Sea-Level Rise, Drinking Water Quality and the Economic Value of Coastal Tourism in North Carolina

Abstract

We estimate the economic benefits of avoiding reductions in drinking water quality due to sea level rise accruing to North Carolina (NC) coastal tourists. Using stated preference methods and responses from recent coastal visitors, we find that tourists are 2%, 8%, and 11% less likely to take an overnight trip if drinking water tastes slightly, moderately, or very salty at their chosen destination. The majority of those who decline a trip would take a trip to another NC beach without water quality issues, others would take another type of recreational trip, with a minority opting to stay home. Willingness to pay for an overnight beach trip declines with the salty taste of drinking water. We find evidence of attribute non-attendance in the stated preference data, which impacts the regression model and estimates of the willingness to pay for trips. Combining economic and hydrological models, annual aggregate benefit losses due to low drinking water quality could be as high as $232 million by 2040.

Key Points

• We estimate the benefits to North Carolina coastal tourists of avoiding reductions in drinking water quality due to sea level rise

• Willingness to pay for an overnight beach trip declines with the salty taste of drinking water

• Annual aggregate benefit losses due to low drinking water quality could be as high as $232 million in 2040

1 Introduction

Tourism is a major component of the U.S. coastal economy, contributing about $143 billion to GDP each year (NOAA, 2023c). Sea-level rise (SLR) is an existential threat to economic viability and environmental sustainability of coastal North Carolina (Poulter et al., 2009), with serious implications for coastal tourism due to inundation of low-lying areas, erosion of beaches and dunes, loss of buildings and public infrastructure, and intrusion of salt water into freshwater aquifers. Tidal data collected in the region by the National Oceanic and Atmospheric Administration (NOAA) indicate rates of annual SLR of 4.78 mm/y at Duck, NC (NOAA, 2023a) and 2.61 mm/y at Wilmington, NC (NOAA, 2023b), as of the writing of this paper, with rates expected to rise in the coming decades. Bin et al. (2011) estimates negative impacts of SLR on property values for four coastal North Carolina counties at up to $7 billion by 2080. Losses from reduced access to shore fishing locations due to SLR are estimated at $430 million between 2005 and 2080 (Whitehead et al., 2009).

An unexplored issue in the context of SLR and coastal tourism is the impact on freshwater supplies. Availability of ample clean and safe drinking water supply can be a challenge for sustainable coastal development (Chen et al., 2021). Fiori and Anderson (2022) found evidence of decreasing viability of North Carolina's barrier-island aquifers due to increasing SLR. Most public water suppliers to towns on the North Carolina coast use some form of desalinization to supply fresh water, often mixing freshwater from surficial aquifers with deeper saline water to reduce the level of desalinization needed. Rising sea levels are compromising this shallow freshwater resource, meaning that future freshwater supplies will require more extensive desalinization treatment and will raise the costs of potable water. Also, desalinization cannot eliminate the salty taste of potable water when there are high chloride levels, as is likely to occur on some parts of the NC coast.

The effect of salty-tasting drinking water is underexplored in the context of SLR and coastal tourism. To our knowledge, only two studies have considered the willingness to pay (WTP) to avoid salinity in household water supply. Ragan et al. (2000) use a damage function approach to estimate the costs of high salinity water on household appliances. Using the contingent valuation method (CVM) to value improvements in drinking water quality in the State of Palestine, Middle East, Alameddine et al. (2018) find that existing salinity levels are determinants of WTP for improved drinking water quality. In this study we combine revealed preference (RP) and stated preference (SP) data on overnight trips to estimate the WTP to avoid SLR-induced effects on the salinity of drinking water in the coastal tourism sector. We utilize a series of dichotomous choice questions that inquire whether survey respondents would continue to take an overnight trip under various trip degradation scenarios, including higher trip costs.

Our survey design builds on the CVM approach to valuing a recreation trip. This literature began with Brown and Hammack (1973) who first asked waterfowl hunters about their total costs on all of their hunting trips over the season. They then asked hunters an open-ended question about the maximum amount the costs would be before they stopped hunting. Following a number of articles that found problems with open-ended willingness to pay data, Bishop and Heberlein (1979) introduced the dichotomous choice question. The first dichotomous choice study with a trip cost payment vehicle is Cameron and James (1987). Survey respondents who had already taken a fishing trip were asked a counterfactual question about whether they would have still taken the trip with higher trip costs. Cameron and James only analyze the stated preference data. McConnell et al. (1999) build on this empirical approach by analyzing both the baseline RP trip and the SP trip decisions in a panel framework.

Park et al. (1991) ask a dichotomous choice trip cost question and then follow-up questions about the quality of the trip, analyzing the data separately. Loomis (1997) extends this approach by analyzing the RP and SP data in a panel framework. More recently, Neher et al. (2017) ask four separate questions with changes in trip costs at different quality levels and find that the results are temporally reliable; willingness to pay estimates are similar to those estimated from the same survey from 20 years earlier. Moreover, Neher et al. (2018) find that willingness to pay estimates from dichotomous choice trip cost questions produce similar values to those from a discrete choice experiment.

Building on this prior work, our empirical analysis first utilizes ex-post (RP) trip responses based on current conditions as a baseline. We then consider an ex-ante (planned) trip response under current conditions, and then under alternative situations with differing quality conditions. We combine the RP and SP data into a quasi-panel. As an extension to the CVM recreation literature we allow for and model attribute non-attendance (ANA). ANA occurs when respondents fail to consider every detail of the attributes in a valuation scenario (Lew & Whitehead, 2020).

The literature includes two approaches for identifying and accounting for ANA behavior in stated preference studies. The stated ANA approach employs self-reported information about ANA behavior, while the inferred ANA approach relies on the use of econometric models to identify ANA behavior. Inferred ANA approaches generally involve flexible econometric models that allow for ANA to be identified directly from patterns in the stated responses to the choice scenarios. In this way, inferred methods do not require the use of potentially endogenous stated ANA information provided by individuals. Rather, the inferred ANA models attempt to let the data “speak for themselves” about whether or not ANA behavior is present.

In the rest of the paper we describe the data, present the model, review empirical results, explore policy implications and offer conclusions. Using an inferred ANA model we find evidence of attribute non-attendance behavior in the data, suggesting significant bias in willingness to pay compared to the naïve (base) model. This bias has significant policy implications. We recommend that researchers routinely consider ANA, and when present, provide adjusted WTP estimates. Various approaches to account for ANA can be utilized for sensitivity analysis and robustness checks.

2 Data

In the spring of 2022 we surveyed 434 North Carolina (NC) residents who had taken an overnight trip to the NC coast in the previous 36 months and who did not own coastal property. The sample is from the Dynata opt-in consumer panel. We pretested the survey in 2021 with over 200 respondents. Results of the pretest helped us revise the survey and adjust the additional trip cost amounts presented to respondents. We do not include these pretest responses in the analysis sample.

Internet surveys with opt-in samples are one of the least expensive survey modes and, as a result, are widely used in the stated preference literature (Champ, 2017). But these data may be lower in quality than probability-based samples. Johnston et al. (2017) assert that the highest quality surveys use probability-based sampling and employ the Dillman repeat-contacts method for quality assurance. A recent special section in the journal Applied Economics Perspectives and Policy examined the use of opt-in survey panels. Goodrich et al. (2023) find that one drawback of data from an opt-in sample is that respondents may rush through the questionnaire, paying little attention to the details of the valuation questions, which results in relatively low-quality data. Sandstrom-Mistry et al. (2023) compared two opt-in panels with a mixed mode mail/internet sample and found that each produced the expected results, but the WTP estimates in an opt-in sample were always greater than the probability-based sample. Penn et al. (2023) compare a probability-based sample with a convenience sample and find differences in the determinants of willingness to pay but no differences in the magnitude of willingness to pay. Whitehead et al. (2023) find that the probability-based sample data are the most likely to pass validity tests with data from a single bounded referendum question.

This research examining opt-in panels generally supports their use but with caveats and a recognition that extra effort must be expended to develop a reliable sample. In order to increase data quality, we first asked for respondents' state of residence. Non-NC residents were deleted. This was followed by an open-ended question about residents' ZIP codes. Respondents who reported ZIP codes outside NC were also deleted. We asked redundant questions to screen out additional respondents who were rushing through the questionnaire (i.e., “speeders”). We deleted 18 respondents who provided inconsistent age and/or income responses. The median time that it took respondents to complete the survey was 7 min.

Eighty-two percent of the original sample took an overnight trip during the previous 12 months, and 87% of the sample planned to take an overnight trip in the next 12 months. Given that our analysis involves stated preference questions about future trip conditions, we focus on the 286 respondents who planned to take an overnight beach trip to the NC coast during the next 12 months. The average age of the respondents is 46 years, and 69% are female (Table 1). The average household size is 2.74 people with 1.24 children. The average years of schooling is 14, and the average household income is $79 thousand.

Table 1. Sample Demographics

Variable	Label	Mean	Std Dev
Age	Age in years	46.38	15.43
Female	1 if female, 0 otherwise	0.69	0.47
House	Household size	2.74	1.20
Children	Number of children	1.24	0.97
Schooling	Years of schooling	14.25	2.17
Income	Household income	79.11	55.63
Sample size		286

Seventy-four percent of respondents had taken an overnight trip to a NC beach in the previous 12 months (Table 2), with an overall average number of 2.8 beach trips in the past 12 months. For their most recent overnight trip, the average number of nights stayed was three and the average travel party size was four people. Respondents spent an average of $749 (self-reported) on their most recent trip. These respondents expect to take an average number of 2.8 beach trips in the next 12 months. The average number of nights that they planned to stay on their next trip is also three, and the average party size remains at four people. Respondents state that they plan to spend an average of $879 (self-reported forecasting) on their next overnight trip.

Table 2. Beach Trips

Variable	Label	Trips over previous 12 Months		Trips over next 12 Months
		Mean	Std Dev	Mean	Std Dev
Trips	Day or overnight trips	2.77	2.38	2.67	2.39
Nights	Number of nights on most recent/next trip	3.09	1.60	3.03	1.57
Party	Party size on most recent/next trip	3.94	1.31	3.99	1.39
Spend	Spending on most recent/next trip	748.83	726.25	879.37	873.37
Sample		213		286

The first stated preference scenario includes up to two questions and considers the most recent trip (Table 3). We first ask respondents who had taken a trip in the past year to a NC beach (n = 213) a stated preference question for their most recent trip. We ask them to suppose that their most recent trip cost more money as a result of higher rental rates, higher prices, or some other reason. We inquire whether they would still have taken the trip if the revised trip cost was higher than the amount that they had previously spent, where the additional cost is a randomly assigned amount that ranged from $100 to $1,000 in increments of $100. Sixty-five percent of the respondents state that they would have still taken the trip, with an average additional cost of $569.

Table 3. Stated Preference Question Scenarios Data Summary

Scenario	Question	Sample size	Yes	Added cost (mean)	Slightly salty	Moderately salty	Very salty
1	1	213	100%	0	0	0	0
	2	213	65%	$569	0	0	0
	3	139	49%	$1306	0	0	0
2	1	286	100%	0	0	0	0
	2	286	57%	$560	0	0	0
	3	164	52%	$1288	0	0	0
3	1	286	87%	0	45%	55%	0
	2	248	79%	0	0	0	100%
	3	196	50%	$724	0	0	100%

In Table 4 we present the frequency tables of yes responses for each cost amount and tests for independence of the yes responses for each SP trip cost question. The percentage of yes responses to the first question (Yes1) fall from 100% at $100 to 60% at $1,000. The sample sizes at each additional cost amount are 30 or below, so it is understandable that the yes responses decrease non-monotonically with the cost amount. But, consistent with demand theory, a chi-square test indicates that the percentage of respondents who state that they would have still taken the trip is non-constant over the cost range.

Table 4. Stated Preference Question Yes Responses by Cost Amount

Cost amount	Yes1			Yes1f			Yes2			Yes2f			Yes3f
	Yes	Total	%Yes	Yes	Total	%Yes	Yes	Total	%Yes	Yes	Total	%Yes	Yes	Total	%Yes
100	19	19	100				27	31	87				13	18	72
200	27	30	90				17	26	65				8	12	67
300	8	14	57				22	31	71				9	12	75
400	10	14	71				13	20	65				13	21	62
500	12	18	67				12	20	60				10	13	77
600	12	25	48				24	38	63				11	17	65
700	14	23	61				13	28	46				4	15	27
800	13	21	62				17	32	53				7	16	44
900	9	24	38				11	33	33				4	11	36
1000	15	25	60				8	27	30				5	15	33
1100				11	23	48				18	34	53	3	9	33
1200				12	27	44				20	37	54	1	4	25
1300				17	35	49				23	39	59	3	11	27
1400				11	27	41				11	22	50	3	11	27
1500				17	27	63				14	32	44	5	11	45
Total	139	213	65	68	139	49	164	286	57	86	164	52	99	196	51
χ^2(df)	30.92*** (9)			3.80 (4)			33.17*** (9)			1.73 (4)			26.94** (14)

• Note. Yes1f and Yes2f are follow-up questions asked to those who respond “yes” to Yes1 and Yes2, respectively. Yes3f is a follow-up question asked to those who would still take the trip if the drinking water was very salty. ***p < 0.01, **p < 0.05.

For those respondents that affirmed they would still have taken the trip at a higher cost we ask a follow-up (f) question with a randomly assigned increased cost amount that ranges from $1,100 to $1,500 in increments of $100. Forty-nine percent of these respondents state that they would have still taken the trip, with an average additional cost of $1,306 (Table 3). At these higher costs, the percentage of respondents who state that they would have still taken the trip does not vary as the cost amount increases (Yes1f, Table 4).

The second stated preference scenario is similar to the first, but focuses on the next planned overnight trip to the NC coast (n = 286). We ask respondents if they would still take the trip if the cost was higher than the amount that they think they will spend, assuming costs are not higher at other potential substitute beach sites. Again, the added cost is a randomly assigned amount that ranged from $100 to $1,000 in increments of $100. The specified additional cost was $560, on average, and 57% of the respondents stated that they would still take the trip (Table 3). The percentage of respondents who state that they would still take the trip (Yes2) falls as the cost increases, again, consistent with demand theory (Table 4).

If the respondent states that they would still have taken the trip we pose another follow-up question, again with a randomly assigned cost increase that ranges from $1,100 to $1,500 in increments of $100. Fifty-two percent of these respondents state that they would still take the trip, with an average additional cost of $1,288 (Table 3). As in the first scenario, at these higher amounts the percentage of respondents to this follow-up question who state that they would still take the trip (yes2f) does not vary as the cost amount increases (Table 4).

The questionnaire then turned to the issue of sea-level rise. Respondents were told: “The National Oceanic and Atmospheric Administration (NOAA) estimates that sea levels along the North Carolina coast have been rising at a rate of about 1/8 inch to almost a 1/4 inch per year over the last several decades. At that rate, sea levels along the entire North Carolina coast will be more than 1 inch to 2 inches higher in the next 8 years.” Then respondents were asked if they were previously aware that sea levels have been rising along the NC coast. Fifty-seven percent of respondents indicated that they were aware of SLR.

Respondents were then told about the problem of saltwater intrusion: “This increase in sea-level poses several issues to coastal communities. One of these issues is drinking water quality. Saltwater can more easily mix with freshwater sources making water undrinkable. This is known as saltwater intrusion. Most of the North Carolina coastal communities are using a desalination treatment process. In this situation, continued saltwater intrusion will increase treatment costs and may make the water taste salty.” In response, 37% of respondents indicated that they were very concerned about drinking water quality at NC beaches in the future.

The hypothetical decrease in drinking water quality at the location of the respondent's next beach trip is then described, as follows: “Now try to imagine a situation where [chosen NC beach] is dealing with saltwater intrusion and drinking water quality in 2022. In this situation the water from the tap is treated by desalination. It is safe to drink and fine for bathing, washing dishes and washing clothes. But, the water would taste salty. The potential salty taste can be described on the following scale:

1. Slightly intense (barely noticeable compared to your usual tap water)

2. Moderately intense (somewhat noticeable)

3. Very intense (definitely noticeable)

An ‘extremely intense’ salty taste is like when you accidently swallow ocean water while swimming. The tap water would never be this salty.” Respondents were then asked how the tap water from their home tastes, with most (56%) stating that it “tastes fine, no complaints.” Only 4% stated that their home tap water tasted salty.

Respondents were then given details about a third stated preference scenario. They were asked what they would do if there were drinking water problems at their chosen NC beach. Then we explained several options: (a) respondents could take the trip because they do not think it would be an issue, or could find another source for drinking water; (b) they could decide to take a trip to another NC beach; or (c) do something else entirely. Respondents were told that the water quality problems in this scenario were isolated to their chosen NC beach and, thus, drinking water at all other NC beaches did not have a salty taste. In addition, respondents were instructed that they could cancel or change their reservations at no cost, and other costs associated with the trip would not change. As an internal quality check, we inquired about attentiveness to the survey scenario/instructions. Seventy-five percent of respondents stated that they read the instructions very closely, 23% said they read them somewhat closely, and 2% said that they did not read the instructions closely. Respondents were not asked to assume that averting expenditures (e.g., purchases of bottled water) would remain constant. As such, the added cost variable may include these costs to the extent that respondents did consider averting expenditures.

Respondents are first presented with one of two drinking water quality scenarios—slightly salty or moderately salty tasting water—and asked if they would still take their planned beach trip. Eighty-seven percent of respondents would still take their planned trip in this scenario (Table 3). We follow-up with those respondents who would still take the trip to assess whether they would take their planned trip if the drinking water tasted very salty; 79% of the 248 respondents would still take the trip. Finally, these remaining respondents are asked if they would still take the trip if the cost increased with the very salty taste. The cost increase was a randomly assigned amount from $100 to $1,500 in increments of $100. Fifty-percent of these remaining respondents would still take the trip if the average cost increase was $724. Again, following economic theory, the percentage of respondents who state that they would still take the trip falls as the cost amount increases (Yes3f, Table 4).

After the last trip question in each of the three scenarios, we inquire about substitution patterns for those respondents who said that they would no longer take their chosen trip (n = 187). Following the third scenario, 42% of the respondents said that they would go to another NC beach; 33% said that they would take a trip somewhere other than a NC beach; 24% said that they would stay home, and 2% said that they would do another activity entirely. Twenty-one percent of the respondents who stated that they would still go to their chosen beach if the water tasted very salty and the trip cost more (n = 99) indicated that they did not think the drinking water problem would be an issue for them. Seventy-eight percent said that they would bring drinking water from home, buy drinking water at the beach, or do both. Those who stated that they would buy drinking water were asked how much they think they would spend on bottled water during the trip. The mean averting expenditure for hauling or buying water is $36 per trip (n = 78). Note that these behaviors are not explicitly accounted for in our empirical models, but respondents are presumably accounting for such behaviors (and the associated costs) when making their decisions. As such, our subsequent WTP estimates implicitly capture anticipated averting or adaptation behaviors by households.

Similar to McConnell et al. (1999) and Loomis (1997), we combine (“stack”) the RP and SP trip data under baseline conditions, with SP trips with posited cost increases and increased drinking water salinity. The data are an unbalanced, quasi-panel with three trip scenarios (1: RP trips with cost increases; 2: SP trips with cost increases; and 3: SP trips with cost increases and increases in drinking water salinity) and up to three trip responses in each scenario (Table 3). The quasi-panel data consist of 2031 observations for the 286 respondents.

3 Model

Suppose that consumers have a quasi-concave, monotonic utility function defined over recreation trips, x (with baseline cost, p, and quality, q), and consumption of a numeraire composite commodity, h, with p_h = 1. The resulting indirect utility function depends upon trip quality and numeraire consumption: v(q, y − p), where y denotes income. If the consumer is observed taking the trip under conditions q then v(q, y − p) > v(y). When faced with additional trip cost, c, the consumer will continue to take the trip if v(q, y − p − c) ≥ v(y), where the trip cost is less than the reservation price (implicitly defined as $$x\left(\overline{p},q\right)=0)$$, $$p+c< \overline{p}$$. When faced with a degradation in trip quality the consumer will continue to take the trip if v(q′, y − p) ≥ v(y), where $$q > {q}^{\prime } > \overline{q}$$, and $$\overline{q}$$ is the reservation quality for a given price, $$x\left(p,\overline{q}\right)=0$$. When faced with a cost increase and a degradation in trip quality, the consumer will continue to take the trip if v(q′, y − p − c) ≥ v(y).

The theoretical model can be operationalized empirically following Hanemann (1984) and Loomis (1997). The individual utility from the choice is expected to be increasing in quality and income (and decreasing in price). Let the utility from alternative j be denoted as v_j(q, y) + ε_j, where v_j is the non-stochastic portion of utility for alternatives j = 0, 1 (i.e., x = 0, 1), and ε is the corresponding error term. The random utility model assumes that the individual chooses the alternative that gives the highest utility, π₁ = Pr(v₁ + ε₁ > v₀ + ε₀), where π₁ is the probability that the respondent would choose alternative j = 1. The probability can be rearranged to show that it depends on the difference in utilities, π₁ = Pr(v₁ − v₀ > ε₀ − ε₁), relative to the difference in error terms.

If the indirect utility function is assumed to be linear-in-parameters, v = β + β_qq + β_yy + ε, then the difference in utility for the first two trip scenarios (where quality is constant and the trip cost changes) is $${\increment}v={\beta }_{1}+{\beta }_{q}q+{\beta }_{y}(y-p-c)-\left[{\beta }_{0}+{\beta }_{q}q+{\beta }_{y}(y-p)\right]+\left({{\varepsilon }_{1}-\varepsilon }_{0}\right)$$ and $${\increment}v=\tilde{\beta }-{\beta }_{y}c+\tilde{\varepsilon }$$, where $$\tilde{\beta }={\beta }_{1}-{\beta }_{0}$$, and $$\tilde{\varepsilon }={\varepsilon }_{1}-{\varepsilon }_{0}$$. Under the linear-in-parameters structure, quality, income and baseline trip cost (p) drop out of the differenced utility equation. The difference in utility for the third scenario where site quality changes is $${\increment}v={\beta }_{1}+{\beta }_{q}{q}^{\prime }+{\beta }_{y}(y-p-c)-\left[{\beta }_{0}+{\beta }_{q}q+{\beta }_{y}(y-p)\right]+\left({{\varepsilon }_{1}-\varepsilon }_{0}\right)$$ and $${\increment}v=\tilde{\beta }+{\beta }_{q}\left({q}^{\prime }-q\right)-{\beta }_{y}c+\tilde{\varepsilon }$$, where c is zero for the initial stated preference question in this scenario.

Estimation of the parameters is achieved by stacking the change in indirect utility functions considering the t ≤ 9 observations (choice occasions) for each respondent, i = 1, …, 286, $${{\increment}v}_{\text{it}}=\tilde{\beta }+{\beta }_{y}{c}_{\text{it}}+{\beta }_{q}{q}_{it}+{\tilde{\varepsilon }}_{\text{it}}$$. Assuming ε are drawn from a joint logistic distribution, the probability that individual i will choose to take the trip in occasion t is

$$$\mathit{Pr}\left({x}_{\text{it}}=1\right)=\frac{1}{1+\mathrm{exp}\left({-{\increment}v}_{\mathrm{it}}\right)}$$$ (1)

The equality-constrained latent class (ECLC) model assumes respondents fall into one of several discrete and latent classes, where each latent class is defined by which attributes are attended to (Scarpa et al., 2009). The model assumes that across classes, utility difference parameters for the attributes that are attended to are equivalent. This contrasts with standard latent class logit models that allow the preference parameters to differ across classes.

The ECLC model is referred to as an inferred ANA model because it gleans ANA behavior directly from the likelihood function and patterns in the choice data, without the aid of stated ANA information from the respondents. In other words, the estimated probability that a respondent belongs to a particular class is based on observed variation in the choice data, rather than as a function of self-reported responses to questions asking about attribute attendance. As with all maximum likelihood estimation, the parameters are chosen to maximize the likelihood that the estimated model best reflects the data. In the case of an ECLC model, the researcher specifies the number of latent classes and imposes ANA restrictions on parameters. Following Koetse (2017), we specify two classes and one restriction (i.e., β_y = 0 for the second class):

$$$\text{Class}\,1:{\increment}v=\tilde{\beta }-{\beta }_{q}q-{\beta }_{y}c$$$ (2)

$$$\text{Class}\,2:{\increment}v=\tilde{\beta }-{\beta }_{q}q-0c$$$ (3)

If ANA behavior is observed in the data then the statistical fit of the model will increase (Scarpa et al., 2009).

A single parameter vector is estimated in the ECLC model, and each latent class is differentiated by which parameters are constrained to be zero and assumed to be ignored. The probability of observing individual i taking the trip at choice occasion t is:

$$$\pi \left({x}_{\text{it}}=1\right)=\sum\limits _{k=1}^{2}\left[\left(\frac{\mathrm{exp}\,\left({\theta }_{l}\right)}{\sum \nolimits_{k=1}^{K}\,\mathrm{exp}\,\left({\theta }_{k}\right)}\right)\times \frac{1}{1+\mathrm{exp}\left(-{{\increment}v}_{\mathrm{it}}\right)}\right]$$$ (4)

The left-most term in the right-hand side of the equation is the probability of membership in latent class $$l=1,2$$, where $${\theta }_{k}$$ is a class-specific constant parameter to be estimated and $$\sum \nolimits_{l=1}^{2}\frac{\mathrm{exp}\,\left({\theta }_{l}\right)}{\sum \nolimits_{k=1}^{2}\,\mathrm{exp}\,\left({\theta }_{k}\right)}=1$$. The probabilities of membership in each class are, again, estimated by maximum likelihood.

In general, if the estimated utility model is $${\increment}v=\tilde{\beta }-{\beta }_{q}q-{\beta }_{y}c$$, where q is a quality vector, q = S, M, V (i.e., slightly intense, moderately intense, and very intense salty taste), then the willingness to pay (WTP) for an overnight beach trip with baseline quality is $$\text{WTP}=-\tilde{\beta }/{\beta }_{y}$$. This is the mean (and median) WTP estimate where respondents are indifferent between taking the trip or not, and can be found by solving for the price that leads to indifference, π(x = 1) = 0.50, in the logit (Hanemann, 1984). An alternative WTP estimate involves truncating the portion of the logit curve with negative WTP: $${\mathrm{WTP}}^{\prime }=\frac{-1}{{\beta }_{y}}\mathrm{ln}\left(1+\mathrm{exp}\left(\tilde{\beta }\right)\right)$$ (Hanemann, 1989). Considering this truncation, WTP’ > WTP and the difference will be decreasing in the constant of the logit model. These differences are slight in our models, so we choose to present the truncated mean WTP estimate since it provides a more conservative estimate of some of the differences in WTP due to changes in drinking water quality. If ANA on the price variable is present in the data, but unaccounted for, then β_y will be biased toward zero and the willingness to pay estimate will be biased upwards. We assume that those in the non-attending class have the same WTP values as those in the attending class.

4 Results

We first estimate a base case binary logit model with clustered standard errors at the individual level: Pr(x_it = 1) = f(c_it, S_it, M_it, V_it), where x = 1 if the respondent would take the trip, c is the added trip cost, S = 1 if the salty taste is “slightly intense,” M = 1 if the salty taste is “moderately intense” and V = 1 if the salty taste is “very intense.” The baseline for the taste variables is no salty taste (S = M = V = 0), which reflects the drinking water quality at the time of the survey. This model is labeled as the naïve model because it assumes no ANA behavior (Table 5). The coefficient on the added trip cost variable is negative and statistically significant. The coefficients on the quality variables are negative and statistically significant. The quality coefficients are increasing (in absolute value) as salty taste becomes more intense, but the differences in the coefficients on the moderately salty and very salty variables are not statistically different (χ²[1 df] = 0.68).

Table 5. Logistic Regression Model of Overnight Beach Trips: Dependent Variable Is Whether Respondent Would Take a Trip With Higher Cost and Salty Water

	Naïve model			ANA (ECLC) model
	Coefficient	Clustered SE	z	Coefficient	SE	z
Constant	2.369	0.444	5.34	3.048	0.149	20.52
Cost	−0.0021	0.0003	−7.06	−0.0054	0.0003	−19.40
Slightly salty	−0.268	0.106	−2.52	−0.947	0.297	−3.19
Moderately salty	−0.722	0.177	−4.08	−1.405	0.281	−4.99
Very salty	−0.939	0.207	−4.53	−1.462	0.186	−7.89
AIC	1943.00			1581.40
Model χ^2	402.99			770.52
Sample size	286			286
Panel size	2031			2031
	Class probabilities
Full Preservation	100%			68%
Cost non-attendance				32%

We then estimate a binary logit ANA model following Koetse (2017) (Table 5). For this approach a 2-dimensional latent class logit model is estimated with a full preservation class (the cost attribute coefficient is estimated) and a class with non-attendance on the cost amount (with the cost coefficient constrained to zero). The class probability in the non-attending class is an estimate of the probability that the respondent did not pay attention to the cost attribute. It is important to note that an alternative explanation to apparent non-attendance behavior in general is that a respondent's utility, and hence choices, are not affected by the attribute changes posed. It is difficult to disentangle these two alternative explanations, but in our setting, economic theory suggests costs should matter and so we posit that attribute non-attendance is driving any differences between the naïve model and our application of Koetse's (2017) ANA model. Other alternative behaviors that would bias the cost coefficient toward zero are possible. For example, strategic behavior where a survey respondent states that they would choose the higher cost amount just to signal their general preference toward a site or a particular attribute. See Alemu et al. (2013) for a catalog of the numerous reasons that might emerge and be observationally equivalent to the attribute non-attendance explanation.

The ECLC variant of the ANA model is statistically superior to the naïve model with a lower AIC and higher model χ² statistics. The estimate of cost non-attendance in the ANA model is 32%, suggesting that almost a third of respondents did not pay attention to the cost attribute. The coefficient on the added trip cost variable is negative, statistically significant, and 165% larger in absolute value than the same coefficient in the naïve model. Thus, controlling for ANA significantly increases the estimate of marginal utility of income and sensitivity to cost changes, suggesting significant bias in the naïve model. The coefficients on the quality variables are negative, statistically significant and increasing (in absolute value) as the posited salty taste increases in intensity. The coefficients on the slightly, moderately and very salty tasting water variables are 255%, 95%, and 56% larger in absolute value than the coefficients in the naïve model. The differences in the coefficients on the slightly salty and moderately salty variables are not statistically different (χ²[1 df] = 1.69). Similar to the naïve model, the differences in the coefficients on the moderately salty and very salty variables are not statistically different (χ²[1 df] = 0.05). Only the difference between the slightly salty and very salty coefficients are statistically different at the p = 0.10 level (χ²[1 df] = 3.41).

5 Willingness to Pay

If the marginal utility of income, β_y, is biased toward zero in a naïve model where the researcher ignores ANA behavior, then the WTP estimate will be biased upwards. Such overstatement of the benefits can lead to suboptimal policy decisions. Even though the numerator coefficients are higher in the ANA model, we still find that the WTP for a trip is biased upwards in the naïve model. The WTP for an overnight trip is $1,173 in the naïve model and $567 in the ANA model (Table 6). This upward bias in the naïve model can be observed in the logistic regression curves (Figure 1). The naïve model has a relatively flat curve with a fat tail that reaches only a 31% probability that the respondent would not take the trip with the highest trip cost increase included in the stated preference question. In contrast, the estimated probability at the highest cost amount is 0.6% in the ANA model. In a two-tailed test, the ANA WTP estimate is statistically different from the base case WTP estimate at the p = 0.058 (t = 1.90) level.

Table 6. Truncated Mean Willingness to Pay Estimates

	Naïve model			ANA (ECLC) model
	Mean	SE	z	Mean	SE	z
Base case	1172.65	314.82	3.72	576.31	25.30	22.78
WTP | Slightly	1057.30	313.09	3.38	412.80	47.64	8.66
WTP | Moderate	869.55	277.26	3.14	339.49	41.12	8.26
WTP | Very	784.48	288.65	2.72	330.10	24.40	13.53

Figure 1

Logistic regression curves for two models with baseline water quality.

The willingness to pay for a trip with a quality degradation is $${\text{WTP}}_{q}^{\prime }=\frac{-1}{{\beta }_{y}}\mathrm{ln}\left(1+\mathrm{exp}\left(\tilde{\beta }+{\beta }_{q}\right)\right)$$, and the difference in willingness to pay from a quality degradation is $${\Delta }{\text{WTP}}_{q}^{\prime }={\text{WTP}}_{b}^{\prime }-{\text{WTP}}_{q}^{\prime }$$, where b is the base case. The patterns that we find in the logit models translate to differences in WTP estimates for quality. The WTP estimates for a trip with slightly salty tasting drinking water are $1,057 in the naïve model and $413 in the ANA model (Table 6). The naïve model and ANA model WTP estimates are statistically different from the base case WTP estimate at the p = 0.014 (t = 2.45) and p < 0.01 (t = 3.39) levels. The WTP estimates for a trip with moderately salty tasting drinking water are $870 in the naïve model and $306 in the ANA model. The moderately salty WTP estimate from the naïve model is statistically different from the slightly salty WTP estimate, p = 0.037 (t = 2.08). The slightly salty and moderately salty WTP estimates from the ANA model are not statistically different. We find the smallest differences in benefit estimates across models for the most extreme scenario. The WTP estimates for a trip with very salty drinking water are $784 in the naïve model and $330 in the ANA model. Neither of these WTP estimates are statistically different from the moderately salty WTP estimates.

6 Policy Implications

In this section we estimate the aggregate lost benefits from saltwater intrusion under two illustrative scenarios. The first scenario links our model results to a hydrogeological model that estimates the future impacts of saltwater intrusion. The second scenario assumes adaptation behavior by providers of drinking water (i.e., public water systems and owners of rental homes). The primary purposes of the policy simulation is to illustrate the potential magnitude of the drinking water quality problem on the tourist economy and illustrate the effects of attribute non-attendance on aggregate damage estimates.

Fiori and Anderson (2022) studied the effects of SLR on the primary source of freshwater to the barrier-island aquifers of North Carolina. Using an analytical model based on low groundwater gradients, limited room for upward expansion of the water table, and applying SLR projections from the Intergovernmental Panel on Climate Change (IPCC, 2014) and NOAA (NOAA, 2020), the authors found decreasing viability of the state's barrier-island aquifers with increasing SLR. Aquifer risk maps based on model output from this research show that most of the state's coastal aquifers are under threat from SLR over the next 60 years, but also that narrower islands and/or high-permeability barrier-island aquifers in areas of faster SLR, such as along the northern North Carolina coast, are the most vulnerable.

We use the model in Fiori and Anderson (2022) to develop estimates of five levels of drinking water quality for the years 2040, 2060, and 2080. The calculations for salt concentrations in the aquifer are based on island width, aquifer thickness, and hydraulic conductivity, and produce estimates of the position of the toe of the saltwater wedge under SLR scenarios (see Fiori & Anderson, 2022, for more detailed information on the model). We then take the model output and calculate average aquifer salinities based on the ratio of the area of the saltwater wedge to the total area of the aquifer. This gives a salinity per unit length of aquifer. There are several important caveats regarding the calculated salinity values: the salinity calculated is based on the area ratio and does not include potential saltwater intrusion induced by pumping, nor does it include the effects of tidal oscillations, wave action, or extreme storm events, including overwash.

We consider 31 beaches in North Carolina for which survey respondents reported the destination of their next beach trip in 2022 (the trip frequencies and results of the salinity calculations for each beach can be found in Tables A1–A3). We estimate that in 2040, 45% of these beaches will continue to experience freshwater in their aquifers, 23% will have slightly salty tasting water, 16% will experience moderately salty tasting water, 3% will suffer very salty tasting water, and 13% of the beaches will be left with no freshwater aquifer (Table 7). In 2060, the number of beaches with no salty taste falls to 39%, 32% have (slightly, moderately, or very) salty tasting water, and the number without an aquifer rises to 32%. Beaches with no salty tasting water falls to 6%, 39% have salty tasting water to some degree, and 55% have no aquifer in 2080.

Table 7. Drinking Water Quality and Weighted Willingness to Pay Per Trip at North Carolina Beaches

Salty taste	Percent of beaches
	2040	2060	2080
Not Salty	45%	39%	6%
Slightly Salty	23%	6%	29%
Moderately Salty	16%	16%	10%
Very Salty	3%	6%	0%
No aquifer	13%	32%	55%
	Weighted WTP^a
Naïve Model	$1094	$1091	$1031
ECLC Model	$495	$509	$436

• ^a Willingness to pay for an overnight beach trip weighted by salty taste and visitation frequency.

We next assign each beach its corresponding WTP for a beach trip from Table 6, based on baseline salinity levels (not salty), and then weight the WTP per beach by its visitation frequency (vf): $$\overline{\text{WTP}}=\sum\limits _{b=1}^{B}{vf}_{b}{\text{WTP}}_{q}$$, where $$\sum\limits _{b=1}^{B}{vf}_{b}=1$$ over b = 1, …, 31 beaches. If the beach is predicted to lose its freshwater aquifer we remove it from the choice set, simulate where North Carolina beach tourists will visit instead from a travel cost demand model (see Appendix A), and assign them the willingness to pay with water quality at that beach in 2040, 2060, 2080 (Our simulation allows respondents to travel to other North Carolina beaches even though a number of respondents told us that they would stay home if the drinking water was very salty. This decision may bias our aggregate benefit loss estimates downward). We then repeat this exercise based on the beach-specific salinity levels projected for 2040, 2060, and 2080. In other words, in this exercise we estimate the benefit losses that could occur if there was an instantaneous decrease in drinking water quality that corresponds to the projected levels for future years. Considering the naïve model, the weighted mean WTP for an overnight beach trip is $1,094 for the predicted salinity levels in 2040, $1,091 for the 2060 levels and $1,031 for the 2080 levels. These represent forgone benefits of 6.7%, 7.0%, and 12%, respectively, relative to the 2022 no saltiness baseline. The weighted WTP estimates in the ANA model are $495, $509, and $436 for the projected salinity levels for 2040, 2060, and 2080. The benefit per trip losses that are estimated to occur if these higher salinity levels are experienced today correspond to a 14%, 12%, and 24% loss, respectively. A counterintuitive result is that the weighted WTP trip estimate increases from 2040 to 2040 as the simulation model reallocates trips from sites with salty drinking water and lower WTP to sites with fresh tasting water and higher WTP. This difference should be considered neither statistically or economically significant.

According to the State of NC's tourism office (Visit North Carolina, 2023), there were 9.8 million overnight trips taken to the NC coast in 2019 (pre-covid), 95% of which were for leisure. Among those overnight vacation trips, 51% originate from NC, of which 60% are for the primary purpose of visiting the beach. Therefore, we aggregate our results over an assumed 2.86 million overnight beach trips taken by NC residents in a given year. We use frequency estimates of trip locations from the survey to create an estimate of the aggregate benefit loss of SLR-induced drinking water quality degradation relative to an aggregate benefit baseline of $3.35 billion and $1.65 billion in the naïve and ANA models.

Considering the naïve model, we estimate that the aggregate annual benefit loss will be 6.7% of the $3.35 billion base case benefit under the 2040 saltiness projections, 7.0% under 2060 levels, and 12.1% under the 2080 levels (Table 8). Annual benefit losses are $225 million, $233 million and $406 million under 2040, 2060, and 2080 projected salinity levels. With the ANA model, the annual benefit loss estimate is 14.1% of the $1.65 billion base case under the 2040 projected salinity levels, 11.7% under the 2060 levels, and 24.4% under the 2080 levels. Aggregate annual losses are $232 million, $193 million, and $402 million under each respective scenario.

Table 8. Estimates of Annual Lost Benefit^a

	Millions of 2021 Dollars
Pessimistic Scenario	2040	2060	2080
Naïve Model	$225 (6.71%)	$233 (6.96%)	$406 (12.1%)
ANA (ECLC) Model	$232 (14.1%)	$193 (11.7%)	$402 (24.4%)

Optimistic Scenario	2040	2060	2080
Naïve Model	$141 (4.21%)	$99 (2.95%)	$237 (7.07%)
ANA (ECLC) Model	$200 (12.2%)	$140 (8.52%)	$336 (20.4%)

• ^a Losses are relative to baseline benefit of $3,354 million in the naïve model and $1,648 in the ANA (ECLC) model.

The illustrative benefit exercise above presumes an instantaneous change where current salinity levels in drinking water increase to the levels that are projected for 2040, 2060, and 2080. Obviously, this increase in drinking water salinity will be more gradual, and it is possible that drinking water technologies and regulations will at least partially curb such degradation. A more optimistic scenario would involve an assumption of an improvement in drinking water technology that would leave drinking water quality at levels no worse than slightly salty. Based on the naïve model, the weighted WTP associated with this assumption is $1,123 under the projected 2040 salinity levels, $1,138 under the 2060 levels, and $1,090 under the 2080 levels; corresponds to benefit per trip losses of 4.2%, 3.0%, and 7.1%. Relative to the 2020 baseline salinity levels, aggregate losses are $141 million, $99 million, and $237 million under the 2040, 2060, and 2080 projected salinity levels, respectively. The weighted WTP estimates in the ANA model are $506, $527, and $459 for the salinity levels projected for 2040, 2060, and 2080. Aggregate annual losses are $200 million under the 2040 salinity levels scenario, $141 million for 2060 scenario, and $336 million for 2080. The annual benefit losses relative to the 2022 baseline are 12%, 9%, and 20% in 2040, 2060, and 2080, respectively.

7 Conclusions

In this paper we find that SLR effects on drinking water taste potentially have significant implications for consumer benefits and the tourist economy in North Carolina. Considering the preferred ANA model, we estimate that North Carolina residents are less likely to take an overnight trip to NC beach towns if drinking water has a slightly, moderately or very intense salty taste. These trip decreases translate into an annual loss in consumer benefits of $232 million, $193 million, and $402 million per year in pessimistic scenarios where salinity levels in the drinking water increase to projected levels in 2040, 2060, and 2080, respectively, due to SLR (As described earlier, several other (potentially critical) factors are held constant under these illustrative scenarios. It is presumed that no innovation in desalinization technologies will emerge, and that drinking water standards will allow for higher salinity levels).

We have assessed the effect of attribute non-attendance in stated preference models of recreational trip-taking. Using latent class models we find a significant amount of inferred attribute non-attendance behavior in the data with only 68% of the sample fully engaged. The ANA behavior reduces the baseline willingness to pay estimates by 50%. This is due to the biased cost coefficient in the naïve model that does not consider ANA behavior. This bias could reflect well-known problems in stated preference data such as hypothetical bias or fat tails (Parsons & Myers, 2016; Penn & Hu, 2023). Our results suggest that the influence of these stated preference behavioral anomalies on the results can be mitigated with ANA models. The annual aggregate benefit losses using the ANA model are similar to the naïve model estimates but the percentage decreases are much lower due to the lower baseline value in the ANA model.

These aggregate loss estimates do not account for all of the potential losses since we did not consider day trips and we do not consider economic surplus losses on the producer side. Our aggregate loss estimates are also conservative since we limited the geographic range of our sample to North Carolina residents, which account for 51% of all overnight trips. This was for two reasons. First, we were constrained by our research budget. Second, sampling only residents from North Carolina may minimize complications associated with multiple-destination trips. Including non-North Carolina residents would increase the population that the household WTP estimates are aggregated over, increasing the aggregate benefit estimates. This is true whether or not the out-of-state WTP estimates are biased due to multi-destination trips.

These results allude to several directions for future research with these data and other applications. First, we restricted our attention to the ECLC variant of ANA models. There are a large number of alternative stated and inferred ANA models in the literature. Studies that have a focus on providing estimates for policy analysis should consider a broader range of models to determine the robustness of estimates from a single ANA approach. Second, our data is from an opt-in panel. Future research should compare attribute non-attendance models with opt-in and probability-based samples to determine if data quality is a factor in studies like this. Finally, attention paid to ANA in SP studies is not widespread, despite a long history of evidence of ANA in the literature (Lew & Whitehead, 2020). Researchers should routinely consider the presence of ANA behavior in their data and, at the very least, estimate ANA models as a robustness check on standard models. We have estimated additional models that account for ANA on the drinking water salinity variables. In these models we find statistically significant differences in the quality coefficients and WTP estimates. The differences in the magnitudes of the quality coefficient estimates are to be expected if ANA behavior is present but we have limited variation in quality in our scenarios. With these models we find only minor differences in the weighted WTP estimates used in our simulation analysis from those presented in the paper. Therefore, we suggest that the effect of ANA on quality change in trip behavior questions is an avenue for additional research.

Climate change is perhaps one of the most difficult issues to assess with nonmarket valuation methods since many of the projected changes are beyond the range of historical experience. With revealed preference methods, one approach is to estimate the effects of weather or environmental attributes on behavior and then counterfactually simulate the effect of climate change (Shaw & Loomis, 2008). Chan and Wichman (2022) illustrate a similar approach with benefit transfer. With stated preference methods, one approach is to present hypothetical scenarios and ask the respondent to imagine that the climate problem might actually happen in a timeframe during which they might need to respond (Richardson & Loomis, 2004). It is likely that some survey respondents, in general, have difficulty with this type of hypothetical question. In our case, some respondents may overreact to a rapidly changing situation instead of one that occurs gradually over time, and in that sense our estimates could be biased upwards. Others might proceed with disbelief and then our estimates would be biased downwards. This is a critical issue in need of future study.

Acknowledgments

This paper benefits from presentation at the Society for Benefit Cost Analysis meetings, the Summer Workshop at the University of Alaska Anchorage, the Workshop on Energy and Environmental Research at the University of Hawaii and the Environmental Science and Policy Seminar at the University of Miami. This research was supported by Appalachian State University through a CONCERT grant from the Research Institute for Energy, Environment and Economics and a Dean's Club grant from the Walker College of Business.

Appendix A

Each location in Table A1 corresponds with a model location in Fiori and Anderson (2022) and overnight trips in our survey. In 2040, 45% of the model locations have viable fresh groundwater resources, but 13% have already lost a freshwater resource. By 2060, 32% of the model locations have lost their freshwater resource, while the percentage with fresh groundwater resources has dropped to 39%. By 2080, only those locations with low SLR rates and low to moderate permeability (e.g., Bald Head Island and Emerald Isle), or wide island widths and/or thicknesses and moderate to high SLR (e.g., Kitty Hawk, Buxton, and Ocracoke) retain their freshwater aquifers. Most other areas, an estimated 55%, are predicted to lose their groundwater resource.

Table A1. Modeled Drinking Water Quality Estimates Based on Fiori and Anderson (2022)

Beach	Trip frequency (%)	Water quality
		2040	2060	2080
Corolla	8.04	Slightly Salty	No Aquifer	No Aquifer
Duck	1.05	Slightly Salty	Moderately Salty	No Aquifer
Kitty Hawk	4.55	Not Salty	Not Salty	Not Salty
Kill Devil Hills	2.45	Slightly Salty	Moderately Salty	No Aquifer
Nags Head	5.24	Moderately Salty	No Aquifer	No Aquifer
Rodanthe	0.35	No Aquifer	No Aquifer	No Aquifer
Waves	1.05	Very Salty	No Aquifer	No Aquifer
Salvo	0	No Aquifer	No Aquifer	No Aquifer
Avon	2.10	Moderately Salty	No Aquifer	No Aquifer
Buxton	1.05	Not Salty	Not Salty	Slightly Salty
Hatteras	3.85	Moderately Salty	No Aquifer	No Aquifer
Ocracoke	2.45	Not Salty	Not Salty	Slightly Salty
Fort Macon	0	Slightly Salty	Very Salty	No Aquifer
Atlantic Beach	8.74	Slightly Salty	Moderately Salty	No Aquifer
Pine Knoll Shores	2.10	Slightly Salty	Moderately Salty	No Aquifer
Salter Path	0	Moderately Salty	Very Salty	No Aquifer
Indian Beach	1.40	Moderately Salty	No Aquifer	No Aquifer
Emerald Isle	10.14	Not Salty	Not Salty	Not Salty
North Topsail Beach	2.80	Slightly Salty	Moderately Salty	No Aquifer
Surf City	3.50	No Aquifer	No Aquifer	No Aquifer
Topsail Beach	5.24	No Aquifer	No Aquifer	No Aquifer
Wrightsville Beach	6.99	Not Salty	Not Salty	Slightly Salty
Carolina Beach	12.94	Not Salty	Not Salty	Moderately Salty
Kure Beach	1.75	Not Salty	Slightly Salty	Moderately Salty
Fort Fisher	1.75	Not Salty	Slightly Salty	Moderately Salty
Caswell Beach	0.70	Not Salty	Not Salty	Slightly Salty
Yaupon Beach	0	Not Salty	Not Salty	Slightly Salty
Long Beach	1.05	Not Salty	Not Salty	Slightly Salty
Holden Beach	1.40	Not Salty	Not Salty	Slightly Salty
Ocean Isle Beach	5.24	Not Salty	Not Salty	Slightly Salty
Sunset Beach	2.10	Not Salty	Not Salty	Slightly Salty

The adaptation simulation is based on a site selection random utility model as in Whitehead et al. (2009). Respondents are asked about the location of their next overnight trip to the North Carolina coast and 27 sites have positive trips (Table A1). Travel distances to each site are from Google Maps. Travel cost is $0.18 per mile. A conditional logit model is estimated with travel costs and alternative specific constants (Table A2). In a simulation analysis we remove sites without aquifers from the choice set in 2020, 2040, and 2060 scenarios and allow the model to reallocate trips to other locations (Table A3).

Table A2. Conditional Logit Site Selection Model

	Coefficient	SE	t-ratio
Travel cost	−0.02	0.01	−2.88
Alternative Specific Constants^a
Corolla	2.31	0.57	4.02
Duck	0.10	0.76	0.13
Kitty Hawk	1.55	0.57	2.73
Kill Devil Hills	0.89	0.62	1.45
Nags Head	1.59	0.54	2.93
Rodanthe	−0.99	1.12	−0.89
Waves	0.16	0.77	0.21
Avon	0.97	0.67	1.43
Buxton	0.33	0.80	0.41
Hatteras	1.70	0.64	2.65
Ocracoke	1.29	0.69	1.88
Atlantic Beach	1.74	0.47	3.69
Pine Knoll Shores	0.35	0.59	0.58
Indian Beach	−0.03	0.66	−0.04
Emerald Isle	1.81	0.46	3.91
North Topsail Beach	0.40	0.54	0.73
Surf City	0.61	0.52	1.18
Topsail Beach	1.06	0.49	2.18
Wrightsville Beach	1.24	0.47	2.66
Carolina Beach	1.91	0.44	4.33
Kure Beach	−0.05	0.61	−0.08
Fort Fisher	−0.04	0.61	−0.06
Caswell Beach	−0.93	0.82	−1.14
Long Beach	−0.52	0.71	−0.73
Holden Beach	−0.43	0.65	−0.66
Ocean Isle Beach	0.89	0.48	1.84
Log likelihood function	−844.65
Constants only	−849.06

• ^a Sunset Beach is the omitted site.

Table A3. Predicted Trip Frequencies With Fiori and Anderson (2022) Drinking Water Scenarios Table A2 and Simulations From the Travel Cost Model (Table A1)

Beach	Trip frequencies (%)
	Stated	Simulated
	2020	2040	2060	2080
Corolla	8.04	8.87	0.00	0.00
Duck	1.05	1.16	1.54	0.00
Kitty Hawk	4.55	5.01	6.69	9.00
Kill Devil Hills	2.45	2.70	3.60	0.00
Nags Head	5.24	5.79	0.00	0.00
Rodanthe	0.35	0.00	0.00	0.00
Waves	1.05	1.16	0.00	0.00
Salvo	0.00	0.00	0.00	0.00
Avon	2.10	2.31	0.00	0.00
Buxton	1.05	1.16	1.54	2.07
Hatteras	3.85	4.24	0.00	0.00
Ocracoke	2.45	2.70	3.58	4.81
Fort Macon	0.00	0.00	0.00	0.00
Atlantic Beach	8.74	9.66	12.74	0.00
Pine Knoll Shores	2.10	2.32	3.06	0.00
Salter Path	0.00	0.00	0.00	0.00
Indian Beach	1.40	1.55	0.00	0.00
Emerald Isle	10.14	10.81	14.27	19.14
North Topsail Beach	2.80	3.09	4.06	0.00
Surf City	3.50	0.00	0.00	0.00
Topsail Beach	5.24	0.00	0.00	0.00
Wrightsville Beach	6.99	7.73	10.10	13.44
Carolina Beach	12.94	14.30	18.68	24.83
Kure Beach	1.75	1.93	2.53	3.36
Fort Fisher	1.75	1.93	2.53	3.36
Caswell Beach	0.70	0.77	1.01	1.34
Yaupon Beach	0.00	0.00	0.00	0.00
Long Beach	1.05	1.16	1.52	2.01
Holden Beach	1.40	1.55	2.01	2.67
Ocean Isle Beach	5.24	5.79	7.55	9.98
Sunset Beach	2.10	2.32	3.02	3.99

Open Research

Data Availability Statement

The questionnaire, data in MS Excel, SAS and Limdep (www.limdep.com) formats, SAS and Limdep program files are available at the OSF webpage: https://osf.io/xrvdn.