Quantifying Recreational Benefits from Fish Consumption Advisories

FCAs

FCAs are public health tools designed to inform the public about the potential health risks associated with consuming fish from certain water bodies. These advisories are typically issued when toxic substances, such as PCBs, mercury, dioxins, or other contaminants, accumulate in fish tissue at levels that pose a risk to human health. Advisories may recommend limiting or completely avoiding the consumption of specific fish species, especially for vulnerable populations, such as pregnant women, children, and those with certain health conditions. In the United States, state environmental and public health agencies are primarily responsible for issuing these advisories, often in collaboration with federal agencies like the Environmental Protection Agency and the Food and Drug Administration. The advisories aim to reduce public exposure to harmful substances while balancing the nutritional benefits of fish consumption. Figure 1 shows an example of FCAs in Bridge Area, Michigan.

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Figure 1

Fish Consumption Advisory Signs in Bridge Area, Michigan

Beyond direct health implications, FCAs can have broader environmental and economic effects, particularly on recreational activities such as fishing and other water-based recreation. While the primary goal of advisories is to safeguard public health from consuming contaminated fish, they may also signal a polluted or degraded water body, influencing public recreational choices. Specifically, even if the advisories apply only to certain fish species and do not reflect the broader ecosystem, recreational visitors, such as anglers and nonfishing visitors, may still interpret them as indicators of poor water quality. The welfare effects of these advisories are therefore multifaceted, depending not only on the severity of contamination and the characteristics of the fishery but also on how visitors perceive the environmental quality of the site.

In this study, we identify three complementary pathways through which FCAs can plausibly affect recreational site choice for anglers and nonanglers. First, they discourage anglers who intend to eat their catch from visiting advisory sites, as shown by angler surveys in the Great Lakes region and elsewhere documenting substantial rates of fish consumption (Imm et al. 2005; Pulford, Polidoro, and Nation 2017). Second, FCAs act as salient signals of water pollution and reduced environmental quality. Prior research has shown that advisories alter perceptions of ecosystem health, aesthetic appeal, and fish abundance, thereby reducing the utility of affected sites even for catch-and-release anglers (Jakus et al. 1997; MacNair and Desvousges 2007). Third, the perceived pollution signaled by FCAs can spill over to nonfishing recreationists who value clean, visually appealing water for swimming, boating, or shoreline activities. Together, these pathways support the causal interpretation that FCAs operate both as direct health warnings and as environmental quality signals influencing site choice decisions across a broad range of recreational users.

Literature Review

The economic literature examining the effects of FCAs on outdoor recreation has grown significantly over the past few decades, with studies highlighting diverse impacts on recreational behavior and welfare. Early research primarily focused on anglers, assessing how the advisories influenced individuals’ fishing site choices and their valuation of fishing experiences (Jones and Sung 1993; Montgomery and Needelman 1997; Chen and Cosslett 1998; Parsons and Hauber 1998). Jakus et al. (1997) and Jakus, Dadakas, and Fly (1998) applied random utility models to evaluate how FCAs affected anglers’ site selection, finding that FCAs led to reduced fishing activity in affected areas and shifts toward alternative, uncontaminated sites. Similarly, Parsons, Jakus, and Tomasi (1999) used discrete-choice models to estimate the welfare losses associated with FCAs, demonstrating that anglers’ willingness to pay to avoid contaminated sites varied significantly depending on the severity of the advisories and the species targeted. Jones and Sung (1993) and Parsons and Hauber (1998) emphasized the heterogeneous effects of FCAs, showing that the extent of the impact depends on factors such as the type of water body (lake vs. river), the proximity of alternative recreation sites, and individual preferences for recreational fishing. Building on previous findings, MacNair and Desvousges (2007) examined the economic impacts of FCAs by integrating revealed and stated preference data to better capture anglers’ behavioral responses. Their joint estimation approach overcomes several difficulties, including hypothetical bias in stated preference surveys and the difficulty of modeling the variation in advisory severity levels across species and catch rates because of collinearity in revealed preference models.

Although the studies above provide important insights into angler behavior, few of them study how FCAs affect the benefits of other recreational uses of water. This may be because anglers, who directly engage in fishing, are the ones most immediately affected by FCAs. The impact of FCAs may extend beyond those who fish. Nonanglers may not directly consume fish but could use water bodies for various recreation activities, such as boating, swimming, and hiking. Negative perceptions of water quality caused by FCAs could deter visitors from visiting certain sites, leading to welfare losses. For instance, Amini, Lloyd-Smith, and Becker (2024) find that water quality at beaches leads to significant welfare loss for campers. Past literature also finds significant WTP for water quality from all recreational users (Egan et al. 2009; English et al. 2018; Johnston et al. 2023;Vossler et al. 2023). These studies highlight the importance of considering the impact of FCAs across a broader range of recreational activities.

This article contributes to this literature by examining how FCAs influence overall recreational visitation, extending beyond fishing-specific impacts. Unlike prior studies that focus on anglers, we leverage large-scale mobility data to capture broader recreational responses to advisories, providing a more comprehensive assessment of FCA effects. In addition, while most research has been geographically constrained to specific water bodies or regions, which are often within a single HUC10, our study analyzes recreational behavior across a wider geographic scale, enabling a more generalizable understanding of FCA impacts. Another empirical limitation in prior work is the potential endogeneity of FCAs, as advisories are more likely in more popular or polluted areas that also exhibit correlated socioeconomic and environmental characteristics, such as urbanization, industrial activity, and recreational site accessibility, which may not always be observable and difficult to control for. We address this concern using an IV approach, leveraging upstream industrial activity as an exogenous predictor of FCA issuance. By combining high-frequency mobility data with an IV strategy, our work provides a robust empirical framework for estimating the causal effect of FCAs on both angler and nonangler recreation demand, advancing the literature on water quality and outdoor recreation.

Recreation Demand Model

We modeled recreational behavior based on a discrete-choice modeling approach following the framework of Berry (1994) and the two-step estimation technique outlined by Murdock (2006). In the first step, we used a random utility model to estimate recreation demand and recover the mean utility gain from visiting each recreational site across all visitors using site-specific alternative-specific constants (ASCs). In the second step, we regress ASCs estimated from the first step on site attributes, including the presence of FCAs, to estimate the impact of FCAs on recreation demand.²

We considered a random utility model in which visitors from different CBGs make discrete choices among all the recreational sites in their choice sets, plus an outside option consisting of alternative leisure activities and nonrecreation choices. We define a market at the CBG-quarter level.³ Our model assumes static preferences, meaning visitors make decisions without considering future changes in travel costs or recreational site characteristics. The utility of visitors from CBG c visiting recreational site j in year-quarter t is given by

1

where TC_cjt denotes the travel cost from the visitors’ home CBG c to site j in year-quarter t, CBG_c represents CBG fixed effects, which accounts for socioeconomic characteristics of visitors at their home CBG level; W_jt represents weather conditions at recreational site j in quarter t, modeled nonparametrically with temperature and precipitation decile bins; Site_j is the ASCs for recreational sites, which capture the mean utility of visiting each site, depending on recreational site j’s attributes. γ_t is the year-quarter fixed effect, which captures the variation of seasonality, and ϵ_cjt follows an i.i.d. type I extreme value distribution.

Under the logit assumption, the difference in expected utility between a site and the outside option can be expressed in a linear form:

2

In the second step, we followed Murdock (2006) to regress the estimated ASCs (Site_j) from the first step on site attributes to identify the effects of FCAs on market share. Because each Site_j is estimated across multiple CBG markets with different choice sets, its identification strength depends on the number of markets in which site j is included in consideration. To ensure robust estimation, we constructed relatively large choice sets (within 300 miles from home CBG), allowing each site to be included by multiple CBG markets (mean = 274; median = 105). Consider the following regression:

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where Advisory_j is a binary indicator for whether site j is under a FCA. Q_j represents observed site attributes that matter to recreational values, such as whether the site is lake- or river-based, and whether it is designated as a fishing site. Because visitors’ preference for recreational sites may also be affected by the involvement of surrounding communities in tourism (Stylidis 2022), we controlled for the characteristics of the local community through X_j, a vector of demographic variables at the CBG level corresponding to the location of the recreational site. The error term ξ_j captures unobserved factors affecting ASCs.

Identification

Handling Zero Market Shares

A common challenge in modeling demand is the occurrence of zero market shares, where some products record zero observed sales in specific markets during certain periods (Ackerberg and Rysman 2005; Quan and Williams 2018; Gandhi, Lu, and Shi 2023; Earle and Kim 2024). This issue is particularly prevalent in studies of retail markets using discrete-choice demand models, where infrequent purchases, niche product offerings, or limited consumer awareness can lead to observed zero sales. Berry, Linton, and Pakes (2004) highlight that traditional demand models often assume positive market shares for all products, making them less suited for datasets with frequent zero observations. Moreover, sampling errors in small datasets or survey-based approaches can further distort demand estimation, exacerbating the challenge of accurately capturing consumer preferences.

To overcome this challenge, previous researchers modified data by aggregation or selective trimming, sometimes unknowingly, leading to potential selection bias and distorted demand estimates that affect policy simulations (Li 2019; Dubé, Hortaçsu, and Joo 2021). In our context, the presence of zero market shares raises concerns about potential bias from two scenarios: (1) the site is available but unvisited, or (2) visits occurred but were not captured in the sampled data. The first scenario can introduce selection bias, as unvisited sites may differ systematically from visited ones in terms of accessibility, attractiveness, or unobserved characteristics, leading to incorrect inferences about site preferences and the impact of advisories. The second scenario, in which visits are missed due to sampling limitations, introduces measurement error, potentially underestimating actual demand and distorting the estimated effect of key variables. Moreover, if zero-market-share observations are correlated with advisory status, where sites with missing visits tend to be smaller and nonadvisory sites, then the missing data are not random. This nonrandom missingness could lead to biased estimates of the effect of advisories, as sites without advisories may be disproportionately underrepresented, causing an overestimation of the advisory effect.

To mitigate the first issue, we limited the choice set to sites that were ever visited throughout the study period, ensuring a comprehensive representation of available options while excluding inaccessible recreational sites. For the second issue, we applied empirical Bayes posterior mean estimation, as proposed by Li (2019). This method refines the visit probability estimates and ensures compatibility of our recreation demand model with the estimation framework of Berry (1994), which requires strictly positive market shares. In practice, to maintain key heterogeneity across markets (CBG-year-quarter), we constructed each market’s empirical Bayes prior using a set of similar CBGs. Specifically, we defined similar CBGs as the 50 closest in travel distance. The market shares for the same recreational site from these similar CBGs serve as the prior distribution. We then fit the observed distribution using a beta-binomial model, applied a Bayesian approach to estimate the posterior distribution, and predicted adjusted market shares based on the posterior distribution. This method enables flexible adjustments by shrinking observed zero market shares toward expected positive values in comparable CBGs, reducing potential downward bias in recreation demand caused by sampling errors and providing a more accurate representation of true recreational behavior.

Formally, let K_jc be the random variable representing the number of visits to the recreational site j from CBG c. The time subscripts t have been suppressed throughout this subsection for simplicity. Assume K_jc follows a binomial random distribution with NK_c trials (the total number of observed visits from CBG c) and possibility (the market share of recreational site j in CBG c). We assume the trip probability follows a beta prior distribution with the two hyperparameters and that need to be estimated:

4

To estimate the hyperparameters and construct the prior beta distribution for the Bayesian approach, we used visitation data from similar CBGs l ∈ P_c, where P_c represents a set of CBGs with similar travel distances or demographic characteristics. The hyperparameters and are estimated by maximizing the log-likelihood over these similar CBGs:

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The posterior distribution of the trip probability s_jc also follows a beta distribution, with the posterior mean given by

6

We use the strictly positive posterior means as the adjusted market shares. In large markets, the empirical Bayes posterior is very similar to the observed shares because the observed sales dominate the prior.⁵ In addition, the empirical Bayes adjustment further stabilizes Site_j estimates for sites observed in a few markets by shrinking sparse or zero market shares toward expected values based on similar CBGs, thereby improving identification precision and mitigating small-sample noise.

Addressing Endogeneity of FCAs

FCAs intend to warn anglers about contamination in fish, but their distribution can be endogenous to fishing behavior and site characteristics. Two main sources of endogeneity are particularly relevant. First, if FCA sites systematically differ from nonadvisory sites in unobserved factors related to visitation, such as fishing conditions, on-site amenities, or aesthetic appeal, these omitted differences may confound the estimated effects. Second, sites that attract more visitors may be tested more frequently and are therefore more likely to receive advisories, introducing potential reverse causality.

To address these concerns, we used the number of TRI facilities located in far upstream HUC12 watersheds as an IV for advisory issuance. A far upstream HUC12 refers to the nearest upstream watershed that is not directly adjacent to the one containing the recreation site. The number of upstream TRI facilities satisfies the relevance condition because industrial activities in upstream areas are major sources of chemical discharges that contribute to downstream contamination, thereby increasing the likelihood of an advisory. At the same time, these far upstream facilities are typically not visible or known to recreational visitors because they are not adjacent to the water body, supporting the exclusion restriction from the perspective of site choice behavior. Industrial activities in such distant upstream watersheds are a well-established driver of downstream contamination and advisory issuance (Keiser 2019; Keiser and Shapiro 2019). This spatial separation ensures that the instrument affects recreation demand only through its influence on the probability of an advisory.

Another endogeneity concern is that confounding may arise from omitted water quality characteristics. If FCAs are associated with visibly lower water quality, the estimated effect of these advisories may partly reflect the influence of observable water pollution.⁶ In the robustness check, we incorporated a direct measure of water quality, Secchi depth derived from Sentinel-2 satellite imagery, into the second-stage regression. This control variable captures observed variation in water clarity and allows the estimated advisory effect to represent the informational or signaling component of advisories rather than the physical quality of the water body.

Consider the following 2SLS model. In the first stage, we model the likelihood of a water body in a recreation site receiving an FCA as a function of the number of far upstream TRI facilities:

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where represents the count of TRI facilities in the far upstream HUC12 watersheds of site j in 2019.⁷ In the second stage, we regress the Site_j estimated from the demand model on the predicted advisory status and other site attributes. This two-stage approach isolates the exogenous variation in advisories driven by upstream industrial pollution and yields a consistent estimate of the behavioral response to advisories. The estimated advisory coefficient thus reflects the reduction in site utility associated with an advisory, holding travel costs and other attributes constant:

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In principle, first-stage estimation error can propagate into second-stage uncertainty. In our setting, the first-stage ASCs are estimated with extremely large samples per site, making their sampling error negligible. Accordingly, the usual robust (clustered) standard errors from the second stage are valid to first order. This practice is standard in recreation demand applications when first-stage noise is small (Murdock 2006). As an additional check, we report a Monte Carlo experiment in Appendix D that uses simulated data to estimate both stages and shows that the second-stage standard errors closely track the true sampling variability and achieve nearly nominal coverage.

By combining the empirical Bayes adjustment for zero market shares and the IV strategy, we address the long-lasting empirical challenges in the literature, ensuring our analysis with a robust identification of the causal effects of FCAs on recreational site choices.

Data Sources and Integration

We obtained FCA data from the 2018 Eat Safe Fish Guide published by the Michigan Department of Health and Human Services, which provides a comprehensive list of all Michigan water bodies subject to advisories.⁸ The guide details fish species, recommended meal frequencies, and specific contaminants, including PCBs, mercury, dioxins, and other pollutants, primarily stemming from industrial discharges and atmospheric deposition. The advisory dataset is structured as a text file consisting of water body names, counties, and advisory details. To map water bodies with advisories, we collected water body shape files from the Michigan Hydrography Polygons, Michigan Hydrography Lines, and the NHD Plus V2 from the US Environmental Protection Agency, providing geolocated polygons and lines representing Michigan’s lakes, rivers, and reservoirs. We matched FCAs to water bodies based on the water body names and counties listed in the advisories. Some FCAs remain unmatched, primarily due to discrepancies in water body names or missing county identifiers. To ensure complete and accurate FCA coverage, we manually identified the corresponding water bodies using geographic information extracted from the text descriptions of these advisories.⁹

The water bodies identified in the FCA dataset may not always correspond to popular recreational sites, and some may be large water bodies, in which recreational activities are concentrated in specific spots. To better determine recreational sites associated with FCAs, we used Advan’s place data, which provides geospatial boundaries for recreational sites across Michigan, defined as the points of interest (POIs) in the “nature park and similar institutions” subcategory.¹⁰ These areas adjacent to water bodies are key water-based recreational sites for fishing, boating, and other water-related outdoor activities that may be influenced by FCAs. In practice, we linked water bodies to recreational sites by performing a spatial join between Advan recreational sites and the water body dataset, applying a 20 m buffer around each site’s boundary. The output of this data process clearly classifies recreational sites as either associated with or without FCAs.¹¹ Through this process, we identified 503 out of 1,605 water-based recreational sites in Michigan that are subject to FCAs.

Recreational demand is measured using anonymized cell phone mobility data from Spectus, which aggregates GPS signals from millions of mobile devices to capture population-scale visitation patterns at fine spatial and temporal resolution.¹² The raw Spectus dataset contains approximately 53 million individual devices in 2019, with information on anonymized device-level dwell events at specific coordinates and timestamps. Two core data products are used in this study. The stop table records device-level location trajectories in the form of device stops for at least two minutes, with associated latitude, longitude, time stamp, and dwell duration. Although the data do not directly provide individual home information, in the home recurring area table, each device is assigned a most likely home CBG based on recurring nighttime locations observed over multiple weeks.

We merged each device’s home CBG with its geographic stops and trajectories using anonymized device IDs to construct a dataset linking individual recreational visits to home CBG locations. Recreational visits are identified by spatially joining stop coordinates with water-based recreational sites obtained from Advan’s place database. To ensure privacy and analytical consistency, we aggregated individual trips to each recreational site at their home CBG level, constructing a quarterly panel dataset that captures variations in visitation patterns over time.¹³ Appendix A provides examples illustrating the data-processing steps, including anonymized stop records, home CBG assignments, and the final CBG-site-quarter aggregated data. These examples clarify the structure of the Spectus mobility data and the data-processing pipeline used to construct the final recreation demand dataset.

Weather plays a critical role in outdoor recreation, as temperature and precipitation influence visitors’ decisions to engage in recreational activities, particularly those involving water. To control for weather, we incorporated high-resolution meteorological data from the PRISM Climate Group, which provides monthly averages of precipitation and temperature at the recreational site level. By linking weather data to recreational sites, we accounted for the effect of weather on visitation, ensuring that our estimates of advisory effects were not confounded by climatic fluctuation.

To address potential endogeneity issues due to the correlations among FCAs, unobserved local characteristics, and recreational demand, we used upstream polluting industrial facilities as the IV. The locations of polluting industrial facilities were obtained from the TRI database, which provides facility-level records of industrial sites that release hazardous chemicals into air, water, and soil. We aggregated the number of TRI facilities in 2019 at the HUC12 watershed level, and used the number of TRI facilities in the far upstream HUC12 watersheds of each water-based recreational site as the IV for FCAs. The upstream HUC12 is identified by the NDLI python package.¹⁴ This IV strategy ensured that we captured industrial pollution sources that contribute to water contamination and FCA issuance while minimizing direct correlations with unobserved local characteristics.

Appendix Figure A2 summarizes the data construction workflow, showing how the raw mobility observations were successively linked and aggregated to create the final estimation dataset. Beginning with approximately 53 million individual devices, we identified about 6.2 million trips to water-based POIs in Michigan, linked them to home CBGs using the home recurring area table, and aggregated them to the CBG-site-quarter level. This level of aggregation defines the market shares used in the later estimation.

Key Variables Construction

We constructed the key variable that defines travel costs, incorporating both monetary and time-related expenses. We calculated the travel costs for visitors choosing a recreation site based on the one-way travel distance and duration from the centroid of the individual’s home CBG to the recreation site using the open source routing machine.¹⁵ Following the common assumption in the recreation demand literature (Palmquist, Phaneuf, and Smith 2010; Lupi, Phaneuf, and von Haefen 2020), we calculated the opportunity cost of time as one-third of the median hourly wage in the home CBG of visitors. The total travel cost TC_ijt is given by

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where Dist_ij is the one-way driving distance between the centroid of visitor i’s home CBG and recreational site j; gs_st captures the state-level average gasoline cost at year t; and f_t denotes the vehicle marginal maintenance cost, repair cost, and depreciation from AAA reports. Medinc_i is the median annual income in the visitor’s CBG. We divided it by 2,080, the annual full-time working hours, to calculate the hourly wage. We assumed γ = 1/3 indicating the cost of travel time is valued at as one-third of work hours.

Because the visitation data from Spectus includes all recreation trips taken by individuals from a CBG and does not differentiate between travel methods, people might fly to a recreation site if it is too far from their home CBG. Since the preference for travel costs in a flight-mode trip could be quite different from that in a car-mode trip, and it is difficult to measure the monetary costs associated with flying (English et al. 2018). Therefore, we restricted our study to short-distance trips within 300 miles, as they are more likely to be taken by car than by flight. Accordingly, we determinded the choice sets for each CBG as all the water-based recreation sites within the 300-mile distance.

To clarify the behavioral rationale for the 300-mile distance band used to define feasible choice sets, we expanded on this modeling assumption in light of established recreation-demand literature. Following Dundas and von Haefen (2020), we selected the 300-mile threshold because trips beyond this distance are rarely undertaken as day trips and often involve air travel, which is not reliably captured in the Spectus mobility data. This cutoff is consistent with common practice in outdoor recreation studies and aligns closely with the empirical distribution of observed trips in our dataset, the vast majority of which fall well below 300 miles. To ensure robustness, we reestimated the model using alternative distance thresholds (150 miles, 200 miles, 250 miles) and find the results qualitatively unchanged.

In traditional recreation demand models, researchers often construct a universal choice set that includes all available sites for every decision maker to ensure a uniform set of alternatives. We did not adopt this approach for two main reasons. First, our mobility data are available only in aggregated form at the CBG-site-quarter level, requiring estimation through a multinomial logit framework in which all market shares must be strictly positive. Although we applied an empirical Bayes adjustment to address zero-market-share observations, a universal choice set would produce an extremely large number of zeros, substantially increasing computational burden and weakening identification for rarely visited sites. Second, we believe that the 300-mile distance cutoff better reflects the behavioral choice set faced by visitors. This distance-based specification aligns with observed travel patterns in our data and more accurately captures the spatial and cognitive constraints that shape recreational decisions. Together, these considerations justify our focus on a distance-based, behaviorally grounded choice set rather than a universal one.

Given the choice sets properly defined, we calculated the market shares of recreation sites using the following steps. We defined the market size of recreational demand for each CBG per quarter. The assumption that individuals make around 30 recreation-related choices per quarter follows conventions in the recreation demand literature, where recreation is commonly modeled as a weekly decision corresponding to weekend and holiday opportunities (Palmquist, Phaneuf, and Smith 2010; Lupi, Phaneuf, and von Haefen 2020).¹⁶ This assumption provides a consistent scaling factor that connects per choice utilities with quarterly and annual welfare measures while reflecting typical seasonal patterns of outdoor activity. The market size for each CBG was obtained by multiplying the estimated visitor population by the number of recreational occasions per quarter, where the visitor population was approximated by the average number of distinct devices observed from each CBG in each quarter.¹⁷ We then computed the market share of each recreation site as the ratio of trips from a given CBG to that site relative to the total market size of the CBG, with the remaining share representing the outside option.¹⁸

Summary Statistics

With these linkages and assumptions, we constructed aggregate data of actual site choices for each CBG from 2019 to 2022. Our final estimation dataset consists of 1,645,724 observations corresponding to CBG-site-year-quarter combinations, covering 7,545 CBG origins, 1,605 water-based recreational sites, and four quarters. Table 1 reports the summary statistics regarding the key variables in our models. An average resident traveled 49.77 miles and took 1.45 hours for a one-way-trip recreational visit. The average travel costs are about $81 in 2019 dollars between 2019 and 2022.

The average number of recreation visits from a home CBG is 0.56, with a wide range from zero to a maximum of 6,347 visits, indicating substantial variation in visitation patterns across communities. The spatial distribution of visits, shown in Figure 2c, reveals that residents from CBGs in the southern and central parts of Michigan’s Lower Peninsula contribute the highest number of visits, particularly those from urban centers and areas near major recreational destinations. In contrast, CBGs in the Upper Peninsula and northern Michigan exhibit lower visit counts, likely due to lower population density and greater travel distances to recreational sites. In addition, CBGs near the Great Lakes coastline and major inland water bodies tend to generate more recreation visits, highlighting the appeal of water-based activities. This variation in visit frequency reflects differences in local population size, accessibility to recreational sites, and regional preferences for outdoor activities.

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Figure 2

Distribution of Water-Based Recreation Sites, Advisory Water Bodies, and Recreation Visits, Michigan.

Note: Map (a) shows all identified water-based points of interest used in the analysis. Map (b) shows rivers and lakes with active fish consumption advisories based on the 2018 Eat Safe Fish Guide. Graph (c) shows the total recreation visits from census block groups, aggregated over the study period.

The posterior estimates of market shares exhibit lower variance and remain strictly positive. The means of the observed and empirical Bayes posterior market shares are closely aligned, at 0.00047 and 0.00046, respectively. Posterior mean estimates of market shares range from 1.63e-17 to 0.9416.

We also compared the summary statistics between FCA sites and nonadvisory sites in Appendix Table B1. The statistics show that advisory sites differ significantly from nonadvisory sites in terms of their geographic and demographic characteristics as well as visitation patterns. They are more likely to be located near lakes (57% vs. 35%), serve as fishing sites (12% vs. 4%), and are situated in CBGs with smaller populations, lower population density, and less urbanization. These CBGs also tend to have more white residents and slightly lower proportions of Black and Asian residents. Advisory sites are also in areas with lower median household incomes compared with nonadvisory sites. In terms of recreation demand, advisory sites experience significantly higher visitation, with an average of 14,832 annual visits compared with 6,555 at nonadvisory sites. Visitors to advisory sites also tend to travel farther, with a median distance of 45.86 miles compared with 26.82 miles for nonadvisory sites. These differences suggest that although advisory sites may be more remote and located in less densely populated areas, they still attract a substantial number of visitors from greater distances, highlighting the importance of understanding how FCAs influence recreational behavior.

Baseline Results

Table 2 presents the first-stage results of our recreational demand model estimated by four different model specifications.¹⁹ Column (1) is the basic model, columns (2) and (4) add site-by-quarter fixed effects to account for any unobserved seasonal and site-specific visitation patterns, and columns (3) and (4) use the far upstream TRI facility number as the IVs for FCA to address endogeneity. The travel cost coefficient is negative and highly significant at the 1% level, with an estimate of −0.006. This result indicates that higher travel costs decrease the likelihood of selecting a given recreational site, aligning with previous findings in recreation demand studies.

The second stage of our analysis examined how FCAs influence site utility by regressing the estimated site-specific ASC from the first stage on the advisory status and other site attributes. A negative coefficient on the advisory dummy reflects the decline in average site utility associated with an advisory, holding travel costs and other characteristics constant. Interpreted in a welfare framework, this coefficient represents the per capita disutility of visiting an advisory site and provides the basis for calculating visitors’ willingness to pay for the removal of advisories. It should be interpreted as an indicator of perceived reductions in recreational quality, rather than as a direct measure of health risk.

The second panel of Table 2 reports these results. In the specifications without IVs (columns (1) and (2)), the coefficients on the FCA variable are small and statistically insignificant, suggesting no clear impact of the advisories on site utility. These results may be subject to bias stemming from several endogenous factors. First, FCAs may be correlated with time-varying local characteristics that affect recreational demand but which our model does not control for, such as water quality, site accessibility, fishing conditions, or other local amenities. Our data from Appendix Table B1 indicate that FCA-designated sites tend to be more remote, have lower population density, be less urban, and receive fewer visits even in the absence of advisories. The second potential endogeneity concern arises from reverse causality. If heavily visited sites are more likely to be tested, advisories are more likely to be issued. Thus, a simple regression without IVs may confound the advisory effect with preexisting recreational demand patterns, leading to an underestimate of the true deterrent effect.

As discussed already, we added the far upstream TRI facility number as the IV for FCA status in columns (3) and (4) to address these endogeneity concerns. The coefficients of FCA variable become negative and statistically significant, with estimates of −0.484 and −0.453, respectively, indicating that FCAs significantly reduce site attractiveness. The strength of our IV strategy is confirmed by the Kleibergen-Paap rk Wald F-statistic of 30.23, which exceeds the conventional weak instrument threshold of 10. Furthermore, the Stock-Yogo critical value for a 10% maximal IV bias is 16.38, reinforcing that our IV provides a strong predictive relationship for advisory status and mitigates concerns about weak instrument bias. As a robustness check, we incorporated site-by-quarter fixed effects in the first stage to control for time-varying site-specific factors. In column (4), including site-by-quarter fixed effects generates similar advisory effect but strengthens its statistical significance, suggesting that although unobserved seasonal site-specific factors may influence visitation, they do not eliminate the negative impact of FCAs.

The estimated coefficients on the weather variables align with expectations and indicate that seasonal conditions play an important role in shaping recreational visitation. As shown in Appendix Figure B1, deviations in average quarterly temperature outside the 10°C–18°C range are associated with lower visitation, and greater precipitation further suppresses recreational visits. Although the magnitudes of these effects are smaller than those of travel costs and advisories, including weather variables, improves model fit and helps isolate the impact of FCAs from broader seasonal patterns in recreational activity.

We translated the estimated coefficients of FCA status into welfare measures by calculating the marginal willingness to pay (MWTP) to avoid sites with FCAs. In the random utility framework, the MWTP values were computed as the ratio of the estimated coefficient on the advisory indicator to the negative of the travel cost coefficient. Because the model does not incorporate direct entry fees or site prices, travel costs (imputed time and fuel expenses) serve as the monetary numéraire. Consequently, the MWTP values should be interpreted as the additional travel-related costs that visitors are willing to bear to avoid sites under advisories. These behavioral measures reflect the revealed component of the value of information disclosure, rather than total welfare gains, including health or psychological benefits. In the basic models (Table 2, columns (1) and (2)), the magnitude of MWTP for avoiding FCAs is small (−$9.21 and −$1.51), reflecting the insignificant advisory effects. However, once endogeneity is addressed using IV (columns (3) and (4)), the MWTP estimates rise substantially to $72.40. These results suggest that on average, visitors are willing to pay approximately $72 per visit to avoid sites under advisory, or roughly $52.60 per capita per quarter.²⁰

Our estimated MWTP appears elevated when benchmarked against relevant prior work. For example, in the context of beach recreation on O‘ahu the study by Peng and Oleson (2017) finds that recreational users were willing to pay roughly US$11.43 per day to reduce waterborne bacterial exceedance from 11 to 5 days per year, and about US$30.72 per day to reduce exceedance to zero, with additional WTP for improved underwater visibility and coral cover. By contrast, a meta‐analysis by Johnston and Thomassin (2010) summarizing stated preference studies of surface water quality improvements in the United States and Canada reports a range of WTP values of roughly $20–$512 per household per year (for large improvements in fisheries, aquatic habitat, or water quality). It is important to note, however, that our estimates are expressed on a per quarter basis, whereas much of the prior literature reports values on a per day or annual basis. When converted to comparable units, our implied per day WTP falls in the range reported in these studies. Because our scenario involves a health-related FCA rather than a marginal quality improvement, we interpret the magnitude of our estimates as plausible and consistent with the elevated stakes associated with health risk avoidance relative to recreation-only contexts.

Seasonal Heterogeneous Impacts

To further explore how FCAs influence recreational behavior across different seasons, we estimated the effects separately for each quarter of a year. Table 3 presents the first-stage and second-stage results for each quarter. Across all four quarters, the first-stage results show that travel costs remain a consistent and significant determinant factor in recreational site choices, with coefficients ranging from −0.005 to −0.007 across quarters, highly significant at the 1% level. This result suggests that recreational visitors’ consideration of travel costs does not fluctuate significantly with seasonal changes.

The second-stage results reveal notable seasonal differences in how FCAs affect the utility of recreational sites. In the third quarter (July–September), FCAs have the strongest negative effect on site attractiveness, with a coefficient of −0.574, significant at the 1% level. This suggests that during the summer, when water-based recreational activities are at their peak, visitors are more responsive to FCAs, likely due to increased engagement in fishing, swimming, and boating. The corresponding MWTP to avoid advisory sites is $87.49 in the third quarter, which is the highest among all quarters. This indicates that visitors’ concerns about water quality and potential health risks are highest in the summer, and they are willing to pay additional premiums to avoid recreation sites with FCAs compared with other seasons.

In contrast, the effects of FCAs in quarters 1, 2, and 4 (representing winter, spring, and fall, respectively) are slightly less pronounced but remain significant. The coefficients of FCA status in these quarters range from −0.353 to −0.509, significant at the 1% level for quarters 1, 2, and 4. The MWTP values for these three seasons hover around $69.46–$73.55, indicating that although visitors are consistently deterred by FCAs, the willingness to avoid is somewhat lower outside the summer months. These seasonal patterns align with our expectations, suggesting that while FCAs have a year-round impact on recreational decisions, the influence is magnified during the peak periods of water-based outdoor activity.

Robustness Checks

We conducted additional analyses to validate the strength and reliability of the IV strategy. Specifically, we tested the sensitivity of our results to the timing of the TRI facility numbers used as IVs. While the primary analysis employs the number of TRI facilities located in far upstream HUC12 watersheds from 2019, we reestimated the models using TRI facility counts from earlier years (2016, 2017, and 2018). This temporal variation allowed us to evaluate whether historical pollution sources have a consistent relationship with FCAs and whether the instrument remains valid over time. Using earlier years also mitigates concerns that contemporary TRI facility numbers may be correlated with unobserved local economic or recreational factors that could directly influence fishing site visitation, thereby strengthening the plausibility of the exclusion restriction.

The first-stage results, reported in Appendix Table B3, show that the number of the far upstream TRI facilities is consistently a strong predictor of FCAs across all years. The coefficients on the IV variable NumFacility_TRI are positive, highly significant at the 1% level, and of similar magnitude: 0.100 (2016), 0.106 (2017), 0.105 (2018), and 0.099 (2019), suggesting that upstream industrial activity is a stable and highly relevant determinant of FCA status regardless of year.

The second-stage results in Appendix Table B3 further confirm the robustness of our findings. The estimated effects of FCAs on recreational site utility are consistently negative and statistically significant across all specifications, regardless of the year of the IV. The coefficients on the predicted advisory variable are −0.463 (2016), −0.425 (2017), −0.387 (2018), and −0.430 (2019), all significant at the 5% level. This consistency in magnitude and significance underscores the robustness of our primary findings. Furthermore, the Stock-Yogo critical value for weak instruments (set at 16.38 for a 10% maximal IV size distortion) is well below the observed F-statistics in all cases, confirming the strength and validity of the instruments. These robustness checks collectively reinforce the credibility of our empirical strategy, demonstrating that our findings of the negative impact of FCAs on recreational demand are properly identified and accurately estimated.

In addition, we assessed whether the two-stage estimation procedure yields valid inference, given that the second-stage regression uses estimated site-specific constants from the first-stage demand model. Although the first-stage ASCs are estimated from millions of observations per site—implying minimal sampling error—we verified this formally through a Monte Carlo experiment (Appendix D). Using synthetic data calibrated to our empirical design, the clustered HC1 standard errors closely match the empirical sampling variability, achieving approximately 93% coverage of nominal 95% confidence intervals. This indicates that first-stage estimation noise contributes negligibly to the overall uncertainty in the second-stage coefficients. Accordingly, standard clustered inference remains valid in our setting without further correction for first-stage uncertainty, consistent with the treatment in Murdock (2006) and related two-step demand applications.

We performed robustness checks with alternative priors for the Bayesian market share estimator to evaluate the sensitivity of our results. As shown in Appendix Table C1, estimates remain stable across different empirical Bayes priors, indicating that the choice of prior does not introduce significant bias. For the nonzero subsample using observed market shares, results align with our main findings, suggesting that excluding zero-market-share observations does not lead to systematic distortion. Meanwhile, incorporating empirical Bayes priors, which leverage varying numbers of nearby markets, substantially increases the sample size, enhancing precision without altering the overall conclusions. These results confirm the robustness of our approach and demonstrate that the Bayesian market share estimator yields consistent demand estimates without introducing bias.

In addition to testing alternative priors and IV specifications, we examined the sensitivity of the results to the assumption about recreational frequency used to define market size. The baseline analysis assumes 30 recreational occasions per quarter, consistent with the recreation demand literature. In Appendix Table B4, when alternative frequencies of 20, 40, and 50 occasions per quarter are applied, the estimated coefficients and welfare measures remain qualitatively similar. This stability indicates that the main findings are not driven by the specific choice of trip frequency and that the model performs robustly across a wide range of plausible behavioral assumptions.

We also assessed the robustness of our results to alternative definitions of the travel distance boundary used to construct choice sets. The baseline specification uses a 300-mile cutoff, following Dundas and von Haefen (2020), which restricts analysis to plausible day‐trip distances primarily undertaken by car. To test the sensitivity of this assumption, we reestimated the model using narrower distance bands of 150, 200, and 250 miles. The results in Appendix Table B5 remain qualitatively similar across these specifications, indicating that the estimated effects are not materially affected by the precise choice of distance cutoff.

Another potential concern is variation in CBG population size and sampling intensity in the mobility data. Such variation may introduce heteroskedasticity, as larger or more frequently sampled CBGs could contribute disproportionately to the estimation of site-level ASCs. We reestimated our main model using sampling weights that scale visitation counts by each CBG’s population. As shown in Appendix Table B6, the weighted estimates (column (2)) are highly consistent with the baseline results (column (1)) in the first and the second stages. This consistency indicates that our findings are not driven by unequal representation across CBGs.

Finally, when Secchi depth is included as a direct control for water quality, the results remain consistent across all specifications. As shown in Appendix Table B7, the coefficient on Secchi depth is positive and statistically significant at the 10% level, indicating that sites with clearer water attract more visitors. The estimated advisory effect remains negative and statistically significant, with coefficients ranging from −0.43 to −0.53 across columns. The magnitudes are nearly identical to those in the baseline IV estimates without Secchi depth, suggesting that including observed water clarity does not materially change the estimated impact of advisories on site attractiveness. The stability of the advisory coefficient across specifications confirms that the IV estimates are robust to including direct water quality measures.