form of consumer surplus (Freeman, 1992).

A single-site TCM recreation demand function corresponds theoretically to the Marshallian demand function of the general form,

(1) $${y^i}_{} = {y_{}}^i*({p_y},M,q),$$

where the dependent variable in (1), y ⁱ, represents annual trips to a recreation site by an individual or group i, p _y represents the full travel cost to an individual or group, M represents socio-economic demographics of an individual or group, and q represents quality of the site (which is constant in the single-site model). Because recreation trips by nature are non-negative integer values, the dependent variable in (1) takes on non-negative integer values. Thus, the ordinary least-squares regression model is inappropriate to estimate the demand model since the data-generating process for non-negative integer values is a count model. The basic model that satisfies the non-negative integer or the count data process is the Poisson model (Hellerstein, 1991).

Predominant problems with on-site samples are truncation, that is, exclusion of non-users (Borzykowski, Baranzini, and Maradan, 2017), and endogenous stratification, that is, oversampling frequent visitors. Shaw (1988) and Englin and Shonkwiler (1995) derived the distribution correcting for the joint effects of truncation and endogenous stratification (on-site) for the Poisson and Negative Binomial distribution, respectively. The conditional probability density for the on-site Poisson model (Shaw, 1988) is given in (2),

(2) $$Pi|s({y_i}|{\beta _s}) = {{{{\rm{exp}}( - {\lambda _i}){\lambda _i}^{\left( {{y_i} - 1} \right)}}}\over {{\left( {{y_i} - 1} \right)!}}}$$

The probability that an individual i belongs to group $s \in \{ 1,...,S)$ is assumed to be logistic ${\pi _s}$ (Baerenklau, 2010, p.804) as shown in (3). In (3), ${\varphi _s}$ is an estimable parameter vector and ${z_i}$ are individual characteristics that influence group membership,

(3) $${\pi _s} = {{{\exp (\phi {'_s}\,{z_i})}}\over {{\sum\limits_{s\,=\,1}^S {\exp (\phi {'_s}\,{z_i})}} }}$$

ϕ ₁ = 0, for identification

The formulation of the probability density in (4) is conditional upon subject i belonging to class s. Considering the observed frequencies of y _i as arising from an unobserved, mixture Poisson distribution, one obtains the unconditional probability density,

(4) $$Pi({y_i}|{\beta _s}) = \sum \nolimits_{s = 1}^S {\pi _s}{{\exp ( - \lambda _{i,s}) \lambda _{i,s}^{(y_i - 1)}}\over {( y_i - 1 )!}}$$

The likelihood function for estimating the parameters in (4) is given by,

(5) $$L = \mathop \prod \nolimits_{i = 1}^n Pi({y_i}|{\beta _s}) = \mathop \prod \nolimits_{i = 1}^n \mathop \sum \nolimits_{s = 1}^S {\pi _s}\left[ { - {\lambda _{i,s}} + \left( {{y_i} - 1} \right)\left( {{X_i}{\beta _s}} \right) - {\rm{ln}}} \right[\left( {{y_i} - 1} \right)!]{\rm{\;}}$$

Based on the estimated parameters, everyone in the population of interest can be assigned to one of the classes based on posterior probabilities. The unconditional posterior probability associated with S latent segments is given by (6):

(6) $$\theta _{is}^* = {{{{{\hat \pi }_s}{{\hat p}_{i|s}}({y_i}|{\beta _s})}}\over{{\sum\limits_{s = 1}^S {{{\hat \pi }_s}{{\hat p}_{i|s}}({y_i}|{\beta _s})} }}}$$

The maximum likelihood estimates of ${\beta _s}$ can be obtained by maximizing the likelihood function in equation (5). Heckman and Singer (1984) advocated the use of an expectation maximization algorithm (Dempster, Laird, and Rubin, 1977) for this type of problem. For the Latent Variable model, the researcher specifies S, the number of segments. The number of S can be determined based on the consistent Akaike information criterion (CAIC) (Bozdogan, 1987) given by (7):

(7) $$CAIC = - 2\sum\limits_{s = 1}^S {L{L_S}} + K(\ln (N) + 1)$$

where LL _S is the log-likelihood value, K is the number of parameters, and N is the number of observations.

Consumer surplus is estimated from the empirical demand model based on the following calculations. Following Shaw (1988), the conditional expected value of y given x (individual characteristics that influence demand) for the on-site Poisson model is given by (8):

(8) $$E\left( {y{\rm{|}}x} \right) = \exp \left( {x\beta } \right) + 1$$

The conditional expected value of y given x for each class in the Latent Variable (latent class) model jointly corrected for truncation and endogenous stratification is therefore given by (9):

(9) $$E\left( {{y_s}users} \right) = \pi s\left[ {\exp \left( {xs\beta s} \right)} \right]$$

Consumer surplus per person visit can be calculated as given in (10) (Shaw, 1988),

(10) $$CS/person/visit = - 1/\beta _S^{TC}$$

where $\beta _S^{TC}$ is the coefficient for travel cost variable.

3. Data Description

Data for estimating the Latent Variable (latent class) recreation demand model discussed above were obtained from the U.S. Forest Service’s National Visitor Use Monitoring (NVUM) program. The NVUM survey is based on a stratified random sampling design (English et al., 2002). The data were collected from the fourth round, which began in 2012 for a period of 5 years, through 2016. Participating National Forests are sampled every 5 years. During the on-site interviews, information was collected from visitors on their annual number of trips to a sampled National Forest in the last 12 months, and also the number of trips to the sampled National Forest for the activity indicated as the respondent’s primary activity.

Information on socio-economic variables was also collected in the NVUM survey, including the gender and age of the respondent. Unlike earlier rounds, primary information on self-reported income and distance was collected for one-third of the sample. Income for the household was recorded as the total annual income of the respondent. Information on travel distance as miles traveled from home to site was also collected from each respondent, and distance from home to substitute location was recorded. Table 1 describes the description of data variables and provides summary statistics of these variables.

Table 1. Descriptive statistics

Although there is a total of 155 National Forests in the U.S., to facilitate data collection some National Forests were combined within given states resulting in 120 sampling units (forests) for the NVUM survey. In any sampling year during a given 5-year sampling period, on-site survey sampling was conducted for roughly 24 National Forests. For our analysis, a single-site recreational demand model was estimated using data collected for the George Washington and Jefferson National Forests. The George Washington and Jefferson National Forests (Figure 2) are located in the southeastern region of the U.S. In 1995, the George Washington National Forest in west central Virginia and the Jefferson National Forest in southwest Virginia were grouped together to form the George Washington and Jefferson National Forests combined management unit. The combined George Washington and Jefferson National Forests management unit (hereafter in this paper referred to as the GW&J National Forest) contains nearly 1.8 million acres of public land with nearly 3 million annual recreation visits. The NVUM survey for GW&J National Forest was conducted in 2015–2016.

Figure 2. Map of George Washington and Jefferson National Forests.

4. Empirical Estimation

4.1. Empirical Model for Recreational Demand

The sampling unit for the NVUM survey is a “group,” which can be a single person or a party of persons traveling together, such as a family (Zarnoch, English, and Kocis, 2005). The NVUM survey measures recreation visits to a National Forest on a 12-month basis. Following the TCM protocol, only visitors who were visiting for the primary purpose of recreation were included in our analysis. Our empirical demand equation was specified as,

(11) $$Visit{s_i} = f(T{C_{\rm{i}}}{\rm{,}}\;Incom{e_{\rm{i}}}{\rm{,}}\;Femal{e_{\rm{i}}}{\rm{,}}\;Ag{e_i})$$

In (11) ² , the dependent variable (Visits _i) represents the annual number of trips from individual i to the sampled National Forest. Socio-economic variables include annual income (Income _i ), age (Age _i), and an indicator for a female survey respondent (Female _i). Income _i is represented by the total annual income of the household. The price of a recreational trip is equal to travel costs for individual i (TC _i ) estimated as the sum of driving and time costs following the equation:

(12) $$TC = (2 \times Distance \times \$ 0.1454/mile)/PeopleVeh + 0.33 \times {{Income\over 2000}} \times {{2 \times Distance\over {40\,mph}}}$$

In (12), driving costs are a function of one-way distance (Distance) from an individual’s origin to the destination, the average operating costs (variable costs) per mile for a typical sedan type car in 2016 of 14.54 cents/mile as defined by the American Automobile Association (AAA, 2016), and the number of passengers per vehicle (PeopleVeh _i). Time costs are a function of travel time estimated by dividing the round-visit distance by an average speed of 40 mph (Rosenberger and Loomis, 1999) and the opportunity cost of time, which was evaluated at one-third of the wage rate (Baerenklau, 2010). The wage rate was estimated by dividing the income variable per annum by 2000 (Hynes and Greene, 2013). All three variables (round-visit distance, income, and time) are considered exogenous.

4.2. Empirical Model for Membership Probabilities

Earlier estimation of latent count models includes Wedel et al. (1993) and Bockenholt (1993) and more recently, Martinez-Cruz and Sainz-Santamaria (2015) who assume the individual class-membership probability to be a function of only a constant term. We use a more generalized framework where class-membership probabilities are a function of covariates. Following Baerenklau (2010), we modeled the membership probability in (13) empirically as follows:

(13) $${\pi _s} = f(Female,\,Age,\,Income,\,Distance,Undeveloped)$$

where Undeveloped in (13) is a dummy variable that takes a value one if visitor engages in wilderness or general forest area settings (undeveloped settings) and zero if they engage in developed settings.

5. Results

Model estimation results are summarized in Tables 2, 3, 4, 5, and 6. Table 2 provides the estimation results for the constrained and unconstrained models for one-group and two-group versions based on the on-site Poisson model ³ . Tables 3 and 4 provide the welfare calculations and the difference in the welfare calculations with bootstrap standard errors, and 95% confidence intervals for estimation results reported in Table 2, respectively. Table 5 provides the estimation results for the three-group version of the on-site Poisson model. Table 6 provides the profile and consumer surplus estimates for the three-group version of the model results reported in Table 5.

Table 2. On-site Poisson regression results: one-group and two-group versions

Notes: ***coefficient significance at 1%, **coefficient significance at 5%, and *significance at 10%.

Table 3. Consumer surplus estimates and bootstrap standard errors (replications = 100)⁵

Table 4. Difference in consumer surplus estimates and bootstrap standard errors (replications = 100)

Table 5. On-site Poisson regression results: three-group version of model 3

Notes: ***coefficient significance at 1%, **coefficient significance at 5%, and *significance at 10%.

Table 6. Trip profile: three−class model

We discuss our results in the following ways. First, in Table 2, we compare our constrained models with the unconstrained models in terms of price behavior and consumer surplus estimates. In Table 2, we restrict our comparisons to only the one-class and two-class model versions ⁴ . We discuss results of the three-class version separately in Table 5, where we discuss the characteristics of different classes of visitors from our three-class models.

Model 1 estimates homogeneous preference without ad-hoc truncation (corresponding to the demand curves labeled PC and P’B’C in Figure 1, Panels A and Panel B, respectively) and estimates a one-class on-site Poisson model. Model 2 imposes a constraint on the estimated model, namely ad-hoc truncation (corresponding to demand curves labeled PBQ_b in Figure 1, Panel B), and estimates a one-class on-site Poisson model with ad-hoc truncation. Model 3 represents the unconstrained model where we relax the assumptions of homogeneous preferences and ad-hoc truncation (corresponding to the demand curves labeled P’D and P’’Q_c in Figure 1, Panel A) and then estimate a two-class on-site Poisson model without ad-hoc truncation ⁷ .

On-site Poisson model regression results for Models 1–3 are shown in Table 2. In all three models, the travel cost coefficient is statistically significant at the 5% level and negative as expected theoretically. The travel cost coefficient of 0.080 in Model 1 (homogeneous preferences) as compared to 0.075 and 0.010 for Class 1 and Class 2, respectively, in Model 3 (heterogeneous preferences) suggests that, on an average, price responsiveness in Model 1 is higher as compared to price responsiveness for both classes in Model 3, thus resulting in flatter demand curve under Model 1 (e.g., PC in Panel A, Figure 1). The travel cost coefficient of 0.040 in Model 2 as compared to 0.080 in Model 1 suggests that, on an average, price responsiveness in Model 2 (homogeneous with ad-hoc truncation) is lower as compared to price responsiveness in Model 1 (homogeneous, no ad-hoc truncation), thus resulting in flatter demand curve under Model 1 (e.g., P’B’C in Panel B, Figure 1).

The model estimation results reported in Table 2 were used to calculate the consumer surplus estimates shown in Table 3, which were then used to calculate the difference in consumer surplus estimates shown in Table 4 ⁸ . In comparing Model 1 (homogenous preferences) with Model 3 (heterogeneous preferences), we quantify the effects of the constraint of homogeneous preferences on consumer surplus estimates. As shown in Table 3, Model 1 resulted in a statistically significant estimate of consumer surplus per individual per trip of about 12 USD. Model 3 resulted in a statistically significant estimate of consumer surplus ⁹ per individual per trip of about 34 USD ¹⁰ .Thus, imposing the constraint of homogeneous preferences on the visitors to the GW&J National Forest resulted in about a 64% underestimation of consumer surplus. Also, as shown in Table 4, the difference in the consumer surplus per trip (22 USD) between the two models is statistically significant ¹¹ .

Thus, we find evidence that leads us to fail to reject Hypothesis 1 which states that the assumption of homogenous preferences will lead to an underestimation of consumer surplus as compared to the assumption of heterogeneous preference. This intuitively means that with homogeneous preferences, the entire probability weight is assigned to one class of visitors who are highly price responsive. Relaxing the assumption of homogeneity of preferences allocates some of the probability weights to a different, less price responsive, class of visitors. Therefore, consumer surplus is higher in the unconstrained model.

In comparing Model 2 (ad-hoc truncation) with Model 1 (no ad-hoc truncation), we quantify the effects of ad-hoc truncation on consumer surplus estimates. As shown in Table 3, Model 2 resulted in a statistically significant estimate of consumer surplus per individual per trip of about 25 USD compared to about 12 USD per individual per trip for Model 1.Thus, imposing the constraint of ad-hoc truncation resulted in an overestimation of consumer surplus by approximately 52%. Also, as shown in Table 4, the difference in the consumer surplus per trip between the two models is statistically significant ¹² .

The statistically significant difference in consumer surplus estimates across Models 1 and 2 points toward the welfare impacts of ad-hoc truncation in our data. Given this statistical difference, we conclude the following about Hypothesis 2 – assuming the constraint of ad-hoc truncation results in the overestimation of consumer surplus in the constrained model. This implies that the visitor group, whose demand is cut-off due to ad-hoc truncation, has a relatively smaller consumer surplus in the unconstrained model (area II + III + IV). For example, including these visitors who take more frequent visits and have relatively smaller consumer surplus per trip makes the unconstrained demand curve flatter (P’B’C in Panel B), price responsiveness higher, and consumer surplus lower. Thus, if these visitors are truncated out of the sample, consumer surplus will be overestimated.

Our final model, Model 4, represents the three-class model for the three class version of the one-site Poisson model with three distinct classes of visitors:1) a group of visitors termed “residents” (Class 1); 2)a distinctly different group termed “recreational enthusiasts” (Class 2); and 3) a group of visitors termed “casual users” (Class 3). The classes are defined based on trip frequency, price responsiveness, and consumer surplus per person. Estimation results for Model 4 are shown in Table 5. For all three classes, the negative and significant estimated coefficients for own travel costs indicate that the number of trips is inversely related to own travel costs for each class, implying a downward-sloping demand curve. An increase in travel costs by 1 USD reduces trips by 6.9%, 1.6%, and 9.7% for local residents, recreational enthusiasts, and casual users, respectively.

The price responsiveness as given by the travel cost coefficient estimates of respective groups in Table 5 is highest for casual users followed by local residents and lowest by recreational enthusiasts. According to economic theory, if a recreational trip to a National Forest is a normal good, we would expect an increase in income to have a positive marginal effect on trips demanded. The positive and significant estimated coefficients for income in Model 4 imply that an increase in income by 1 USD increases trips by 0.4%, 0.7%, and 0.5% for local residents, recreational enthusiasts, and casual users, respectively. The coefficient for age is positive and statistically significant for all the three classes. The positive and statistically significant coefficient for the gender variable (Female) for local residents suggests that for this population female respondents, on average, take 33% more trips ceteris paribus than male respondents.

Though, in the NVUM data, we do not have data on substitute visits to state/local parks, price responsiveness of casual users intuitively implies that casual users substitute their visits to National Forest recreation sites with other recreational facilities (may be local or state parks) as compared to recreational enthusiasts. Based on their engagement in day trips that may be more in the nature of a convenient site for casual day-use visits, the casual user may decide at the spur of the moment to go, say, to a local town park instead. Our definitions of these two types (classes) of visitors and findings in terms of price responsiveness and consumer surplus are consistent with Baerenklau (2010).

Table 6 shows that local residents tend to visit more frequently as compared to recreational enthusiasts and casual users. Local residents, on average, take 113 annual visits as compared to recreational enthusiasts who on an average take 31 annual visits and casual users who take three annual visits. Recreational enthusiasts value each visit more than local residents and casual users. Their consumer surplus per person per trip is about 62 USD as compared to 14 USD for local residents and 10 USD for casual users. Casual users, recreation enthusiasts, and local residents constitute about 61%, 31%, and 8% of total visitors, respectively.

We further use group membership coefficients estimated in Table 5 to define the characteristics of different classes of visitors ¹³ . The statistically significant positive one-way travel distance coefficient in the membership probability for the recreational enthusiasts and casual users suggests that these visitors travel greater distances to visit the GW&J National Forest as compared to local residents, which is likely attributable to the endogenous spatial sorting discussed by Baerenklau (2010) ¹⁴ . If an individual travels an additional mile of one-way distance, it increases the relative probability of belonging to the class of recreational enthusiasts as compared to local resident by 0.036.

Descriptive statistics corroborate these membership model estimation results, showing, for example, that the average one-way distance traveled by recreational enthusiasts is about 55 miles compared to about an average of 19 miles by local residents. The negative coefficient on the settings variable suggests that local residents engage more in undeveloped activities as compared to casual users. However, this coefficient estimate was not statistically significant.

The estimation results in Table 5 ¹⁵ suggest that local residents and casual users differ in terms of their price-responsive behavior and trip frequency. Casual users travel less frequently than local residents. Casual users on an average take three annual visits. They live further away from the GW&J National Forest as compared to local residents and visit developed settings such as day-used settings as compared to local residents who visit undeveloped settings. Casual users have a flatter demand curve than local residents and thus their price responsiveness is higher (40% more) than local residents. As compared to local residents, casual users derive lower consumer surplus per visit.

6. Implications and Conclusions

In this paper, we compare the effects of ad-hoc truncation and homogeneous preference constraints on recreation demand and welfare measure estimates associated with trip to the GW&J National Forest in the southeastern U.S. In most cases, observations that are dropped due to constraints imposed on the definition of visitors constitute a relatively small proportion of the visitor population but have a significant impact on consumer surplus estimates. In our analysis, we found that differences in consumer surplus per person per trip are contingent on assumptions regarding visitor preferences (homogenous vs. heterogeneous), the elasticity (slope) of the demand curve constrained by homogenous preferences, and the binding ad-hoc truncation point set by the researcher.

In general, we found that the assumption of homogenous preferences resulted in the underestimation of consumer surplus, and right-hand side ad-hoc truncation resulted in the overestimation of consumer surplus. Thus, these constraints could lead to inaccurate (biased) estimates of the benefits of recreation sites such as the GW&J National Forest. Inaccurate (biased) estimates of benefits, in turn, could lead to incorrect policy and management decisions based on, for example, benefit-cost analysis.

We also found that consumers surplus estimates are sensitive to different types or classes of visitors based on distance traveled to the recreation site (GW&J National Forest) and the particular forest setting visited (e.g., developed site vs. undeveloped site). These results imply that visitors can be segmented into different user-groups or “markets” based on different visitor (and visit) characteristics and preferences.

The ability to segment visitors into different types or classes can facilitate differential pricing policies, should that be something natural resource management agencies may want to consider in cases where user fees (e.g., entrance fee, parking fee) are charged for access to recreation sites. For example, our results show that recreation enthusiasts have a substantially higher consumer surplus (willingness-to-pay) per person per trip as compared to casual users and local residents. Also, casual users have a slightly higher consumer surplus per person per trip as compared to local residents. Thus, from both economic efficiency and equity perspectives, natural resource management agencies may want to consider charging a different user fee per trip or annual user fee to different types of users such as local residents, casual users, and recreational enthusiasts identified by the latent variable (latent class) analysis in this study. For example, local residents, who are also the most frequent users, might be charged a relatively low “local resident” daily or annual visit fee as compared to recreation enthusiasts who are non-local residents and travel less frequently to the site from greater distances.