ECONOMIC DAMAGES OF WATER QUALITY WARNINGS AT GREAT LAKE BEACHES By Greg ory Boudreaux A THESIS Submitted to Michigan State University i n partial fulfillment of the requirements f or the degree of Agricultural, Food, and Resource Economics Master of Science 20 21 ABSTRACT ECONOMIC DAMAGES OF WATER QUALITY WARNINGS AT GREAT LAKE BEACHES By Greg ory Boudreaux This thesis estimates welfare impacts of two types of water quality warnings using a combined revealed - stated preference approach. The data was collected in a survey that randomly sampled visitors to 28 public beaches in Michigan and Ohio. The first essay uses a discrete choice experiment to measure preferences for common beach attributes including the presence of active or recent warnings for harmful algal blooms (HAB) or bacterial contamination. We find respondents are willing to drive over 200 miles to a void a site with either of these warnings, with a negative lag effect for both hazards that remains at least 6 days after warnings are lifted. of beaches, by modeling site substitution behavior when beachgoers face warnings. We use a multi - site demand model that explicitly accounts for site substitution to estimate welfare impacts of site closures and HAB and bacterial warnings. A contraction map identifies the disutili ty of warnings by calibrating changes in site demands to match contingent behavior questions. The findings show that, at the average beach, season - long bacterial or HAB warnings cause losses of about 1.4 million dollars per year for either hazard. For 2019 , the observed HAB and bacterial lagged aversion to recently lifted warnings; omitting lagged effects would understate welfare losses by 34 percent. Together, the essays show that cost - benefit analyses that fail to account for the dynamic disamenity effects of HAB and bacterial warnings will likely understate the costs of these events, which are projected to increase in frequency and intensity under climate change. Copyright by G REGORY BOUDR EAUX 2021 iv ACKNOWLEDGEMENTS This work is the result of a long and collaborate process of scholarship, during which I have benefitted from the support of countless friends and colleagues. I would like to mention a ience Foundation, NOAA, and the Ohio Sea Grant for their generous funding and research support. I sincerely thank my major professor, Dr. Frank Lupi, for his guidance and reassurance d vision for this thesis has been humbling, and his willingness to assist at every turn has helped me become a better researcher. He is truly a model for scholarship in this profession. Dr. Brent Sohngen and Alan Xu of Ohio State University have been fantastic collaborators throughout this project and have taught me the boundless value of being part of a ping me Swinton for agreeing to serve on my thesis committee, and for his fruitful research suggestions and words of encouragement. I am especially grateful to Henry Leto, Will Vaughn, Debra Johnson , Kristi Tabaj , Adam Swint , Jacob Zinkhon , Emily Anderson , Hannah Below , Michelle Bock , Rachel Dufresne , Madeline Franz , Paige Lampman , Leah Roginski , Alexis Scharrer , and Sarah Sutton for assisting with data collectio n. Without your hard work and dedication, this research would not exist. Sara thank you for tolerating our bi - weekly drives around Lake Michigan, and for going on this adventure with me. Mom and Dad any successes I experience in life are the direct e more grateful to be your son . v TABLE OF CONTENTS LIST OF TABLES ................................ ................................ ................................ ...................... vi i LIST OF FIGURES ................................ ................................ ................................ ..................... ix CHAPTER 1 : Great Lake B each V isitor P references T oward W ater Q uality, B acteria, and H armfu l A lgal B looms ................................ ................................ ............................ 1 1.1 : Introduction ................................ ................................ ................................ .......................... 1 1.2 : Backgroun d ................................ ................................ ................................ .......................... 4 1.3 : Random Utility Theory ................................ ................................ ................................ ...... 10 1.4 : Data and Choice Experiment ................................ ................................ .............................. 1 5 1.5 : Results ................................ ................................ ................................ ................................ 22 1.6 : Robustness Checks ................................ ................................ ................................ ............. 29 1.7 : Discussion ................................ ................................ ................................ .......................... 31 1.8 : Conclus io n ................................ ................................ ................................ .......................... 39 CHAPTER 2 : Economic Welfare Effects of Harmful Algal Blooms and Bacterial Contamination Warnings in the Great Lakes ................................ ........................ 4 0 2.1 : Introduction ................................ ................................ ................................ ........................ 4 0 2.2 : Background ................................ ................................ ................................ ........................ 45 2.3 : Onsite Counts and Intercept Survey ................................ ................................ ................... 49 2.4 : Follow - up Survey and Contingent Behavior Data ................................ ............................. 5 4 2.5 : Zonal Dataset ................................ ................................ ................................ ...................... 57 2.6 : Site Choice Model and Calibration to Stated Preference Data ................................ .......... 6 3 2.7 : Results ................................ ................................ ................................ ................................ 7 0 2.8 : Simulation of 2019 Season ................................ ................................ ................................ . 8 2 2.9 : Conclusion ................................ ................................ ................................ .......................... 86 APPENDICES ................................ ................................ ................................ .......................... 89 A PPENDIX A : Intercept Survey Instrument ................................ ................................ ............ 90 A PPENDIX B : Online Follow - up Survey ................................ ................................ ............... 1 00 A PPENDIX C : Data Collection ................................ ................................ .............................. 1 25 A PPENDIX D : Pilot Survey ................................ ................................ ................................ ... 1 27 A PPENDIX E : Follow - up Disposition Tables and Item Non - response ................................ .. 1 34 A PPENDIX F : Follow - up Responses to Contingent Behavior and COVID - 19 questions ..... 1 4 6 A PPENDIX G : Follow - up Robustness Checks for Choice Experiment ................................ . 1 36 A PPENDIX H : 2019 Respondent Summary Statistics ................................ ........................... 1 41 A PPENDIX I: Mixed Logit Conditional Parameter Regressions ................................ ........... 1 42 A PPENDIX J : Choice Experiment Simulation Results ................................ .......................... 1 43 A PPENDIX K : Creation of T rip E stimates from I ndividual W eights ................................ .... 1 44 A PPENDIX L : Observed HAB and B acterial W arnings in 2019 S eason ............................... 1 47 A PPENDIX M : Re - calibrated B aseline ASC A djustments and W elfare E stimates ............... 1 48 A PPENDIX N : Contraction M apping S ubstitution P redictions ................................ .............. 1 52 vi A PPENDIX O : Comparison of I mpaired ASCs and R e - calibrated B aseline ASCs ............... 1 54 REFERENCES .. ................................ ................................ ................................ ......................... 155 vii LIST OF TABLES T able 1.1 : Beach S ites S ampled in 2019 ................................ ................................ ....................... 1 5 Table 1.2 : Choice E xperiment A ttribute L evels ................................ ................................ ........... 2 0 Table 1.3 : Mixed Logit Estimates ................................ ................................ ................................ . 2 2 Table 1.4 : Contingent Behavior Response Percentages ................................ ................................ 3 4 Table 2.1 : Beach S ites S ampled during the 2019 I ntercept S urvey ................................ .............. 5 2 Table 2.2 : Contingent Behavior Scenarios ................................ ................................ .................... 55 Table 2.3 : Zonal Dataset Descriptive Statistics ................................ ................................ ............ 6 2 Table 2.4 : Average Contingent Behavior Responses Percentages and Standard Errors ............... 7 0 Table 2.5 : Revealed Preference Recreation Demand Model Estimates ................................ ........ 7 2 Table 2.6 : Site Closure Welfare Estimates ................................ ................................ ................... 75 Table 2.7 : Average ASC A djustment and T rip - W eighted A verage W elfare L oss , A cross A ll S ites, for E ach W ater Q uality S cenario ................................ ................................ ......................... 8 0 Table 2. 8 : Simulation of W elfare L osses A ttributable to B acterial and HAB W arnings d uring the 2019 R ecreation S eason ................................ ................................ ................................ ................. 8 3 Table D.1 : Conditional Logit E stimates from Pilot S urvey ................................ ........................ 1 30 Table D.2 : Mixed Logit Estimates from Pilot S urvey ................................ ................................ 1 32 Table D.3 : Contingent Behavior Response Percentages from Pilot S urvey ............................... 1 33 Table D.4 : C OVID - 19 question response percentage s from Pilot S urvey ................................ .. 1 33 Table E.1 : Case D isposition A cross B each S ites S ampled in 2019 ................................ ............ 1 34 Table E.2 : Stat ed Preference Item Non - Response ................................ ................................ ...... 1 34 Table F.1 : Contingent Behavior Response Percentages (2019 R espondents) ............................ 1 35 Table F.2 : COVID - 19 Q uestion R esponse P ercentages (2019 R espondents) ........................... 1 35 Table G.1 : Mixed Logit Robustness Checks ................................ ................................ .............. 1 36 Table G.2 : Ordering Effects in Mixed Logit Model ................................ ................................ ... 1 38 Table G.3 : Ordering Effects in Contingent Behavior Response Percentages ............................. 1 39 Table G.4 : Choice Model Estimate Comparisons ................................ ................................ ....... 1 40 viii Table H.1 : 2019 Respondent Summary Statistics ................................ ................................ ....... 1 41 Table I .1 : Summary of M ixed L ogit P osterior P arameter R egressions ................................ ...... 1 42 Table J.1 : Choice Experiment Simulation Results ................................ ................................ ..... 1 43 Table K.1 : Strata Used in Visitation Estimation ................................ ................................ ......... 1 46 Table L.1 : Observed HAB and B acterial W arnings in 2019 S eason ................................ .......... 1 47 Table M.1 : Recalibrated ASC E stimates and A djustments for A ll S ites and S cenarios ............ 1 48 Table M.2 : Recalibrated V alue per L ost T rip E stimates for A ll S ites and S cenarios ................. 1 50 Table N.1 : Comparison of C ontingent B ehavior D ata and N ested L ogit P redictions ................ 1 53 Table O.1 : Comparison of I mpaired ASCs and R e - calibrated B aseline ASCs .......................... 1 54 ix LIST OF FIGURES Figure 1.1 : Example Choice Experiment Table ................................ ................................ ............ 1 8 Figure 1.2 : Mean W illingness to D rive to A void S ites with R ecent W ater Q uality E vents and 95% C onfidence I ntervals around the M eans ................................ ................................ ................ 2 6 Figure 1.3 : Average P ercent D ecrease in the P robability of V isiting I ntercepted S ite, R elative to B usiness - as - S cenario ................................ ................................ ................................ ........ 3 7 Figure 1.4 : Simulated P ercentages of R espondents W ho W ould G o to the S ame S ite G iven a HAB or B acterial S cenario, and C ontingent B ehavior Q uestion R esponse P ercentages .............. 3 8 Figure 2.1 : Study A rea and S ites U sed in A nalysis ................................ ................................ ...... 5 1 Figure 2.2 : Nesting Structure for Repeated Nested Logit Model of Great Lakes Beaches .......... 6 3 Figure 2.3 : Contraction Mapping Algorithm ................................ ................................ ................ 69 Figure A.1 : Lake St. Clair & Belle Isle Intercept Survey ................................ ............................. 91 Figure B.1 : Online Follow - Up Survey ................................ ................................ ........................ 1 01 1 CHAPTER 1 : Great Lake B each V isitor Pr eferences T oward W ater Q uality, B acteria, and H armful A lgal B looms 1. 1 : Introduction shores stretching over 4000 miles across eight US states and two Canad i a n pr ovinces , these five also a large driver of economic activity, and their maritime economy generates an average of 8.8 billion dollars in yearly wages across the tour ism, recreation, and transportation sectors (NOAA 2019). Though the immediate economic impact of the Great Lakes on surrounding communities is widely understood and researched, it is much less clear how valuable the Great Lakes are to those who use their w aters and shores for outdoor recreation. Because budgets for managing the Great Lakes are limited, understanding how beach and lake users value their experiences is useful information for policy makers when deciding how to use funds. This paper adds to the information about beach user preferences available to policymakers and beach managers by estimating how beach users value different beach attributes and levels of water quality. In recent years, the health of the Great Lakes has come under threat due to increasing incidences of harmful algal bl ooms , large masses of plant matter which are driven in part by agricultural runoff. This runoff interacts with other environmental drivers to produce cyanobacteria, which in turn produce harmful algal blooms (also known as HABs) . Additionally, the Lakes ha ve faced perennial difficulties concerning high bacterial concentrations, chiefly caused by E. coli - contaminated runoff from urban wastewater, septic tanks, and livestock operations. Exposure to E. coli bacteria can cause cramps, diarrhea, vomiting, and li fe - threatening kidney failure (Mayo Clinic 2019), while exposure to HABs can cause liver damage 2 and gastrointestinal illness (NIEHS 2020). To protect the public from the health effects of bacterial contamination and harmful algal blooms, the eight Great La kes states have established state - level procedures for warning beach users about these events. This paper aims to further examine how Great Lakes beach users value beach attributes, with a focus on user preferences toward HAB and bacterial warnings, and i t is one of the few studies that uses a discrete choice experiment to elicit beach user preferences regarding harmful algal blooms. This study is also unique in the way that it approaches the question of how to frame these welfare effects. While most of th e previous studies use beach closings to approximate the damage caused by HABs, closures are not the usual course of action taken by beach managers, at least in the short term. When a HAB is observed it is much more common for state agencies to issue HAB w arnings than to close the affected beach. Accordingly, we estimate beach user preferences to avoid beaches with HAB and bacterial warnings in effect, as well as the effect that the amount of time since the expiration of a past warning has on these preferen ces. We find that both HAB and bacterial warnings have the potential to affect beach visitation behavior for significantly longer than the warning is in place. While large HAB events have dominated the news cycle in recent years, we find that beach users are willing to drive longer distances to avoid beaches with bacterial warnings in effect, relative to similar sites with HAB warnings in effect. We also find that preferences to avoid HAB - and bacteria - affected beaches behave differently over time, with th e disutility of visiting a site with a recent HAB warning dying off more quickly in comparison to a site with a recent bacterial warning. The structure of this paper is as follows. Section 1.3 outlines random utility theory and its application to questions in environmental and resource economics, and summarizes the techniques used in this paper for modeling preferences. Section 1.4 describes our data collection 3 process, survey pretesting and th e choice experiment. Section 1.5 presents the results of the study , and Section 1.6 discusses robustness checks . Finally, Section 1.7 discusses possible policy implications of this work and explores validity and further implications of our results using au xiliary survey data. Section 1.8 concludes. 4 1.2 : Background Lake Erie and Lake St. Clair, a smaller lake which lies between Erie and Lake Huron to the north, are the focus of our analysis. Lake Erie is connected to Lake St. Clair by the Detroit River, and in turn the St. Clair River connects Lake St. Clair with Lake Huron. Bordered by the lake by surface area (Ohio Geological Survey 2014). The Ohio Geological Survey estimates that - mile coast. Over the past decade, Lake Erie has become a locus of severe and widely publicized HAB incidents. In the summer of 2011, Lake Erie experienced its largest HAB on record, hypothesized by researchers to be caused by increased nutrient loadings brought on by heavy rainfall as well as above - average temperatures (Michalak et al. 2013). Just three years later in August 2014, another HAB event in Lake Erie contaminate affecting over 400,000 people and resulting in the declaration of a state of emergency by then - Ohio governor John Kasich. This marked increase in HAB events is far from a recent and isolated occurrence. Using satellite data of 71 lakes around the world, researchers at the Carnegie Institute for Science found that in 68% of these lakes, peak summertime bloom intensity has been steadily increasing since the 1980s (Ho et al. 2013). Additionally, in 2019 the United Nations Intergovernmental Panel on Climate Change reported that increasing global water temperatures, in conjunction with business - as - usual agricultural practices, have the potential to increase this upward trend (IPCC 2019). This possibility is worrisome, especia lly for coastal communities in areas like Ohio which depend on already HAB - prone waters for drinking water, tourism, and recreation. 5 Ohio and Michigan both maintain active, publicly available BeachGuard websites, where daily updates about beach warnings and closures are posted. Since HAB events are not very prevalent in Lake St. Clair or along the Michigan coast of Lake Erie, the Michigan BeachGuard website mostly functions as a bacterial contamination warning system. If dangerous levels of bacteria are detected off the coast of Michigan, a notification is posted to the website, a warning sign is posted on the beach in question, and in some cases the beach is closed to the public. Ohio follows a similar procedure for cases of bacterial contamination. Addi tionally, when toxins from harmful algal blooms are observed beyond a certain threshold, the Ohio Environmental Protection Agency declares a Recreational Public Health Warning, and a sign is posted on the affected beach warning visitors of the possible health impacts of coming in c ontact with HABs (Ohio EPA 2019). To estimate Lake s series of regional ly common beach characteristics including harmful algal bloom warnings and bacterial warnings, we use a discrete ch oice experiment administered to Lake Erie and Lake St. Clair beach users. In the experiment, respondents are presented with five different choice situations, in which they are asked to choose which of two beaches they would rather visit. In each choice sit uation, respondents can also select that they would not visit either beach. Each proposed beach alternative is described by a set of attributes, and the levels of the attributes vary between and across alternatives. By observing how respondents choose betw een site alternatives, we will be able to estimate marginal utility parameters, and willingness to drive (WTD) metrics, for each attribute (Haab and McConnell 2003, Freeman et al. 2014). In the case of beach attributes that may negatively impact utility, s uch as the presence of a HAB or bacterial warning, the hazard . 6 If a researcher decides to use a revealed - preference approach such as a travel cost model, identifying the effe cts of differing levels of environmental attributes on beach use requires significant sample variation across in the levels of these attributes (Haab and McConnell 2003 ) and the variation needs to be independent of any unmeasured site attribute . However, d ue to the logistic and time constraints of primary data collection, researchers are often un able to sample over long - enough time scales for gathering sufficient variation in environmental attributes in observed trips . In the case of assessing the welfare i mpacts of harmful algal blooms and bacterial contamination , this problem is exacerbated since these events are largely stochastic and typically only occur a few times per season in any given body of water. Stated preference approaches are well suited to this type of research, as they allow analysts to identify and evaluate the effects of environmental s Previously, researchers have used several different valuation techniques, including choice experiments, to measure how much beach users value changes in water quality and other beach at tributes. Loomis and Santiago (2013) use both a choice experiment and a contingent valuation survey to estimate per - visitor, per - day values of both water clarity and the elimination of trash on Puerto Rican beaches, finding that the estimates of these valu es ($51 and $103, respectively) are statistically robust to the elicitation method. Beharry - Borg and Scarpa (2010) use a choice water quality, and then examine p reference heterogeneity using a mixed logit model and a latent class model. Hilger and Hanemann (2006) also use a latent class model to infer consumer valuations of water quality from self - reported trip data collected from visitors to Southern California b eaches. While most of these studies rely on respondent - perceived water quality metrics, Egan et al . (2009) combine visitation data collected from Iowa beachgoers with an 7 extensive dataset detailing biological water quality measures and use a mixed logit ap proach to link the two. While the use of recreation demand models to value changes in environmental quality is common in the environmental economics literature, much less of this work is focused on the Great Lakes (and freshwater beaches in general). In o ne of the earlier studies to focus on the value of Great Lakes beaches, Sohngen et al. (1999) use data from intercept surveys conducted at Maumee Bay State Park and Headlands Beach State Park, both Ohio beaches on the Erie coast, to value single day trips to both sites. They find average single - day trip values of $25 for Maumee and $16 for Headlands, which aggregate to $6.1 and 3.5 billion dollars in annual value, respectively. In another early study, Murray et al. (2001) estimate the value of reducing E. c oli advisories using intercept data collected from visitors at 15 Lake Erie beaches. Importantly, the ir intercept survey asked beach users whether or not they take advantage of publicly - available data on current beach advisories when deciding whether or no t to make a trip, and the researchers found that visitors who use this data would gain on average $24 per year from one less beach advisory. Meanwhile, beach users who only use signs posted at the beach during an advisory would gain more from the reduction of an advisory, roughly $38 per year. Song et al. (2010) use a survey of a web - based consumer panel of Michigan residents to calculate the welfare effects of beach closings at Great Lakes beaches in Michigan , including Lake Erie and Lake St. Clair . They find that closing one of Michigan beaches would result in a loss of around $ 50 per person, per trip. Additionally, the researchers use the number of beach advisories and closures at a given beach during 2006 as a proxy variable for the water quality at that beach, although the number of beach advisories was not significant in their demand model and they did not control for possible correlation with unobserved beach attributes . 8 In one of the first studies to focus explicitly on the welfare impacts of HABs in western Lake Erie, Palm - Forster et al. (2016) build on earlier work by Chen (2013) which estimated beach visitation for Great Lakes beaches in Michigan. Palm - Forster et al. use two benefit transfer approaches, a value transfer and a function trans HAB - induced closures of 67 Ohio beach sites on the coast of Lake Erie. They find that the typical day trip to a w estern Lake Erie beach is worth about $18 per trip, and total seasonal visitation is worth roughl y $2 million per year. In another study focused on the welfare effects of Erie HABs, Zhang and Sohngen (2018) use choice experiment data from a survey of Ohio anglers to estimate angler willingness to pay to avoid HABs. Using several different discrete cho ice models including mixed logit and latent class logit to account for angler preference heterogeneity, the researchers find anglers are willing to pay $8 - $11 more to avoid boating through a HAB on the way to a fishing site. Finally, Wolf et al . (2019) use survey data and a latent - class framework to simulate the welfare effects of HABs and E. coli events in Lake Erie on both beach users and anglers. By simulating the full closure of all western Lake Erie beaches due to poor water quality conditions, the res earchers find that beachgoers and anglers would annually lose $7 million and $69 million, respectively, as a result of these closures. Additionally, they find that while beachgoers are more averse to E. coli , anglers are more averse to algae. This prior research has shown that water quality is a valuable good for which the public is willing to E. coli warnings has advanced this understanding in the context of Great La kes beaches, but there are still relatively few studies in this area . Additionally, much of th is research uses beach closings as a proxy for warnings , yet warnings rarely result in full beach closures. Our work contributes to this literature by estimating beachgoer preferences for the presence or absence of 9 HAB and bacterial warnings and by specifically distinguishing between warnings and closings. This work is also the first study to consider the lagged effects of recent warnings on beachgoer preferences. 10 1.3 : Random Utility Theory To estimate beachgoers preferences toward beach attributes such as water clarity, HAB warnings and bacteria warnings, we use a discrete choice experiment based on random utility theory, which is widely used in transportation, environmental, and other areas of applied microeconomics. Pioneered by the early work of psychologists L.L. Thurstone (1927) and R. Duncan Luce (1959), random utility theory was formalized in an economic context by Daniel McFadden (1974). Random utility models provide a framework for m odeling economic choices over discrete alternatives, such as which recreation site to visit. Assume that we observe an individual i making a choice between J distinct alternatives. can be represented as follows: (1) w he re is a vector of site - specific variables for site j , is a vector of individual characteristics that do not vary by alternative, is the income, and is i j . is a Hicksian composite commodity, and is an indicator function equal to 1 if individual i chooses alternative j , and 0 otherwise. For utility - maximizing individual i , the conditional indirect utility of choosing alternative j can be written as: ( 2) 11 w here we have substituted i . is made up of the deterministic portion of the utility function and the random error term . can be a function of both attributes of the individual and attributes of the alternative, and is commonly written as a linear - in - parameters function: (3 ) where represents the marginal utility of income. When analyzing the estimated parameters in this indirect utility function, it is useful to compute a marginal rate of substitution (MRS) between a given attribute and the marginal utility of income. This provides an empirical estimate of the implicit trade - off individuals face between direct expenditures and attributes of the alternative . Taking the total differential of Equation (3) for optimizing choices and recognizing so that the attribute - expenditure tradeoff we are considering keeps utility constant for individual i , we have : (4) Setting the differentials for all attributes besides and price e qual to zero and rearranging , we have: (5) In E quation ( 5 ), this MRS between attribute and represents the willingness to pay (WTP) for a marginal increase in attribute , conditional on choosing j . Since the model only captures use values, i f the individual does not choose j , marginal willingness to pay for is zero. 12 As the error term is random from the perspective of the researcher, a natural way to conceptualize individual i - making process is in terms of probabilities. The probabil ity that individual i chooses alternative j over any other alternative in the choice set J is given by: ( 6 ) If the researcher assumes that the error terms are independent and identically distributed as type 1 extreme value, these choice probabilities take on the familiar conditional logit form (McFadden 1974): (7) which can be thought of as the expected demand for site j . In this context, individual i willingness to pay for an increase in attribute is a function of the probability that i chooses alternative j and modifies the result in Equation ( 5 ) as follows : (8) In our empirical analysis, we generalize the MRS concept and estimate respondent willingness to drive for certain beach characteristics, although we later convert our results to willingness to pay measures , in both cases using Equation (5) as is common in choice experiments, while recognizing the importance of Equation (8) for actual choice settings . Although the conditional logit model possesses several intuitive and desirable features for modeling discrete choices, it exhibits a statistical property known as independence of irrelevant alternatives (IIA): the probability ratio of choosing alternative j to alternative k remains unchanged when another alternative is added to the choice set, which can lead to unrealistic predictions of substitution behavior. A common way to relax IIA is to use a mixed logit model. Mixed logit models are a type of finite mixture model that assume the relevant preferences are 13 drawn from a mixture of underlying population distributions (Greene 2018). In contrast to the conditional logit, which produces point estimates for the preference parameters , the mixed logit model estimates the mean and standard deviation of each parameter across the sample. Thus, while the conditi onal logit model inherently assumes that preferences are The mixed logit probability of individual i choosing alternative j can be written as follows: (9) where g( ) is the mixing distribution specified by the analyst and represents the parameters of this distribution. g( ) can be specified as any distribution of preferences in the underlying population. The analyst can also allow for correlation among the individual attribute preferences. tandard deviation is estimated to be significantly different from zero, there is evidence of preference heterogeneity for that attribute in the sample. The analyst can use the mixing distribution g( ) to further examine the shares of respondents with either positive or negative preferences for each attribute level, and this is the approach we take in our analysis. In addition, following Revelt and Train (2000), it is possible to further isolate where particular individuals lie in the sample distributio n of preferences when the analyst possesses repeated choice data for each individual. By specifying the mixing distribution g( ) , the analyst assumes that the true parameter vector follows this distribution in the population. Suppose individual i i s observed to choose between alternatives across t repeated choice situations. Let denote the particular sequence of choices that person i makes across the T observed choice situations, and let denote the attributes of the unique sequence of alternatives from which the individual chooses . 14 We can then define h( ) as the distribution of parameters in the segment of the population that would make the sequence of choices when faced with . The probability that individual I chooses when faced with can be written in a modified mixed logit form: (10) - population distribution h( ) can now be computed as follows: (11) The analyst can now use this distribution to compute the conditional mean parameter vector in the sub - population of people who would make the sequence of choices when faced with : (12) This term does not have a closed form solution, so Revelt and Train lay out a simulation process to recover the conditional expectation. With large T , the conditional mean above consistently estimates the parameter vector of any individual who is observed to choose when faced with (Train 2009) . In the survey, e ach respondent was offered five choice situations, allowing us to examine the determinants of preference heterogeneity using the process outlined in Equations (10) through (12). 15 1.4 : Data and Choice Experiment The d ata used in this work was collected in a two - stage survey of Michigan and Ohio beach users. In the summer of 2019, we performed intercept interviews with beach users at 25 sites along the Ohio shore of Lake Erie, as well a s 3 sites on the coast of Lake St. Clair and the Detroit River (Table 1.1). The 28 sites reflect coastal areas most heavily affected by harmful algae blooms and bacterial contamination. These 28 sites include all sandy beaches in this area that we could id entify as open for public use during our sample period. Table 1.1: Beach S ites S ampled in 2019 Lake or River County, State Site Detroit River Wayne, MI Belle Isle Beach Lake St. Clair Macomb, MI Lake St. Clair Metropark Walter & Mary Burke Park Lake Erie Monroe, MI Lucas, OH Sterling State Park Luna Pier Beach Maumee Bay State Park Erie Beach Maumee Bay State Park Inland Beach Ottawa, OH Camp Perry Beach Port Clinton City Beach East Harbor State Park Erie, OH Nickel Plate Beach Old Woman Creek Beach Sherod Park Beach Main Street Beach Showse Park Beach Lorain, OH Lakeview Park Beach Century Park Beach Cuyahoga, OH Huntington Beach Edgewater Park Beach Euclid State Park Sims Beach Lake, OH Ashtabula, OH Headlands Beach State Park Fairport Harbor Walnut Beach Geneva State Park Lakeshore Park Beach Conneaut Beach Intercept surveys were conducted on randomly selected days between May 27 th and September 1 st , and each sampled day was divided into morning and afternoon shifts. After 16 arriving at a site, interviewers walked the shoreline and counted beachgoers both in the water and on the sandy portions of the beach. Boaters in the water were e xcluded from these counts. Intercept interviews were then conducted with a random sample of visitors. Intercept respondents were asked about their beach recreation behavior, demographic information, and whether they would provide an e - mail address for a fo llow - up survey. The intercept survey resulted in 4239 interviews for an 86% response rate (see Appendix E for a complete disposition of attempted interviews). In total, we collected 2538 (60%) usable emails of sampled beach users from the intercept survey . In May and June of 2020, these 2538 respondents were each e - mailed up to 5 invitations to the online follow - up survey. Of these invitations, 252 were undeliverable and 3 people explicitly refused to take the survey. 127 people partially completed the sur vey (i.e., did not answer any stated preference questions), and 1067 respondents completed the survey (47% of valid email invitations). These 1067 respondents answered an average of 4.7 out of 5 possible choice experiment questions see Appendix E for a com plete item non - response table for the stated preference questions. In the follow - up survey, we used a discrete choice experiment to elicit stated preferences for common beach attributes, including sand quality, crowding, water quality, and the presence of harmful algal bloom and bacterial warnings. The choice experiment presented respondents with five pairs of possible sites with varying levels of beach characteristics, and asked them to ndents were also asked questions about their demographic information and various other items. As part of the survey design process, we pre - tested the follow - up survey instrument via one focus group and several cognitive interviews with Michigan and Ohio be ach users. Focus groups and cognitive interviews ensure that respondents from the target population can 17 understand the questions and tasks that they are being asked to complete and are an essential part of stated preference survey development (Kaplowitz et al . 2004, Johnston et al . 2017). In August 2019, we conducted the focus group with 14 Ohio beach users using an early version of the choice experiment. To further refine the survey instrument, we conducted 15 cognitive interviews with eligible Ohio and Mi chigan beach users. Interview participants were recruited from Amazon Mechanical Turk (MTurk) and the undergraduate student populations of Ohio State University and Michigan State University. The one - on - one cognitive interviews were done iteratively onlin e via screensharing, so we were able to watch as participants completed the survey and assess how well they comprehended the questions and choice scenarios in real time. After respondents completed the survey, we further probed them on the survey instrumen t, focusing on the stated preference sections. The cognitive interviews resulted in several substantive changes to the choice experiment and survey. 1 1 clarity and a harmful algal bloom warning in effect and considered this situation implausible. Our final experimental design was specified to exclude such i mplausible attribute combinations. Additionally, the presence of either a harmful algal bloom warning or a bacterial warning at one of the beaches in the choice experiment caused almost all respondents to choose the other beach. Thus, we expanded HAB and b acterial warning levels to include intermediate levels for the days passed since the warning was lifted. 18 In the choice experiment, respondents were instructed to assume that the two beaches presented in each choice set were the only beaches available to visit, and that choosing the attributes, as well as one - of the choice experiment tables presented in the follow - up survey is shown below in Figure 1.1. Figure 1.1: Example Choice Experiment Table 19 The follow - up survey instrument began with a series of questions explaining each beach attribute and its levels, and then asked each respondent which attribute levels best described the beach where he or she was intercepted. This was done early in the surv ey to inform respondents about the attribute levels in a way which facilitated participation and minimized survey fatigue. Directly before the choice experiments, respondents were reminded of the attributes presented before and were offered the option to click a hyperl ink that opened a summary of the attribute levels that looked similar to Table 1.2. Sand quality was presented in three levels: mostly sand, half sand/half pebbles, and mostly pebbles, and each level was accompanied by a corresponding picture of sand taken at one of the 28 beaches included in the study. Pictures and levels of sand quality reflect the actual range of sand quality along the coasts of Lake Erie and Lake St. Clair. Water clarity was also presented in three levels: clear, somewhat murky, and ver meanings, we defined each water clarity level as the maximum depth at which a beach visitor can clearly see his or her submerged feet on a typical trip to the beach. Similarly, we specified the three levels of crowding ( not crowded, somewhat crowded, and very crowded ) in terms of how easy it is to find a spot to sit on a typical day at the given beach. During pre - test cognitive interviews, most beachgoers indicated that these descriptions made sense to them and were simi lar to how they usually think about these beach attributes. The beaches presented in the choice experiment also varied in terms of harmful algal bloom and bacterial warnings (Table 1.2). The HAB and bacterial warning attribute levels indicated: there is no t and has not been a warning at the site this season; there is a warning at the site, or that there is not currently a warning but there was a recent warning that expired either 1, 3 or 6 days earlier. The three intermediate levels are meant to reflect the possibility that 20 beachgoers may care about the amount of time since the last warning was lifted, in addition to the presence of a warning. Finally, the choice experiment included the one - way distance (in miles) from the e final distance levels varied individually for each respondent i Table 1.2: Choice Experiment Attribute Levels Attribute Levels Sand quality Mostly sand Half sand/ half pebbles Mostly pebbles Water clarity Clear Somewhat murky Very murky Crowding Not crowded Somewhat crowded Very crowded Presence of bacterial warning No warning, none this season No warning, last warning lifted {1, 3, 6} days ago Warning in effect Presence of HAB warning No warning, none this season No warning, last warning lifted {1, 3, 6} days ago Warning in effect One - way distance to site {10, 50, 100, 150} miles + minimum distance from respondent zip code to any site in the sample frame Sand Quality Pictures Mostly sand Half sand/ half pebbles Mostly pebbles 21 we used Ngene (ChoiceMetrics 2018) to generate an experimental design that minimized D - error subject to several conditions imposed on the design. Although such des igns result in efficient estimates of the preference parameters used to build the design, researchers generally do not know the true distribution of preferences in the population. Therefore, when generating D - efficient designs researchers must supply prior estimates of these parameters. To ground our experimental design in empirical evidence, we conducted a pilot study to generate more informed priors and used the estimated parameter distributions from the pilot data to generate a Bayesian design for the fi nal survey. In addition to providing evidence - based preference priors, the pilot study allowed us to troubleshoot other early issues with the survey. We conducted the pilot in two stages. The first - stage pilot survey presented respondents with a list of t he 28 beaches in our sample frame, asked respondents to indicate whether they were familiar with each beach, and which beaches (if any) they visited in 2019. If a given respondent indicated that he or she had visited any of the 28 sampled beaches at least once during 2019, the respondent was invited to complete the second - stage pilot survey containing which contained the five choice experiment questions. The second - stage pilot survey was designed to mirror the structure and information treatments of the fin al follow - up survey to be sent to intercept respondents. 176 respondents completed the pilot survey, supplying 880 unique choices that were used to estimate a conditional logit choice model for the Bayesian priors in our final experimental design. The fina l design consisted of 35 choice sets total, organized into 7 blocks of 5 choice sets each. In the follow - up survey, each respondent was randomly shown one of these 7 blocks for their 5 choice experiment tables. 22 1.5 : Results To examine we estimate a mixed logit choice model for panel data (Train 2009). The mixed logit parameter estimates are reported below in Table 1.3. Table 1.3 : Mixed Logit Estimates 2 (1) (2) (3) (4) Variables Mean parameter estimate Std. deviation estimate % with parameter > 0 3 W illingness to drive (WTD ) at mean parameter s (miles) Distance from home (miles) - 0.0148*** (0.000721) Mostly sand 1.177*** 0.680*** 96 80 (0.0892) (0.120) Half sand/half pebbles 0.380*** 0.0412 26 (0.0734) (0.145) Clear water 1.500*** 0.662*** 99 101 (0.103) (0.158) Somewhat murky water 0.707*** 0.226*** 99 48 (0.0738) (0.0836) Not crowded 1.011*** 0.780*** 90 68 (0.0925) (0.108) Somewhat crowded 0.643*** 0.0873 43 (0.0780) (0.0829) Bacterial warning in effect - 3.938*** 0.605 - 266 (0.267) (0.699) - Lifted 1 day ago - 1.732*** 0.554** 1 - 117 (0.119) (0.236) - Lifted 3 days ago - 1.211*** 0.180 - 82 (0.0931) (0.150) - Lifted 6 days ago - 1.136*** 0.00744 - 77 (0.0900) (0.165) HAB warning in effect - 3.855*** 1.971*** 3 - 260 (0.314) (0.475) - Lifted 1 day ago - 1.280*** 0.200 - 86 (0.102) (0.149) - Lifted 3 days ago - 0.873*** 0.332** 1 - 59 (0.0870) (0.166) - Lifted 6 days ago - 0.454*** 0.214 - 31 (0.0780) (0.173) Neither - 0.554*** 1.657*** 37 (0.127) (0.0881) Respondents 1048 1048 1048 Choice Occasions 5082 5082 5082 2 Robust standard errors in parentheses, *** p <0.01, ** p <0.05, * p <0.1. Each attribute level preference parameter 3 These values are only calculated for attribute levels with significant standard deviation estimates and rely on the assumption that attribute preferences are normally distributed, which may not hold at the tails for some attributes. 23 Each attribute level parameter other than distance was assumed to follow a normal distribution. Mean parameter estimates for all attribute levels are significantly different from zero at the 1% level and have the expected signs, i.e., are positive on level s of attributes thought to be valued by beach users, such as sand quality, and negative on driving distance and levels of HAB and bacterial warnings. Each parameter estimate represents the marginal utility of a site attribute level relative to the relevant excluded attribute level. For example, our results indicate that, on average, respondents value a site with a half sandy/half pebbly beach more than one with mostly pebbles, all else equal. Similarly, on average respondents value a somewhat crowded beach relative to a crowded beach. The estimated distance parameter is negative and significant at the 1% level, indicating the familiar result that respondents would prefer to go to a closer beach, all else equal. Across the site attributes, all but one adjace nt pair of attribute level parameters are statistically different from one another 4 based on a Wald test, implying an intuitive and about the relative rankings o f respondent preferences; however, it is useful to express estimates into meaningful information about travel behavior. Following E quation ( 5) , the estimated willingness to drive (WTD) for each attribute level provide a way to discuss our parameter estimat es in a more immediate and policy - relevant context. Average respondent WTD for each attribute level is reported in the final column of Table 1.3. The most striking WTD results involve the presence of a harmful algal bloom warning and the presence of a bac terial warning. These values are - 260 and - 266 respectively, indicating that on average respondents would be willing to drive 260 miles to avoid a beach where a 4 The bacterial statistically different. This relationship is examined in detail later in this section. 24 harmful algal bloom warning is in effect, and 266 miles to avoid a beach where a bacterial warn ing is in effect. Considering that the state of Ohio is roughly 250 miles wide and that the median distance respondents live from the nearest beach in our sample is 15 miles 5 , the magnitude of these estimates demonstrates their high importance. Additionally, these estimates indicate that to avoid either type of warning, on average respondents are willing to drive more than double the distance they would drive for a mostly sandy beach (80 miles), a beach with clear water (101 miles), or a beach th at is not crowded (68 miles). It should be noted that these estimates do not account for the substitution observed in a non - hypothetical demand system. Because substitute sites exist in the real world, respondents likely would not need to drive the full di stance they are willing to. Thus, the distance they incur is not the same as their willingness to drive, a difference that is akin to why willingness to pay for a good exceeds payments and yield s consumer surplus. The average respondent WTD values to avoid a site with a HAB warning in effect and a site with a bacterial warning in effect are not statistically different from one another. However, differences in preferences begin to emerge when the other three warning attribute levels are considered. Our estimates indicate that respondents are willing to drive on average 86, 59, and 31 miles to avoid a site with a HAB warning that expired 1, 3, or 6 days earlier, respectively. Similarly, respondents are willing to drive on average 117, 82, and 77 miles to avoid a site with a bacterial warning that expired 1, 3, or 6 days earlier. Estimated willingness - to - drive values at each attribute level are significantly different from one another across both types of warning. Taken together, these results imply that th e disutilit y of each type of water quality warnings exhibit strong lag effects, and do not disappear immediately after a warning is lifted. 5 Respondents live an average of 69 miles from their closest site in our s ample. However, the median and mean travel distances for the sites where respondents were interviewed was 58 and 154 miles. 25 While respondents seem to be equally as averse to sites with a current HAB warning as they are to sites with a curre nt bacterial warning, this aversion fades more quickly for HAB warnings. Respondents are willing to drive 36% farther to avoid a site with a 1 - day expired bacterial warning relative to a site with a 1 - day expired HAB warning and 39% farther to avoid a site with a 3 - day expired bacterial warning relative to a site with a similarly recent HAB event. Additionally, respondent WTD estimates for 3 - day and 6 - day expired bacterial warnings are the only adjacent attribute level WTD estimates in our results that are not statistically different. In comparison, WTD to avoid a site with a recent HAB warning steadily decreases as time since the HAB warning increases. This disparity, along with the difference in magnitude between the HAB and bacterial warning WTD estimates , indicates that the preference effects of past bacterial warnings are significantly more intense, and last longer after an event, than those of HAB warnings. The behavior of respondent WTD estimates over time (at the mean parameter estimates), as well as their 95% confidence intervals, is plotted below in Figure 1.2. Our mixed logit model allows the attribute level parameters to vary according to a multivariate normal distribution and estimates a standard deviation for each parameter. A statistically sig nificant standard deviation estimate provides evidence of preference heterogeneity kes intuitive sense, as it is likely that different beachgoers value certain beach characteristics more than others, which in turn affects their choice of sites and travel behavior. 26 Figure 1.2: Mean W illingness to D rive to A void S ites with R ecent W ater Q uality E vents and 95% C onfidence I ntervals around the M eans 6 The standard deviation estimates also reveal it is unlikely that any of the warning attributes are positively valued by beachgoers. Although the vast majority of respondents are estimated to have positive marginal utility for the best levels of crowding, sand quality, and water clarity, 7 the magnitude of this positive valuation significantly varies in the sample. The marginal utility of a site with the intermediate water clarity one with murky water, also exhibits heterogeneity in the sample. This is the only intermediate 6 - wtp - postestimation command (Hole 2007a) 7 1.3 for further details. 0 50 100 150 200 250 300 350 0 1 3 6 WTD (miles) Days since water quality event WTD to avoid - bac. advisory. WTD to avoid - HAB warning. 27 attribute level parameter across the water clarity, sand quality, and crowding attributes estimated to significantly vary ac ross sampled beachgoers. The estimated heterogeneity in both water clarity attributes makes sense in that not all beach users enter the water during a typical beach trip, while all of our beach users interacted with the sandy portion of the beach at some t ime during their visit. Alternatively, regardless of whether they plan to enter the water, people are unlikely to prefer murky water at the beach; 99% of respondents are estimated to positively value somewhat murky water relative to murky water. Preference s for sites with a 1 - day lifted bacterial warning, 3 - day lifted HAB warning, and current HAB warning also exhibit significant heterogeneity among sampled beachgoers. Since the mean WTD estimates for the current HAB and bacterial attribute levels are not st atistically different, this heterogeneity indicates that roughly half of sampled beachgoers would be willing to drive a longer distance to avoid a site with a HAB warning in effect than they would be to avoid a site with a bacterial warning in effect. One possible reason for this is that respondents in our sample tended to have more experience with bacterial warnings relative to HABs; while 44% of respondents indicated that they have seen a bacterial warning sign on a beach, only 34% of responde nts indicated having seen a HAB warning sign. Additionally, most respondents (56%) had seen news reports of people getting sick due to bacterial contamination in bodies of water. This greater level of familiarity with bacterial contamination events may con tribute to The significant standard deviation estimates for several marginal utility parameters reveal that for some beach characteristics there is a distribution of preferences a cross individual beachgoers , but the standard deviations do not reveal how this preference heterogeneity relate s to observable characteristics of beachgoers. To examine possible determinants of preference 28 t command (Hole 2007b) to predict each E quation (1 2 ). For each of the 15 attribute level parameters ress the predicted individual - specific parameter on a constant and a vector of 15 demographic and attitudinal variables from the survey that may influence the distribution of beachgoer preferences. These variables include respondent age, income, race, and years each respondent has regularly visited area beaches, and whether each respondent entered the water on their intercepted trip, among others. Significant results from these regressions could assist policymakers and managers understand possible market segments of beachgoers with distinct preferences . The results of these regressions are summarized in detail in Appendix I. The available demographic and attitudinal variables do not explain much of the variation in the conditional marginal utility parameters the 15 regressions have an average of 0.015 with an average adjusted of 0.004. Out of the 225 estimated parameters in these regressions, 8 are significant at the 5% level, and 4 are significant at the 1% level. These results are not unprecedented; s everal recreation studies examining heterogene ity show that attitudes explained preference heterogeneity but demographics did not (Ehrlich et al. 2017; Campbell et al. 2014) or that demographics had substantially less explanatory power that attitudes (Komossa et al. 2019) . Since our current data ident ifies significant preference heterogeneity but is largely unable to explain the determinants of this heterogeneity, this remains fertile ground for future research. 8 8 Indeed, we examined several specifications of mixed logits with discrete preference distributions (also called latent class models); these latent class models often did not converge, and those that did failed to reveal substantial differences in preferences across classes with class memberships poorly explained by demographics. 29 1.6 : Robustness Checks To test the sensitivity of the mixed logit estimates to different model specifications, we estimate a conditional logit model and a nested logit model with trip/no - trip nests. The results are provided in Table G.1 of Appendix G . Preference parameter estima tes are stable across all three models, and estimated parameter vectors are highly correlated ( > .99 for all pairwise combinations). Consequently, our WTD estimates are robust to different distributional specifications, with an average 7% difference be tween the mixed and conditional logit WTD estimates and an average 4% difference between the mixed and nested logit WTD estimates. To test the sensitivity of our estimates to sample definitions, we re - estimate mixed logit models on the following subsets of the full sample: (1) respondents that completed the survey in less than 29 minutes (the 75 th percentile of task duration), (2) respondents that completed the survey in more than 8 minutes (the 10 th percentile of task duration), (3) respondents that live within 50 miles of their intercept beach (the 75 th percentile of distances ), and (4) respondents that did not exhibit intransitive preferences in their choice experiment responses. Subsets (1) and (2 ) were chosen because an influence due to especially fast or slow respondents may be indicative of inattention or poor comprehension, respectively . Subset (3) was chosen to test whether preferences were swayed by differences in non - local respondents . Final ly , subset (4) is tested because choices of respondents with intransitive preferences may be indicative of either irrationality or in attention. Sensitivity analysis estimates are reported in Appendix Table s G.1 through G.4 . The mean preference parameter estimates are highly stable across the four robustness sub samples, and the patterns of preference heterogeneity are similar, though as expected when sample sizes shrink there are generally fewer parameters with significant d istributions. In all cases the 30 estimated mean parameter vectors are highly correlated ( > .99 for all pairwise combinations). In addition, model estimates were compared across alternative randomized question orderings that were present in the survey (Tab le VIId), and the results are similarly robust to ordering effects with the pooled mean parameter vector again being similar and highly correlated with the randomized orders ( > .99). 31 1.7 : Discussion The estimates discussed in the previous section provide useful information about how Lake Erie and Lake St. Clair beachgoers value different beach attributes, and how their preferences for certain attributes behave in comparison to others. By forming ratios of marginal utility parameter estimate s, we can further examine how the average beach user implicitly trades off different levels of environmental quality, in the form of marginal rates of substitution (MRS) of driving for quality attributes. These MRS estimates have the potential to be valuab le for beach managers and state financial planners, who must make decisions about how to manage public funds and want to do so in a manner that enhances societal and environmental benefits. Consider the mixed logit estimation results. The average beachgoer has a MRS of clear water for sandy beaches of about 1.3 and MRS estimates of the absence of bacterial warnings for sandy beaches and the absence of HAB warnings for sandy beaches of about 3.3 each 9 . These clear preferences for water - related attributes su ggest that the marginal dollar of state funding would likely be better spent on pollution control than local beach maintenance . However, because sand quality affects beach recreation on every trip while HAB and bacterial warnings are comparatively rare, more detailed analysis would be needed for the purposes of program evaluation and cost - benefit analysis. While the ratios of the WTD estimates and their ordering in relation to one another are potentially useful in a policy context, one must exercise caution when interpreting the absolute magnitude of the individual WTD estimates for different beach attribute levels. As mentioned previously, many of our estimates indicate that beach users w ould be willing to drive large 9 The estimated marginal rates of substitution of the absence of HAB warnings for sandy beaches and the absence of bacterial warnings for sandy beaches are not statistically different. This is consistent with our prior result that . 32 distances to avoid a beach with a HAB or bacterial warning in place. The largest estimates produced by our mixed logit model indicate that the average respondent would be willing to drive almost 300 miles to avoid a beach wit h either a bacterial or HAB warning in effect. To further contextualize the magnitude of our results, we can compare our WTD estimates with previous WTP estimates from the water quality valuation and recreation demand literature by converting distances to dollars. After using the cost of travel to convert the results to round trip dollar values, our WTD estimates can be viewed as roughly equivalent to WTP. 10 In one of the few studies to use a choice experiment to value HABs in Lake Erie, Zhang and Sohngen (2018) find that Lake Erie anglers would be willing to pay up to $80 per trip to avoid boating through 8 miles of a HAB. Although we have no directly comparable result for beach ute which used very similar levels to those in our study. They found that boaters would be willing to pay about $96 per trip for clear water relative to murky water, which is very similar to our estimate for the id a beach with very murky water. While Zhang and Sohngen offer the closest point of comparison to our estimates, other stated preference valuation work conducted in marine and international settings can help to examine the validity of our results. Marsh (2012) uses a household - level choice experiment to 10 1897 unique zip - site combinations were observed in our intercept data. Round - trip travel distances (in miles) and travel times (in minutes) were computed for each observed combination using Georoute (Weber and Péclat 2017). For each combination, we com puted the travel cost from zip code z to site j as follows: TC zj =dist zj *$0.27 +time zj *(1/3)*(median income z /2000) Per - average across vehicle types and assuming 15,000 miles driven per year. Opportunity cost of time is specified using zip code z ined from the 2018 ACS 5 - year Estimates (US Census Bureau 2019) and assumes 50 weeks worked per year and 40 hours worked a week. To obtain the factor to convert WTD to WTP, we divide round - trip travel cost by travel distance and average across all observed combinations. The resulting cost is $0.47 per mile. Since a WTP measure using travel cost would typically be a round trip value, we can convert our one - way distance value by a factor of 0.5, making our one - way WTP about the same as round trip WTP. 33 examine how New Zealand residents value reduced probability of algal bloom warnings in two inland lakes, and finds that the average household would be willing to pay up to $138 (USD 2020) a year to reduce the probability of HAB warnings by 40%. The choice experiment was 35% of respondents indicated that they had visited either of the lakes in the last year. Consider ing that this relatively large WTP estimate was obtained from a sample which included non - users and was for a reduction in probability rather than a certain HAB as in our case, the relative value compared to our results for observed beach users make intuit ive sense. Using data from a mail survey of Finnish households, Kosenius (2010) similarly estimates yearly WTP for a series of policies designed to reduce concentrations of cyanobacteria t model indicate that the average household would be willing to pay $596 per year (USD 2020) to reduce cyanobacteria and other algal biomass in Finnish coastal waters by 15 - 35%. To value reduction of HABs in - Sauvageau et al . (2018) use choice experiment responses of beach users (via intercept interviews) and residents (via door - to - door interviews) in coastal cities that had been affected by cyanobacteria blooms within the past ten years. The researchers estimate mean yearly m arginal WTP for reduction of common attributes of algal blooms, such as smell, recreational impacts, and low water clarity using a mixed logit model, and aggregate these measures. They conclude that the average coastal resident in the sampled area would be willing to pay roughly $269 per year (USD 2020) to reduce the incidence of HABs. While these studies differ from ours in important methodological ways and in their focus on annual WTP for reductions of negative events, the magnitude of these WTP estimates help provide further context for our results. 34 Johnston et al . (2017) suggest that auxiliary evidence collected in stated preference surveys can be useful in assessing the validity of the preference elicitation mechanism. In our case, supplemental informat ion can be used to assess how much respondents care about common beach attribute levels outside of the context of the choice experiments because our survey respondents also answered a series of contingent behavior (CB) questions The CB questions asked resp ondents if they would still have made the same trip to the beach where they were intercepted if faced with certain HAB and bacterial warning s at th at beach on the day of their trip . The CB questions covered the same eight scenarios as covered by the HAB an d bacterial warning attribute levels in the choice experiment. Table 1.4 summarizes each contingent behavior scenario and the percentage of respondents that indicated that they would have made the same trip if faced with each scenario. Table 1.4 : Continge nt Behavior Response Percentages CB Scenario I would have gone to the same beach. (%) Bacterial warning - day of trip 19 - Lifted 1 day before trip 35 - Lifted 3 days before trip 53 - Lifted 6 days before trip 76 HAB warning - day of trip 19 - Lifted 1 day before trip 39 - Lifted 3 days before trip 62 - Lifted 6 days before trip 80 Table 1.4 shows that as the time since the last water quality event grew, more CB question respondents indicated they would have gone to the same beach. However, about 20 % of 35 respondents indicate that they still would not have gone to the same beach if a H AB warning had been lifted for 6 days, and 24% indicate they would not have gone to the same beach if a bacterial warning had been lifted for 6 days. For each time - since - event level, fewer respondents would have made the same trip given that the event was a bacterial warning, relative to if the event was a HAB warning. Each of these percentage estimates is statistically different from its adjacent level; however, the percentage of respondents who would have made the same trip given a bacterial warning and t he percentage of respondents who would have made the same trip given a HAB warning are not statistically different from one another. Although these insights from our CB questions are consistent with and corroborate the results and patterns of the choice e xperiment, the CB percentages are not yet directly comparable to the parameters of the choice models. To more directly compare the preference data gathered in the choice experiment and CB questions, we use the estimated parameters from our mixed logit mod el to simulate the effect of current/recent HAB and bacterial warnings on the probability of visiting a site, relative to a baseline scenario with no warning s . This requires specifying a simulation choice set and attribute levels analogous to what was shown in the choice experiments, and then using this structure to compute changes in choice probabilities corresponding to the CB scenarios . Specifically, f or each follow - up respondent who answered every CB question (n = 907), we created a sim ulation choice set with three alternatives. The first alternative represented the site where the respondent was interviewed, and the beach attribute levels for this alternative were populated using averages of subjective environmental quality assessments c ollected earlier in the survey 11 . The first 11 In th e follow - up survey, respondents were asked to report the typical levels of crowding, sand quality, and water the average levels of sand q uality, water clarity, and crowding reported by beachgoers intercepted at the same beach 36 - way distance from th at intercept site. The second alternative in each choice set represented an average substitute si intercept intercept site to any of the other 27 sites in our sample. The third alternative in each simulation like the one offered in the choice experiment. To compute baseline choice probabilities for the simulation , within each simulation c hoice set we set the HAB and bacterial attribute levels to zero for intercept parameters to compute the probability of each respondent visiting the be ach where he or she was interviewed . In the simulation, this represented the baseline scenario with no current or recent HAB or bacterial warnings. The simulation then create d 8 counterfactual beach quality scenarios to correspond to each of the 8 CB scena rios . For each counterfactual, w e set the levels of the HAB and bacteria variables for to match the CB levels, and we computed the probability that each respondent would visit their intercept beach under the counterfactual. Next, we computed percent change in probability of visiting their intercept site relative to the baseline scenario. These percent changes we re then averaged across all respondents for each of the 8 scenarios. Figure 1.3 plots the average percent decrease in the probability a respondent would visit the same site for each HAB and bacterial warning scenario. as the given respondent. The second alternative in each choice set used the average reported levels of each attribute across the whole sample. 37 Figure 1.3 : Average P ercent D ecrease in the P robability of V isiting I ntercepted S ite, R elative B usiness - as - S cenario These simulated visitation probabilities are very consistent with the WTD estimates plotted previously in Figure 1.2 and offer a way to evaluate the validity of the choice experiment (CE) preference estimates. For each scenario, our CE estimates also imply that a percentage of respondents would go to the same site, and these percentages are highly correlated with the contingent beha vior response percentages ( 12 . The graphs in Figure 1.4 plot the implied percentage of CE respondents who would go to the same site given a HAB or bacterial warning 12 The similarity is part icularly reassuring given the different framing of the questions the CB question was explicitly framed about the site and time of the intercept trip whereas the CE question was about a more generic trip occasion. For a detailed table comparing the implie d percentages from our choice experiment simulation with the contingent behavior response percentages, see Appendix J . 0 10 20 30 40 50 60 70 80 90 100 0 1 3 6 Avg. % decrease in probability of trip Days since water quality event Bacterial warning HAB warning 38 against the CB response percentages to further illustrate the high correlation bet ween the two. Even though t he mixed logit preference parameters were estimated in the context of a choice between hypothetical beaches, they are able to approximate contingent behavior scenarios concerning observed trip s . Figure 1.4 : Simulated Percentages of Respondents Who Would Go to the Same Site Given a HAB or Bacterial Scenario, and Contingent Behavior Question Response Percentages Taken together, these observations lend credence to our previous hypothesis that a temporal preference lag effect exists for HAB and bacterial warnings, and that this lag has the potential to affect travel behavior even after warnings have been lifted. The fact that such a large percentage of respondents would not make the same trip if either type of warning were in effect indicates the presence of a substantial aversion to these hazard events. Considering this auxiliary evidence, the magnitude of the estim ated respondent WTD values make more sense, as such an aversion would naturally equate to a larger willingness to incur avoidance costs, all else equal. 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 0 1 3 6 Days since warning Bac CE Bac CB 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 0 1 3 6 Days since warning HABs CE HABs CB 39 1.8 : Conclusion This paper demonstrates that beachgoers are willing to drive farther for beaches that are less crowded, are less rocky, have higher water clarity, and do not have current or recent warnings for bacteria or HABs. In particular, the results demonstrate a significant preference lag effect concerning HAB and bacterial warnings, i.e. these even ts affect the visitation and welfare of beach users even after they are lifted. While respondents are willing to drive similar distances to avoid current bacterial and HAB events, the disutility of a bacterial warning lingers for much longer than a HAB war ning, and the results show a remarkably similar pattern is observed in findings have ramifications for future research and policy analyses seeking to quantify benefit s of non - point source pollution control programs. If the costs of HAB and bacterial warnings are solely measured in terms of value - per lost trip during warning events, these costs will be understated. 40 CHAPTER 2 : Economic Welfare Effects of Harmful Algal Blooms and Bacterial Contamination Warnings in the Great Lakes 2.1 : Introduction While some may consider climate change to be a distant concern, global water resources have already been impacted by climate change - induced extreme weather patterns through the increasing frequency of harmful algal bloom events. A lgal blooms are water - born e masses o f plant matter, which can be caused by excess agricultural nutrient runoff. Under certain environmental conditions, this runoff contributes to cyanobacteria growth in waterways, which in turn contributes to the growth of h armful algal blooms (als o known as HABs) . HABs can cause liver damage, gastrointestinal illness, and skin irritation for people who come into contact with them (NIEHS 2020), and they have severe ecological impacts on the bodies of water in which they appear. HAB growth routinely oxygen that would otherwise nourish aquatic wildlife (NOAA 2020 ). Fish or shellfish that are not killed by this lack of oxygen and nutrients can be rendered poisonous by algal toxins, with potentially devastating effects on coastal communities who depend on aquaculture and the fishing industry for their livelihoods (CDC 2020 ). Hi gh bacterial concentrations in ambient waterways, caused by runoff from untreated urban wastewater, septic tank overflow, and concentrated animal feeding operations (CAFOs), often affects the same communities which deal with HABs on a regular basis. One of the most well - known bacteria that commonly reaches unsafe levels in waterbodies is Escherichia coli ( E. coli ), exposure to which can cause cramps, diarrhea, vomiting, and in older people and children, life - threatening kidney failure (Mayo Clinic 2019). Because climate variability has been linked to more intense precipitation and more frequent flood events, increase d water - borne bacterial 41 contamination events will be a natural consequence of these changes without a large national overhaul in flood protection infrastructure and agricultural practices (Rose et al . 2001, Jung et al . 2014, Patz et al . 2008). Extreme prec ipitation events have been shown to be linked to past water - borne disease outbreaks (Curriero e t al . 2001), underscoring the potentially large impacts of bacterial contamination on human health in the wake of rapidly changing weather patterns. In light of the potential impacts of climate change on the frequency and intensity of HABs and bacterial contamination, policy makers and resource managers would likely benefit from information concerning the economic costs and welfare effects of these events. Howeve r, a relatively small amount of empirical research in environmental economics has sought to quantify the specific damages of HABs and bacterial contamination. With few exceptions, the existing literature devoted to estimating the costs of HABs and bacterial contamination has used stated preference methods. Stated preference methods are useful when valuing changes in environmental quality because they allow the analyst to value quality changes t Hanemann 2005) or may be correlated with unobserved attributes of sites . This is especially true of HAB and bacterial events, which are random and, in the case of HAB events, usually only occur a few times per season. Despite their relative benefits, however, a drawback to stated preference studies is that they often produce willingness - to - pay estimates which may exceed what respondents would be willing to pay in real life, a concept known as hypothetical bias (List and Gallet 2001; Murphy et al . 2004; Loomis 2011). To mitigate possible effects of hypothetical bias while taking advantage of the flexibility of stated preference methods, the use of combined RP - SP approaches in empirical valua tion studies has become more common. In applications of combined RP - SP models, researchers have 42 commonly augmented revealed preference data with contingent valuation surveys (Cameron 1992) and choice experiments (Adamowicz et al . 1994; Cheng and Lupi 2016; Whitehead and Lew 2020). E nglin and Cameron (1996) was the first recreation demand study to suggest combining RP travel cost data with contingent behavior (CB) data, which asks respondents about their expected trip behavior after a price or quality change . The authors posit that CB questions may be more practical than the contingent valuation approach, as respondents may be better able to conceptualize future trips compared to the future prices offered in a contingent valuation survey. Since Englin and Cam - CB methods have proven useful for answering questions in coastal resource management and environmental economics (Cameron et al . 1996; Eiswerth et al . 2000; Hanley et al . 2003). In most of the contingent behavior literature, researchers ask respondents to report hypothetical future trips or demand behavior. An alternative approach ask s respondents if they would still engage in the observed behavior given a change in price or quantity ( Tanner et al. 2019 ; P arsons and Stefanova 2011) and seeks to ground CB scenarios in observed behavior respondents are familiar with . We take t his approach and embed contingent behavior data in a revealed - preference site choice model to value Great Lakes recreation and water qu ality . The work is one of the few studies to value Great Lakes beaches and is one of the few to estimate the recreational costs of harmful algal blooms and bacterial contamination in freshwater more generally. We utilize a multi - stage research strategy to examine the welfare effects of freshwater harmful algal blooms and bacterial warnings. Using responses to a rigorously designed intercept survey conducted at 28 Great Lake beaches over the course of the 2019 recreation season, we construct a multi - site, zo nal dataset following the strategy developed by von Haefen et al . 43 (2019) . Using this revealed preference data, we estimate a multi - site nested logit model of recreation demand and simulate the welfare effects of beach closures. In a follow - up survey, we el icited contingent behavior data concerning various HAB and bacterial scenarios asking beachgoers if they would have made the trip on which they were interviewed if certain HAB and bacterial events were in effect. We use the CB responses in a contraction - ma pping algorithm to identify the disutilities of HAB and bacterial events, and then produce seasonal estimates of the average welfare effects of each contingent behavior scenario. We fin d that season - long HAB and bacterial warnings each cause welfare losses of roughly $1.4 million at the average site in our sample. We then use our estimates to simulate the welfare effects of the observed HAB and bacterial events that occurred during the 2019 recreation season, finding that these events caused roughly $ 5.8 million dollars in losses. We show that this estimate is about 3 4 % larger than welfare losses computed under the assumption that beachgoers only reap disutility when of beachgoer preferences in welfare estimation and policymaking . Finally, after standardized by the number of days affected by each type of warning, recreational welfare loss can be attributed to bacter ial warnings, beachgoers reap more than three times more disutility from the sites that had HAB warnings than those that had bacterial warnings. The structure of this essay is as follows. Section 2.2 provides background on water quality issues in Lakes Er ie and St. Clair and reviews the available literature. Section 2.3 summarizes the on - site sampling plan used to collect intercept data, and details how the intercepted trip data is used in our revealed - preference site choice model. Section 2.4 introduces t he follow - up survey, with a particular focus on the contingent behavior questions and their 44 motivation. Section 2.5 summarizes how intercept probabilities derived from our sampling scheme are used to create our multi - site zonal dataset, and Section 2.6 out lines the theory underpinning our empirical estimation strategy. Finally, Section 2.7 and 2.8 present our results and discuss their practical significance. Section 2.9 concludes. 45 2.2 : Background According to the Environmental Protection Agency, HABs have been observed in all 50 US states (EPA) and are a significant and growing problem worldwide (Anderson 2012). Using satellite data of 71 lakes around the world, researchers found that in 68% of the se lakes, peak summertime bloom intensity has been steadily increasing since the 1980s (Ho, Michalak, and Pahlevan 2013). Additionally, in 2019 the United Nations Intergovernmental Panel on Climate Change reported that increasing global water temperatures brought on by climate change, in conjunction with business - as - usual agricultural practices, have the potential to increase this upward trend (IPCC 2019). Because HABs can occur in freshwater, saltwater, and the brackish water between the two, the entirety Despite the relatively small amount of research concerning the welfare effects of HABs and bacterial contamination, the wide international scope of the existing literature reflects the global nature of this problem. In one of the few articles focused on measuring the welfare effects - Sa u vageau et al . (2019) use a choice experiment on a convenience sample of - reduction policies, finding an average household willingness to pay of $269 per year (USD 2020) for eliminating the visual, recreational, odorous, and ecological consequences of HABs on local lakes . In a s imilar study, Kosenius (2010) uses a mail survey administered to Finnish households to estimate preferences for reduction of eutrophication in the Baltic Sea. Using a mixed logit model, the researchers find that the average household would be willing to pa y $596 per year (USD 2020) for a 15 - 35% reduction in cyanobacteria biomass. Marsh (2012) also uses a household - level choice experiment lakes, and finds that the aver age household would be willing to pay up to $138 (USD 2020) a 46 - Sauvageau et al . and Kosenius frame their choice experiments by asking respondents about nutrient reduction pol icies and biomass levels, Marsh focuses on the reduction of HAB warnings, which is a central focus of our analysis in this paper. Finally, Taylor and Longo (2010) use a ay region for HAB reduction. While the previously referenced studies find comparatively large WTP for nutrient abatement policies and HAB reduction, Taylor and Longo estimate a more modest figure, as their average respondent would be willing to pay a one - o ff tax of $13 (USD 2020) to fund the elimination of HABs in the Varna Bay. In the United States, the western Lake Erie basin (consisting of Lake Erie, Lake St. Clair, and the surrounding watersheds) is one of the areas most frequently affected by HAB and bacterial events, and it is the focus of our analysis. In the summer of 2011, Lake Erie suffered from its largest HAB on record. Three years later in August of 2014, another HAB event people and forcing immune to the threat of climate change, and the nutrient loading reductions needed to manage icult to achieve under business - as - usual agricultural practices in the coming decades (Scavia et al . 2014; IJC 2014). In one of the earliest studies to focus on the value of Lake Erie beaches, Sohngen et al. (1999) use revealed preference intercept data to value single day trips to Maumee Bay State Park and Headlands Beach State Park, both sites on the northern coast of Ohio. They find average single - day trip values of $25 for Maumee and $16 for Headlands and aggregate these values to $6.1 and 3.5 billion d ollars in annual surplus value, respectively. While Sohngen et al . do not 47 model the effects of HAB or bacterial events on the value of these sites, Murray et al. (2001) estimate the value of reducing E. coli advisories using intercept data collected from visitors at 15 Lake Erie beaches. They find that beachgoers would benefit between $24 and $38 per year from one less E. coli advisory, and that the relative value of these welfare gains is dependent on the met hods by which beachgoers learn about advisories. Zhang and Sohngen (2018) use choice which boaters likely only must do once or twice each season, and find anglers a re willing to pay $8 - $11 more to avoid boating through a HAB on the way to a fishing site. research concerning the value of Erie beaches uses data from Ohio sites and beac hgoers. However, within a larger study of all Great Lakes beaches in Michigan, Song et al. (2010) use self - reported trip data from a consumer web - based panel of Michigan residents to calculate the welfare effects of beach closings at Michigan Great Lake be aches, including Lake Erie and Lake St. Clair. They find that closing an average public beach would cause losses of roughly $ 50 per person per trip. The researchers suggest that these large values are likely due to the small number of substitute sites on t he Michigan coasts of Erie and St. Clair (10 were considered in the study) coupled with the larger number of potential beach users in the Detroit metropolitan area. While Song et al . use the number of beach advisories and closures at a given beach during 2 006 as a proxy variable for the water quality at that beach, because they do not control for unobserved beach attributes and the number of advisory days is not significant , welfare loss of an advisory is not calculated. In one of the first studies to expl icitly focus on the welfare impacts of HABs in Lake Erie, Palm - Forster et al. (2016) use a benefit transfer approach to apply an existing model of 48 Michigan beach recreation (Chen 2013) to valuing HAB - induced closures of 67 Ohio beach sites on the coast of Lake Erie. They find that the typical day trip to a Lake Erie beach is worth about $18 per person per trip, and they aggregate this to roughly $2 million per year in total seasonal value. In recent work, Wolf et al . (2019) use self - reported visitation data and a latent - class modeling framework to simulate the welfare effects of HAB and E. coli events on both beachgoers and anglers in Lake Erie. By simulating the full closure of all western Lake Erie beaches due to poor water quality conditions, the researchers find that beachgoers and anglers would annually lose $7 million and $69 million, respe ctively, as a result of these closures. Additionally, they find beachgoers to be comparatively more averse to E. coli , and anglers more averse to HABs. While Palm - Forster et al . and Wolf et al . each reach important conclusions about the impacts of common water quality events in Lake Erie, both studies frame their discussion of worst - case welfare scenarios in terms of beach closures, and their analys e s do not consider the welfare effects of HAB and E. coli advisories when beaches stay open. This distinction is important, as Lake Erie and Lake St. Clair beach managers typically do not close sites in response to HAB and bacterial events. This comparative infrequency of beach closure, and its implications for accurate welfare estimation, are discussed in detail later in this paper. 49 2.3 : Onsite Counts and Intercept Survey On randomly selected days d uring the 2019 summer recreation season, we conducted visitor counts and collected intercept data from Ohio and Michigan beach users at all 25 sandy public beaches along the southern and western coasts of Lake Erie, as well as 3 beaches on the coast of Lak e St. Clair and the Detroit River. Interviewers approached randomly selected beachgoers at each site and asked if they would be willing to participate in a short interview about their beach visitation. At the end of each interview, respondents were given t he option to participate in an online follow - up survey about their experiences with water quality at the beach. If they agreed, respondents were asked to provide an email address. The counts and intercept surveys provided revealed - preference data on beach visitation that is used to construct a recreation demand system grounded in observed travel behavior. The online follow - up survey collected contingent behavior data on trip responses to possible HAB and bacterial contamination events, which is used to iden tify dis utilit ies of these events and simulate the welfare impacts within the structure of the revealed - preference site choice model. The intercept survey was conducted randomly selected days between May 27 th and September 1 st , 2019. Interviews were condu cted at the 25 Lake Erie sites for the entire summer season, and interviews were conducted at the 3 Lake St. Clair/Detroit River sites between June 29 th and September 1 st . A map of our study area is pictured in Figure 2.1 , and a full list of the sites sam pled in our analysis can be found in Table 2.1 below. The sites were randomly sampled within strata for weekend or weekdays and morning or afternoon shifts. After arriving at a site, interviewers walked the length of the beach and counted the number of beachgoers both in the water and on the sandy portion of the beach. Boaters in the water were excluded from these 50 counts. After the counts, interviewers were instructed to approach every third person or group on the beach and ask if they would complete a short interview about their visit. 51 Figure 2.1 : Stu dy A rea and S ites U sed in A nalysis 52 Table 2.1 : Beach S ites S ampled during the 2019 I ntercept S urvey Lake or River County, State Site Lake St. Clair Macomb , MI Walter & Mary Burke Park Lake St. Clair Metropark Detroit River Wayne , MI Belle Isle Beach Lake Erie Monroe, MI Lucas, OH Sterling State Park Luna Pier Beach Maumee Bay State Park Erie Beach Maumee Bay State Park Inland Beach Ottawa, OH Camp Perry Beach Port Clinton City Beach East Harbor State Park Erie, OH Nickel Plate Beach Old Woman Creek Beach Sherod Park Beach Main Street Beach Showse Park Beach Lorain, OH Lakeview Park Beach Century Park Beach Cuyahoga, OH Huntington Beach Edgewater Park Beach Euclid State Park Sims Beach Lake, OH Ashtabula, OH Headlands Beach State Park Fairport Harbor Geneva State Park Walnut Beach Lakeshore Park Beach Conneaut Beach If an interviewer approached a group of beachgoers, he or she was instructed to ask to speak to the person 18 years or older with the most recent birthday, to ensure that respondent selection was random. Respondents were asked questions about their beach recreat ion behavior, including how many people traveled to the beach in the same vehicle with them. After asking would participat e in a follow - up survey. If they agreed, respo ndents were asked to provide an email address for the follow - up survey. 53 The 2019 intercept survey resulted in 4239 initial observations and an 86% response rate, and of these, 4159 usable intercept observations 13 were used to create a multi - site zonal dat aset, designed to model beach site choice s across the 2019 recreation season. Taking advantage of the rigorous sampling plan, each observed trip could be assigned an individual weight equal to the inverse probability of being selected for an intercept interview on a given day at a given site. Thes e weights were then aggregated to estimate seasonal visitation from zip code z to destination site j , for all observed zip - site combinations in the usable intercept data. These estimated trips serve as the dependent variables in our repeated random utility model of site choice, which treats each origin zip code as a representative agent. The creation of the weights and zonal dataset is described in further detail later in this essay. 13 Excluded interviews included 69 that refused to provide a zip code or provided foreign or nonexistent zip codes ; 4 zip codes only accessible by boat ; 4 zip codes for which the round - trip driving cost could otherwise not be obtained, and 3 zip codes over 2500 miles from the site where they were intercepted. 54 2.4 : Follow - Up Survey and Contingent Behavior Data An online follow - up survey was used to gather the contingent behavior data. The follow - up survey began by asking respondents questions about their perceptions of several beach characteristics at the site where they were intercepted. Respondents were then shown information co ncerning the causes of HAB and bacterial warnings, as well as the possible effects of each type of event on human health and the environment. After each information page, respondents were asked questions about their personal experiences with HAB and bacter ial warnings to encourage them to interact with the survey instrument. Respondents were then shown the contingent behavior questions. The survey development and questionnaire testing process followed recommendations for revealed and stated preference studi es (Lupi et al. 2020; Johnston et al . 2017) and included a focus group with 14 participants, 15 individual cognitive interviews conducted in March and April of 2020, and a 176 - respondent pilot survey conducted via Amazon MTurk in May 2020. In May and June 2020, respondents who provided email addresses during the intercept survey were invited to participate in the follow - up survey. Out of the 4159 intercept participants who provided usable trip data in 2019, 2538 provided an email address. After the initial invitation email, non - respondents were sent up to 5 reminder messages over the course of a month. After the first reminder email, non - respondents were offered a $20 completion incentive. Of the 2538 contacted via email, 1067 respondents 14 (46% of deliverable emails) completed the survey, and these 1 067 respondents answered an average of 8 contingent behavior questions. An item non - 14 251 email addresses were undeliverable; 3 respondents refused; 3 opened the survey but did not click past the first page, 1194 clicked through the consent form , and 127 partially completed the survey ( did not answer any stated preference question s ). 55 questions is available in Appendix E . The nine contingent behavior scenarios used in the follow - up survey are listed below in Table 2.2 . Table 2.2 : Contingent Behavior Scenarios Type of water quality e vent Contingent Behavior Scenario Harmful algal bloom A harmful algal bloom warning is in effect at the beach where you were interviewed. A harmful algal bloom warning was issued at the beach where you were interviewed 7 days before your trip, and was lifted 1 day before your trip. A harmful algal bloom warning was issued at the beach where you were interviewed 7 days before your trip, and was lifted 3 days before your trip. A harmful algal bloom warning was issued at the beach where you were interviewed 7 days before your trip, and was lifted 6 days before your trip. A harmful algal bloom warning was issued for the next beach along the shore on the day you were interviewed, but no warning was issued for the beach you visited. Bacterial contamination A bacterial warning is in effect at the beach where you were interviewed. A bacterial warning was issued at the beach where you were interviewed 7 days before your trip, and was lifted 1 day before your trip. A bacterial warning was issued at the beach where you were interviewed 7 days before your trip, and was lifted 3 days b efore your trip. A bacterial warning was issued at the beach where you were interviewed 7 days before your trip, and was lifted 6 days before your trip. For each contingent behavior question, respondents were asked if, given the scenario described, they still would have made the same beach trip they made on the day they were interviewed. Each question had three possible answers : respondents could either indicate they would have gone to the same beach, gone to a different beach, or stayed h ome. The contingent behavior questions were written to reflect the hypothesis that the average beachgoer is less likely to visit a beach if he or she knows a HAB or bacterial warning is in effect at that beach. As part 56 of our larger goal of identifying the welfare impacts of these water quality events, the questions about recently lifted warnings were used to examine whether these events have a lag effect on visitation. 57 2.5 : Zonal Dataset Our revealed preference site - choice model is specified as a repeated random utility model (Morey et al . 1993) to capture both site choices and seasonal participation. Traditionally, repeated RUMs estimated using individual - level data require detailed data on the number of trips taken by each person to each relevant site in order to model both the intensive and extensive margins of recreation behavior . O ur model treat s each origin zip code as a representative agent (English 2008) and use s site - selection and intercept probabilities derived from our original sampling design to estimate seasonal trips for each origin zip - destination site combination observed in the intercep t data. Using zip code population data, we can then estimate the number of no - trip choice occasions in each zip code across the 2019 recreational season. Developed for intercept data by von Haefen et al . (2 019 ), this approach allows us to use the survey de sign weights to estimate demand in a two - level nested logit framework which includes a non - participation alternative in each choice set . Each beach user who completed a full interview at an intercept site reported his or her home zip code, and so we were able to compile a list of the unique zip - site combinations observed in the intercept data. Using the intercept data, we derive the trip es timates from each origin zone to each intercept site using inverse selection probabilities (Leggett 2017 , Tourangeau et al . 2017 ). With the estimated number of trips from each origin zip code to each site for every unique zip - site combination, we form our zonal dataset . Let represent the sites in our dataset, with j= 0 representing the no - total number of possible destination sites in each choice set is J = 28 , and the total number of alte rnatives in each choice set is J+1 = 29. 58 To form the inverse selection probabilities, each sampled trip is assigned to one of ten mutually exclusive strata, based on the day of the week and month when the trip was intercepted, as well as on which intervie wer team (Michigan State or Ohio State) conducted the interview. The list of strata used in our trip estimation is available in Appendix K . The selection probabilities also use the trip counts conducted during each site visit. Since multiple interviewers w ere usually present at a site on any given day, daily beachgoer counts for each site were obtained by averaging the individual counts. Additionally, trip durations are derived from the ture times. Finally, because each interviewed beachgoer was asked if recreation was the primary purpose for their visit, we are able to construct , the probability that any given beachgoer in stratum h was engaging in recreation. These quantities are the main components used to construct our zonal trip estimates. F ollowing Leggett (2017) and Tourangeau et al . (2017) , we first create a weight for each beachgoer k intercepted on date i at site j in stratum h, as follows: (1) (2) Each individual weight is equal to the in verse of the probability that beachgoer k was sampled. is the average instantaneous count of beachgoers at site j on day i, and is the number of beachgoers interviewed at site j on day i . is the length of time, in minutes, during whic h instantaneous counts could have taken place on day i. is the total number of days in stratum 59 h 15 , and is the total number of days in stratum h that sampled site j . is the harmonic mean of the average trip duration across the sample, which is used instead of the arithmetic mean to account for the fact that visitors who stay at a site longer have a larger probability of being intercepted 16 . The harmonic mean (Equation 2) is calculated as the inverse of the mean of the inverse trip durations, and denotes the number of intercepted trips. Once is obtained for every intercepted beachgoer, we sum these weights over the beachgoers in a given stratum h to re cover an estimate of the total visitation in each stratum: (3) For each origin zip - destination site combination, are the trips taken to j from z for each zip - code representative agent in our zonal dataset. We use the stratum - specific visitation estimates to construct , and this process is explained in detail in Appendix K . Additionally, we define the total estimated trips to each site ( and from each origin zip code ( by summing over the Z total origin zips and J sites in the choice set: (4) (5) Following von Haefen et al . (201 9 ) and Tanner et al . (2019), we construct , the number of times in zip z the no - trip option was chosen during the season, using and the total population of z : (6) 15 The total number of days in each stratum varies, as the sample was stratified by month and weekend/weekday 16 For detailed discussions of the use of the harmonic mean to estimate trips in the context of recreation demand modeling , see Leggett (2017), Deacon and Kolst ad (2000), an d Tourangeau and Ruser (1999). 60 (7) where A is a scaling factor which ensures that the number of choice occasions for each zip code can never be less than the number of estimated visits and is always at least 10% larger . Peclat 2017) to compute the round - trip travel time (in minutes) and distance (in miles) between the centroid of each origin zi p code and each site in our sample. Using the 2019 AAA Your Driving Costs report (AAA 2019), we construct the travel cost for each zip - site combination in each individual choice set. The travel cost accounts for per - mile driving costs as well as the opport unity cost of time 17 , and is specified as follows: (8) where z indexes the origin zip and j indexes the destination site. Median annual income for each - year estimates (US Census Bureau 2019). Our per - mile driving cost of $0.27 is computed using a weighted average of costs across vehicle types from the AAA Your Driving Costs report for 15,000 miles driven each year. The driving cost is made up of maintenance costs as well as marginal depreciation costs (Lupi et al. 2020) . The hourly value of time for recreation travel is specified as one - third of zip z - hour work week and 50 weeks worked each year. The zonal dataset was constructed using the intercept interviews and is described in detail in Table 2.3 below. The dataset was made up of 41 59 indivi dual beachgoers from 999 origin zip codes. Within this data, we observed 1 896 unique origin zip - destination site combinations. At the individual level, 95 percent of respondents indicated that recreation was the primary purpose of 17 For a survey of the recreation demand literature concerning how to construct travel costs, as well as a discussion of the challenges inherent in measuring the value of travel time, see Lupi, Phaneuf, and von Haefen (2020). 61 their visit. Respondents spent a harmonic average of 104 minutes at sites. The 999 origin zip codes had an average median income of $ 61,938 , and an average median age of about 41 years old . The average origin zip code was predominantly white (82%) and was 5 % Hispanic. At the trip - site level, the average estimated number of trips from origin zip z to destination site j ( ) was 7 77 . Estimated total tri ps from zip code z ( ) range from 28 to 38,465 with an average of 1 475 and estimated total trips to any site j ( ) range from 1717 to 262,944 , with an average of 52,638 trips . 62 T able 2.3: Zonal Dataset Descriptive Statistics Arithmeti c Mean Harmonic Mean Median Min Max N Individual Variables Recreation primary purpose of beach visit? (0/1) 0.95 1 0 1 4159 Time spent at site (minutes) 175.9 104.4 165 5 870 4159 Trip Variables Visits from origin zip z to destination site j ( ) 777 356 28 31,301 1896 Visits from origin zip z ( ) 1475 495 28 38,465 999 Visits to destination site j ( ) 52,638 35,478 1757 262,94 4 28 Origin Zip Demographics Median household income ($) 61,938 58,495 11,049 201,23 2 999 College degree (%) 29.5 25 3 85 999 Median age (years) 40.8 41 19 66 999 Hispanic (%) 5.1 3 0 69 999 White (%) 82.3 90 2 100 999 Unemployment rate (%) 5.9 5 0 30 999 Trip Statistics Round trip distance to any site (miles) 571 33 6.2 1.2 5126.4 27,972 Round trip distance to visited site (miles) 308.5 115.5 1.2 4975.9 1896 Round trip travel cost to any site ($) 259.9 148. 6 1.2 3313 27,972 Round trip travel cost to visited site ($) 143 52.7 1.2 3212.4 1896 63 2.6 : Site Choice Model and Calibration to Stated Preference Data Our site choice model is rooted in random utility maximization theory and uses revealed preference data to model the recreation decision process in a two - level nested logit framework. In each choice occasio n, individuals decide whether to make a trip and conditional on a trip, they decide which of the 28 sites ( j of RUM theory, we assume that an agent chooses alternative j if it yields the most utility out of all the available alternatives in the choice set. Figure 2.2 below illustrates the nests w ithin our model , where the site nest alternatives may have errors that are more correlated with one another - . Figure 2.2: Nesting Structure for Repeated Nested Logit Model of Great Lakes Beaches The conditional indirect utility an individual from zip code z receives from choosing the no - trip option ( j = 0) is composed of an observable representative utility component and a random error term, unobservable to the researcher. Representative utility for t he no - trip option is specified as a function of zip - level demographic variables obtained from the 2018 American Community Survey five - year estimates : 64 (9) The conditional indirect utility an individual from zip code z receives from choosing to visit site j utility term is specified as a function of the travel cost from zip code z to site j (10) Here, is an alternative - specific constant ( ASC ), a site - level fixed effect that captures the influence of site - specific characteristics omitted from the utility function. Because random utility models are defined in terms of utility differences, of the J+1 alternatives in the repeated RUM, only J =28 constants are identified for esti mation ( one for each site in the choice set ) . The probability that a person from zip z chooses site j can be expressed as the product of , the probability that a person from z takes a trip, and , the conditional probability o f choosing site j : (11) Because w e model the site - choice process in a nested - logit framework, we assume the random error terms follow a generalized extreme value (GEV) distribution, and write the components of as follows: 65 (12) Train (2009) shows how these probabilities are obtained by decomposing the structural term derived from the multivariate GEV distribution. The dissimilarity coefficient reflects the degree to which the random error terms in each site utility are correlated, with a lower value of indicating more correlation. The term , which appears in the numerator of , is often called the log - sum or inclusive value term. The inclusive value represents the expected ut ility that a representative agent reaps from the ability to choose between the site alternatives in the trip nest and is a central quantity in our empirical welfare estimat ion later in this essay . As the inclusive value increases, the probability that an agent chooses to make a trip increases as well, an intuitive result that connects the upper and lower nests of the choice structure. In our empirical estimation, we first examine the welfare effects of site closure. To do so, we use the concept of compensating variation (CV) . Following a change in the price or quality of a good, the compensating variation is the amount of money that leave s an economic agent as well off, in terms of utility, as they were before the change. Specifically, consider a set of recreation sites which are substitutes, and with level of environmental quality Now suppose a policy change or natural event shif ts the quality level and number of viable sites from ( ) to ( ). Defining as a vector of demographic variables for representative agent z, the compensating variation per choice occasion for agent z can be implicitly defined as follows: (13) Specifying the linear functional form of our site - choice model and rearranging, we can isolate the CV term. Because our model accounts for site - specific environmental quality variation using 66 alternative - specific constants, we represent the change to by adding a term to the relevant c onstant: (14) (15) To aggregate this welfare measure to a full recreation season, we multiply per - choice occasion CV by each choice occasions , 18 and sum over all agents Z : (16) For the analyst, the best sites and the error terms are unknown, so expectations are taken. Given our model is a nested logit, the expected compensating variation for site closures or quality changes can be written as a function of the monetized difference between two inclusi ve value terms , which represent the maximum expected utilities that can be achieved under baseline and post - change conditions. For our purposes, let denote an adjustment to site j which represents a quality change , or in the case of a closure , a large r change that drives predicted trips to j to zero. Here, [ ] is an indicator function which equals if site j is affected, and zero otherwise: (17) 18 For events which vary over the season, we can sum the measure over the relevant choice occasions rather than simply multiplying by choice occasions. 67 The average seasonal welfare effect of a given scenario s at site(s) j is evaluated using E quation (1 7 ) above (English et al . 2018) . Because harmful algal bloom and bacterial warnings do not usually result i n beach closings, we are interested in the welfare effects of these events when sites stay open. To estimate the welfare effect of beach closures contingent behavior questions in the online follow - up survey. Respondents were asked whether, given each of the algae/bacterial scenarios in Table 2.2 , they would have gone to another site on the day they we re interviewed. quality attributes that affect site utility, we adjust different warning scenarios. Following Tanner et al . (2019) and English et a l. (2018) , we adjust the alternative - specific constant for each site j and each scenario s : (18) For each site in the choice set, we can obtain , the percentage of follow - up respondents who indicated they would have gone to the same site under scenario s . The above adjustments to the alternative specific constants are ma de to replicate the pattern of demand predicted by the contingent behavior res ponses; in other words, the adjustments solve for the value of that satisfies the following equation: (19) For each site - scenario combination, we recalibrate the initial ASCs and solve for using an iterative contraction mapping algorithm. This method has been most notably used to calibrate automobile market share data for demand forecasting (Berry, Levins ohn, and Pakes 1995) 19 , and has been applied to recreation demand by Murdock (2006) , English et al. (2018) and Tanner et 19 For a discussion of this technique as applied to empirical industrial organization, see pp. 32 - 33 of T rain (2009). 68 al . (2019) 20 . The contraction mapping estimates values of , which are then used to repeatedly compute guesses of u ntil it is as close as possible to . The algorithm begins by guessing , adjusting the ASC, and estimating . Then for each successive iteration k , the algorithm calculates as follows: (20) Once the constants have been recalibrated, we can use them to estimate the welfare effects of the 9 different water quality scenarios . For each scenari o s we compute the weighted average of the ASC adjustment term s across the J = 28 sites . Figure 2.3 below illustrates the contraction mapping graphically in price - quantity space, and it shows how the algorithm iteratively guesses values of until is reached. The movement from to reflects the downward shift in recreation demand induced by warning scenario s at site j . In the illustration, , the algori demand, overstates the target, and once again understates the target but less dramatically than . This pattern continues until is reached . is the disutility adjustment that moves the original ASC to the calibrated term, . 20 Anciaes, Metcalfe, and Sen (2020) also use the same contraction mapping algorithm to calibrate choice experiment responses to an RP model to estimate the preferences of UK anglers for site attributes. 69 Figure 2.3 : Contraction M apping A lgorithm Naturally, high - use beach sites will likely incur higher recreational welfare losses from HAB and bacterial scenarios, relative to less popular sites. To standardize our welfare estimates and compare the impacts of different water quality scenarios at both high - use and low - use sites, we divide the CV term in E quation (1 7 ) b y the predicted change in trips under scenario s to recover an estimate of the value per lost trip associated with s : where is equal to the specified number of choice occasions for zip code z . 70 2.7 : Results Table 2.4 lists the percentage breakdown of responses to the contingent behavior questions, along with the standard errors of these percentages. Roughly 81 percent of respondents indicated that they would have not taken the same trip if a HAB or bacterial warning wa s in effect at the site where they were intercepted. 46 percent of respondents would not have gone to any site if a bacterial warning was in effect at the site they visited, and similarly 42 percent would not have gone to any site if a HAB warning was in e ffect at the site they visited. For both types of water quality event s , the percentage of respondents who indicate d that they would have made the same trip gradually increased grew . However, roughly 24 % of respondents still would not have made the same trip if a bacterial warning had been lifted 6 days before their trip, and roughly 20 % would not have made the same trip in a similar HAB warning scenario. Table 2.4 : Average Contingent Behavior Response Percentages and Standard Errors CB Scenario I would have gone to the same beach. % I would have gone to another beach. % I would not have gone to any beach. % Bac. warning - day of trip 18.97 34.81 46.23 (1.32) (1.62) (1.69) - Lifted 1 day before trip 34.55 31.95 33.51 (1.62) (1.58) (1.60) - Lifted 3 days before trip 52.62 25.79 21.59 (1.69) (1.48) (1.39) - Lifted 6 days before trip 76.22 11.42 12.36 (1.44) (1.08) (1.10) HAB warning - day of trip 19.23 38.12 42.65 (1.33) (1.65) (1.68) - Lifted 1 day before trip 39.03 30.02 30.95 (1.66) (1.56) (1.56) - Lifted 3 days before trip 62.24 22.10 15.66 (1.64) (1.40) (1.23) - Lifted 6 days before trip 80.10 11.03 8.87 (1.34) (1.06) (0.95) HAB warning - next beach along the shore 56.29 (1.68) 15.18 (1.22) 28.52 (1.53) 71 At all warning attribute levels, fewer respondents would have made the same trip in a bacterial scenario compared to a HAB warning scenario. For each level of lifted warnings (1, 3, and 6 day - lifted warnings) we reject the null hypothesis of equality between the percentages of respondents who would make the same trip given a HAB or bacterial warning. However, the percentages of respondents who would have made the same trip if either a HAB or bacterial warning were currently in effect are not statistically different from one another. Consistent with findings from the first paper in this thesis , these results indicate that respondents in the samp le are similarly averse to current HAB and bacterial events, but this aversion seems to linger more intensely and for a more sustained period after a bacterial event. The results of our nested logit site - choice model are shown in Table 2.5 . The choice of whether to take a trip (the participation nest) is modeled as a function of zip code - level demographics obtained from the American Community Survey 2018 five - year estimates. Our parameter estimates imply that, all else equal, potential beachgoers from zip codes with a higher median age are more likely to make a trip, as are potential beachgoers from zip codes with a higher percentage of college graduates. Beachgoers from zip codes with a higher share of white and H ispanic residents, as well as higher unempl oyment rates, are also more likely to make a trip . The estimated parameter on median income is positive and implies that potential beachgoers from zip codes with higher incomes have a lower probability of making a trip to these beaches, all else equal. 72 Table 2.5: Revealed Preference Recreation Demand Model Estimates Nest Variable Coefficient Std. Error 21 95% Confidence Interval Trip Travel cost - 0.0072*** 3.62E - 05 ( - 0.0073, - 0.0072) Dissimilarity coefficient 0.111*** 5.16E - 04 (0.109, 0.111) No Trip Median income (/10k) 0.078*** 8.58E - 04 (0.077, 0.080) Median age - 0.056*** 2.7E - 04 ( - 0.059, - 0.058) % college graduate - 0.0054*** 9.43E - 05 ( - 0.0056, - 0.0052) % unemployed - 0.031*** 4.45E - 04 ( - 0.032, - 0.030) % white - 0.0098*** 7.15E - 05 ( - 0.0098, - 0.0095) % Hispanic - 0.027*** 9.51E - 05 ( - 0.027, - 0.026) (***) denotes significance at the 1% level. Estimated s ite constants are reported in Table 2.6 . In the trip nest, we estimate a negative and significant coefficient on the round - trip travel cost, indicating that a higher travel cost lowers the probability of choosing a site, all else equal. We also estimate a full set of = 28 alternative specific constants, which are listed in Table 2.6 . As discussed earlier, the dissimilarity coefficient reflects the degree of correlation between the alternatives in the trip nest. We estimate a value of that is between 0 and 1 and significantly different fro m 1, indicating significant correlation between the random error terms in the trip nest site utilities. This result confirms that a nested logit model is better suited to explain the observed variation in site utilities than the standard conditional logit model , and it implies that when prices or site qualities change, the sites are closer substitutes for one another than the no - trip option. We use the results of our site - choice model to examine the welfare effects of site closures. The disutility of closing a site j is equal to the expected maximum utility of the choice 21 The reported standard errors and confi dence intervals were obtained via bootstrap estimation on 127 replicate datasets. However, these estimates do not yet take into account the underlying variation in our trip estimates, and future efforts will account for this variation. 73 between the original set of J sites, less the expected maximum utility of the choice between the J - 1 sites other than s ite j . As explained earlier, the measure is given by Equation (21) and produces the monetized value of lost surplus due to the closure of j . For each site, we estimate the lost surplus value of site closures across a single recreation season, and the loss in trips that these closures would induce (Table 2.6). We also report each Total seasonal welfare loss from the closure of a single beach range s from $ 24 , 000 to $3, 915 , 000 across each of the sites , with a trip - weighted average loss of $ 1,779 , 000 . Value per lost trip across one season averages $ 16.34 value per lost trip at $19. 48 . Using a welfare computa tion for multiple site closures based on Equation (17) , we calculate that the closure of all 28 beaches in our sample would induce roughly $ 208 million in welfare losses per year. While a closure of this magnitude is extremely unlikely to occur, and so policy analysis using this value would be unwise, this estimate illustrates the total recreational value of the public beaches in our sample area. To illustrate how beach goers make tradeoffs between environmental quality and the price of site access in the presence or absence of substitute sites, consider the estimated site ASCs from our site choice model ( Table 2.6 ) . A comparatively small ASC ind icates a lower level of level of environmental attributes at other sites. To more readily compare ASCs across sites, the last column of Table 2.6 normalizes each constant relative to the lowest estimated ASC. The lowest ASC of any beach in the sample belongs to Showse Park Beach, a site in Vermillion, Ohio with a relatively small sandy area. This low ASC makes sense given Sh 74 and proximity to larger, more sandy public beaches such as Main Street and Lakeview Park. Showse Park also has the smallest value per lost trip in the sample ($15.28). 75 Table 2.6 : Site Closure Welfare Estimates Site Welfare loss from seasonal site closure Lost trips due to site closure Value per lost trip ASC/site fixed effect Normalized ASC Walter & Mary Burke Park $659,000 38,000 $17.27 - 6.268 0.163 Lake St. Clair Metropark $1,118,000 64,000 $17.41 - 6.228 0.203 Belle Isle Beach $3,014,000 155,000 $19.48 - 6.126 0.305 Sterling State Park $2,221,000 122,000 $18.21 - 6.106 0.325 Luna Pier Beach $389,000 25,000 $15.70 - 6.274 0.157 Maumee - Erie Beach $775,000 47,000 $16.44 - 6.144 0.287 Maumee Inland Beach $250,000 16,000 $15.62 - 6.264 0.167 Camp Perry Beach $229,000 15,000 $15.53 - 6.194 0.237 Port Clinton City Beach $284,000 18,000 $15.58 - 6.175 0.256 East Harbor State Park $1,756,000 101,000 $17.42 - 5.935 0.496 Nickel Plate Beach $767,000 48,000 $16.10 - 6.06 0.371 Old Woman Creek Beach $93,000 6,000 $15.35 - 6.3 0.131 Sherod Park Beach $59,000 4,000 $15.31 - 6.337 0.094 Main Street Beach $463,000 29,000 $15.69 - 6.118 0.313 Showse Park Beach $24,000 2,000 $15.28 - 6.431 0 Lakeview Park Beach $650,000 41,000 $15.84 - 6.075 0.356 Century Park Beach $96,000 6,000 $15.34 - 6.286 0.145 $84,000 5,000 $15.33 - 6.3 0.131 Huntington Beach $1,137,000 70,000 $16.22 - 6.039 0.392 Edgewater Park Beach $3,915,000 215,000 $18.22 - 5.937 0.494 Euclid State Park $287,000 19,000 $15.46 - 6.176 0.255 Sims Park Beach $117,000 8,000 $15.34 - 6.269 0.162 Headlands Beach St . Park $1,410,000 86,000 $16.49 - 5.952 0.479 Fairport Harbor Park Beach $1,398,000 86,000 $16.27 - 5.951 0.48 Geneva State Park $1,154,000 71,000 $16.26 - 5.926 0.505 Walnut Beach $1,397,000 83,000 $16.92 - 5.945 0.486 Lakeshore Park Beach $311,000 20,000 $15.61 - 6.114 0.317 Conneaut Beach $1,343,000 76,000 $17.74 - 5.939 0.492 Min $24,000 2,000 $ 15.28 Max $3,915,000 215,000 $19. 48 Mean ( trip - weighted ) $1,779,000 53,000 $1 6 .34 76 ($19.48), its ASC is only the 14 th largest among the 28 sampled beaches. These results indicate that while Belle Isle does not have the most desirable beach attributes to the average beach user, its closure would have the largest welfare effects. This result is likely attributable to the f act that Belle Isle is the only public beach in the city of Detroit, and accordingly has much higher baseline visitation than any other site in our sample due to the surrounding population density 22 . Park, are 24 and 48 miles away, and the absence of close substitutes likely also contributes to Park exhibit a similar pattern, as both have high values per lost trip and low ASCs relative to the other sites in our sample. While there are only 5 public beaches on the roughly 100 miles of shoreline which extend - mile Erie coast has 23 public beaches. This denser spatial ordering of Ohio sites is reflected in the welfare estimates above. Edgewater Park Beach, East Harbor State Park Beach, and Conneaut Beach have the highest values per lost trip of all sites in Ohio, however the highest value among these three ($18.22 at Edgewater Park Beach) is st ill over a dollar less per lost trip than Belle Isle. All three sites have higher ASCs than Belle Isle, and so the most likely explanation for the relatively lower values of Ohio sites despite higher levels of unobserved environmental amenities is the dens e clustering of substitute sites nearby. Edgewater Park can be most readily compared to Belle Isle given its location in downtown Cleveland, and its $18.22 value per lost trip estimate is likely influenced by the large number of Cleveland residents who use the site (Edgewater Park has the highest number of estimated lost trips in our sample). 22 Indeed, Belle Isle is estimated to lose the second highest number trips across all sites, over 1 55 ,000 , in the event of a seasonal closure. 77 The above welfare estimates offer important information about the value of Lake Erie and Lake St. Clair beaches. However, because HAB and bacterial events do not usu ally result in the closing of sites, 23 these estimates do not best reflect the welfare impacts of HABs and bacterial contamination in the region. To estimate these impacts, we use the disutilities identified by the contraction mapping procedure described e arlier. B efore doing so, we correct the initially estimated constants to account for the HAB and bacterial events which were observed during the 2019 recreation season. If the contraction mapping was computed using the estimated constants without correcti on , this procedure would implicitly assume that the initial site - choice model was estimated using data from sites unaffected by HAB or bacterial warnings during the 2019 recreational season. However, this is not the case, as 21 of the 28 sites used in our analysis experienced at least one type of warning from May 27 th to September 1 st . 24 Given the purpose of this study and the regularity of HAB and bacterial warnings in the area, this complication is not unexpected. However, since this discrepancy can potentially influence the absolute magnitude of total welfare loss and lost trips, the A SCs are adjusted water quality before using the contraction mapping to identify the true disutility parameters associated with different HAB and bacterial scenarios. For each site j in our analysis, we estimated an alternative - specific constant which captured the effect of unobserved environmental quality attributes on site - specific utility. In the 23 Across the 28 sampled sites, 115 HAB and bacterial events were reported on the Michigan and Ohio BeachGuard websites from May to August 2019. Of the 115 events reported , only 3 were closings and 112 were warnings. 24 115 total warnings were observed at the se 21 sites during the season, according to Michigan BeachGuard and Ohio BeachGuard. 110 of these were bacterial warnings, and 5 were HAB warnings. Here, we only consider warnings directly attributed to observed bacterial contamination or algal blooms in t he BeachGuard system. Warnings informed by predictive modeling are excluded from our analysis. 78 case of the 21 sites where HAB and bacterial warnings were observed during the 2019 season 25 , do not represe nt the counterfactual, unimpaired levels of environmental quality at each site in the absence of HABs and bacterial warnings. Let denote the unknown ASC for site j which captures this level of unobserved environmental quality in the absence of warnin gs. For the 7 sites where no warnings were issued in 2019, . For all 28 sites, we also obtain , the contraction mapping adjustment to which calibrates the site choice model to the pattern of demand observed in the CB responses for scenario s . Suppose that site j only suffers from one type of warning during the season, the fraction of days in the season affected by a warning s is given by , and assume for the moment that beachgoers do not derive any disutility from a site with a recently - lifted warning. Further, let by the quanti ty , and simulates the effects of a season - long warning. In this case, the can be written as: (22) All terms on the right side of this final equation are known 26 , except for , the calibration adjustment to the baseline unimpaired ASC of site j , . However, noting that for the 7 is precisely equal to the known adjustment p roduced by the contraction mapping, . Let the average of 25 Defined as May 27 th through September 1 st , the length of the summer 2019 intercept survey. 26 is obtained from the BeachGuard websites. 79 these calibration adjustments across the 7 unimpaired sites be denoted . Then, for any site j which experienced a warning during the season, can be used to estimate the baseline AS C , as follows: (23) This process is similarly expanded to account for the disamenity effects of recently lifted HAB and bacterial warnings. The adjusted baseline ASCs can then be fed back into the contraction mapping algorithm and welfare formulas to recover correctly scaled estimates of total welfare loss and lost trips for each HAB and bacterial scenario . For each contingent behav ior scenario s , we obtain , the proportion of respondents who indicated that they would have gone to the same site if the given scenario were in effect. For , a constant which replicates the pattern of demand predicted by the contingent behavior responses within the structural demand system. These individual ASC adjustments are listed in Table M.1 of Appendix M . For each scenario, we compute the average of across the J = 28 sites, weighted by predicted trips to each site, to obtain . The outcome of the site adjustments from the contraction map allows us to produce estimates of seasonal welfare losses and lost trips for each site - scenario combination. Table 2.7 repor ts average welfare estimates for each HAB or bacterial scenario, weighted by predicted trips to each site, as well as the bootstrapped confidence intervals for these welfare estimates. 80 Table 2.7 : Average ASC A djustment and T rip - W eighted A verage W elfare L oss , A cross A ll S ites, f or E ach W ater Q uality S cenario Water Quality Scenario Seasonal welfare loss Lost trips Value per lost trip Bacterial warning - day of trip - 0.2 06 ( - 0.22, - 0.19 2 ) $1,4 48 , 823 ($1,36 1 , 575 , $1,5 51 ,25 3 ) 82, 170 (7 7,167 , 88,113 ) $17. 27 ($17. 19 , $17. 33 ) - Lifted 1 day before trip - 0.1 3 2 ( - 0.14 2 , - 0.12 3 ) $1, 172 , 656 ($1,09 7 , 839 , $1,2 56 , 520 ) 65, 286 ( 61,014 , 70,044 ) $17. 57 ($17. 50 , $17. 64 ) - Lifted 3 days before trip - 0.0 81 ( - 0.09, - 0.07 5 ) $ 853,871 ($78 0 , 057 , $ 932,242 ) 4 6,596 (4 2,388 , 50,942 ) $1 7.90 ($1 7.81 , $1 7.96 ) - Lifted 6 days before trip - 0.03 5 ( - 0.04, - 0.031) $4 34 , 521 ($37 3,109 , $4 90 , 907 ) 23,137 (19, 824 , 2 6,200 ) $18. 32 ($18. 24 , $18. 39 ) HAB warning - day of trip - 0.2 03 ( - 0.2 19 , - 0.18 6 ) $1,4 4 1, 475 ($1,34 6 , 812 , $1,5 21 , 045 ) 81, 712 (7 6,248 , 84, 451 ) $17. 28 ($17. 21 , $17. 34 ) - Lifted 1 day before trip - 0.1 18 ( - 0. 129 , - 0.1 09 ) $1, 096 , 386 ($1,0 22 , 130 , $1,1 90 , 257 ) 6 0,742 ( 56,256 , 6 6,285 ) $1 7.65 ($17. 56 , $ 17.75 ) - Lifted 3 days before trip - 0.06 ( - 0.06 7 , - 0.05 3 ) $68 1 , 624 ($61 6 , 538 , $7 56,165 ) 3 6,815 (3 3,165 , 40,926 ) $18. 07 ($1 7.98 , $18. 17 ) - Lifted 6 days before trip - 0.0 29 ( - 0.03 3 , - 0.02 4 ) $3 63 , 875 ($3 10,308 , $4 21,638 ) 19,2 99 ( 16,432 , 2 2,426 ) $18. 38 ($18. 31 , $18. 46 ) 81 These estimates represent the average welfare losses which would occur if each scenario were in effect for an entire summer recreational season. On average, a HAB or bacterial warning which affects the average site for an entire season is estimated to result in losses of about $17. 30 per lost trip , and roughly $1.4 million in seasonal welfare losses. Our estimates of seasonal welfare loss and lost trips behave as expected current HAB and bacterial warnings resul t in higher welfare losses and more lost trips than day - old warnings, and so on. However, as the time since either type of warning grows, total estimated welfare losses decrease at a faster rate than lost trips, which causes our value per lost trip estimat es to increase. The gap between value per lost trip for a current warning and a 6 - day expired warning is relatively small in both cases (just over $1). While our welfare estimates for season - long HAB and bacterial warnings are easy to - long 1 - practic e . In the next section , we develop a more easily interpretable method for using these estimates to simulate the temporal welfare impacts of observed warnings in 2019 . 82 2.8 : Simulation of 2019 Season In addition to estimating the welfare losses associated with a full season of HAB and bacterial warnings , our results can be used to move from modeling the abstract notion of season - long warnings to simulating the effects of actual observed events. The Michigan and Ohio BeachGuard websites provide the number of warnings in effect at each site during the 2019 seas on, as well as the dates and durations of each warning. Once total seasonal welfare loss estimates are obtained for each HAB or bacterial scenario at each site, these estimates can be prorated across a season to match the number of days with an observed wa rning (or days within 1, 3, or 6 days after a warning) at each site. Appendix L summarizes the bacterial and HAB warnings observed during the 2019 season. Dividing each seasonal welfare loss estimate by the number of days in the season produces a rough e stimate of the per - day welfare loss of each scenario. By multiplying each of these estimates by the number of days in which the respective warning scenario is in effect and summing these products, we recover an estimate of the total recreational welfare lo ss caused by the observed HAB and bacterial warnings during the 2019 season. W e treat days which fall 2 - - 27 By executing this process on 127 bootstrapped datasets, losses. The results of this estimation process are shown below in Table 2.8 . 27 This welfare loss is calculated assuming that the welfare effects of a 2 - day lifted warning are the same as a 1 - day lifted warning, and likewise the effects of a 4 - 5 day lifted warning are the same as a 3 - day lifted warning, but it assumes no effect after 6 days. An alterna tive approach that maintained the assumption of no losses after 6 days, losses for 2 - day lifted warnings = 3 - day lifted warnings and 4 - 5 day lifted warnings = 6 - day lifted warnings found welfare losses totaling 93% of the above approach. A linear interpola tion of the values from these two approaches totaled 96% of the above approach. 83 Table 2.8 : Simulation of W elfare L osses A ttributable to B acterial and HAB W arnings during the 2019 R ecreation S eason Simulated Scenario Welfare loss attributable to observed warnings in 2019 All bacterial and HAB warnings, including welfare losses from up to six days following a warning $ 5,802,336 ($ 5,461,049 , $ 6,184,385 ) All bacterial and HAB warnings, only accounting for day - of welfare losses $ 3,848,011 ($ 3,619,996 , $ 4,111,074 ) % Understatement of not accounting for lagged welfare effects 33.68 ( 32.91 , 34.67 ) All HAB warnings , but no bacterial warnings , including welfare losses from up to six days following a warning $ 854,585 ($ 787,797 , $ 928,934 ) All HAB warnings , but no bacterial warnings , only accounting for day - of welfare losses $ 750,408 ($ 689,515 , $ 818,426 ) All b acterial warnings , but no HAB warnings , including welfare losses from up to six days following a warning $ 4,947,751 ($ 4,636,671 , $ 5,283,923 ) All bacterial warnings , but no HAB warnings , only accounting for day - of welfare losses $ 3,097,603 ($ 2,894,187 , $ 3,305,886 ) Note: 95% confidence intervals are in parentheses. We find a mean total seasonal welfare loss of about $ 5 . 8 million during the 2019 recreational season which can be attributed to HAB and bacterial warnings 28 . This information can be used by policy makers to begin to quantify the effects of E. c oli and HAB warnings on public beach recreation. This amounts to roughly 2.8 % of the total annual value of recreation at these beaches. Eliminating warnings would provide benefits to beachgoers as well as the nearby businesses that benefit from their patronage due to the additional trips that would be taken. 28 See footnote 27 for robustness of this method. 84 We have also establi shed that the recreational welfare effects of bacterial and HAB warnings do not immediately dissipate over time . There are two important implications of this finding . First, any warning, even if only a day, has long er - term consequences for recreation . Th is finding heightens the need to develop policies that work to eliminate warnings themselves, not just the length of warnings. Second, and consequentially for welfare measurement, the failure to s the r esulting welfare estimates. To illustrate the effect of days on which a warning was in effect and find a mean total welfare loss of about $ 3 . 8 million . This estim ate is roughly 3 4 % lower than our initial estimate that which explicitly illustrat es the importance of accounting for the full costs of HAB and bacterial warnings in policymaking and cost - benefit analysis. Additionally, accounting for the disamenity effects of recently lifted warnings, we find that bacterial warnings are responsible for 8 5 % of total 2019 welfare losses ( roughly $ 4 . 9 5 million ), while HAB warnings are responsible for 15 % of seasonal welfare losses ( roughly $855 , 000 ). These estimates indicate that while HAB events often command significant media attention and possess a visual aspect that bacterial contamination events do not, bacterial contamination currently represents a much larger proportional threat to beach recreation i n the region. While this information is useful from a policy standpoint, it is also worthwhile to note that the magnitude of welfare losses attributable to bacterial contamination is driven by the large number of bacterial warning days in the 2019 seas on, relative to HAB warning days. Rather than relying solely on absolute welfare loss estimates, we obtain standardized measures of the disamenity value of HAB and bacterial warnings to more reliably compare how beachgoers value the presence of these warni ngs. The mean day - of welfare loss attributable to warnings in 85 the 2019 season is about $3 million for bacterial contamination and $ 750, 000 for HABs; likewise , 475 days of the season were directly affected by a bacterial warning in 2019, and 73 were directly affected by a HAB warning. The quotient of these values produces a standardized - of $ 6,5 00 per day for bacterial warning event s and $ 10, 30 0 per day for HABs events . Despite the larger share of total losses attributable to bacterial warnings, these standardized values indicate that beachgoers reap much larger disutility from the site s where HAB warning s were effect, as opposed to th e one s with a bacterial warning in effect. 86 2.9 : C onclusion In this paper, we have shown that the welfare costs of water - borne health hazard warnings are high and persist for at least six days after warnings are lifted. Our research contributes to the relatively small number of studies that estimate the economic value of Great Lakes recreation and is one of the few studies to use contingent behavior data embedded within a revealed prefe rence model to value environmental quality at freshwater beaches. This work also contributes to the limited number of studies estimating welfare impacts of freshwater HABs and bacterial contamination, events projected to worsen in frequency and intensity u nder global climate change. While prior studies have used beach closings as a proxy for season - long HABs, we estimate the welfare effects of HAB events when beaches stay open, which more accurately reflects observed beach management . We utilized a combine d stated preference and revealed preference approach to estimate the welfare impacts of water quality warnings that are common in the western Lake Erie Basin. Revealed preference data on observed trips to 28 public beaches was collected using an intercept s urvey during the summer of 2019. Each randomly selected respondent was recruited for an online stated preference survey that included contingent behavior questions asking about stated travel behavior in the face of possible harmful algal bloom (HAB) and ba cterial warnings. The RP data was used to create a zonal dataset that treated each observed origin zip code as a representative agent , and inverse probability weights were created to estimate trips from each origin zip code to each destination site. We est imated a repeated random utility zonal site choice model on this dataset and were able to isolate the welfare effects of seasonal site closures, finding an average loss of $16.34 per lost trip across all sites. The model also produced a full set of alterna tive - specific constants, which capture the influence of unobserved environmental 87 quality attributes. After estimating the site - choice model, we identified the disutilities of HAB and bacterial warnings using a contraction mapping algorithm that calibrated the ASCs until the predicted pattern of demand matched the pattern implied by the stated preference responses to our follow - up survey. This calibrated model was used to examine the welfare impacts of season - long HAB and bacterial warnings, finding that th ese scenarios would each result in welfare losses of $1.4 million at the average site in our sample. We also used our seasonal welfare estimates to show that the observed HAB and bacterial events in the western Lake Erie Basin caused over $ 5.8 million in losses during the 2019 season, and we demonstrated that not accounting for the disamenity effects of recently lifted warnings would underestimate these damages by roughly 3 4 percent. Additionally, we find that 85 % of the estimated 2019 welfare losses ( 4,9 00 ,000 ) are attributable to bacterial events, while the 2019 HABs are responsible for 15 % of seasonal welfare losses ($855,000 ). However, when these estimates are standardi zed by dividing by the number of days on which each type of warning was in effect, we find that beachgoers reap more than three times as much daily disutility from the sites that had a HAB warning in effect, compared to sites that had a bacterial warning. These results can aid state agencies and policy makers in understanding the full costs of current freshwater HAB and bacterial events, especially as both are projected to increase as a direct result of climate change. Our results are descriptive of the 2019 recreation season that was marked by high water levels which may have affected overall visitation and that was a relatively mild HAB season relative to years like 2011 and 2014. Accordingly, our results serve as a rough lower bound estimate of the ye arly recreational welfare impacts to beachgoers of HAB and bacterial warnings. Without serious investment in runoff control technology or policy change, the welfare impacts of these events will likely continue to grow. In planning for the future, 88 government agencies need improved u nderstand ing of the discounted future benefits resulting result from the up - front costs of environmental protection. Accordingly, future interdisciplinary research can build on our work by examin ing how the economic costs of point and non - point source water pollution will likely behave over time, and this dynamic consideration may also apply to other pollution costs such as non - use values. These dynamic cost estimates can then serve as empirical b enchmarks for governments to use when making water quality policy in the face of a warming world . 89 APPENDICES 90 A PPENDIX A : Intercept Survey Instrument The survey below was read to Michigan beachgoers who agreed to participate in a survey about their beach visit, and who indicated they were over 18 years of age. This version of the survey was administered to beachgoers at two public Lake St. Clair beaches , Lake St. Clair Metropark and Walter & Mary Burke Park Beach , as well as Belle Isle Beach in Detroit. The version of the intercept survey administered to beachgoers at the other 2 6 beaches in our sample was essentially identical to this version. To ensure that potential respondent selection was unbiased, interviewers approached every third beach goer and asked if they would be willing to participate in the survey. app, and then responses were recorded by the interviewer. 91 Figure A.1 : Lake St. Clair and Belle Isle Intercept Survey 92 Figure A.1 : 93 Figure A.1 : 94 Figure A.1 : 95 Figure A.1 : 96 Figure A.1 : 97 Figure A.1 : 98 Figure A.1 : 99 Figure A.1 : 100 A PPENDIX B : Online Follow - Up Survey The following survey was sent to Ohio and Michigan beachgoers who provided their emails during the intercept survey and indicated they would be willing to participa te in the follow - up. Each follow - up instrument was specifically written to show the individual site where the respondent was interviewed; in this example the site has been specified as Belle Isle Beach. Similarly, the intercept year in this example has bee n specified as 2019. In the follow - up instrument, each respondent was shown 5 choice situations as part of the discrete choice experiment. For the sake of brevity, only one choice occasion is presented here. Individuals intercepted by the Ohio teams were s end a version branded by Ohio State University. 101 Figure B.1 : Online Follow - Up Survey 102 Figure B.1 : (cont.d) 103 Figure B.1 : (cont.d) 104 Figure B.1 : (cont.d) 105 Figure B.1 : (cont.d) 106 Figure B.1 : (cont.d) 107 Figure B.1 : (cont.d) 108 Figure B.1 : (cont.d) 109 Figure B.1 : (cont.d) 110 Figure B.1 : (cont.d) 111 Figure B.1 : (cont.d) 112 Figure B.1 : (cont.d) 113 Figure B.1 : (cont.d) 114 Figure B.1 : (cont.d) 115 Figure B.1 : (cont.d) 116 Figure B.1 : (cont.d) 117 Figure B.1 : (cont.d) 118 Figure B.1 : (cont.d) 119 Figure B.1 : (cont.d) 120 Figure B.1 : (cont.d) 121 Figure B.1 : (cont.d) 122 Figure B.1 : (cont.d) 123 Figure B.1 : (cont.d) 124 Figure B.1 : (cont.d) 125 APPENDIX C : Data Collection The intercept surveys were conducted on randomly selected beaches and days between May 27 th and September 1 st , with the exception of the 3 sites on Lake St. Clair and the Detroit River, where intercept surveys were conducted between June 29 th and August 29 th . For the 25 sites on the coast of Lake Erie, interviewer schedules were determined by a random sampling sch eme, stratified by weekend (Saturday and Sunday) and weekday days. All weekend days were sampled, 4 of the 5 weekdays in any given week were sampled, and a random - number generator was used to determine the order of non - sampled weekdays. Each sampled day wa s then divided into two possible sampling shifts : a morning shifts from 10am to 4pm, and an afternoon shift from 1pm to 7pm. Two teams of interviewers were allocated to each sampled day and were randomly assigned to either both work the morning shift, both work the evening shift, or individually work both shifts. The se 2 5 Lake Erie sites were then divided into 8 groups composed of 3 sites each (Group 1 had 4 sites), and each unique interviewer team/shift combination was randomly assigned one of these groups to determine which sites were sampled during each shift. Finally, the order in which the interviewers visited each site within the selected group was randomized, to avoid systematically visiting certain sites only at certain times of day. The 3 beaches on Lake St. Clair and the Detroit River were sampled differently to accommodat e less - frequent local interviewer availability. For these sites, three days were sampled per week in one of two arrangements : either both weekend days and one weekday were sampled, or one weekend day and two weekdays were sampled. The first week of samplin g was randomly chosen to follow the two weekend - day/one weekday pattern, and each following week alternated between the day - sampling arrangements. Each day then was divided into a morning shift from 10am to 4pm and an afternoon shift from 2pm to 8pm. Only one interviewer team 126 conducted interviews each day, and weekend shifts were selected using random number generation. Likewise, if a given week was selected to sample one weekday, the particular shift was randomly drawn from the ten possible shift - day combi nations. If a given week was selected to sample two weekdays, the above process was completed to select the first day - shift combination, and then a sampled shift was randomly selected from the remaining eight shifts. Similar to the method used when samplin g the 2 6 Lake Erie beaches, the order in which the interviewers visited the three sites was randomized for each shift. 127 APPENDIX D : Pilot Survey In order to avoid using up respondent emails gathered in our initial intercept survey, we complete our pilot survey. In mid - April, we used MTurk to recruit Ohio residents via a short, five - minute Qualtrics screening survey concern ing their visits to Lake Erie beaches in 2019. This first - stage survey was used to isolate Ohio residents who had actually visited one of the 28 beaches in our sample, before inviting them to take a second - stage survey which included the choice experiments questions. Accordingly, the first - stage survey was analogous to our summer 2019 intercept survey and allowed us to ensure that the pilot survey drew from a similar population of Ohio beach users. The first - stage survey presented respondents with a list of the 28 beaches in our sample frame, and it asked respondents to indicate whether or not they were familiar with each beach. For each beach that a given respondent indicated he or she was familiar with, the respondent was asked how many times he or she vis ited the beach in 2019. Respondents were then asked to provide their zip code, gender, and indicate if they had a college degree. If a given respondent indicated that he or she was not familiar with any of the sites and/or visited none of the beaches in th e sample during 2019, the survey ended. However, if a given respondent indicated that he or she had visited at least one of the 28 beaches during 2019, they were asked two questions about their typical 2019 beach trip. These included whether recreation was the primary purpose for the respondent's typical trip in 2019, and how many people typically ride in the same car with the respondent when driving to the beach. The demographic questions, as well as the questions about analogous to questions posed to respondents during the initial intercept interviews. The first - stage screener was administered in two parts, hereby referred to as 128 1A and 1BC, to maximize the number of prospective respondents to invite to the second - stage survey. Out of 276 responses to the first - stage 1A instrument, 179 were eligible for the second - stage instrument. Out of 232 responses to the first - stage 1BC instrument, 161 were eligible for the second - stage instrument. The second - stage pilot survey was designed to mirror the final follow - up survey sent to intercepted respondents from summer 2019. The survey began with a series of questions designed to educate respondents about harmful algal blooms and E. c oli contamination in Lake Erie and Lake St. Clair . These questions also asked respondents about their experiences visiting area beaches, and about their attitudes concerning different beach attributes. Respondents were then asked to complete the five choice experiments and contingent behavior questions. The order in which these two sections were presented to respondents was randomized, to avoid any systematic ordering effects across the sample which could influence respondent answers to either section. Finally, respondents were asked a series of questions about their demographics, and their typical spending during beach trips. The second - stage survey was distributed in three parts, hereby denoted instruments 2A, 2BC, and 2BC - Corona (this version included several questions related to the coronavirus pandemi c, which will be discussed later). The five choice experiments in instrument 2A were utility parameter and insights from the qualitative efforts . The 179 responde nts to instrument 1A who had visited at least one of the sampled beaches during 2019 were invited via MTurk to complete instrument 2A, and this resulted in 105 conditional logit choice model and used the estimated parameters from this model to generate a 129 new D - efficient experimental design in Ngene. This design was subsequently used in instruments 2BC and 2BC - Corona. The remaining 74 eligible respondents to instr ument 1A, as well as the 161 eligible respondents to instrument 1BC, were then invited to complete instrument 2BC, and this instrument resulted in 77 usable responses. At this stage, we designed instrument 2BC - Corona, which was identical to instruments 2A and 2BC but included the six additional coronavirus - related questions. These questions concerned whether respondents believed the Covid - 19 pandemic influenced their answers, and whether they expected their future beach recreation behavior to change as a co nsequence of the pandemic. After making these changes, the remaining non - respondents from both instruments 1A and 1BC were invited to complete instrument 2BC - Corona, which resulted in 62 additional usable responses. In total, the final model used to genera te the Ngene design for our follow - up survey used data from 176 respondents, and 880 unique choice situations. 130 Table D.1 : Conditional Logit E stimates from Pilot S urvey (1) (2) (3) (4) Variables Neither Interactions Distance Interactions Model 1 WTD (in miles) Mostly sand 0.888*** 0.905*** 0.898*** 91 (0.158) (0.159) (0.160) Half sand/half pebbles 0.303** 0.305** 0.301** 31 (0.151) (0.152) (0.151) Clear water 0.852*** 0.878*** 0.871*** 87 (0.182) (0.183) (0.183) Somewhat murky water 0.440*** 0.462*** 0.459*** 45 (0.161) (0.162) (0.163) Never crowded 1.016*** 1.035*** 1.011*** 104 (0.169) (0.167) (0.168) Somewhat crowded 0.396*** 0.404*** 0.389*** 40 (0.148) (0.149) (0.149) Bac. warning in effect - 2.446*** - 2.497*** - 2.468*** - 250 (0.284) (0.285) (0.282) - Lifted 1 day ago - 1.307*** - 1.331*** - 1.316*** - 134 (0.216) (0.217) (0.214) - Lifted 3 days ago - 0.678*** - 0.681*** - 0.684*** - 69 (0.153) (0.153) (0.153) - Lifted 5 days ago - 0.755*** - 0.756*** - 0.760*** - 77 (0.149) (0.148) (0.150) HAB warning in effect - 2.208*** - 2.239*** - 2.214*** - 226 (0.332) (0.329) (0.332) - Lifted 1 day ago - 1.171*** - 1.195*** - 1.176*** - 120 (0.207) (0.207) (0.209) - Lifted 3 days ago - 0.809*** - 0.813*** - 0.806*** - 83 (0.150) (0.150) (0.151) - Lifted 5 days ago - 0.837*** - 0.817*** - 0.818*** - 85 (0.151) (0.150) (0.152) Neither 0.0967 1.008** 0.0902 (0.271) (0.479) (0.270) Distance - 0.00979*** - 0.0102*** - 0.0201*** (0.00268) (0.00266) (0.00619) nindist_neither - 0.00426** - 0.00409** - 0.00417** (0.00189) (0.00189) (0.00187) neither_income - 1.17e - 06 (2.26e - 06) neither_white - 0.564 (0.351) neither_hispanic - 1.043** (0.520) neither_male - 0.350 (0.236) neither_collgrad - 0.209 (0.237) 131 Table D.1 : (cont.) dist_income 1.93e - 09 (3.04e - 08) dist_white 0.00786 (0.00537) dist_hispanic 0.00739 (0.00596) dist_male 0.00248 (0.00336) dist_collgrad 0.00233 (0.00356) Respondents Choice Sets 176 880 176 880 176 880 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 132 Table D.2 : Mixed Logit Estimates from Pilot S urvey (1) (2) (3) (4) Variables Parameter Estimate SD Estimates % with Parameter >0 WTD at mean parameter est. (miles) Mostly sand 8.237*** 1.619*** 100 118 (2.834) (0.558) Half sand/half pebbles 3.783** 1.794** 98 54 (1.698) (0.826) Clear water 4.862*** 1.720** 100 69 (1.643) (0.840) Somewhat murky water 1.282* 7.921*** 56 18 (0.688) (2.291) Never crowded 6.395*** 5.913*** 86 91 (1.712) (1.611) Somewhat crowded 4.966*** 7.893*** 74 71 (1.258) (2.251) Bac. warning in effect - 19.933*** 16.863*** 11 - 285 (5.960) (4.683) - Lifted 1 day ago - 7.348*** 10.191*** 24 - 105 (2.670) (2.988) - Lifted 3 days ago - 2.794** 7.147*** 35 - 40 (1.157) (1.929) - Lifted 5 days ago - 3.342*** 9.153*** 36 - 48 (1.120) (2.622) HAB warning in effect - 15.935*** 14.078*** 13 - 228 (4.078) (3.414) - Lifted 1 day ago - 4.785*** 9.067*** 30 - 68 (1.481) (2.613) - Lifted 3 days ago - 5.559*** 10.789*** 30 - 79 (1.432) (3.087) - Lifted 5 days ago - 4.462*** 12.706*** 36 - 64 (1.265) (3.881) Neither 4.713*** 7.849*** 73 (1.779) (2.026) mindist_neither - 0.030*** 0.489*** 48 (0.011) (0.149) Distance - 0.070** (0.030) Respondents Choice Sets 176 880 176 880 176 880 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 133 Table D.3 : Contingent Behavior Response Percentages from P ilot S urvey (1) (2) (3) CB Scenario I would have gone to the same beach. I would have gone to another beach. I would not have gone to any beach. E. coli advisory - day of trip 8.52 35.23 56.25 HAB warning - day of trip 10.23 39.77 50 - Lifted 1 day before trip 23.3 39.77 36.93 - Lifted 3 days before trip 35.23 34.66 30.11 - Lifted 5 days before trip 56.82 26.7 16.48 HAB warning - next beach along the shore 32.95 28.41 38.64 Table D.4 : COVID - 19 Q uestion R esponse P ercentage s from P ilot S urvey As a result of the coronavirus Disagree Somewhat disagree Neutral Somewhat agree Agree I will be more likely to avoid all beaches. 22% 28% 14% 18% 18% I will likely visit beaches as much or more than in the past. 21% 24% 20% 16% 19% I will be more likely to go to different beaches than in the past. 20% 24% 24% 27% 5% I will be less likely to avoid crowds at beaches 51% 10% 15% 14% 10% I will be more likely to avoid beaches with warnings and advisories. 2% 7% 25% 25% 41% 134 APPENDIX E : Follow - up Disposition Tables and Item Non - response Table E.1 : Case D isposition A cross B each S ites S ampled in 2019 *729 interviews were attempted at the 3 Detroit River and Lake St. Clair sites, and 4253 were attempted at the 25 Lake Erie sites. Table E.2 : Stated Preference Item Non - Response Contingent Behavior Questions # of questions answered 0 1 2 3 4 5 6 7 8 9 % of respondents 7.69 0.66 0.28 0.56 0.37 0.37 3.56 1.31 3.84 81.35 Choice Experiments # of questions answered 0 1 2 3 4 5 % of respondents 1.78 1.87 0.84 0.84 3.09 91.57 Includes only respondents intercepted in 2019 who completed the follow - up survey, i.e. provided an answer to at least one stated preference question (n = 1067). Onsite Interviews* Follow - Up Interviews Lake or River County, State Site Completed Emails Invites Partial Complete Complete Detroit River Wayne, MI Belle Isle Beach 366 262 259 10 113 Lake St. Clair Macomb, MI Lake St. Clair Metropark 164 113 113 5 31 Walter & Mary Burke Park 88 63 62 5 22 Lake Erie Monroe, MI Lucas, OH Sterling State Park Luna Pier Beach Maumee Erie Beach 106 38 48 56 19 20 56 19 19 0 2 0 19 6 4 Maumee Inland Beach 20 11 11 0 5 Ottawa, OH Camp Perry Beach 19 9 9 1 4 Port Clinton City Beach 30 17 17 1 6 East Harbor State Park 120 56 54 2 24 Erie, OH Nickel Plate Beach 129 89 85 6 39 Old Woman Creek Beach 41 24 24 2 16 Sherod Park Beach 24 14 14 0 7 Main Street Beach 178 118 118 7 42 Showse Park Beach 10 6 6 0 2 Lorain, OH Lakeview Park Beach 193 115 115 0 48 Century Park Beach 32 19 19 2 6 Beach 29 17 16 1 7 Cuyahoga, OH Huntington Beach 256 161 158 8 88 Edgewater Park Beach 445 295 289 12 109 Euclid State Park 133 77 76 5 25 Sims Beach 54 38 38 2 10 Lake, OH Ashtabula, OH Headlands State Park Fairport Harbor Walnut Beach Geneva State Park Lakeshore Park Beach Conneaut Beach 378 318 305 321 80 310 210 202 176 187 50 152 207 202 172 185 49 147 11 9 10 17 4 4 97 93 78 75 20 71 135 APPENDIX F : Follow - Up Responses to Contingent Behavior & COVID - 19 Questions Table F.1 : Contingent Behavior Response Percentages (2019 respondents) (1) (2) (3) (4) CB Scenario I would have gone to the same beach. I would have gone to another beach. I would not have gone to any beach. N E. coli advisory - day of trip 18.97 34.81 46.23 928 - Lifted 1 day before trip 34.55 31.95 33.51 961 - Lifted 3 days before trip 52.62 25.79 21.59 954 - Lifted 6 days before trip 76.22 11.42 12.36 963 HAB warning - day of trip 19.23 38.12 42.65 905 - Lifted 1 day before trip 39.03 30.02 30.95 966 - Lifted 3 days before trip 62.24 22.10 15.66 964 - Lifted 6 days before trip 80.10 11.03 8.87 970 HAB warning - next beach along the shore 56.29 15.18 28.52 922 Table F.2 : COVID - 19 Q uestion R esponse P ercentages (2019 Respondents) As a result of the coronavirus Disagree Somewhat disagree Neutral Somewhat agree Agree N I will be more likely to avoid all beaches. 42.68 16.82 14.19 16.93 9.38 874 I will likely visit beaches as much or more than in the past. 16.57 17.15 20.02 19.79 26.47 869 I will be more likely to go to different beaches than in the past. 33.56 16.27 29.1 15.12 5.96 873 I will be less likely to avoid crowds at beaches 44.27 14.68 11.70 11.93 17.43 872 I will be more likely to avoid beaches with warnings and advisories. 9.74 6.07 22.57 22.22 39.4 873 136 APPENDIX G : Follow - Up Robustness Checks for Choice Experiment Table G.1 : Mixed Logit Robustness Checks Variables (1) All 2019 Respondents (2) Under 29 mins. to complete (75 th pctl.) (3) Over 8 mins. to complete (10 th pctl.) Mean SD Mean SD Mean SD Distance - 0.0148*** - 0.0145*** - 0.0153*** (0.000721) (0.000848) (0.000770) Mostly sand 1.177*** 0.680*** 1.179*** 0.559** 1.135*** 0.614*** (0.0892) (0.120) (0.107) (0.250) (0.0922) (0.123) Half sand/half pebbles 0.380*** 0.0412 0.407*** 0.463** 0.373*** 0.0335 (0.0734) (0.145) (0.0899) (0.186) (0.0794) (0.159) Clear water 1.500*** 0.662*** 1.419*** 0.708*** 1.520*** 0.573*** (0.103) (0.158) (0.122) (0.209) (0.102) (0.197) Somewhat murky water 0.707*** 0.226*** 0.628*** 0.0359 0.747*** 0.107 (0.0738) (0.0836) (0.0870) (0.251) (0.0744) (0.144) Never crowded 1.011*** 0.780*** 0.892*** 0.780*** 1.041*** 0.755*** (0.0925) (0.108) (0.108) (0.139) (0.0943) (0.103) Somewhat crowded 0.643*** 0.0873 0.550*** 0.114 0.660*** 0.00920 (0.0780) (0.0829) (0.0888) (0.116) (0.0810) (0.0912) Bac. warning in effect - 3.938*** 0.605 - 3.792*** 0.607 - 4.056*** 0.705 (0.267) (0.699) (0.381) (1.212) (0.283) (0.613) - Lifted 1 day ago - 1.732*** 0.554** - 1.679*** 0.392 - 1.746*** 0.412 (0.119) (0.236) (0.139) (0.380) (0.119) (0.324) - Lifted 3 days ago - 1.211*** 0.180 - 1.192*** 0.328** - 1.177*** 0.0239 (0.0931) (0.150) (0.108) (0.153) (0.0908) (0.323) - Lifted 6 days ago - 1.136*** 0.00744 - 1.192*** 0.187 - 1.137*** 0.219 (0.0900) (0.165) (0.105) (0.203) (0.0953) (0.299) HAB warning in effect - 3.855*** 1.971*** - 3.501*** 1.783*** - 3.813*** 1.788*** (0.314) (0.475) (0.312) (0.481) (0.261) (0.379) - Lifted 1 day ago - 1.280*** 0.200 - 1.158*** 0.169 - 1.245*** 0.0204 (0.102) (0.149) (0.115) (0.267) (0.104) (0.195) - Lifted 3 days ago - 0.873*** 0.332** - 0.812*** 0.315 - 0.899*** 0.227 (0.0870) (0.166) (0.100) (0.235) (0.0902) (0.255) - Lifted 6 days ago - 0.454*** 0.214 - 0.490*** 0.293 - 0.441*** 0.0543 (0.0780) (0.173) (0.0922) (0.199) (0.0822) (0.172) Neither - 0.554*** 1.657*** - 0.691*** 1.659*** - 0.568*** 1.707*** (0.127) (0.0881) (0.144) (0.112) (0.134) (0.0875) Respondents 1048 779 944 Choice Occasions 5082 3775 4640 Correlation with model 1 means 0.9988 0.9997 137 Table G. 1 : (cont.) Variables (1) All 2019 Respondents ( 4 ) Respondents who live within 50 miles of a beach (75 th pctl.) (5) Only respondents with transitive preferences Mean SD Mean SD Mean SD Distance - 0.0148*** - 0.0161*** - 0.0151*** (0.000721) (0.000844) (0.000819) Mostly sand 1.177*** 0.680*** 1.084*** 0.722*** 1.198*** 0.697*** (0.0892) (0.120) (0.104) (0.158) (0.0941) (0.132) Half sand/half pebbles 0.380*** 0.0412 0.350*** 0.166 0.376*** 0.160 (0.0734) (0.145) (0.0881) (0.319) (0.0796) (0.186) Clear water 1.500*** 0.662*** 1.425*** 0.734*** 1.493*** 0.798*** (0.103) (0.158) (0.116) (0.171) (0.107) (0.151) Somewhat murky water 0.707*** 0.226*** 0.653*** 0.0100 0.724*** 0.0876 (0.0738) (0.0836) (0.0850) (0.156) (0.0775) (0.132) Never crowded 1.011*** 0.780*** 0.863*** 0.774*** 0.986*** 0.708*** (0.0925) (0.108) (0.108) (0.116) (0.0992) (0.121) Somewhat crowded 0.643*** 0.0873 0.482*** 0.165 0.612*** 0.0343 (0.0780) (0.0829) (0.0906) (0.120) (0.0843) (0.0933) Bac. warning in effect - 3.938*** 0.605 - 4.323*** 1.840*** - 4.045*** 1.002* (0.267) (0.699) (0.456) (0.616) (0.318) (0.583) - Lifted 1 day ago - 1.732*** 0.554** - 1.675*** 0.182 - 1.716*** 0.497** (0.119) (0.236) (0.132) (0.467) (0.126) (0.244) - Lifted 3 days ago - 1.211*** 0.180 - 1.299*** 0.144 - 1.199*** 0.180 (0.0931) (0.150) (0.117) (0.494) (0.0977) (0.149) - Lifted 6 days ago - 1.136*** 0.00744 - 1.185*** 0.106 - 1.155*** 0.395* (0.0900) (0.165) (0.106) (0.162) (0.0982) (0.225) HAB warning in effect - 3.855*** 1.971*** - 3.596*** 2.135*** - 3.829*** 1.976*** (0.314) (0.475) (0.335) (0.507) (0.291) (0.414) - Lifted 1 day ago - 1.280*** 0.200 - 1.238*** 0.104 - 1.257*** 0.223 (0.102) (0.149) (0.119) (0.224) (0.119) (0.255) - Lifted 3 days ago - 0.873*** 0.332** - 0.870*** 0.327* - 0.849*** 0.302* (0.0870) (0.166) (0.100) (0.181) (0.0941) (0.182) - Lifted 6 days ago - 0.454*** 0.214 - 0.363*** 0.0446 - 0.469*** 0.240 (0.0780) (0.173) (0.0907) (0.149) (0.0859) (0.146) Neither - 0.554*** 1.657*** - 0.704*** 1.515*** - 1.109*** 1.753*** (0.127) (0.0881) (0.143) (0.0961) (0.144) (0.0967) Respondents 1048 801 1016 Choice Occasions 5082 3881 4465 Correlation with model 1 means 0.9963 0.9962 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.10 138 Table G.2 : Ordering Effects in Mixed Logit Model Variables (2) CB|CE - contingent behavior appeared first (3) CE|CB choice experiment appeared first Mean SD WTD (miles) Mean SD WTD (miles) Distance - 0.0151*** - 0.0149*** (0.00104) (0.00101) Mostly sand 1.205*** 0.521* 80 1.172*** 0.742*** 79 (0.127) (0.288) (0.127) (0.169) Half sand/half pebbles 0.476*** 0.157 32 0.316*** 0.458 21 (0.104) (0.225) (0.118) (0.293) Clear water 1.316*** 0.568*** 87 1.703*** 0.685** 114 (0.141) (0.213) (0.145) (0.288) Somewhat murky water 0.732*** 0.0858 48 0.684*** 0.408** 46 (0.105) (0.187) (0.105) (0.177) Never crowded 0.807*** 0.832*** 53 1.150*** 0.710*** 77 (0.130) (0.116) (0.132) (0.174) Somewhat crowded 0.583*** - 0.0790 39 0.635*** 0.0859 43 (0.115) (0.161) (0.109) (0.166) Bac. warning in effect - 3.820*** 1.100* - 253 - 4.480*** 1.306* - 301 (0.415) (0.582) (0.435) (0.697) - Lifted 1 day ago - 1.608*** 0.442 - 106 - 1.874*** 0.574 - 126 (0.165) (0.384) (0.173) (0.449) - Lifted 3 days ago - 1.107*** 0.218 - 73 - 1.263*** 0.0224 - 85 (0.131) (0.203) (0.133) (0.285) - Lifted 6 days ago - 0.924*** 0.308 - 61 - 1.331*** 0.0763 - 89 (0.125) (0.354) (0.131) (0.197) HAB warning in effect - 3.540*** 1.360** - 234 - 3.677*** 1.568 - 247 (0.384) (0.652) (0.489) (1.018) - Lifted 1 day ago - 1.163*** 0.00477 - 77 - 1.409*** 0.136 - 95 (0.148) (0.306) (0.144) (0.234) - Lifted 3 days ago - 0.889*** 0.0804 - 59 - 0.855*** 0.00345 - 57 (0.126) (0.664) (0.122) (0.347) - Lifted 6 days ago - 0.428*** 0.231 - 28 - 0.543*** 0.506*** - 36 (0.114) (0.154) (0.114) (0.178) Neither - 0.612*** 1.817*** - 0.572*** 1.581*** (0.185) (0.133) (0.189) (0.121) Respondents 508 540 Choice Occasions 2483 2599 Correlation with Model 1 means 0.9983 0.9963 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 139 Table G.3 : Ordering Effects in Contingent Behavior Response Percentages (1) (2) (3) CB Scenario I would have gone to the same beach. I would have gone to another beach. I would not have gone to any beach. CE|CB CB|CE CE|CB CB|CE CE|CB CB|CE E. coli advisory - day of trip 18.14 19.75 39.38 30.46 42.48 49.79 - Lifted 1 day before trip 37.42 31.85 33.33 30.65 29.25 37.50 - Lifted 3 days before trip 60.00 45.75 24.35 27.13 15.65 27.13 - Lifted 6 days before trip 82.19 70.62 9.87 12.88 7.94 16.50 HAB warning - day of trip 16.97 21.38 43.44 33.05 39.59 45.57 - Lifted 1 day before trip 42.92 35.40 29.61 30.40 27.47 34.20 - Lifted 3 days before trip 68.25 56.69 20.73 23.35 11.02 19.96 - Lifted 6 days before trip 85.26 75.30 8.97 12.95 5.77 11.75 HAB warning - next beach along the shore 61.61 51.27 13.39 16.88 25.00 31.86 Comparison with pooled data results from Table IVa Average difference - 3.72 3.47 - 0.29 0.30 4.02 - 3.77 Min absolute difference 0.83 0.78 0.41 0.38 3.06 2.88 Max absolute difference 7.38 6.87 5.32 5.07 5.94 5.54 Correlation 0.9996 0.9963 0.9926 0.9835 0.9979 0.9980 140 Table G.4 : Choice Model Estimate Comparisons Variables (1) Mixed Logit (3) Conditional Logit (4) Nested Logit Mean Estimate SD Estimates WTD (miles) Estimate WTD % diff. from m. logit WTD Estimate WTD % diff. from m. logit WTD Distance - 0.0148*** - 0.0112*** - 0.00941*** (0.000721) (0.000501) (0.000638) Mostly sand 1.177*** 0.680*** 80 0.834*** 74 - 7% 0.758*** 81 1% (0.0892) (0.120) (0.0674) (0.0624) Half sand/half pebbles 0.380*** 0.0412 26 0.297*** 26 3% 0.273*** 29 13% (0.0734) (0.145) (0.0584) (0.0472) Clear water 1.500*** 0.662*** 101 1.053*** 94 - 8% 0.911*** 97 - 5% (0.103) (0.158) (0.0727) (0.0756) Somewhat murky water 0.707*** 0.226*** 48 0.524*** 47 - 2% 0.441*** 47 - 2% (0.0738) (0.0836) (0.0560) (0.0537) Never crowded 1.011*** 0.780*** 68 0.725*** 65 - 6% 0.681*** 72 6% (0.0925) (0.108) (0.0706) (0.0612) Somewhat crowded 0.643*** 0.0873 43 0.501*** 45 3% 0.439*** 47 7% (0.0780) (0.0829) (0.0621) (0.0546) Bac. warning in effect - 3.938*** 0.605 - 266 - 2.733*** - 243 - 9% - 2.427*** - 258 - 3% (0.267) (0.699) (0.145) (0.164) - Lifted 1 day ago - 1.732*** 0.554** - 117 - 1.195*** - 106 - 9% - 1.095*** - 116 - 1% (0.119) (0.236) (0.0805) (0.0803) - Lifted 3 days ago - 1.211*** 0.180 - 82 - 0.801*** - 71 - 13% - 0.709*** - 75 - 8% (0.0931) (0.150) (0.0673) (0.0640) - Lifted 6 days ago - 1.136*** 0.00744 - 77 - 0.756*** - 67 - 12% - 0.653*** - 69 - 10% (0.0900) (0.165) (0.0683) (0.0639) HAB warning in effect - 3.855*** 1.971*** - 261 - 2.256*** - 201 - 23% - 2.022*** - 215 - 18% (0.314) (0.475) (0.133) (0.143) - Lifted 1 day ago - 1.280*** 0.200 - 87 - 0.942*** - 84 - 3% - 0.789*** - 84 - 3% (0.102) (0.149) (0.0754) (0.0798) - Lifted 3 days ago - 0.873*** 0.332** - 59 - 0.646*** - 57 - 3% - 0.549*** - 58 - 1% (0.0870) (0.166) (0.0656) (0.0614) - Lifted 6 days ago - 0.454*** 0.214 - 31 - 0.294*** - 26 - 15% - 0.276*** - 29 - 4% (0.0780) (0.173) (0.0595) (0.0498) Neither (nest in n. logit) - 0.554*** 1.657*** - 0.240** - 0.302*** (0.127) (0.0881) (0.0960) (0.0816) Nesting parameter 0.759*** 0.062 Respondents 1048 1048 1048 Choice Occasions 5082 5082 5082 Corr. w/ Model 1 means .996 .999 Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1 141 APPENDIX H : 2019 Respondent Summary Statistics Table H.1 : 2019 Respondent Summary Statistics Mean Min Max N Variable (1) (2) (3) (1) (2) (3) Male (0/1)* . . 0.24 0 1 . . 964 Hispanic (0/1)* . . 0.03 0 1 . . 853 White (0/1)* . . 0.94 0 1 . . 847 Income (in thousands)* . . 80.9 12.5 250 . . 854 Age 42.9 41.1 42 22 70 4159 2535 1195 College graduate (0/1) 0.58 0.62 0.58 0 1 4140 2524 959 Have you, or do you plan to, enter the water? (0/1) 0.69 0.73 0.73 0 1 4157 2534 1196 Is rec. the primary purpose of visit? (0/1) 0.95 0.95 0.95 0 1 4163 2538 1196 (1) Intercept survey participants (2) Intercept participants who provided an email (3) Follow - up respondents used in analysis *These variables are only available for follow - up respondents 142 APPENDIX I: Mixed Logit Conditional Parameter Regressions Table I .1 : Summary of M ixed L ogit P osterior P arameter R egressions Conditional Beta for Dependent Variable Adjusted P - value for regression F test Number of demographic regressors significant at 5% Demographic regressors significant at 5% Number of demographic regressors significant at 1% Demographic regressors significant at 1% Mostly sand 0.008 0.005 0.86 0 0 Half sand/half pebbles 0.021 0.009 0.055 0 1 Employed full time (0/1) Clear water 0.009 0.003 0.74 0 0 Somewhat murky water 0.017 0.005 0.16 1 Male (0/1) 0 Never crowded 0.017 0.005 0.17 1 College grad (0/1) 1 Visits to intercepted beach each season Somewhat crowded 0.007 0.005 0.87 0 0 Bac. warning in effect 0.014 0.001 0.35 1 Years visit area beaches 0 - Lifted 1 day ago 0.016 0.003 0.22 1 Visits to intercepted beach each season 0 - Lifted 3 days ago 0.012 0.0004 0.48 0 0 - Lifted 6 days ago 0.018 0.005 0.14 0 0 HAB warning in effect 0.017 0.004 0.18 2 College grad (0/1) & Num. children in hh. 0 - Lifted 1 day ago 0.014 0.002 0.32 1 White (0/1) 0 - Lifted 3 days ago 0.015 0.003 0.24 0 1 Years visit area beaches - Lifted 6 days ago 0.024 0.011 0.025 1 College grad (0/1) 1 Enter water during intercepted trip? (0/1) Average 0.015 0.004 0.57 0.29 143 APPENDIX J : Choice Experiment Simulation Results Table J.1 : Choice Experiment Simulation Results Scenario (1) Avg. % change in prob. of visiting same site (2) Implied percentage of CE respondents who would go to same site (3) Percentage of CB respondents who would go to the same site Bac. warning in effect - 94% 6% 19% - 13% - Lifted 1 day ago - 60% 40% 39% - 1% - Lifted 3 days ago - 44% 56% 62% 6% - Lifted 6 days ago - 41% 59% 80% 21% HAB warning in effect - 93% 7% 19% 12% - Lifted 1 day ago - 46% 54% 35% - 19% - Lifted 3 days ago - 32% 68% 53% - 15% - Lifted 6 days ago - 17% 83% 76% - 17% Correlation between (2) and (3) 0.85 144 APPENDIX K : Creation of T rip E stimates from I ndividual W eights Once the individual weight is obtained for every intercepted beachgoer, these weights are summed over the beachgoers in a given stratum h to recover an estimate of the total visitation in each stratum: Total estimated v isits to the 3 sites where Michigan State interviewers conducted interviews is computed by summing over the 4 MSU - specific strata, and the same strategy is used for the 25 sites in the 6 OSU - specific strata: Because the Michigan State interviewer team did not conduct interviews from May 27 th to June 28 th , at this stage we are only able to construct , which estimates site visitation from June 29 th to September 1 st at Belle Isle, St. Clair Metropark, and Burke Park. Conversely, the Ohio State team conducted interviews from May 27 th to September 1 st , and so estimates visitation across the full summer season at the 25 Erie sites. In order to estimate full seaso nal visitation to all 28 sites in our sample, we needed to recover estimated visitation to the 3 MSU sites during the period of May 27 th to June 28 th . Accordingly, we first partition estimated visits to OSU - sampled sites into two mutually exclusive groups based on the sampling date: 145 We then compute , the ratio of total estimated visits to OSU - sampled sites to the number of estimated visits to OSU - sampled sites in July and August. Note that multiplying by returns the total estimated seasonal trips for the OSU - sampled sites. To adjust for the lack of data on May and June trips to MSU - sampled sites, we first assume tha t the constant also characterizes the relationship between the known and the unknown Operating under this assumption, we inflate each individual weight assigned to a beachgoer in the MSU - specific strata by and sum these weights to recover : 146 Tabl e K.1 : Strata Used in Visitation Estimation Stratum Interviewer Team Time Period Day Period # Intercepted Trips 1 MSU June 29 - August 1 Weekday 83 2 MSU August 1 September 1 Weekday 134 3 MSU June 29 - August 1 Weekend 289 4 MSU August 1 September 1 Weekend 103 5 OSU May 27 July 1 Weekday 638 6 OSU July 1 August 1 Weekday 766 7 OSU August 1 September 1 Weekday 632 8 OSU May 27 July 1 Weekend 320 9 OSU July 1 August 1 Weekend 650 10 OSU August 1 September 1 Weekend 544 147 APPENDIX L : Observed HAB and B acterial W arnings in 2019 S eason Table L.1 : Observed HAB and B acterial W arnings in 2019 S eason Warning type Affected site Number of warnings during 2019 season Number of affected days Number of days 1 - 2 days after warning Number of days 3 - 5 days after warning Number of days 6 days after warning Bacterial Camp Perry Beach 3 22 6 9 3 Century Park Beach 13 56 14 11 3 Conneaut Beach 1 3 2 1 0 East Harbor State Park 3 9 6 7 2 Fairport Harbor Park Beach 1 3 2 3 1 Geneva State Park 2 6 4 6 2 Headlands Beach St. Park 1 3 2 3 1 Lakeshore Park Beach 2 6 4 6 2 Lakeview Park Beach 12 45 14 17 5 Main Street Beach 13 47 14 18 6 Maumee Inland Beach 9 74 8 7 2 Nickel Plate Beach 4 15 6 9 3 Old Woman Creek Beach 4 13 8 12 4 Sims Park Beach 5 32 10 11 3 Sherod Park Beach 12 46 13 11 6 Showse Park Beach 10 37 13 16 5 15 58 18 20 6 HAB Edgewater Park Beach 1 9 2 3 1 Euclid State Park 1 9 2 3 1 Huntington Beach 1 10 2 3 1 Maumee - Erie Beach 2 45 2 3 1 Total 115 548 152 179 58 Mean 5.48 26.1 7.24 8.52 2.76 Max 15 74 18 20 6 Min 1 3 2 1 0 148 APPENDIX M : Re - calibrated B aseline ASC A djustments and W elfare E stimates Table M.1 : Recalibrated ASC E stimates and A djustments for A ll S ites and S cenarios (* denotes unaffected site/ no ASC adjustment) Site Baseline ASC HAB warning HAB 1 day ago HAB 3 days ago HAB 6 days ago HAB next beach Bac. warning Bac. 1 day ago Bac. 3 days ago Bac. 6 days ago Belle Isle* - 6.126 - 0.235 - 0.147 - 0.072 - 0.036 - 0.086 - 0.241 - 0.159 - 0.084 - 0.040 Walter & Mary Burke Park* - 6.268 - 0.215 - 0.130 - 0.061 - 0.031 - 0.074 - 0.221 - 0.142 - 0.073 - 0.033 Luna Pier Beach* - 6.274 - 0.195 - 0.115 - 0.052 - 0.026 - 0.064 - 0.200 - 0.126 - 0.062 - 0.028 Lake St. Clair Metropark* - 6.228 - 0.216 - 0.131 - 0.062 - 0.031 - 0.075 - 0.222 - 0.143 - 0.074 - 0.034 Sterling State Park* - 6.106 - 0.218 - 0.133 - 0.063 - 0.031 - 0.076 - 0.224 - 0.145 - 0.075 - 0.034 Camp Perry Beach - 6.128 - 0.194 - 0.114 - 0.052 - 0.026 - 0.064 - 0.200 - 0.125 - 0.062 - 0.028 Century Park Beach - 6.131 - 0.193 - 0.113 - 0.052 - 0.025 - 0.063 - 0.199 - 0.124 - 0.062 - 0.028 Conneaut Beach - 5.929 - 0.221 - 0.135 - 0.064 - 0.032 - 0.077 - 0.227 - 0.147 - 0.076 - 0.035 East Harbor State Park - 5.9 - 0.210 - 0.126 - 0.059 - 0.029 - 0.072 - 0.216 - 0.138 - 0.070 - 0.032 Edgewater Park Beach - 5.913 - 0.220 - 0.135 - 0.064 - 0.032 - 0.077 - 0.226 - 0.147 - 0.076 - 0.035 Euclid State Park - 6.152 - 0.193 - 0.114 - 0.052 - 0.025 - 0.063 - 0.199 - 0.125 - 0.062 - 0.028 Fairport Harbor Beach - 5.939 - 0.202 - 0.120 - 0.056 - 0.028 - 0.068 - 0.208 - 0.132 - 0.066 - 0.030 149 Table M.1: (cont.) Geneva State Park - 5.902 - 0.204 - 0.122 - 0.057 - 0.028 - 0.069 - 0.209 - 0.133 - 0.067 - 0.031 Headlands Beach State Park - 5.94 - 0.204 - 0.122 - 0.057 - 0.028 - 0.069 - 0.210 - 0.134 - 0.067 - 0.031 Huntington Beach - 6.013 - 0.200 - 0.119 - 0.055 - 0.027 - 0.066 - 0.205 - 0.130 - 0.065 - 0.030 Lakeshore Park Beach - 6.09 - 0.196 - 0.115 - 0.053 - 0.026 - 0.064 - 0.201 - 0.126 - 0.063 - 0.028 Lakeview Park Beach - 5.939 - 0.204 - 0.122 - 0.056 - 0.028 - 0.068 - 0.209 - 0.133 - 0.067 - 0.031 Main Street Beach - 5.977 - 0.201 - 0.119 - 0.055 - 0.027 - 0.067 - 0.206 - 0.131 - 0.066 - 0.030 Maumee Bay State Park - Erie - 6.041 - 0.210 - 0.127 - 0.059 - 0.030 - 0.072 - 0.216 - 0.138 - 0.071 - 0.032 Maumee Bay State Park - Inland - 6.08 - 0.204 - 0.122 - 0.057 - 0.028 - 0.069 - 0.209 - 0.133 - 0.067 - 0.031 Nickel Plate Beach - 6.01 - 0.199 - 0.118 - 0.054 - 0.027 - 0.066 - 0.205 - 0.129 - 0.065 - 0.029 Old Woman Creek Beach - 6.248 - 0.192 - 0.113 - 0.051 - 0.025 - 0.062 - 0.198 - 0.124 - 0.061 - 0.028 Port Clinton City Beach* - 6.17 5 - 0.193 - 0.113 - 0.052 - 0.025 - 0.063 - 0.199 - 0.125 - 0.062 - 0.028 Sims Park Beach - 6. 174 - 0.193 - 0.113 - 0.052 - 0.025 - 0.063 - 0.198 - 0.124 - 0.062 - 0.028 Sherod Park Beach - 6. 205 - 0.192 - 0.113 - 0.051 - 0.025 - 0.063 - 0.198 - 0.124 - 0.061 - 0.028 Showse Park Beach - 6. 316 - 0.191 - 0.112 - 0.051 - 0.025 - 0.062 - 0.197 - 0.123 - 0.061 - 0.027 - 6. 127 - 0.194 - 0.114 - 0.052 - 0.025 - 0.063 - 0.199 - 0.125 - 0.062 - 0.028 Walnut Beach* - 5.945 - 0.207 - 0.125 - 0.058 - 0.029 - 0.071 - 0.213 - 0.136 - 0.069 - 0.032 150 Table M.2 : Recalibrated V alue per L ost Tr ip E stimates for A ll S ites and S cenarios (* denotes unaffected site) Site HAB warning HAB 1 day ago HAB 3 days ago HAB 6 days ago HAB next beach Bac. warning Bac. 1 day ago Bac. 3 days ago Bac. 6 days ago Belle Isle* $19.85 $20.70 $21.88 $22.60 $21.62 $19.81 $20.55 $21.65 $22.52 Walter & Mary Burke Park* $17.64 $18.00 $18.48 $18.76 $18.37 $17.63 $17.94 $18.38 $18.73 Luna Pier Beach* $15.60 $15.65 $15.73 $15.78 $15.71 $15.59 $15.64 $15.71 $15.77 Lake St. Clair Metropark* $17.76 $18.17 $18.75 $19.11 $18.62 $17.74 $18.09 $18.64 $19.07 Sterling State Park* $17.95 $18.39 $18.99 $19.37 $18.86 $17.93 $18.31 $18.87 $19.33 Camp Perry Beach $15.55 $15.60 $15.66 $15.71 $15.65 $15.55 $15.59 $15.65 $15.71 Century Park Beach $15.45 $15.48 $15.53 $15.56 $15.52 $15.45 $15.48 $15.52 $15.56 Conneaut Beach $18.22 $18.68 $19.28 $19.64 $19.15 $18.20 $18.59 $19.16 $19.60 East Harbor State Park $17.10 $17.38 $17.77 $18.01 $17.68 $17.09 $17.33 $17.69 $17.98 Edgewater Park Beach $18.20 $18.69 $19.39 $19.82 $19.23 $18.17 $18.60 $19.25 $19.77 Euclid State Park $15.47 $15.50 $15.55 $15.59 $15.54 $15.47 $15.50 $15.54 $15.58 Fairport Harbor Park Beach $16.34 $16.51 $16.76 $16.93 $16.70 $16.34 $16.48 $16.71 $16.91 Geneva State Park $16.50 $16.69 $16.98 $17.17 $16.92 $16.49 $16.66 $16.92 $17.15 151 Table M.2: (cont.) Headlands Beach State Park $16.56 $16.75 $17.03 $17.21 $16.97 $16.55 $16.72 $16.98 $17.19 Huntington Beach $16.10 $16.23 $16.42 $16.55 $16.38 $16.10 $16.21 $16.38 $16.54 Lakeshore Park Beach $15.69 $15.76 $15.86 $15.93 $15.83 $15.69 $15.74 $15.84 $15.92 Lakeview Park Beach $16.48 $16.67 $16.95 $17.12 $16.88 $16.48 $16.64 $16.89 $17.11 Main Street Beach $16.21 $16.35 $16.57 $16.71 $16.52 $16.20 $16.32 $16.52 $16.70 Maumee Bay State Park - Erie $17.15 $17.45 $17.89 $18.17 $17.79 $17.14 $17.40 $17.80 $18.14 Maumee Bay State Park - Inland $16.50 $16.69 $16.98 $17.17 $16.92 $16.49 $16.66 $16.92 $17.15 Nickel Plate Beach $16.05 $16.16 $16.34 $16.46 $16.30 $16.04 $16.14 $16.30 $16.45 Old Woman Creek Beach $15.35 $15.36 $15.38 $15.40 $15.38 $15.35 $15.36 $15.38 $15.39 Port Clinton City Beach* $15.46 $15.49 $15.53 $15.56 $15.52 $15.46 $15.48 $15.52 $15.56 Sims Park Beach $15.43 $15.46 $15.49 $15.52 $15.49 $15.43 $15.45 $15.49 $15.52 Sherod Park Beach $15.36 $15.38 $15.40 $15.42 $15.40 $15.36 $15.37 $15.40 $15.42 Showse Park Beach $15.29 $15.30 $15.31 $15.31 $15.30 $15.29 $15.30 $15.31 $15.31 $15.49 $15.53 $15.58 $15.62 $15.57 $15.49 $15.52 $15.57 $15.61 Walnut Beach* $16.87 $17.13 $17.52 $17.78 $17.43 $16.86 $17.08 $17.44 $17.75 152 APPENDIX N : Contraction M apping S ubstitution P redictions The contraction mapping algorithm calibrates a change in the ASCs so that the site choice model generates the same pattern of demand implied by the contingent behavior responses. This pattern of demand depends on the proportion of respondents who indicated that they would visit the same site given each HAB or bacterial scenario. However, respondents could also select that they would have gone to another beach or stayed home. The proportions of agents in the recalibrated demand model that select each of thes e two options are dictated by the estimated site choice model structure, rather than the pattern of demand reported in the CB responses. Table XIV compares the responses from the follow - up survey with the predictions from our nested logit model. In the cas e of the percentage of respondents who selected that they would go to the model predicts that the majority of respondents who elect to not go to the same site wo uld substitute to other sites, rather than stay home. Indeed, for each contingent behavior scenario, under 1 percent of beachgoers are predicted to stay at home. In comparison, the stated preference results indicate that a fairly large percentage of respon dents would stay home for each scenario (26.7% on average). A similar pattern of visitation predictions was observed by Tanner et al. (2019), who estimated a similar calibrated RP - SP model of southern California forest recreation. Taken together, these results provide evidence that models like the one used in this paper are useful in terms of estimating the welfare effects of environmen tal quality changes but may not as be accurate in forecasting patterns of site substitution. 153 Table N.1 : Comparison of C ontingent B ehavior D ata and N ested L ogit P redictions Survey Responses Model Predictions, weighted by predicted trips CB Scenario I would have gone to the same beach. I would have gone to another beach. I would not have gone to any beach. I would have gone to the same beach. I would have gone to another beach. I would not have gone to any beach. Bacterial warning - day of trip 19.0 34.8 46.2 16.95 83.03 0.02 - Lifted 1 day before trip 34.6 32.0 33.5 32.91 67.07 0.016 - Lifted 3 days before trip 52.6 25.8 21.6 57.60 42.39 0.01 - Lifted 6 days before trip 76.2 11.4 12.4 77.9 22.10 0.005 HAB warning - day of trip 19.2 38.1 42.7 17.82 82.16 0.019 - Lifted 1 day before trip 39.0 30.0 31.0 36.32 63.37 0.015 - Lifted 3 days before trip 62.2 22.1 15.7 62.94 37.05 0.009 - Lifted 6 days before trip 80.1 11.0 8.9 79.67 20.33 0.005 HAB warning - next beach 56.3 15.2 28.6 56.92 43.07 0.01 154 APPENDIX O : Comparison of I mpaired ASCs and R e - calibrated B aseline ASCs Table O.1 : Comparison of I mpaired ASCs and R e - calibrated B aseline ASCs Observed Warning Site Impaired ASC Re - calibrated ASC Absolute % change Bacterial Camp Perry Beach - 6.194 - 6.128 1.1 Century Park Beach - 6.286 - 6.131 2.5 Conneaut Beach - 5.939 - 5.929 0.2 East Harbor State Park - 5.935 - 5.9 0.6 Fairport Harbor Park Beach - 5.951 - 5.939 0.2 Geneva State Park - 5.926 - 5.902 0.4 Headlands Beach St. Park - 5.952 - 5.94 0.2 Lakeshore Park Beach - 6.114 - 6.09 0.4 Lakeview Park Beach - 6.075 - 5.939 2.2 Main Street Beach - 6.118 - 5.977 2.3 Maumee Inland Beach - 6.264 - 6.08 2.9 Nickel Plate Beach - 6.06 - 6.01 0.8 Old Woman Creek Beach - 6.299 - 6.248 0.8 Sims Park Beach - 6.27 0 - 6.174 1.5 Sherod Park Beach - 6.337 - 6.205 2.1 Showse Park Beach - 6.431 - 6.315 1.8 - 6.3 00 - 6.127 2.7 HAB Edgewater Park Beach - 5.937 - 5.913 0.4 Euclid State Park - 6.176 - 6.152 0.4 Huntington Beach - 6.039 - 6.013 0.4 Maumee - Erie Beach - 6.144 - 6.041 1.7 155 REFERENCES 156 REFERENCES AAA (American Automobile Association). 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