Revenue and Distributional Consequences of Alternative Outdoor Recreation Pricing Mechanisms: Evidence from a Micropanel Data Set

Empirical Model

We use a demand system model based on Poisson-distributed trip counts (Englin, Boxall, and Watson 1998; von Haefen and Phaneuf 2003) to study the effects of counterfactual fee increases using the Iowa lakes data. Specifically, we assume that the expected demand for trips by household i during year y to lake j is given by [2] Our specification includes a full set of time-by-site alternative specific constants α_jy, which control for all characteristics of recreation sites (e.g., water quality, visitor facilities, surface area, depth of the lake) that are constant over people for that site-year pair. For consistency with integrability conditions (von Haefen 2002), we allow the own-travel cost parameter β_j to vary across sites, restrict the coefficient γon annual income Y_iy to be constant across sites, and restrict all cross-travel cost parameters to zero. This last restriction has important ramifications for how the model accommodates substitution across sites. The variable X_iy is a set of household demographics, including age, gender, educational attainment of the respondent, and the average weekend weather variables (temperature and precipitation) at the household’s home county. The functional form of the demand system in equation [2] gives rise to an expected indirect utility function of the form [3]

To estimate the parameters in equation [3], we assume that trips_ijy has a univariate Poisson distribution so that [4] where the first moment of the distribution is equal to expected trips: [5] With this assumption, the contribution to the log-likelihood for household i in year y is [6] We use equation [6] to derive the sample log-likelihood for all households and years and estimate the demand equation parameters using maximum likelihood.

Raising Revenue

Our primary interest is studying how alternative revenue-raising schemes perform using this trip demand structure. We assume it is possible to impose a lake-specific per visit user fee t_j for each lake j = 1,…,J. With this, the expected revenue from household i during year y is [7] The fee system also reduces visitors’ welfare. Based on the indirect utility function in equation [3], the welfare loss from the fee system without any feedback to improved site quality is [8] The compensating variation (CV) from the fee system is a willingness to accept. It is the income transfer the person would need to receive to restore baseline utility. Computationally for our utility function, CV is the increase in income under the fee system that makes V₀ = V₁ in equation [8], which we solve as [9]

Optimal User Fees without Revenue Recycling for a Quality Improvement

We use equations [7] and [9] to predict the individual and population revenue and welfare consequences of an arbitrary set of site user fees. We are also interested in the optimal user fees when there is a specific revenue goal. For this, we apply the Ramsey (1927) logic to derive user fees that minimize the welfare cost of obtaining a revenue goal. Specifically, in the case of a single household, we select user fees t₁,…,t_J to minimize equation [8] subject to a revenue constraint based on equation [7]. Because the first three terms in equation [8] are constant with respect to the user fees, the formal problem can be written as [10] where R is the revenue target and λis the Lagrange multiplier on the revenue constraint. In Appendix A, we examine the first-order conditions for this problem and show that the optimal user fees are characterized by [11] This result matches the standard Ramsey intuition that an optimal tax system should reduce the quantity demanded for all taxed commodities by the same proportion. Here, β_j is the proportionate reduction in trips to site j from a one-unit change in the fee, and so t_j · β_j is the overall proportionate reduction from the fee level t_j.

The formulas for revenue, welfare loss, and optimal user fees are derived in reference to a single household. In our empirical analysis, we are also interested in understanding aggregate outcomes. The predictions for household revenue and welfare losses in equations [7] and [9] can be directly aggregated using the properties of our sample. The population analog to the optimal user fees, however, requires a separate calculation when households are not identical. We show in Appendix A that equation [11] holds approximately in our context when income effects are small.

Optimal User Fees with Revenue Recycling for a Quality Improvement

Banzhaf and Smith (2022) derive two relationships conditioned on weak complementarity that determine whether a user fee accompanied by a site quality improvement is welfare enhancing. First, if weak complementarity holds and the combined effect of the user fee and the resulting site quality improvement leads to an increase in trip demand, consumer surplus is positive (this is exact for Hicksian demand and holds for Marshallian demand if the Willig condition also holds).

To examine this situation in our context, we need a way for site quality to enter our system of demand equations. Fortunately, the alternative specific constant, α_jy, can be interpreted as a site quality index that nonparametrically captures all nonprice and household-constant determinants of demand for site j during year y. Similar to Murdock (2006) and Phaneuf, Carbone, and Herriges (2009), we assume the quality index is a function of observable, policy-relevant quality variables q_jy (e.g., ambient water quality) as well as unmeasured or unobservable (to the researcher) attributes ξ_jy, so that [12] We consider changes in the quality index α_jy that could be brought about by an unspecified change in an element of q_jy, given the structure in equation [12]. With this addition to our basic model in equation [2], we can analyze the effects of a simultaneous site user fee and quality change.

If we posit a set of user fees t₁,…,t_J and an increase in site quality of Δα_j, Banzhaf and Smith’s (2022) condition that welfare is improved if site demand increases can be written as [13] where we have dropped the time subscripts to reduce clutter.

Their second insight relevant for our work is that if the cost structure of the quality improvement is unknown, it is still possible to solve for the welfare-enhancing change in site quality. The break-even quality change falls out naturally from equation [13] and can be written as [14] or equivalently as [15] The second form of this break-even condition corresponds to equation [6] in Banzhaf and Smith (2022), which shows that the break-even tax is a product of the change in quality and the marginal willingness to pay for a trip, since the per trip consumer surplus in the semi-log model is simply . Thus equation [15] provides a prediction for the change in the site quality index that is required to offset the trip-reducing impact of a site fee.

Parameter Estimates

Table 2 displays selected parameter estimates for two versions of our demand system model. Both models include a full set of site-by-year fixed effects (the α_jy terms in equation [2]) that are not shown. Model 1 corresponds to a standard specification: we estimate 139 own-travel cost parameters, 139 parameters for each of 12 demand-shifting variables, and a single income coefficient. Model 2 generalizes the specification to allow the travel cost and income coefficients to vary with household membership in one of five income categories. Specifically, we estimate separate parameters and γ^a for the a = 1,…,5 income categories defined in Table 1. That is, we estimate 139 own-travel cost parameters for each income category and five separate income parameters while maintaining homogeneity in the demand-shifting parameters. The table of results shows median and interquartile ranges for the travel cost and demand shift parameters across the range of values for the recreation sites. Point estimates and z-statistics constructed using robust standard errors are displayed for the income coefficients.

Our estimates are generally as expected. The travel cost parameters are in $100 units and are negative across their interquartile ranges (and are, in fact, negative for all sites). The distance between the 25th and 75th percentiles for these parameters shows that there is substantial heterogeneity across sites in the responsiveness of trip demand to travel cost. In model 1, the log-linear functional form and travel cost units imply the demand for trips at the median value of β_j decreases 5.7% from a $1 increase in travel cost; this changes to 7.3% and 4.3% at the endpoints of the interquartile range. In model 2, we see similar variation for the β_js in the income categories and find that the median and interquartile endpoints are smaller in absolute value for households in the upper income categories. This suggests higher-income households are less sensitive to travel costs than are households in the lower-income categories. These findings are similar in spirit to Kim, Shaw, and Woodward (2007), who allow the travel cost parameters in a random utility model to differ with income levels.

The income parameters are positive in general, with model 2 showing smaller income responsiveness for higher-income households. The direction of heterogeneity in travel cost and income effects in model 2 suggests that important distributional aspects may be masked when the simpler specification from model 1 is used, a point to which we return below. The demand shift variables show substantial heterogeneity across sites in how they affect demand, with the interquartile range going from negative to positive for nearly all variables. This heterogeneity implies it is difficult to draw general conclusions about the household, precipitation, and temperature variables, so we treat them mainly as controls and do not discuss them further.

In Table 3, we explore the behavioral implications of the different models by examining how aggregate trip demand responds to marginal price and income changes. Specially, we construct total trip price arc elasticities by increasing the travel cost to each site for each respondent in the 2014 cross section by 1%. With this, we predict the change in total trips for each respondent. The change is divided by expected baseline trips and multiplied by 100. We similarly construct total trip income arc elasticities by predicting the change in trips to all sites from a 1% increase in income. The sample averages for these calculations are reported in Table 3. Two observations are clear from the predictions. First, total trip demand is elastic with respect to travel cost for all income categories, so site entry fees may generate a comparatively large decrease in visits. Model 1 by construction captures little variation in price responsiveness across income categories, whereas for model 2, higher-income households are moderately less price elastic. Second, total trip demand is inelastic with respect to income. The log-linear functional form that we use implies that the income elasticity of trip demand for all sites is the product of income and the coefficient on income. The heterogeneity in income elasticities across income categories in model 1 is therefore mechanical. The heterogeneity in model 2 is based on differences in coefficients and income levels, so it is a more genuine representation of differential elasticities. We find that the lowest and highest income households’ total trip demand is the least responsive to a change in income, while the middle three categories are similar and somewhat more responsive.

Uniform User Fees

To further investigate the behavioral responses implied by the model specifications, we consider three different uniform fee structures and their consequences for changes in trip-taking behavior, revenue collected, and consumer welfare. The scenarios include:

• ■ Scenario 1: entry fee of $20 per trip at all lake sites in the model (Fees All $20).

• ■ Scenario 2: entry fee of $20 per trip at all lakes sites that have a boat ramp (Fees Boat $20, 105 sites).

• ■ Scenario 3: entry fee of $20 per trip at all lakes sites that are designated as state parks (Fees Park $20, 47 sites).

• ■ Scenario 4: entry fee of $5 per trip at all lake sites in the model (Fees All $5).

Table 4 provides point estimates of the average household responses to the four price change scenarios for the two model specifications. For these average effects, there is little difference between the homogeneous (model 1) and heterogeneous (model 2) specifications. In all cases, the estimates illustrate that entry fees decrease recreation visits and private consumer welfare (defined as deadweight loss plus the transfer payment). The predicted change in trips to lakes with a fee is equivalent to the overall change in trips. This absence of substitution toward nonfee lakes is a direct consequence of the limited cross-site substitution patterns captured by the log-linear functional form and is a disadvantage of this modeling approach. Nonetheless, our estimates suggest that entry fees can provide revenue to support recreation infrastructure. For the Fees All $20 scenario, for example, the per household total fee payment ranges from $49 to $52 across the two models. The per household revenue amounts are smaller for the boat ramp and park site scenarios, in that fewer lakes have a fee. Likewise, the $5 fee generate correspondingly less revenue. The $20 fee scenario revenue figures come at a relatively high private welfare cost. For the Fees All scenario, for example, the private welfare loss to revenue ratio is 1.67 and 1.61 for models 1 and 2, respectively. For both models and all the $20 scenarios, the ratio is larger than 1.5, implying that uniform fees of this size are a relatively inefficient means of raising revenue for recreation infrastructure. We note, however, that a $20 fee represents an average tax rate of 33%, based on the average travel cost of $60 for trips taken (see Table 1). For the more modest $5 entry fee—an 8.3% rate—the ratio of welfare loss to revenue raised is 1.16 for both models. This suggests that modest uniform fees can generate (smaller) revenue amounts at relatively smaller welfare loss ratios.

Table 5 presents aggregate annual estimates scaled up to the population of Iowa, assuming that our unit of observation is a household and there are 1.267 million households in the state. In aggregate, the two models once again imply similar conclusions. For the most extensive Fees All $20 scenario, the fee program would reduce trips by over 5 million visits, generate $62-$65 million in new revenue, and reduce visitors’ welfare by over $100 million annually. The predictions are similar for the Fees Boat $20 scenario. While lakes with boat ramps make up around 80% of lakes in our data, these sites are popular destinations, thus yielding similar revenue and welfare effects as the more expansive scheme. The less expansive Fees Park $20 scheme generates correspondingly less revenue at a smaller welfare cost. Finally, the Fees All $5 scheme can provide $32 million per year in revenue with comparatively modest aggregate welfare loss.

The average effects shown in Tables 4 and 5 are likely to mask heterogeneity in the incidence of user fees. To examine distributional aspects, Table 6 breaks out household-level averages for the five income categories in our models (see Table 1). Appendix Figure B2 shows the income share of fees paid for each income category across the two models and four fee scenarios. For all fee scenarios and both models, the revenue raised and welfare lost increase with higher income levels, meaning that higher-income households contribute more to overall revenue. Appendix Figure B2 shows, however, that the fee structures are regressive in the sense that households in lower-income categories pay a higher proportion of their income in fees. Comparing panels A and B shows that the extent of regressivity is smaller when we construct predictions using the income-differentiated travel cost coefficient model (model 2). A second way of looking at incidence is to examine heterogeneity in the ratio of private welfare loss to revenue. For model 1, these ratios are largely constant across income categories for any fee scenario. For model 2, this ratio falls with movements to higher-income categories. Thus, our most general specification illustrates two ways that user fees may be regressive: lower-income groups pay higher fees as a percentage of income while also experiencing higher welfare loss per dollar raised.

Optimal User Fees

Here we consider the efficiency properties of uniform versus differentiated fees for raising a fixed amount of revenue. For illustration, we fix a revenue goal of $60 million per year to raise via user fees at all of the lakes in our model. This is our Fees All scenario. For this goal, we consider three possible revenue schemes:

• ■ Uniform: a fixed entry fee for all visitors at all sites.

• ■ Income Group: fixed entry fees at all sites that are differentiated by five income categories.

• ■ Ramsey: site-differentiated entry fees.

The Income Group scheme is a hybrid that we include to consider revenue raising that optimally differentiates user fees (in terms of minimizing welfare loss) for a population based on income categories. Its relevance is illustrated by common price discrimination fee structures, such as senior citizen and student discounts. We examine each revenue scheme for our models and compare the resulting user fees, per household revenue and private welfare loss, and the efficiency ratio, defined as the ratio of welfare loss to revenue raised. We consider average effects and distributional elements.

The analytical characteristics of the Ramsey scheme are described above and in Appendix A. Actual computation for the Uniform, Income Group, and Ramsey schemes for the Iowa population relies on numerical search algorithms. For the Uniform scheme, an iterative approach is used whereby the single entry fee is incrementally changed up or down until a fee is located that results in $60 million in revenue from the Iowa population of households. For the Ramsey scheme, we use a minimization algorithm in Matlab. The objective function in Appendix A equation [A5] is coded with AR = $60 million and scaling up our sample to represent the population. The search algorithm locates the user fees by minimizing aggregate welfare loss subject to the revenue constraint. A similar algorithm is used for the Income Group, but instead of searching for site-differentiated users fees, it searches for five income category-differentiated fees.

Table 7 shows average results for the three schemes and two models, which each raise the $60 million in targeted revenue. In all cases, households contribute on average $47 per year, but there are substantial differences in how the different schemes accomplish this. For model 1, a uniform fee of nearly $16.50 per visit generates an average welfare loss per household of $72 per year. Differentiating the fees based on income leads to modest differences across income groups and similar aggregate welfare losses.⁶ In contrast to the Uniform and Income Group schemes, optimally site-differentiated user fees reduce the welfare loss to $63 on average—a 12.5% reduction for the same revenue outcome. This is accomplished using a wide range of user fees with median, 5th, and 95th percentiles of $9.30, $4.40, and $25, respectively. These predictions are qualitatively similar for model 2, with the main difference arising for the income-differentiated scheme. Here we see that parameterizing demand based on income category generates more substantial differences in the optimal income category fees. Nonetheless, the average welfare consequences of the non-Ramsey revenue-raising schemes are qualitatively similar to model 1. Specifically, for model 2, the ratio of average private welfare loss to average revenue per household falls from 1.43 for the Uniform and Income Group schemes to 1.29 for the Ramsey scheme.

The distributional properties of the three schemes are shown in Table 8 and Appendix Figure B3. Because model 2 provides income-differentiated estimates, we focus our discussion on the results for this specification. We once again find evidence of regressivity for the Uniform and Ramsey fee schemes in that higher-income households pay a smaller percentage of income and have lower welfare loss to revenue ratios. This regressivity is partially mitigated by the Income Group scheme. Although lower-income households still pay a higher percentage of income in total fees, the magnitude is smaller relative to the other schemes. In addition, the welfare loss to revenue ratio is smaller for the lowest income group (1.36) than for the highest income group (1.53). These findings suggest there is a trade-off between the efficiency gains from optimally differentiated site fees and the distributional benefits from differentiating based on income categories.

User Fees and Quality Changes

Our empirical analysis of user fees has thus far abstracted from the primary motivation for implementing a fee system: to raise revenue to improve recreation infrastructure and site quality. In this section, we consider the magnitude of quality changes necessary to offset the welfare losses implied by specific revenue goals and fee structures following Banzhaf and Smith (2022). Because we do not have access to reliable estimates of the costs required to increase site quality, we consider how overall site quality would need to change to achieve specific revenue targets while structuring welfare-neutral site fees as described in equation [16].

We examine the distribution of these quality changes for a suite of aggregate revenue goals and fee structures. Since the quality index α_j does not have meaningful units, we summarize our results using the percentage change in quality relative to average site quality in the landscape: [16] where is the average of the ASCs for the reference year.

Focusing on the results in model 1, we consider revenue targets of $60, $40, and $20 million and examine the quality-change equivalents necessary to make uniform and optimal user fees welfare neutral. Table 9 summarizes the distribution of for each revenue target/fee structure pair. Two patterns are apparent. First, the comparatively inefficient uniform fee approach to raising revenue requires substantially greater site quality improvements to generate welfare gains from a given revenue target. This is especially so for larger revenue targets: for a $60 million target with uniform fees, the average site requires a 94% quality improvement to be welfare neutral; this falls to 54% for the optimal fee structure. Second, the size of site quality improvements needed for welfare neutrality decreases nonlinearly with the aggregate revenue goal. Although this pattern is likely functional-form dependent, it is noteworthy that relatively modest quality improvements (10% and 16% at the average site for Ramsey and uniform fee, respectively) would justify a program targeting $20 million in revenue raised from visitors to lakes in Iowa. That the approximately 135 estimated ASCs have a mean of −1.07 and a standard deviation of 1.7 (far exceeding a 16% difference) suggests that this magnitude of quality improvement may be realistic.