Distributional Effects of Entry Fees and Taxation for Financing Public Beaches

Survey Data and Model Specification

The data come from the Great Lakes Beaches Survey,² which was conducted in 2011 and 2012 and was a statewide general population survey that consisted of two stages: a short screener survey and a web survey. To identify beachgoers, the screener survey was mailed to 32,230 Michigan adults randomly drawn from a driver’s license list. To reduce potential self-selection bias, the screener survey covered a broad range of indoor and outdoor leisure activities, among which there was only one screening question for Great Lakes beach recreation. Respondents who answered that they had visited a Great Lakes beach during two summers in 2010 and 2011 were invited to take a follow-up web survey.

The web survey asked respondents for detailed monthly trip information on three types of trips from Memorial Day weekend to September 30, 2011: day trips (lasting a day or less), short overnight trips (less than four nights), and long overnight trips (four nights or more). For up to eight beaches visited, the survey elicited site-specific trips per month and a trip count to any remaining beaches. Respondents were also asked for more detailed questions on up to two randomly selected trips, such as date and main purpose of the trip. For trips with multiple beach destinations, we specify the destination as the beach where they spent the most time. Although most trips are day trips, short and long overnight trips are about 13% and 8% of the 19,284 total trips, respectively.

In the mail survey data set with 9,591 observations, 3,838 indicated they did not visit any Great Lakes beaches in 2010 or 2011, so they are defined as “nonusers” for beach recreation but were retained for modeling. The 5,737 respondents who indicated they had visited a Great Lakes beach were invited to the web survey. A total of 3,196 people responded to the web survey, for a response rate of about 59%. For demographics, respondents were asked if they were the person to whom the web survey was addressed or if they were another household member or “someone else.” To maintain consistent demographic information, we only kept the respondents to whom the web survey was addressed, which left 2,537 effective respondents from the web survey. Following the definition in Shonkwiler and Shaw (1996), we define the respondents of the web survey who took at least one trip to Great Lakes beaches from Memorial Day weekend to September 30, 2011, as “users” and those who had taken trips to Great Lakes beaches before but did not take any trip during the indicated season as “potential users.” Including the nonusers from the screener survey and users and potential users from the web survey, the effective sample size is 6,375. Among the 6,375 observations, 3,838 nonusers had not taken trips to Great Lakes beaches before. After applying the weights to the data, about 42% of the sample were nonusers during the sample season or in the two previous seasons.

The choice set is composed of reported beaches on Lake Erie, Lake St. Clair, Lake Huron, and Lake Michigan, and it does not include reported beaches on Lake Superior, inland lakes, or outside Michigan. After matching the reported beaches to the Michigan DEQ beach database, the universal choice set for each individual contains J = 451 beaches (Appendix Figure A1) and the “don’t go” alternative. On each occasion, indirect utility for visiting beach j at lake l is V_jlt = β_tc * travel cost_jl + β_l * log(beach length_jl) + ω_t* temperature_jlt + ω_cd* closure days of 2010_jl + ω_r* regional dummies. The regional dummies divide Michigan into seven regions R = {UP, Upper Peninsula (the baseline), Lower Peninsula (LP) Northeast, LP Mid-East, LP Southeast, LP Northwest, LP Mid-West, LP Southwest}. The indirect utility for individual n for not taking a trip is V_No = γ_malemale + γ_ageage + γ_whitewhite + γ_eduedu + γ_fulltimefulltime + γ_retireretire + γ_under17under17 + γ_incomeincome + constant.

Table 1 reports descriptive statistics for site attributes in the indirect utility V_jlt and individual characteristics in V_No. Table 1 includes rows for the travel cost for all sites as well as the visits. The computation of travel cost is Travel cost = distance × 2 × $0.2422 + time × 2 × (income/2,000) × (1/3), where travel cost is the sum of driving cost and time cost. Roundtrip travel distance and round-trip travel time are calculated using PC Miler. Driving cost is calculated as $0.2422 per mile, based on the 2011 AAA report and consists of per mile marginal costs for fuel, tires, maintenance, and marginal depreciation for an average vehicle (Lupi, Phaneuf, and von Haefen 2020). The value of time in recreation travel is approximated using the convention of one-third of hourly income, which is annual income divided by 2,000 hours per year of work.

The trip data as described consist of the regular matched beach data and observations with partial information about the destinations visited. The resulting structure for the probabilities for this irregular data set cannot be accommodated using standard software packages for the nested logit model. Moreover, the panel data contain a time-variant variable (water temperature), and the choice set consists of 452 alternatives for each observation. Owing to the complexity, the standard errors were bootstrapped.

Estimation Results

The estimated parameters of the repeated nested logit model for all trip data are presented in Table 2. Results indicate that travel cost has a negative and statistically significant effect on the probability of choosing a site, consistent with expectation. An increase in beach length increases the probability of choosing a beach at a decreasing rate; likewise, an increase in water temperature increases the probability of choosing a beach. The number of closure days in the previous year negatively affects the probability of visiting the beach. Although the estimates for these site variables make intuitive sense, we treat them as controls to improve model fit and because they may be correlated with other omitted site characteristics. Regional dummies reveal that Lake Michigan attracts the most Michiganders, whereas Lake St. Clair and Lake Erie are less popular, all else equal.

The nesting parameters measure the degree of independence in nests of each level and are related to the correlation among alternatives in a nest. Results show that error terms for beaches are more correlated in each lake than across lakes. Both nesting parameters show that the nested logit provides a significant improvement over conditional logit.

The signs for all the estimated demographic parameters also make intuitive sense. In particular, the parameter for having a higher income significantly and negatively affects the decision of not taking a trip in a choice occasion at a statistical confidence level of 99%. That is, Michiganders with higher incomes take more Great Lakes beach trips, all else equal. Households with children aged 17 or younger were significantly less likely to take trips at the 5% level, a result consistent with findings for Gulf Coast beaches (English et al. 2018) and boating (English et al. 2019a). At a 10% level of significance, all else equal, males take more trips, while those employed fulltime take fewer trips.

For context, the model can be used to assess welfare benefits of beach access (i.e., for avoiding a beach closure). The model implies values for beach access of about $26-$27 per lost trip to the closed site in 2012 dollars, which is slightly lower than from a model without the income effect (Cheng 2016). Closures that affect large areas, such as an entire Great Lake, will limit substitution possibilities and result in values per lost trip that can be more than twice as large as single site closures. For example, Cheng (2016) shows that a closure of Lake Michigan induces substantial trip loss and yields a value of $66 per lost trip (2012 dollars).

Beach Pricing and Financing Scenarios

For pricing policy scenarios, we simulate increases in gate fees where prices rise at all beaches by the same amount. We also compute state income tax rate changes that would generate equivalent revenue from the general population. For computing the state income tax equivalent to the revenue generated by each pricing scheme (reported in the last column of Table 3), note that Michigan has a single, flat state income tax rate (4.25%) with fewer deductions than allowed for federal taxes, although the existing deductions mean the effective share of state incomes collected is lower than the tax rate. For the equivalent income tax calculations, we assume that all resident adults would pay, since they all face the same marginal rate.

In Table 3, the second column shows the change in trips as gate fees rise, which decline as expected. The third column shows the percentage loss of trips relative to the no fee baseline as the gate fee rises at all sites. The fourth column shows the arc elasticity (midpoint formula) for demand with respect to changes in the total price (gate fee plus travel cost), where each elasticity is computed for a $1 price change at all sites (e.g., the elasticity at the $10 fee was computed for a change from a $9 fee, not shown in the table). We find that total trip demand is elastic with respect to total price and averages −1.5 across the range of fees from $1 to $20. However, note that with respect only to fees, total demand is inelastic, with the fee elasticity averaging about −0.16 over the same range. Fee elasticity does not become elastic until fees reach about $60 at each site. This suggests a substantial potential to raise revenues, assuming people respond to gate fees the same as travel costs and assuming the fees are imposed at all sites. Indeed, if we impose a fee at only one site, site demand is much more elastic to total price (with typical site demands’ elasticity of −3.4) and less inelastic with respect only to fees (fee elasticity of −0.38) for fees of $1-$20. A typical site demand becomes elastic to fees imposed on it alone at about $26, which is lower than for fees at all sites because of the substitution potential.

The relative responsiveness to fees is shown in Figure 2, which shows the effect of fees on relative demand for all sites and for a single site. In the figure, the “all sites” demand is for total demand to all sites with the fee at all sites, whereas the “typical site” demand is for a single site that faces a fee while other sites do not. To plot the relative demands on the same scale, each was normalized by dividing by their respective baseline trips without fees. As expected, demand at a single site is much more elastic to a fee than is total demand when all sites charge a fee, which has bearing on policies that apply fees differentially across sites.

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Figure 2

Demands for All Sites When Each Site Has Gate Fee and for a Typical Site That Solely Has Gate Fee

The final columns of Table 3 show the revenue raised by fees and the statewide increase in income tax rate that would generate the equivalent revenue as the fees. Of note is that, while the burden of user fees is borne by visitors, income tax changes are borne by all taxpayers. Notably, in our data, 42% had not visited a Great Lakes beach in the past three seasons.

Interestingly, the user fee is regressive when we look at the lost welfare as a percentage of income. In Table 4, we show the lost welfare and trips from the $10 fee (compared with no fee) as a percentage of income across income quartiles. The table shows that the share of trip losses is largest for the people in the lowest- and highest-income groups. Because the model estimates revealed a significant effect of income on trip taking, the result is potentially counterintuitive. It can be explained by the observation that many of our other demographic variables are correlated with income in ways that influence trip taking. Specifically, compared with the lowest quartile, the highest-income individuals in our sample are significantly whiter (by 11%), more likely to be employed fulltime (by 40%), less retired (by 23%), and more likely to have children younger than age 17 in the household (by 16%). Also relevant to trip taking are travel costs, which increase with income and depend on where one lives relative to coasts. For example, Michigan has several large lower-income urban areas directly on or close to the Great Lakes (e.g., Detroit), which contribute to much lower travel costs, thereby increasing trip demand. Some of these areas have higher unemployment relative to other areas in Michigan, and these factors combine to partially offset the fact that higher-income people are more likely to take trips, all else equal. Consequently, welfare and trip losses from gate fees are borne relatively similarly across all income quartiles. Nevertheless, as a share of income, the welfare losses accrue significantly more to lower-income households, making the fees regressive. Similar findings about the regressivity of recreation fees were found by von Haefen and Lupi (2022) and Ji et al. (2022) and for taxes on recreation gear (Walls and Ashenfarb 2022).

Table 5 examines the excess burden associated with the fee increases.³ As expected, the revenue increases are accompanied by larger surplus losses (i.e., the excess burden of the financing scheme). The results show that excess burden grows at a slightly increasing rate. Caution is warranted when interpreting these results, since welfare loss depends on how the counterfactual is specified—much larger losses would be incurred if sites were to close because of lack of financing—so keeping the sites open at a fee is a welfare gain relative to closure. Alternatively, if sites were to remain open at the current quality, gate fees could be crafted that would not reduce welfare for visitors by reinvesting those fees into site quality in a way that offsets the welfare effect of the fee (Banzhaf and Smith 2022; Chan and Kotchen 2022; Ji et al. 2022). Regardless, a key point to note in our comparison is that any gains from keeping sites open (or reinvesting fees) accrue to the users, whereas the state income tax is borne by all residents.