TWO ESSAYS ON THE ECONOMIC VALUE OF ELK VIEWING IN MICHIGAN By Paul Austin Hunt A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Agricultural, Food, and Resource Economics ŠMaster of Science 2019 ABSTRACT TWO ESSAYS ON THE ECONOMIC VALUE OF ELK VIEWING IN MICHIGAN By Paul Austin Hunt This thesis examines the value of wilderness recreation in the context of Michigan™s Elk Range. The Michigan Elk Range is a near -wilderness area located in the northern Lower Peninsula of Michigan, and it is home to one of the largest free -roaming elk herd s east of the Mississippi River. The first essay takes a broad look at the value of wilderness recreation in the area by estimating a single -site travel cost model. After estimating the mean overall consumer surplus value ($86 per trip) for a population of Michigan Elk Range users , we segment the model by each respondent™s interest in the elk herd and by their primary activity . The se results show that the value for elk viewing is higher than the overall value, and this accords with economic theory about hig her values for goods/services with few or no substitutes. The second essay takes a closer look at elk viewing itself by evaluating elk viewing preferences using a discrete choice experiment. The choice experiment asks respondents to choose between two recreation areas that are identical apart from their distance from the respondent and the chances of experiencing some elk -related attributes. The results show that there is significant variation in respondents™ preferences. To explain this variation, visitors are segmented by their primary activity in the Michigan Elk Range as well as their elk viewing experience . Unsurprisin gly, elk viewers place a higher value on the elk -related attributes than other activity groups, and all activity groups have a significant positive preference for at least one elk attribute suggesting the presence of elk may also incidentally affect activi ties besides elk viewing. Additionally, respondents with more elk viewing experience place a higher value on the elk -related attributes. iv ACKNOWLED GMENTS Funding support for this research was provided by the Michigan Department of Natura l Resources and the U.S. Fish and Wildlife Service through the Pittman -Robertson Wildlife restoration Act Grant MI -155-R. This research benefited from assistance provided by Clay Buchanan (Michigan Department of Natural Resources), Melissa Nichols (Michigan Department of Natural Resources), Scott Whitcomb (Michigan Department of Natural Resources), Brian Mastenbrook (Michig an Department of Natural Resources), Cody Stevens (Michigan Department of Natural Resources), Aren Calton, and Tara Buehler. I™m also grateful for the members of the fall survey team: Tom Giesemann, Joe and Judi Jarecki, Sarah Topp, and Lija Krievs. I wou ld thank my committee members, Drs. Joseph Herriges, Soren Anderson, and Frank Lupi, for their guidance in the preparation of this thesis. My adviser, Dr. Frank Lupi, has provided indispensable guidance, support, and assistance throughout this process, and I feel fortunate to have been able to learn from him. Lastly, I™m grateful to my father, Paul Hunt, my late mother, Lorraine Hunt, and my brother, Jason Hunt, for their love and support. v TABLE OF CONTENTS LIST OF TABLES .................................................................................................................... vi LIST OF FIGURES ................................................................................................................ viii INTRODUCTION ...................................................................................................................... 1 REFERENCES ............................................................................................................................ 4 CHAPTER 1 : Segmented Recreation Demand Models for the Michigan Elk Range ................ 6 I. Introduction .......................................................................................................... 6 II. Survey and Data ................................................................................................. 12 III. Theory of Recreation Demand ........................................................................... 15 IV. Poisson Count Model ......................................................................................... 19 V. Results ................................................................................................................ 22 VI. Discussion .......................................................................................................... 34 REFERENCES .......................................................................................................................... 36 CHAPTER 2 : Preferences and Values for Elk -Related Attributes among Visitors to the Michigan Elk Range .......................................................................................... 40 I. Introduction ........................................................................................................ 40 II. Study Area and Survey ...................................................................................... 45 III. Choice Experiment ............................................................................................. 49 IV. Random Utility Maximization Theory ............................................................... 55 V. Modelling Heterogeneity in Random Utility Models ........................................ 56 VI. Overall Results ................................................................................................... 59 VII. Identifying and Exploring Classes of Elk Range Visitors ................................. 64 VIII. Reflections on the Results using Auxiliary Data ............................................... 71 IX. Discussion .......................................................................................................... 74 REFERENCES .......................................................................................................................... 77 APPENDICES .......................................................................................................................... 81 Appendix I : Survey Disposition Tables .................................................................................... 82 Appendix II : Intercept Survey ................................................................................................... 85 Appendix III : Follow -Up Online Survey .................................................................................. 93 Appendix IV: Strategies for Defining a Target Population ..................................................... 112 Appendix V : Robustness Checks ............................................................................................ 116 Appendix VI : Robustness Check using a Single Elk Attribute Variable ................................ 120 vi LIST OF TABLES Table 1.1 : One-Way Distances from the Michigan Elk Range (unweighted) .............................. 21 Table 1.2 : Descriptive Statistics for Respondents (Unweighted) ................................................. 22 Table 1.3: Overall Travel Cost Mod el (Poisson Maximum Likelihood Model) ......................... 23 Table 1.4: Summary Statistics by Respondents™ Answers to the Question fiWhat role did the chance of seeing elk play in your decision to visit?fl .................................................................... 26 Table 1.5: Travel Cost Model Segmented by Answer to Elk Importance Question .................... 27 Table 1.6: Summary Statistics by Primary Activity Groups ........................................................ 29 Table 1.7 : Travel Cost Model Segmented by Primary Activity ................................................... 30 Table 2.1: Elk-related Attribute Levels ........................................................................................ 51 Table 2.2 : Overall Conditional Logit Estimates with fiNonefl and fiOutside of Elk Rangefl Interactions .................................................................................................................................... 59 Table 2.3: Overall Mixed Logit Estimates ................................................................................... 61 Table 2.4 : Primary Activities ( per respondent ) in Choi ce Experiment ....................................... 64 Table 2.5 : Conditional Logit Estimates by Primary Activity Group ........................................... 65 Table 2.6 : Summary of Elk Experience Variables used in Latent Class Logit ............................ 68 Table 2.7: Class Members hip for Latent Class Logit Model for Two Classes when using Elk Experience as Explanatory Variables ( Class 2=Reference Class) ............................................... 69 Table 2.8 : Preferences for Latent Class Logit Model for Two Classes ....................................... 70 Table 2.9 : Cross Tabulation for questions on experience with elk -related attributes and importance of elk -related attributes for future recreation ............................................................. 73 Table A1.1: Intercept Survey Method of Contact ........................................................................ 82 Table A1.2 : Response Rate for Paper Surveys ( by season ) ......................................................... 83 Table A1.3 : Response Rate for Paper Surveys ( by select sites ) ................................................... 83 Table A1.4 : Follo w up Survey Email Distribution ...................................................................... 84 vii Table A1.5: Distribution of Follow -Up Survey Invitations ......................................................... 84 Table A5.1: MRS using Conditional Logit Models ................................................................... 117 Table A5.2: MRS using Conditional Logit separated by Activity Group ................................. 118 Table A5.3: MRS using Mixed Logit ........................................................................................ 119 Table A5.4: SD of Elk -Related Attributes using Mixed Logit .................................................. 119 Table A5.5: MRS using Latent Class Logit (Elk Experience Class Membership) .................... 119 Table A6.1: Overall Correlation of Elk -Related Attributes ....................................................... 120 Table A6.2: Principal Component Analysis of Elk -Related Attributes ..................................... 121 Table A6.3: Overall Conditional Logit Estimates with fiNonefl and fiOutside of Elk Rangefl Interactions .................................................................................................................................. 122 Table A6.4: Overall Mixed Logit Estimates .............................................................................. 123 Table A6.5: Conditional Logit Estimates by Primary Activity Group ...................................... 124 Table A6 .6: Class Membership for Latent Class Logit Model for Two Classes when using Elk Experience as Explanatory Variables ( Class 2=Reference Class) ............................................. 125 Table A6.7: Preferences for Latent Class Logit Model for Two Classes Explained by Elk Experience ................................................................................................................................... 125 viii LIST OF FIGURES Figure 1.1 : Michigan Elk Range .................................................................................................. 12 Figure 1.2: Demand Curve for Overall Recreation Demand Model (unweighted, using average trip characteristics) ........................................................................................................................ 24 Figure 1.3 : Demand Models for Wildlife Viewing and Hunting (Using the average trip to the Michigan Elk Range) .................................................................................................................... 33 Figure 2.1 : Michigan Elk Range .................................................................................................. 45 Figure 2.2: Example Choice Experiment ( with hunting as the primary activity ) ........................ 49 Figure 2.3 : Choice Experiment Response Questions ................................................................... 54 Figure A2.1: Intercept Survey (Paper Version) ........................................................................... 86 Figure A2.2 : Map of Recreation Sites and Map of Entrance/Exit Roads .................................... 90 Figure A2.3 : Intercept Survey Outer Envelope ........................................................................... 92 Figure A3. 1: Screen Shot of Online Follow -Up Surve y .............................................................. 93 1 INTRODUCTION Animals have been a source of wealth and value throughout human history and across all cultures. While this notion is not disputed, history is replete with examples of extinction events caused by the mismanagement of animal capital stock. Environmental and natural resource economics emerged in the second half of the 20 th century, in part, to identify and promote welfare -enhancing wildlife management practices. One key insight that informed this effort was the recognition that animals and other natural resources provide multiple values and benefits, and this came to be kno wn as a Total Economic Value (TEV) framework. Under this framework, people can hold both use and nonuse values for different animal species. Use values typically involve some sort of direct interaction with an ecosystem resource, while nonuse values relate to people™s intrinsic or existence value for an ecosystem resource. Use values can be further subdivided into consumptive and non-consumptive use values, where consumptive use typically involves extraction of the resource and non -consumptive use does not (Heal et al. 2005; Segerson 2017). This thesis contributes to knowledge about the TEV of elk in Michigan. After going extinct in the 19 th century, elk were reintroduced to Michigan in 1918 and can now be found in a 600 square -mile elk range in the northe rn Lower Peninsula. Given the uniqueness of this particular elk herd, there is likely some nonuse value for Michigan residents. As an example of this, the state of Michigan recently introduced specialty elk themed license plates as a way to commemorate the 100th anniversary of the elk reintroduction. Consumptive use values are derived from an annual Michigan elk hunt. Each year, thousands of Michigan residents enter a lottery to win one of 200 Michigan elk hunt licenses. Though the Michigan Department of Natural Resources (MDNR) actively seeks to minimize negative values created by the elk herd, 2 the herd has been known to cause crop damage to neighboring farms and to be involved in vehicular collisions on Michigan roads and highways. This study directly per tains to the non -consumptive use value of the Michigan Elk Herd, which is elk viewing. Elk viewing can occur anywhere throughout the elk range, but it tends to take place around areas that the MDNR has cleared and planted for elk feeding and elk viewing areas. Elk viewing typically occurs at dawn or dusk, when the animals are most active, and fall is the peak elk viewing season, as this time of year corresponds to the elk rutting season. Additionally, elk viewing can occur simultaneously with the many other recreational activities that occur within the Michigan Elk Range. The first essay presents a recreation demand model for visitors to the Michigan Elk Range. Because the Michigan Elk Range is large, dispersed, and has many entrance roads, it is difficult to identify and estimate the underlying population of Michigan Elk Range users. Generally, the population is composed of Michigan residents (with lesser numbers from neighboring states) who hunt, fish, or engage in some other type of remote outdoor recrea tional activity . The essay will identify consumer surplus values per trip to the Michigan Elk Range, and Appendix IV presents some strategies and insights that could be used in future research to identify the target population. The recreation demand model uses data from an intercept survey conducted in major recreation areas of the Michigan Elk Range during the summer and fall of 2018. Because the area is also used for a variety of other forms of recreation (e.g., hunting, fishing, hiking, camping, etc.), t his essay also presents separate models based on respondents™ primary activities in the Michigan Elk Range as well as their stated attitudes concerning the elk herd. 3 The second essay presents the results of a discrete choice experiment that was completed by a sample of Michigan Elk Range visitors in a follow -up survey conducted in the spring of 2019.1 The choice experiment tasked respondents with choosing between two possible recreation areas that differed in their distance from the respondent™s home and t he likelihood of experiencing various elk -related attributes. There was significant variation in respondents™ preferences for the various elk -related attributes, so the essay also reports strategies for segmenting respondents into different classes. 1 The follow -up online survey was sent to visitors who completed the intercept survey and provided an email address. 4 REFERENCES 5 REFERENCES Heal, G. M., Barbier, E. B., Boyle, K. J., Covich, A. P., Gloss, S. P., Hershner, C. H., ... Shrader -Frechette, K. (2005). Valuing ecosystem services: toward better environmental decision -making . National Academies Press. Segerson, K. (2017). Valuing Environmental Goods and Services: An Economic Perspective. In P. A. Champ, K. J. Boyle, & T. C. Brown (Authors), A primer on nonmarket valuation (pp. 1-25). Springer. 6 CHAPTER 1 : Segmented Recreation Demand Models for the Michigan Elk Range I. Introduction The idea of wilderness has long captivated the American imagination. When the possibility emerged that America™s wilderness could disappear due to urbanization and over extraction of natural resourc es in the first half of the 20 th century, Congress responded by setting aside public land to be preserved in perpetuity through the Wilderness Act of 1964. This act defines wilderness as fian area where the earth and its community of life are untrammeled by man, where man himself is a vis itor who does not remainfl, and part of the motivation behind wilderness preservation was to provide fiopportunities for solitude or a primitive and unconfined type of recreationfl (Wilderness Act of 1964). This definition of wilderness recreation inherently requires trade -offs. Most notably, managers of wilderness areas are tasked with striking a balance between visitor accessibility and comfort, on the one hand, with solitude and protection of plant and animal life, on the other (Lawson and Manning 2001). Wh ile wilderness recreation is diverse and continually changing, one significant subset is wildlife -based recreation. Over 35 million Americans fished and over 11 million Americans engaged in some form of hunting in 2016. Additionally, over 86 million Americ ans engaged in wildlife viewing, including 23 million Americans who travelled at least one mile away from their home with the primary purpose of wildlife viewing (Cordell et al. 2008; USFWS 2016). 2 In this spirit, the aim of this study is to estimate the economic value, or consumer surplus, of recreational trips taken to the Michigan Elk Range. This specific application is a useful case 2 fiWildlife watching is defined here as closely observing, feeding, and photographing wildlife, visiting parks and natural areas around the home because of wildlife, and maintaining plantings and natural areas around the home for the benefit of wildlife– secondary or incidental participation, such as observing wildlife while doing something else, was not included in the survey (USFWS 2016). 7 study in valuing wilderness recreation because the Pigeon River Country State Forest, the core of the Michigan Elk Range , is one of the largest undeveloped areas in Michigan™s Lower Peninsula (MDNR 2007). Most distinctively, this area is home to Michigan™s only free -roaming elk herd, and the herd provides visitors with both consumptive value (through the annual elk hunt) as well as non -consumptive value (through elk viewing). To accomplish this valuation, we report the results of a survey of Michigan Elk Range visitors conducted in the summer and fall of 2018 and estimate several single -site travel cost models of recreation demand. Our first model is for overall Michigan Elk Range visitors, and we find that the mean consumer surplus value for a visit (per -household, per -trip) is $86.21, and this corresponds to a per -day average value of $20.28. Th is estimate is an unbiased e stimate of the average consumer surplus value per trip , because we use methods to correct for the intercept sampling . However, in order to estimate an aggregate consumer surplus value for recreational visits to the Michigan Elk Range, we would need to quan tify the total trips or the population of Michigan Elk Range users. This is challenging given the dispersed nature of recreation in the region, so Appendix IV includes some strategies and insights that could be used in future efforts to estimate the target population. In order to approximate the value of the elk herd to visitors, our second set of demand models segment respondents by their reported interest in seeing elk on their visit. The third set of demand models segment respondents into groups based o n the primary activity of their intercepted visit. Given the uniqueness of the elk herd, we would expect that elk viewers have a higher consumer surplus value for accessing the Michigan Elk Range than other visitors because there are no nearby substitutes. This is indeed what we find. Visitors reporting that the chance of seeing elk was their primary motivation for visiting the area exhibit higher consumer surplus 8 values than those who say that the elk either played some role or no role in their decision to visit. This finding is repeated when we run separate models by visitors™ primary activities, and we find that visitors coming to the area primarily for wildlife viewing have the highest consumer surplus values of any activity group. This study is situa ted in two areas of the recreation demand literature. Because of the unique presence of the elk herd, this study is linked to the literature on the demand for wildlife viewing. There have been many papers that have examined the economic value for various t ypes of wildlife viewing, and one of the more popular subjects has been bird watching. For example, studies on the value of bird watching include Edwards et al. (2011), which estimated the value of migratory shorebird viewing in Delaware using a single -sit e travel cost model, and Kolstoe and Cameron (2017), which used data from an online bird watching social media platform to estimate the consumer surplus value or willingness to pay (WTP) for additional bird species using a multi -site travel cost model. The y also explored how novelty and variety -seeking preferences influence visitor site choice when bird watching. Other studies have explored the value of viewing large charismatic mammals, and these include studies on bear viewing (Richardson et. al 2014; Ric hardson et. al 2017), whale watching (Loomis et. al (2000), and African safari animals (Mladenov et al. (2007). A few studies have looked directly at elk viewing. Donovan and Champ (2009) used a single -site travel cost model to estimate the value of elk vi ewing in Oregon during winter supplemental feedings, and their study reported a mean per -day consumer surplus value of $138 ($170.45 in 2019 dollars). 3 This is likely to be higher than the Michigan elk range use value 3 Donovan and Champ report a sample mean per day access value of $369. We are unsure how they reached this number. Consumer surplus for an individual is defined as =. Donovan and Champ report that their travel 9 because the authors of this study assu med a higher travel cost, but it could also differ because of different preferences, site quality, and other factors. Their paper defined direct vehicle costs as $0.485 per mile, which was the IRS standard mileage rate in 2007. This represents an average vehicle operation cost, which includes full coverage insurance and any vehicle taxes and registration fees. Alternatively, we will use a marginal travel cost instead of an average cost (see section III for details on how we determine travel cost), so our di rect vehicle costs are much lower (Hang et al. 2016). Additionally, elk viewing was the only activity in the Donovan and Champ study area, whereas the present study in the Michigan Elk Range includes visitors participating in a whole range of activities. Other studies that estimate values for elk viewing include Loomis and Caughlan (2004), which estimated a mean consumer surplus of $52 per -day ($74 in 2019 dollars) for elk and bison viewing in the National Elk Refuge in Wyoming, and Shafer et al. (1993), w hich estimated consumer surplus for elk viewing in Pennsylvania to be just over $20 per -day for intercepted visitors ($43.30 in 2019 dollars). It should be noted that the Shafer study used a stated preference approach (i.e. visitors were asked open -ended q uestions about their WTP for elk viewing), while this study uses a revealed preference approach based on actual behavior. Another strand of relevant literature includes studies that provide additional insights to the single -site travel cost model. Aside f rom simply determining site access values, these studies use the single -site travel cost model to answer additional research questions. Boxall et al. (2003) combined a single -site travel cost model (revealed preference) with contingent behavior questions ( stated preference) in order to estimate the economic value of aboriginal pictographs on wilderness canoe trips in Manitoba. Respondents were asked to answer a question about their actual number of trips to the park as well as a hypothetical question about how many additional 10 trips they would take provided that they would see a pictograph. This results in two dependent variables, and they were able to determine the added value of the pictographs by taking the difference between consumer surplus with the actu al trips versus consumer surplus with the hypothetical trips. Of course, this method depends on the hypothetical pictograph question introducing new information to the respondent. If a respondent had already factored in the presence of pictographs, then be ing informed about them in the survey would not change his trip behavior. Another approach that contributes insights beyond the simple single -site travel cost model involves running segmented models for different visitor groups, and this is an approach tha t we adopt in this study. Benson et al. (2013) did this in the context of visits to Yellowstone National Park. Apart from estimating consumer surplus values for the entire sample of respondents, they estimated values for distinct types of visitors to Yello wstone. Using activities reported in a survey, the authors used cluster analysis to group respondents into activity -based clusters, and their demand models showed that activity clusters had different consumer surplus values for their respective trips to Ye llowstone, with backcountry enthusiasts having about twice the surplus values as picnickers. The present study contributes to the small number of studies that estimate consumer surplus values for wilderness recreation. Additionally, this is one of the onl y studies to estimate the value of elk viewing in the Eastern United States. Originally native throughout the eastern half of North America, Eastern Elk went extinct by the end of the 19 th century. Michigan and Pennsylvania were early states to reintroduce elk, which they did in the 1910s. Apart from Michigan and Pennsylvania, there are now elk herds in Arkansas, Kentucky, Missouri, Minnesota, North Carolina, Tennessee, Virginia, West Virginia, and Wisconsin (RMEF 2019). 11 Many of these herds have been establ ished in the past 30 years through partnerships between the Rocky Mountain Elk Foundation (RMEF) and state wildlife agencies. Elk reintroduction results in the creation of consumptive use values (from hunting), non -consumptive use values (from elk viewing and ecosystem services), and existence values (Segerson 2017). Elk reintroduction can also result in negative values, and two salient examples of this would be vehicular collisions and crop damages (Hegel et al. 2009). 12 II. Survey and Data Figure 1.1 : Michiga n Elk Range Though the Michigan Elk Range is made up of both public and private land, this study only surveyed visitors in portions of the Pigeon River Country State Forest (PRCSF) and Atlanta State Forest (ASF) where recreation is known to occur. In the summer, recre ation centers on lakes, rivers, and seven state forest campgrounds. Boating, swimming, and fishing occur in area lakes, and the most popular lakes include Cornwall Flooding, Pickerel Lake, various sinkhole lakes, and Foch Lakes (in the ASF). Both the PRCSF and the ASF have numerous access points to highly rated fly -fishing sections of the Pigeon, Sturgeon, and Black rivers. There are several hiking, biking, and equestrian trails in the Michigan Elk Range. The most prominent is the High -Pigeon River Country SF Atlanta SF 13 Country Pathway, an 8 0-mile trail that circumnavigates the Michigan Elk Range. The most popular form of recreation in the fall is hunting, which is highly dispersed throughout the forests. Elk Viewing is another popular activity in the fall, as well, and it peaks in popularity in late September Š during the elk rutting (or mating) season. The MDNR maintains about 1,000 acres of grass openings and planted fields for elk feeding. Some of these openings are publicized as fielk viewing areasfl on MDNR maps and brochures, along with ot her helpful information on elk viewing (MDNR 2012). There is a total of 13 elk viewing areas identified throughout the Michigan Elk Range (MDNR 2019). Some have dirt parking areas that allow visitors to view elk from their cars, while others require a shor t hike to reach. In general, PRCSF recreation guidelines require that recreation is low impact, is not noisy or something that lessens the enjoyment of others, does not lead to further development of facilities, and is consistent with the overall wild char acter of the forest (MDNR 2007). The data used in this study comes from an intercept survey conducted in the summer (June, July, and August) and fall (September, October, and November) of 2018 along predetermined routes in the Michigan Elk Range. The route s were not all -encompassing (due to the dispersed nature of recreation in the area), but they were chosen to balance the need for interviews and the need for a representative sample. The summer intercept surveys were conducted between June 7 th and Septembe r 1st, and the sampling was scheduled on a rotational basis - 4 days of sampling followed by 4 days without sampling. The fall intercept surveys were conducted between September 9 th and November 24 th, and the sampling was scheduled on random days adjusted f or interviewer availability. We interviewed visitors seen along routes and left paper surveys on the windshields of parked cars when the vehicle owners were not present. These paper surveys were individually numbered so that returned surveys could be match ed with 14 route vehicle count records to determine when and where the survey was distributed. The response rate for interviews was nearly 100% and the return rate for paper surveys left on windshields was 28% in both the fall and summer. All total, the inter cept survey collected 756 usable observations. See Appendix I for disposition tables that detail the response rates for the survey. 4 Whenever a group of visitors was encountered, we only interviewed one member. In order to minimize bias, the adult with the most recent birthday was asked to complete the interview. The survey included questions on home zip code, the recreational activitie s participated in over the course of the visit, sites visited within the Michigan Elk range, total hours of visit (if day trip), total nights of visit (if overnight trip), lodging type, whether recreation was the main reason for the overall trip, how many times the visitor left and reentered the forest, the importance of seeing elk for the visit, whether/where they saw elk, how many people travelled with them to the forest, how many trips they took to the Michigan Elk Range in the past year, and the respond ent™s age, gender, and highest level of education. 68% of the sample is male, and the mean age is 51.7. The most common primary activities were (in order of popularity): hunting, camping, fishing, and hiking. Close to 80% of visitors in our sample were int ercepted on an overnight trip away from their primary home. One of the overall objectives of this study is to understand values for elk viewing, so it was important to interview visitors whose primary recreational activity was elk viewing. This was done by including elk viewing areas at the end of evening shifts. One challenge in intercepting elk viewers is that some of them drive around the elk range looking for elk, as 4 Appendix IV reports 367 completed interviews and 393 returned paper surveys for a total of 760 completed surve ys. The completed survey count (760) differs slightly from the usable (756) survey count because four respondents returned a paper survey in which they indicated that they had already completed a survey. 15 opposed to parking in one location for the duration of the activity (like fishing, hi king, biking, etc.). Additionally, elk viewing typically occurs at dusk, when the elk are most active. This relatively short window made it difficult to cover all the elk viewing areas in one shift. In total, 35% of sampled visitors reported elk viewing as one of the activities they participated in on the visit when they were surveyed, and 10% reported that elk viewing was the primary activity (alone or in combination with another activity) on the surveyed visit. One reason to believe that elk viewing may b e more common than what is indicated in the survey data is that a follow -up survey of elk range visitors indicated that about 80% of them had gone elk viewing at least once sometime in the past. 5 III. Theory of Recreation Demand For goods and services traded o n a market, prices can reveal information about the value that people place on that good or service. Because most environmental amenities in wilderness recreation are not traded in markets, there are no corresponding prices to reveal value. Forests, beache s, rivers, and mountains facilitate outdoor recreation and are welfare enhancing, but for a variety of reasons, access tends to be free or only requires a small fee that does not reflect users™ values. The PRCSF does not have any access fee, although it do es require a Michigan Recreation Passport to access some trailheads and boat ramps. The job, then, for researchers is to estimate consumer surplus values in the absence of market prices. Typically, this is done in one of two ways. Researchers can directly elicit information using survey questions on hypothetical scenarios relating to recreation Š referred to as stated preference. Another approach infers values using data on actual recreational behavior Šreferred to as revealed preference. This study will 5 The follow -up survey was an online survey conduc ted in the spring of 2019. It was made up of about 300 respondents from the intercept survey who provided us with email addresses. 16 use respondents™ reported trips and travel costs to estimate a demand curve for recreation in the Michigan Elk Range. One form of revealed preference valuation uses travel cost as a proxy for the price of recreational site access. The idea, first proposed by Harold Hotelling in a letter from 1947, is that visitors to any given recreational site pay an explicit price (for fuel costs, tolls, entrance fees, and vehicle depreciation or maintenance) and face an opportunity cost for the time spent travelling to the site (Freeman et al. 2014). This means that a sample of visitors to a recreational site cover a whole range of latent site -access prices, and researchers can use this information along with various demographic characteristics and a dependent variable (the number of actual trips each visitor took to the site over a given period) to estimate a demand curve for recreational site access. All else equal, we would expect that someone living 20 miles away from a given recreational site would take more trips to th at site than an identical person living 40 miles from that same site. When analyzing a cross -section of data from a single recreational site, this idea can be expressed formally as a single -site travel cost model. This model says that the number of trips an individual takes to a given recreational site over the course of a season ( ) is a function of the individual™s cost in reaching that site ( ), trip costs to substitute sites, various demographic characteristics of t he individual ( ), and the individual™s income () (Parsons 2017). We were not able to get data on substitute sites as there are a large number of alternatives sites for most activities , but we do explore the issue of heterogeneity in the consumer surplus values by segmenting the recreation model. Therefore, our model can be expressed as : =(,,) (1) 17 Consumer surplus for that same individual is simply the integral of equation 1 with being the current access price and being the choke price (i.e. the travel cost at which the individual would not take any trips to the site). =(,,) (2) Travel cost is made up of two components: di rect, out -of-pocket costs as well as an opportunity cost of time. In order to estimate the opportunity cost of time, we follow a common approach in the literature and define it as 1/3 of the respondent™s hourly wage rate (Freeman et al. 2014; Parsons 2017) . To get an hourly wage, we divide each respondent™s annual household income (which we define as the mean household income in the respondent™s home zip -code) by 2,080. The direct, out -of-pocket costs are calculated as $0.285 per mile multiplied by the roun d-trip distance divided by the number of adults in the vehicle group. 6 This out -of-pocket travel cost is lower than driving costs sometimes seen in the literature because we only include expenses that were solely incurred for the recreational trip (i.e. th e marginal driving costs), so this would not include money paid for vehicle purchase, insurance, or registration. Distances are measured from the respondents starting zip -code to the location in the Michigan Elk Range where they were interviewed or received a paper survey. Distances and travel times are calculated using the Stata georoute module (Weber and Péclat, 2017). Travel cost is formally defined as follows (where is annual household income in dollars, is round -trip travel time 6 The $0.285 per mile figure assumes fuel efficiency of 22 mpg (U.S. BTS 2019), average fuel price of $2.80 per gallon (U.S. EIA 2019), $0.0756 per -mile vehicle marginal depreciation costs, and $0.0821 per -mile vehicle marginal maintenance costs (AAA 2018). 18 in hours, is round -trip distance in miles, and is the number of adults travelling in the vehicle): =2,08013+0.285 (3) A common empirical challenge that researchers face when estimating travel cost models is how to use multiple purpose and /or multiple destination trips, as it is not clear how to delineate travel costs among separate components of an overall trip (Parsons 2017; Freeman et al. 2014). This problem is more common in cases where the respondent is on an overnight trip, as is the case with 80% of Michigan Elk Range visitors in our sample. Our solution, then, was to ask respondents to report whether recreation in the Michigan Elk Range was their primary purpose for making the overall trip away from home. If a respondent answered fiye sfl, then we used the respondent™s home zip -code as their starting zip -code. If a respondent answered finofl, then we used the distance from their primary destination to the Michigan Elk Range. 7 Out of the 756 total responses, 4 respondents did not include a zip -code and 54 (7.1%) respondents indicated that recreation was not their main reason for visiting. Of these respondents, 26 provided the location of their primary destination (allowing us to give them a new starting zip - code), 28 respondents were given a n imputed distance and 9 were removed because they reported not having a main destination. 8 In total, 743 (96.3%) of the 756 respondents were included in the travel cost analysis. Fourteen respondents did not provide their age, and 14 respondents did not provide their education level. We replaced these missing values with the respective mean values. 7 The primary destination location is determined from one of two ways. In the fall intercept survey , we asked respondent s staying in lodging outside of the forest to report the city t hat t hey stayed in. We also asked respondents to report the city where their primary destination was located in a follow -up online survey we did in early 2019. 8 The imputed distance was the m ean distance of visitors who had a starting zip -code other than their home zip -code. 19 IV. Poisson Count Model In order to estimate our model, we use a truncated Poisson count model that is adjusted for endogenous stratification ( i.e. the over -sampling of high use visitors ). This structural solution corrects for potential bias in the parameter estimates (provided that the data generating process for trips does indeed follow a Poisson distribution), but it does not correct for potential bias in visitor characteristics (e.g., age, income, seasonal trips, etc.). Because of that, the results provide an unbiased estimate of the p er-trip consumer surplus values (Haab and McConnell 2003) , but by themselves do not provide an unbiased aggregate value. To estimate demand curves for the average visitor and aggregate the values , we would need to weight the intercept ed data by the probability of being intercepted. We assume that a Poisson specification is appropriate for estimating trips for our underlying target population (Michigan Elk Range visitors) . However, it is highly likely that this specification does not represent the trip data generating process for a population defined as all Michigan adults since the vast majority of Michigan adults would never visit this area ; rather it applies to some population of potential visitors . Appendix IV provides a discussion about how future research might estimate the target population of Michigan Elk Range visitors and/or the total number of trips . A Poisson speci fication is commonly used in recreation demand modelling because it handles non -negative discrete count data well. The disadvantage of a Poisson specification is that it assumes that the mean and variance (both defined by the parameter ) are the same, which is not always the case (Haab and McConnell 2003). 9 A standard Poisson model defines the probability of a household taking trips over the course of a season as: 9 To check for overdispersion , we ran a negative -binomial model with a correction for endogenous stratification . The resulting dispersion coefficient ( ) was not significant, so we were justified using a Poisson specification . 20 pr()=exp ()×! (4) Running this Poisson regression results in coefficients for each of the explanatory variables (travel costs, demographic variables, and income). The expected number of overall trips in a year (semi -log demand function) is given as follows: ()==exp++ (5) The consumer surplus per season can be calculated as = and, likewise, consumer surplus per trip can be estimated as =.10 Two common approaches to sampling include random population sampling ( i.e. sending survey invites to random members of the general public) and on -site sampling (Haab and McConnell 2003). We chose to use an on -site sampling approach because the Michigan Elk Range is a sparsely visited recreation area, and if we had used a random sample of Michigan residents, the vast majority of respondents would have likely told us that they have never visited the Michigan Elk Range. That being said, the biggest disadvantage to on -site sampling comes from endogenous stratification. Endogenous stratification , as mentioned above, simply means that when employing an on-site survey, interviewers are more likely to encounter visitors with high use levels than visitors with low use levels. Our sample is more likely to include the person who visits the Michigan Elk Range everyday than the person who only ever visited a single time. Failing to adjust for endogenous stratification would mean that the sample average of trips and the 10 Consumer surplus is the area under the demand curve (see equation 2). Since the Poisson specification uses an exponential demand function, the choke price is infinite. Thus, = exp (+ ) = ( ) = (Haab and McConnell 2003). 21 estimated demand parameters would be biased. To account for endogenous stratification, one needs to account for the intercept probabilities based on the stochastic process that generates the trip taking data for the population (Haab and McConnell 2003). It has been shown that when the data generating process for tr ip taking is itself a Poisson process, then the unbiased population parameters can be estimated from a standard Poisson regression of the number of trips minus one (1) on the independent variables (Haab and McConnell 2003), as in equation (6). This correction does not change the upward bias in the sample average of trips, but it does yield unbiased parameter estimates of the demand function. pr()=exp ()×1! (6) Table 1. 1: One -Way Distances from the Michigan Elk Range (unweighted) Distance ( miles ) Frequency Percent 0-20 99 13.32% 20-40 134 18.03% 40-60 39 5.25% 60-120 48 6.46% 120-180 82 11.04% 180-240 219 29.48% 240+ 122 16.42% Total 743 Table 1.1 shows the breakdown of visitor one -way travel distances to the Michigan Elk Range. One thing to note is that 30% of visitors live between 180 and 240 miles from the 22 Michigan Elk Range. This range contains much of the Michigan population center sŠ Detroit and its surrounding suburbs, Lansing, and Grand Rapids. A similar proportion of visitors live in nearby communities in Northern Lower Michigan (i.e. those between 0 and 40 miles away). Out of state visitors are a small, but not insignificant, su bset of the overall sample. V. Results Table 1.2 : Descriptive Statistics for Respondents (Unweighted) Variables Description Mean SD Annual Trips Trips to Michigan Elk Range in last year 8.47 23.31 Male Male=1 Female=0 0.69 0.46 Income Mean household income by zip -code ( in thousands of dollars ) 71.46 22.43 Trip Length Length of visit to Michigan Elk Range ( in days ) 4.25 3.15 Vehicle Group size Total vehicle group size (net children under 18) 1.90 1.01 Travel Cost See equation 3 120.38 156.66 Distance One -way distance from Michigan Elk Range 152.81 177.61 23 Table 1.3 : Overall Travel Cost Model (Poisson Maximum Likelihood Model) Variables (1) (2) Travel Cost -0.0116*** -0.0116*** (0.000276) (0.000276) Income -0.00800*** -0.00807*** (0.000964) (0.000956) Age 0.00360*** 0.00361*** (0.000914) (0.000909) Education Level -0.00506 (0.00562) Male 0.0230 (0.0288) Constant 3.274*** 3.220*** (0.105) (0.0741) Log -Likelihood -7759.3718 -7760.1481 Observations 743 743 Consumer Surplus 86.21*** 86.21*** Income Elasticity -0.57*** -0.58*** Own-Price Elasticity -1.4*** -1.4*** Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 24 Figure 1.2 : Demand Curve for Overall Recreation Demand Model (unweighted, using average trip characteristics) Table 1.3 includes results of the single -site travel cost model we used to estimate per -trip consumer surplus values for all recreation in the Michigan Elk Range. As we would expect, the coefficient on travel cost is negative and significant, and the mean consumer surplus per -trip to the Michigan Elk Range is $86.21. Given that the mean trip length from our intercept survey was 4.25 days, the mean consumer surplus per -day is $20.28. The coefficients on age and income are significant, and they indicate that older visitors are expected to take more trips in a year and that wealthier visitors are likely to take less trips in a year. The education level and gender variables were not significant, and it made no practical difference to the results when these varia bles were dropped in model 2. Figure 1.2 maps out a demand curve for the overall model using mean values for all demographic values. Income and own -price elasticity measures are calculated by multiplying the respective parameter estimates with the sample m eans for income and travel cost. 25 The income elasticity ( -0.57) is negative, and this indicates that recreational trips to the Michigan Elk Range is an inferior good. The own -price elasticity ( -1.4) is elastic, indicating the presence of many substitutes. T his idea will be explored later in the segmented model approach. The travel cost model summarized in Table 1.3 tells us the expected per -trip values for the Michigan Elk Range population, but it does not easily lend itself to comparison or tell us anythin g about how visitor segments value the area differently. One way to segment visitors is to run separate travel cost models based on survey respondents™ attitude toward the elk herd. This first segmented model uses the following question from the intercept survey: fiWhat role did the chance of seeing elk play in your decision to visit?fl Respondents were given three possible options as answers. The first was fithe chance of seeing elk was my primary reason for visitingfl. The second option was fithe chance of see ing elk played a role in my decision to visit, but it was not my primary reasonfl. The third option was, fiThe chance of seeing elk played no role in my decision to visitfl. Some summary statistics about the three groups are shown in Table 1.4. It is importan t to remember that this question was asked specifically in reference to the visit when the visitor was surveyed. Therefore, it does not necessarily represent any given individual respondent™s attitude toward elk for all of their visits to the Michigan Elk Range over a given year. Still, by assuming that our sample is representative of all recreation trips to the Michigan Elk Range in summer and fall, this question provides a useful metric for estimating the value of elk viewing. 26 Table 1.4 : Summary Statistics by Respondents™ Answers to the Question fiWhat role did the chance of seeing elk play in your decision to visit?fl Mean Trip Length ( days ) Mean Trips in Past year (trips ) Mean Travel Cost ( dollars ) Mean Distance (miles ) Mean Income (thousands of dollars ) Primary reason for visiting (n=113) 4.71 6.99 $104.70 145.7 69.91 Played a role, but not primary (n=294) 4.45 6.07 $137.00 173.7 73.83 Played no role (n=333) 3.94 11.14 $111.60 137.5 69.98 27 Table 1.5 : Travel Cost Model Segmented by Answer to Elk Importance Question Variables Elk -Very Important Elk -Somewhat Important Elk -Not Important Travel Cost -0.00813*** -0.00859*** -0.0150*** (0.000665) (0.000425) (0.000464) Income -0.0218*** 0.000920 -0.00904*** (0.00302) (0.00153) (0.00145) Age -0.0551*** 0.0104*** 0.0125*** (0.00274) (0.00182) (0.00116) Education Level -0.155*** -0.00757 0.0240*** (0.0201) (0.0107) (0.00722) Male 0.0163 -0.329*** 0.0580 (0.0827) (0.0529) (0.0394) Constant 8.970*** 2.181*** 2.728*** (0.345) (0.199) (0.140) Log -Likelihood -822.54542 -2050.877 -4296.3416 Observations 113 294 333 Consumer Surplus 123.00*** 116.41*** 66.67*** Income Elasticity -1.52*** 0.07 -0.63*** Own-Price Elasticity -0.85*** -1.18*** -1.67*** Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Table 1.5 displays separate travel cost models for each of the three responses to the question on elk importance in the intercept survey. The highest per -trip consumer surplus comes from visito rs who indicated that the presence of elk was their primary motivation for visiting the Michigan Elk Range, and their consumer surplus per -trip is $123.00. The second group ( elk played some role ) has a mean per -trip consumer surplus of $116.41, and the thi rd group ( elk played no role ) has a mean per -trip consumer surplus of $66.67. When adjusted for mean trip lengths, the per -day consumer surplus values are $26.11 ( elk were primary reason for visiting ), $26.16 (elk played some role ), and $16.92 ( elk played no role ). 28 When only looking at those respondents who answered that elk viewing was their primary motivation for visiting, those who take the most trips to the Michigan Elk Range are, on average, younger and have less education and income. When only lookin g at those respondents who answered that elk viewing played some role in their decision to visit, those who take the most trips to the Michigan Elk Range are, on average, older and more likely to be female. When only looking at those respondents who answer ed that elk viewing played no role in their decision to visit, those who take the most trips to the Michigan Elk Range are, on average, older and have higher education levels but less income. Although there is little difference in the consumer surplus esti mates between the fielk were primaryfl group and fielk played some rolefl group, the large difference in consumer surplus estimates between the fielk played some rolefl group and the fielk played no rolefl group indicate that elk viewing is a non -trivial component of the overall value of Michigan Elk Range recreation. Segmenting Michigan Elk Range visitors by their answers to a question on elk importance was helpful, but this approach is limited insomuch that it is based on respondents™ answers to a subjective mult iple -choice question and tells us nothing about visitor motivation apart from elk viewing. Another way to segment respondents is to use their self -reported primary activity on the intercepted visit. Respondents were asked to report all of the activities th ey participated in as well as the primary activity or activities from the intercepted visit. 29 Table 1.6 : Summary Statistics by Primary Activity Groups Mean Trip Length ( days ) Mean Trips in Past year ( trips ) Mean Travel Cost (d ollars ) Mean Distance (miles ) Mean Income (thousands of dollars ) Path Activities ( n=140 ) 3.34 9.36 $120.30 153.7 74.23 Wildlife Viewing ( n=88 ) 4.30 5.500 $106.20 153.0 68.55 Hunting ( n=133 ) 5.62 13.38 $146.10 167.1 70.47 Water Activities ( n=174 ) 3.67 6.55 $128.00 158.2 73.78 Camping ( n=176 ) 4.86 5.06 $111.20 151.7 69.34 30 Table 1.7 : Travel Cost Model Segmented by Primary Activity Variables Path Activities Wildlife Viewing Hunting Water Activities Camping Travel Cost -0.0122*** -0.00215*** -0.00991*** -0.0116*** -0.0148*** (0.000632) (0.000751) (0.000456) (0.000644) (0.000808) Income -0.0326*** -0.00588* -0.00173 -0.00408* 0.00812*** (0.00242) (0.00312) (0.00167) (0.00235) (0.00303) Age 0.00761*** -0.00377 -0.0134*** 0.00832*** -0.000683 (0.00207) (0.00389) (0.00188) (0.00232) (0.00263) Education Level -0.267*** -0.0945*** 0.123*** 0.109*** -0.0784*** (0.0136) (0.0235) (0.0106) (0.0124) (0.0175) Male -0.900*** -0.475*** 0.248** 0.764*** 0.701*** (0.0618) (0.105) (0.108) (0.103) (0.0862) Constant 9.090*** 3.883*** 2.116*** 0.231 2.703*** (0.280) (0.428) (0.220) (0.253) (0.314) Log -Likelihood -1681.6223 -555.5855 -1394.1801 -1228.7362 -816.9303 Observations 140 88 133 174 176 Consumer Surplus 81.88*** 465.95*** 100.86*** 85.97*** 67.63*** Income Elasticity -2.42*** -0.40* -0.12 -0.30* 0.56*** Own-Price Elasticity -1.47*** -0.23*** -1.45*** -1.49*** -1.65*** Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 31 Table 1.6 displays some summary statistics by primary activity group and Table 1.7 displays the results of the separate models. To better facilitate analysis, primary activities were grouped into similar activities. fiPath Activitiesfl incl ude hiking/backpacking, bicycling, and horseback riding, and driving for pleasure. fiWildlife Activitiesfl include elk viewing, bird watching, and a more generic category for viewing wildlife and/or scenery. 81 of the 88 respondents in the fiWildlife Activiti esfl category reported elk viewing as their primary activity. fiCamping Activitiesfl include camping, relaxing, and picnicking. fiHunting Activitiesfl include hunting and mushroom picking. Lastly, fiWater Activitiesfl include stream fishing, lake fishing, swimmin g, and boating/kayaking/canoeing. Some respondents did not include a primary activity, and because of that, 58 (7.8%) of the respondents in the overall model are not included in this model. Some respondents (7.5%) indicated multiple primary activities. 11 Respondents that reported primary activities from two different activity groups (as defined above) show up twice in this model (one for each of their reported activities). The order of the mean consumer surplus values per trip by activity group are as fo llows: Wildlife Viewing ($465.12), Hunting ($100.91), Water Activities ($86.21), Path Activities ($81.97), and Camping ($67.57). Intuitively, the high value for wildlife viewing make sense. The wildlife viewing category is primarily composed of elk viewers , and since there are no substitute sites for elk viewing in the state, it would follow that mean consumer surplus are correspondingly higher than the activities with more substitute sites. This same type of insight similarly follows with regards to the ot her activity categories. In a rural area, such as Michigan™s 11 9 respondents are in both the path and wildlife viewing groups. 5 are in both the path and camping groups. 2 are in both the path and wa ter activity groups. 6 are in both the wildlife viewing and camping groups. 3 are in both the wildlife viewing and water activity groups. 1 is in both the wildlife viewing and hunting groups. 14 are in both the camping and water activity groups. 1 is in th e camping and hunting groups. 2 are in both the water activity and hunting groups. 32 northern Lower Peninsula, there are many available options for camping. Similarly, there are many nearby trails where one could go hiking, biking, or horseback riding. Hunting or participating in a water activity (fishing, boating, and swimming) in the Michigan Elk Range arguably has fewer apparent substitutes in the region. One possibility is that tradition, nostalgia, or past experience plays a role. In a follow -up survey we asked about the impo rtance of tradition when choosing to visit the Michigan Elk Range. 53% of overall respondents said that tradition was very important. For those that reported hunting in the Michigan Elk Range during the previous year, 64% said that tradition was very impor tant for visiting. Similarly, 63% of respondents who reported fishing in a stream in the Michigan Elk Rang during previous year and 62% of respondents who reported fishing in a lake reported that tradition was very important in their decision to visit. The high consumer surplus value for wildlife viewing is less clear, however, when approaching it from the perspective of the summary statistics found in Table 1.6. Wildlife viewers are, on average, the closest activity group to the Michigan Elk Range. Corres pondingly, they have lower average travel costs as well. Additionally, wildlife viewers, on average, have the second fewest (after camping) number of yearly trips to the Michigan Elk Range. Given this information alone, it does not follow that wildlife vie wing would have the highest consumer surplus value. The answer, then, as to why this group has such a high consumer surplus estimate is found when looking at the overall shape of the demand curve. 33 Figure 1.3 : Demand Models for Wildlife Viewing and Hunti ng (Using the average trip to the Michigan Elk Range) Figure 1.3 displays both the average trip demand curve s for wildlife viewing (the highest value activity group) and camping (the lowest value activity group), and the differences are striking. 12 The wildlife viewing trips exhibit a steep demand curve, indicating that changes to travel costs have less of an effect on the total number of trips demanded than does that same change for camping . Even though the average wildlife viewing trip has a close r starting point, the wildlife viewing trips that start from farther away have a (relatively) similar overall demand, and this is consistent with the intuitive understanding from above. The camping group, on the 12 The graph uses values from the average trip . This is different from the average visitor. 0200 400 600 800 1000 1200 1400 1600 1800 024681012Travel Cost Expected Trips Wildlife Viewing Camping 34 other hand, exhibits a flat demand curve. Th is means that camping trips are more sensitive to travel cost, and this likewise confirms the intuitive understanding that the relatively lower value for camping is driven primarily by an abundance of substitute sites in the area. In order to drive this po int home, it is worth noting that the own -price elasticity for wildlife viewing trips is -0.23 and the own -price elasticity for camping trips is -1.64, over 7 times larger. VI. Discussion The goal of this essay was to estimate the value of recreational access to the Michigan Elk Range, a near -wilderness area in the northern Lower Peninsula of Michigan. We found that the average per -trip consumer surplus value for a visit to the Michigan Elk Range is $86.21 (or $20.28 per recreation -day). In a follow -up survey (composed of 316 respondents to the intercept survey) we learned a little more about why visitors value the Michigan Elk Range. 80% of respondents reported that the quiet/solitude that characterizes the area was a very important reason in their decisions to visit. Similarly, 76% of respondents indicated that the non -developed nature of the area was a very important reason for visiting, and 70% reported that that the opportunity for remot e recreation was very important. This suggests that our consumer surplus estimate s capture some benefits of wilderness that could be lost with the possible development of roads, buildings, or other man -made facilities. We also ran segmented travel cost mo dels for visitor classes. The first segmented model split up the visitor sample by their reported interest in seeing elk on their intercepted visit. We found that there was a fairly large increase in consumer surplus estimates for visitors answering that t he elk presence played some role in their decision to visit as opposed to no role in their decision to visit. The consumer surplus estimate was nearly identical for respondents indicating that the elk presence played some role in their decision to visit as opposed to the primary role. 35 When segmenting visitors by their primary activity on the intercepted visit, we found that wildlife viewers had substantially higher consumer surplus estimates, and this was due to their inelastic demand for visits to the Mich igan Elk Range. Visitors primarily visiting to camp, on the other hand, have a very elastic demand for visits to the Michigan Elk Range. These results make economic sense given that there are no comparable substitute sites for the wildlife viewing (as this is the only elk herd in Michigan) yet there are many nearby camping sites . The results of this chapter rely on using an econometric technique to correct for our intercept sampling . While this approach yields and unbiased estimate of demand parameters an d per -trip consumer surplus values , additional research is needed to allow the values to be aggregated . Further work in this area should define the target population and sub -populations (based on primary activities) and compute aggregate consumer surplus v alues (see Appendix IV). Doing this would allow for better decision -making when managers find themselves dealing with a user conflict. Additionally, further work in this area should develop a scheme to weight the intercept survey by the likelihood of being intercepted. The intercept survey routes were roving , and certain areas received more coverage than others. Weighting each survey by the probability of interception would allow us to estimate demand curves using the average visitor to the Michigan Elk Ran ge. 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The Stata Journal: Promoting Communications on Statistics and Stata, 17(4), 962 - 971. doi:10.1177/1536867x170170041 40 CHAPTER 2 : Preferences and Values for Elk -Related Attributes among Visitors to the Michigan Elk Range I. Introduction While hunting and fishing participation rates have been stagnant or falling, more Americans than ever are engaging in wildlife viewing. In 2016 fi86.0 million U.S. residents, 34 percent of the U.S. population 16 years or older, participated in wildlife -watching activitiesfl, and this includes 23.7 million people who took trips away from their home to go wildlif e viewing (USFWS 2016). Despite the apparent value of wildlife viewing, the economics of wildlife viewing are generally not well -understood. Some of this is due to the ubiquitous nature of wildlife viewing around the home and in daily routines. Another com plication is that wildlife viewing can be enjoyed in conjunction with other recreational activities (e.g. , hunting, fishing, hiking, etc.). Additionally, the nature of wildlife viewing varies considerably depending on the animal in question. Whale watching is quite different from bird watching on one™s back porch, which is quite different from viewing elephants on an African safari. Accordingly, the best way to foster a better understanding of wildlife viewing is to build up a set of studies diverse in both geographic region and in the particular animal being viewed. In this spirit, this essay will examine elk viewing in Michigan. Michigan is one of the few eastern states with an elk herd, and this herd currently occupies over 100,000 acres in the northern Lower Peninsula, hereafter referred to as the Michigan Elk Range. The Michigan Elk Range is primarily located on state forest la nd, meaning that the area has a variety of other recreational and extractive uses. Given what we know about wildlife viewing and the unique characteristics of the Michigan Elk Range, our research questions are as follows. Does the chance of seeing Michigan ™s elk herd affect visitors™ 41 recreational decisions? What do preferences look like when we break up elk viewing into some component attributes? Is there variation in visitors™ preferences for elk viewing? If there is, can we use any known characteristics t o explain the variation? To answer these questions, we will use a discrete choice experiment (DCE) that was conducted with known visitors to the Michigan Elk Range. A choice experiment presents respondents with a survey choice scenario where they are taske d with choosing between two or more alternatives. Each alternative is described by a set of attributes, and these attributes vary between alternatives. By analyzing the respondents™ choices and their respective attributes, researchers can estimate preferen ces for the attributes and marginal rate of substitution values between pairs of attributes (Freeman et al. 2014). There have been many papers that have studied the economic value for various types of wildlife viewing, and one of the more popular subjects has been bird watching. Two studies on the value of bird watching include Edwards et. al (2011), which estimated the value of migratory shorebird viewing at a few Delaware beaches using a single -site travel cost model, and Kolstoe and Cameron (2017), whic h used data from an online bird watching social media platform to estimate willingness to pay (WTP) for additional bird species using a multiple -site travel cost model. Kolstoe and Cameron also explored how novelty and variety -seeking affects bird watching site choice. Other studies have explored the value of viewing large charismatic mammals, and these include studies on bear viewing (Richardson et. al 2014; Richardson et. al 2017), whale watching (Loomis et. al 2000), and African safari animals (Mladenov et al. 2007). Within this group, a few studies have estimated the value of elk viewing. Donovan and Champ (2009) used a single -site travel cost model to estimate the value of elk viewing in Oregon, and they estimated a sample mean per -day consumer surplus value of $138 ($170.45 in 2019 42 dollars). 13 Other studies that estimate values for elk viewing include Loomis and Caughlan (2004), who estimated a mean WTP of $52 per -day ($74 in 2019 dollars) for elk and bison viewing in the National Elk Refuge in Wyoming, and Shafer et al. (1993), who used an ope n-ended contingent valuation question to estimate a consumer surplus for elk viewing in Pennsylvania to be just over $20 per -day ($43.30 in 2019 dollars). Apart from the Shafer study, there have been no other studies on the economic value of elk viewing in the Eastern United States. Another strand of relevant literature is made up of studies that have used choice experiments to estimate the values of recreational site attributes. Horne et al. (2005) used a spatially explicit choice experiment to examine vis itors™ preferences for forest management. Christie et al. (2007) similarly used a choice experiment approach to value potential improvements in British forests, and they were able to segment their results by specific user types. A few studies have used cho ice experiments to estimate values for wildlife viewing attributes. Boxall and Macnab (2000) used a choice experiment to estimate forest management preferences of moose hunters and wildlife viewers in Saskatchewan, where wildlife viewing conditions was one of the attributes. In particular, they found that wildlife viewing had had an average welfare value of up to 75 dollars a trip ($129 in 2019 dollars). 14 Boxall and Adamowicz (2002) utilized a choice experiment to value Canadian wilderness recreation, and t hey were able to segment respondents using a latent class approach. Brock et al. (2017) utilized a DCE to estimate values for backyard bird feeding and found that respondents were principally motivated 13 Donovan and Champ report a sample mean per day access value of $369. We are unsure how they reached this number. Consumer surplus for an individual is defined as =1/ . Donovan and Champ report that their so this would result in a consumer surplus value per trip of $138. 14 This value was associated with places with the following attribute: fiSee common species of wildlife, one or two species never seen before, and a chance to see a rare or endangered specie s.fl 43 by non -consumptive use values (i.e. seeing the birds a nd engaging with them) as opposed to existence or intrinsic values. 15 They also found that respondents tended to value aesthetics over rarity and that people with more bird -feeding experience had higher engagement values than people with less bird -feeding e xperience. Besides implementing one of the few discrete choice experiments principally about wildlife viewing, this study is unique because it segments the wildlife viewing experience into various attributes related to elk. These attributes include seeing at least one elk, hearing an elk bugle, seeing a bull elk, and seeing 10 or more elk. One reason for doing this is that the elk - related attributes identified in this study have different levels of rarity. Elk bugling, for example, is mainly associated wit h the fall rutting (i.e. mating) season, a period in late September when the elk are most active. Similarly, seeing a bull (male) elk is rarer than seeing a female elk due to the natural sex ratio of the species. Ultimately, we found that there is high var iation in the values that Michigan Elk Range visitors place on experiencing the elk -related attributes, and we found that we could characterize Michigan Elk Range visitors into two types of visitors. The first type of visitor valued seeing at least one elk , hearing an elk bugle, and seeing 10 or more elk. The second type of visitor did not value the elk -related attributes as much as the first type and were more likely to either choose a recreational site outside of the elk range or choose to not recreate at all. Of all the attributes, seeing a bull elk was consistently insignificant for most visitors. This result is surprising because it goes against prior expectations, though we note in the discussion 15 The study describes the value of interacting with outdoor wildlife as a type ficonsumption valuefl. This is non -standard terminology. Typically, consumptive use values imply that one™s use of the good precludes use by another (e.g. , hunting, fishing, a nd harvesting). Non -consumptive use values, on the other hand, does not diminish resource use by others. Bird watching, as is discussed in this study, fits the non -consumptive use value benefit (Segerson 2017). 44 some reasons why the study design may not provide us wit h the power to confidently identify this effect. The structure of this paper is as follows. Section II provides and overview of the study area and details the data collection processes. Section III of the paper details the choice experiment, including mot ivation, experimental design, and pre -testing. Section IV covers the theoretical underpinnings of this study, that is random utility maximization (RUM) theory, and Section V covers the econometric theory used to estimate parameter values and variants that account for preference heterogeneity. Section s VI and VII analyze the overall results and identifies significant variation in elk -related coefficient estimates, and Section VII I reflects on and tempers the findings using auxiliary data. Our empirical str ategy for doing this will employ several different techniques for modeling preferences. The first model employs the simplest approach without heterogeneity, i.e. a conditional logit model. In order to check for variation in preferences for the elk -related attributes, the next step will be to estimate the model using a mixed logit approach. This approach provides standard deviation estimates for the elk -related attribute coefficients. After proving that there is significant variation in our estimates, the re st of the essay will look for visitor types that explain the variation. The first approach for doing this will be to return to a conditional logit model approach. However, this time it will be run using separate models that segment respondents by their pri mary activity from a previous visit to the Michigan Elk Range. The last approach will employ a latent class logit model that will use respondents™ elk viewing experience in order to explain class membership. 45 Figure 2.1 : Michigan Elk Range II. Study Area and Survey Following extinction in the 19 th century, elk were reintroduced into Michigan a little over 100 years ago. Today almost 1,200 elk live in a 600 square mile elk range in Michigan™s northern Lower Peninsula, and this makes it one of the largest elk herds east of the Mississippi River. Much of the Michigan Elk Range is accessible for public recreational access at the Pigeon River Country State Forest (PRCSF) and portions of the Atlanta State Forest (see Figure 2.1). The PRCSF is known for maintaining a near -wilderness state (MDNR 2007). Comp ared with other state forests, the PRCSF is more continuous, has a lower road density, and Pigeon River Country SF Atlanta SF 46 maintains more stringent restrictions on the kinds of recreation they allow (e.g. , ORV and equestrian restrictions). The MDNR maintains about 1,000 acres of grass op enings and planted fields for elk feeding. Some of these openings are publicized as fielk viewing areasfl on MDNR maps and brochures, along with other helpful information on elk viewing (MDNR 2012). There is a total of 13 elk viewing areas identified through out the Michigan Elk Range (MDNR 2019). Some have dirt parking areas that allow visitors to view elk from their cars, while others require a short hike to reach. In addition to elk viewing, other popular recreational activities in the Michigan Elk Range in clude hunting, fishing in lakes and rivers, kayaking and boating, camping, horseback riding, hiking and backpacking, as well as morel mushroom hunting. Aside from recreation, portions of the Michigan Elk Range are used for logging and oil drilling. This essay uses data collected in a two -stage survey of Michigan Elk Range visitors. The first phase of our survey consisted of an intercept survey conducted in the summer (June, July, and August) and fall (September, October, and November) of 2018. Respondents were intercepted along predetermined routes in the Michigan elk range. The routes were not all -encompassing due to the dispersed nature of recreation in the area, but they were chosen to balance the need for interviews as well as a representative sample o f visitors. The summer intercept surveys were conducted between June 7 th and September 1 st, and sampling was scheduled on a rotational basis Š 4 days of surveying followed by 4 days without surveying. The fall intercept surveys were conducted between Septem ber 9 th and November 24 th, and sampling was scheduled on random days adjusted for interviewer availability. We interviewed visitors seen along routes and left paper surveys on the windshields of parked cars when visitors were not present. Paper surveys wer e individually numbered so that returned surveys could be matched with our records to determine when and where the survey was distributed. The response rate for 47 interviews was nearly 100%, and the return rate for paper surveys left on windshields was 28% in both the fall and summer. Ultimately, the intercept survey resulted in 756 usable observations. 16 A disposition table detailing survey response rates can be found in Appendix I. A key finding from the intercept survey was that 35% of visitors reported el k viewing as one of the activities they participated in on the visit when they were surveyed, and only about 10% reported that elk viewing was the primary activity (alone or in combination with another activity) on the surveyed visit. When asked what role the chance of seeing elk played in their decision to visit the Michigan Elk Range on the trip when they completed the intercept survey, 15% of respondents replied that the chance of seeing elk was their primary reason for visiting, 40% of respondents repli ed that the chance of seeing elk played some role (though not primary) in their decision to visit, and 45% of respondents replied that the chance of seeing elk played no role in their decision to visit. These results suggest that visitors to the Michigan E lk Range exhibit heterogeneity in their preferences for elk attributes when making site choices. Through the intercept survey, we were able to collect 580 email addresses for an online follow -up survey, and this was the second phase of the survey. These 580 contacts were emailed with up to 6 survey invites in March and April of 2019. Of the 580 survey invites sent out, 24 were undeliverable, 39 resulted in surveys that were started but not completed, and 316 surveys were successfully completed (see Appendix I). The first section in this online follow -up survey asked respondents several questions about the visit when they received the intercept survey. The second section asked about respondents™ forest related experience and attitudes. The third sect ion 16 Appendix I reports 367 completed interviews and 393 returned paper surveys for a total of 760 completed surveys. The completed survey count (760) differs slightly from the usable (756) survey count because four respondents returned a paper survey in which they indicated that they had already completed a survey. 48 included questions about the respondent™s elk viewing history and experiences, and asked questions about the importance of the elk attributes which also introduced the attributes. The fourth section included the choice experiment, and the fina l section included a few demographic questions. 49 III. Choice Experiment Figure 2.2 : Example Choice Experiment ( with hunting as the primary activity ) In the choice experiment, respondents were asked to think about future recreational trips in Michigan. These recreational trips were presented in the context of a designated activity, and 50 this activity was assigned to match each respondent™s reported prima ry activity from the intercept survey. 17 Each respondent was shown three choice sets. In each choice set, respondents chose between two possible recreational areas (hereafter referred to as the left -side area and right -side area) along with the choice to vi sit neither area, an opt -out option. All the possible recreational areas were given identical non -elk related attributes: campgrounds, hiking/biking trails, equestrian trails, and places for hunting, fishing, and morel hunting. Thus, the left -side and righ t-side areas only differ in their distance from the respondent and in their levels of elk -related attributes. The elk -related attributes included: seeing at least one elk, seeing 10 or more elk, seeing a bull elk, and hearing an elk bugle. In order to mak e the choice scenarios realistic, we employed several feasibility constraints. They are as follows: 1. The chance of seeing a bull elk and seeing 10 or more elk is always lower than the chance of seeing at least one elk. 2. The chance of hearing an elk bugle i s independent of seeing at least one elk. That is, it is free to occupy its entire range. 3. If any of the elk -related attributes are zero, all the other elk -related attributes must also be zero, and fiOutside the Elk Rangefl is listed above the elk -related att ributes. 4. Similarly, if any elk -related attribute is greater than zero, all the other elk -related attributes must also be greater than zero, and fiInside Elk Rangefl is listed above the elk - related attributes. 5. Each of the elk -related attributes for the righ t-side area must be equal to or greater than the same elk -related attribute for the left -side area. 17 Some respondent™s primary activities were changed to better suit the choice experiment. For example, fiDriving for Pleasurefl was changed to fiViewing/Photographing Wildlife or Sceneryfl. 51 6. The distance to the left -side area is the approximate driving time to the Michigan Elk Range from the respondent™s home. The right -side area requires some additional driving time beyond the left -side area. For example, a respondent from Gaylord, Michigan is approximately 30 minutes from the left -side area. If the right -side area requires an additional 60 minutes of driving time beyond the left -side area, thi s means the left -side area is 30 minutes away from the respondent™s home and the right -side area is 90 minutes away from the respondent™s home. Table 2.1 : Elk -related Attribute Levels The rules above ensure that the design exhibits a trade -off between the likelihood of experiencing elk related attributes and longer driving times (i.e. travel costs). The attribute levels are displayed in Table 2.1. The range of the elk -related attributes was chosen to be realistic and credible to respondents. The chance of seeing at least one elk goes up to 60%, and the chances for the other elk -related attributes can go up to 50%. We chose these values as the high end of the range because elk sightings a re not guaranteed on every visit. The range on the distance (additional driving time ) attribute goes up to 120 minutes, because two hours is close to the maximum time it takes to travel between any two given sites in the area. Travel in the area can be slo w due to poor road quality, but the area is not large enough for journeys over two hours. Attribute Level Seeing at least one elk {0, 15, 20, 25, 40, 60} % chance Seeing 10 or more elk {0, 5, 10, 15, 20, 50} % chance Seeing a bull (male) elk {0, 5, 10, 15, 20, 50} % chance Hearing an elk bugle {0, 5, 10, 20, 35, 50} % chance Distance ( Additional Driving Time Beyond Area A ) {15, 30, 60, 90, 120} minutes 52 In order to increase the credibility of the choice scenarios, we assigned respondents into one of three groups for the experimental design process. For each group, we created 15 choice sets divided into five blocks of three, and each respondent was randomly assigned to one of the 5 blocks. The choice sets were created using the Ngene software to minimize D -error and make our parameter estimates as efficient as possible , given the feasibility constraints. The first group was made up of those respondents who indicated in the intercept survey that their primary activity was elk viewing. Since these respondents were being asked about possible elk viewing trips, it didn™t ma ke sense to have any of their choice sets include areas outside of the elk range (i.e. 0% chance of experiencing any of the elk -related attributes), so all of their alternatives (both left -side and right -side) were included in the elk range and featured on ly positive elk -related attributes. The second group was based off an auxiliary question that immediately preceded the choice experiment. This auxiliary question asked respondents how important the various elk -related attributes are to them when choosing where to recreate in the Michigan Elk Range. Respondents who selected finot importantfl for all four elk -related attributes were assigned choice sets where all of the left -side areas were fioutside the elk rangefl (i.e. 0% chance of experiencing any of the elk related attributes). Even for this group, however, the right -side area was always in the elk range. 18 The last group, a base group, was made up of those respondents that did not fall into either of the two groups from above. Members of this base group were sometimes given left -side areas inside the elk range and sometimes they were given left -side areas outside of the elk range. Just like the other two groups, all of their right -side areas were in the elk range. Given that 18 Another purpose of the auxiliary question was to acquaint all respondents to the various elk -related attributes before they viewed the three choice scenarios. 53 these differences were minor, we w ere able to pool together all responses, regardless of group, in the analysis stage. As part of the survey design process, we conducted cognitive interviews to pretest the online follow -up survey, and we paid particular attention to the choice experiment p ortion of the survey. In May 2018 we conducted pre -tests for the intercept survey with visitors to the Michigan Elk Range, and we acquired approximately 25 email addresses. In December 2018 we sent out invitations to these email addresses, and 9 individual s responded and completed individual cognitive interviews to pre -test the follow -up survey. The pre -test respondents completed the survey while on a video -phone call with us. This was advantageous because it allowed us to watch respondents as they answered survey questions and to probe respondents about their decision -making process and understanding using cognitive interviewing techniques. The pre -tests resulted in several changes to the choice experiment. Importantly, complexity was reduced by putting al l the choice questions in a common format (originally two of the questions had different seasons and the other used a different format to address trips in/out of the elk range). To further reduce complexity, the number of attributes was reduced (e.g. elimi nating rare items like fiseeing elk sparringfl). The final survey version presents respondents with three choice scenarios of the exact same setting and format. This allows us to pool responses together and thus increase overall efficiency of the elk -related attrib ute parameter estimates (three observations for every respondent). Another advantage is that this format is easier for respondents because it can fiprovide respondents an opportunity to develop a better understanding of the task at handfl (Johnston et al. 20 17). 54 Figure 2.3 : Choice Experiment Response Questions It is worth noting the format for how we elicited responses to the choice experiment due to formatting constraints within the online survey program. Figure 2.3 displays the three questions respondents were asked to answer following the presentation of each choice scenario. The first question elicits a binary choice between the two areas. The second and third questions asks respondents to choose between each of the respective areas in comparison to fido something elsefl, an opt -out option. If a respondent answ ers fido something elsefl to both the second and third question, their recorded choice is finonefl, the opt -out option. If respondents do not select fido something elsefl to the second and third questions, their recorded choice is whichever area was selected in the first question. This type of choice experiment elicitation set - up is advantageous in that it records a binary choice (the first question) from all respondents while also allowing respondents the option to opt -out. The disadvantage of this elicitation s et-up is that it can be a cognitive burden for some respondents, and it allows the respondents the option 55 of selecting intransitive responses to the three questions. Of the 913 total choice sets, 24 were intransitive. Appendix V displays robustness checks for the models presented in this study. One robustness check runs all of the models used in this study without intransitive responses, and another robustness check runs all of the models used in this study with only binary responses. IV. Random Utility Maximi zation Theory We expect that, when faced with a choice, people make decisions that maximize their expected utility. This is the key insight behind random utility maximization (RUM) theory which was first proposed by Daniel McFadden (1974). Individual deci sion makers make utility maximizing choices with certainty, whereas analysts have an incomplete view of any given choice occasion. From the analyst™s perspective, an individual™s utility derived from a given choice is made up of both observed and unobserve d portions. Holmes et al. (2017) states this relationship formally as: = (,)+ (1) where total indirect utility ( V) for individual k when he selects alternative i is composed of both an observed portion ( v) and an unobserved portion ( ). Z is a vector of attributes for alternative i, p is the price for alternative i, and y is individual k™s income. The observed potion of the indirect utility function is commonly specified as a linear function of the alternative attributes. Th us, equation 1 can be rewritten as follows: =++()+ (2) where is the marginal utility of income. The stochastic nature of the unobserved portion of indirect utility ( ) naturally lends itself to the use of probabilist ic statements. From the analyst™s perspective, the probability that individual k selects alternative i over any other alternative ( j) is given by: 56 =Pr > (3) A common way to interpret the resulting attribute parameter estimates is to calculate a marginal rate of substitution (MRS) between each of the attributes and the marginal utility of income (or driving time, as we will discuss below). MRS can be defined as follows: ,=/= (4) It should be no ted that in this study, costs are presented to respondents in terms of driving time as opposed to direct monetary expenditures. Thus, is a coefficient that represents the marginal utility of minutes spent driving, a value that is likely negative. Framin g costs in this manner is more realistic and credible for respondents because visitors to the Michigan Elk Range do not face direct monetary costs for site choices. However, they do indirectly pay for recreation site choice in terms of additional travel co sts incurred as well as possible accessibility issues. Throughout the pretesting phase, respondents had no problem conceptualizing the costs of different sites in terms of additional driving time (Johnston et al. 2017). Appendix V estimates MRS values for the elk -related attributes and money (using estimated travel costs). In sum, RUM theory says that decisions are based upon the relative attribute levels of two or more choices as well as unobserved stochastic elements influenced by personal preferences. V. Modelling Heterogeneity in Random Utility Models When conducting choice experiments, analysts must make modelling assumptions regarding the unobserved, stochastic component ( ) of decision makers™ choices. The simplest approach is to assume that this compo nent is independently identically distributed (IID) and follows a Type -I extreme value distribution. Conditional logit models also assume a substitution pattern known as independence from irrelevant alternatives (IIA). This means that the probability ratio for choosing between two alternatives is independent of any other alternatives in the choice 57 set. This is not always a realistic assumption, as the probability ratio for two alternatives is likely to change when a substitute good is added to the choice se t (Train 2009). When these conditions do hold, however, a conditional logit model is an appropriate estimation technique. According to a conditional logit model, the probability that individual k selects alternative i over alternatives (where is t he individual™s choice set) can expressed as: =exp ()exp () (5) The assumptions required to use conditional logit models are strict and not always realistic. A second way to model choice is to use a latent class approach (Boxall and Adamowicz 2002). This estimation approach uses additional information to divide the population into classes (s). Within each class, it is assumed that the unobserved heterogeneity of the unobserved component ( ) follows an IID Type -I extreme v alue distribution, and the IIA assumption is weakened. Under a latent class logit model, the probability that individual k selects alternative i over alternatives given that the individual belongs to class s can be expressed as: |=exp ()exp () (6) This differs from the conditional logit estimate in that it results in separate attribute coefficients for each class. Membership to these classes follows from a latent membership likelihood function. This membership function is made up of a vector of membership explanatory variables ( X), a vector of parameters ( ), and a vector of error terms ( ). The membership explanatory variables can include psychometric data, sociodemographic data, and other known latent attitu des or values. The probability that individual k is a member of class s can be expressed as: =+ (7) 58 Assuming that the error term ( ) follows an IID Type -I extreme value distribution, the probability that individual k is a member of segment s can be restated as: =exp ()exp () (8) One can combine the probability of an individual belonging to class s with the probability of choosing alternative i given membership in class s to express the overall, unconditional probability of choosing alterative i for individual k. This is stated as follows: =exp ()exp ()exp ()exp () (9) Another way to address heterogeneity in the unobserved, stochastic component of the indirect utility function is to use a mixed logit model. Whereas the conditional logit results in a point estimate for the parameter ( ) values, the mixed logit provides those same parameter ( ) estimates over a density. A mixed logit m odel can be expressed as follows: =exp ()exp () (10) The latent class logit (mentioned above) is just a special type of the mixed logit that uses a discrete set of parameter ( ) values. The mixing distribution ( ()) can be specified using any distribution. The most common distribution to use is normal, but analysts have been known to use lognormal, triangular, uniform, and gamma distributions as well. The biggest advantage of a mixed logit model is that it captures preferenc e heterogeneity and allows for more flexible substitution patterns (the model does not exhibit IIA). Mixed logit models are also advantageous 59 when using panel data, as is the case in this study, because it can control for correlation errors across repeated choices from the same respondent (Hole 2007; Train 2009) . VI. Overall Results Table 2.2 : Overall Conditional Logit Estimates with fiNonefl and fiOutside of Elk Rangefl Interactions Variables (1) (2) (3) See One Elk 0.0279*** 0.0279*** 0.0271*** (0.00497) (0.00496) (0.00498) Hear Elk Bugle 0.0299*** 0.0298*** 0.0303*** (0.00528) (0.00528) (0.00524) See Bull Elk 0.00431 0.00430 0.00456 (0.00417) (0.00417) (0.00419) See 10 Elk 0.00649 0.00646 0.00700 (0.00514) (0.00515) (0.00510) Distance (additional driving time) -0.0117*** -0.0117*** -0.0117*** (0.00233) (0.00232) (0.00230) Outside of Elk Range 1.418*** 1.420*** 3.192** (0.296) (0.297) (1.460) None -1.632*** 0.949 -1.647*** (0.346) (2.302) (0.347) None x Driving Time -0.00383 (0.00419) None x Male 0.00726 (0.585) None x Education Level -0.152 (0.130) None x Income 0.00276 (0.00664) Outside of Elk Range x Driving Time -0.00727*** (0.00257) Outside of Elk Range x Male -0.519 (0.424) Outside of Elk Range x Education Level -0.0424 (0.0939) Outside of Elk Range x Income 0.00279 (0.00396) Respondents Choice Sets 309 913 309 913 309 913 Standard errors clustered by respondent reported in parentheses *** p<0.01, ** p<0.05, * p<0.1 60 The simplest estimation approach involves using a conditional logit model, and these results are reported in Table 2.2. 19 Table 2.2 shows both the fiNonefl (opt -out option indicating when respondents prefer neither area) variable interacted with several demograph ic variables as well as the fiOutside of Elk Rangefl (selection of an area where all elk -related attributes have a 0% chance of occurring) variable interacted with the same demographic variables. These interactions are included to see whether respondents are more likely to opt -out or pick an area outside the elk range based on individual characteristics. Neither of these sets of interactions result in significant differences to the parameter estimates, and the one significant interaction (fiOutside of Elk Rang efl x Driving Time) will be explored in a later section. The most important finding from these results is that the parameter estimates for seeing at least one elk and hearing an elk bugle are significant while the parameter estimates for seeing a bull elk and seeing 10 or more elk are not significant. This is not entirely surprising given the feasibility constraints we imposed on the design. Both significant attributes, seeing at least on elk and hearing an elk bugle, were allowed to independently assume th eir entire range whereas the other two attributes, seeing a bull elk and seeing 10 or more elk, were constrained to be less than the probability of seeing at least one elk (i.e., since there is less independent variation in these two attributes, the design has less power to identify these effects with the available sample size). In the simple case without interactions, the MRS between seeing at least one elk and additional driving distance is 2.38. This can be interpreted to mean that, on average, respond ents would be willing to drive an additional 2.38 minutes for a one percent increase in the chance of seeing at least one elk. Put another way, respondents would be willing to drive an additional 23.8 minutes for a 10% increase in the chance of seeing elk. Hearing an elk bugle appears to have a 19 The standard errors are clustered by respondents 61 higher value, as respondents would be willing to drive an additional 25.5 minutes for a 10% increase in the chance of hearing a bugle. It should also be noted that the variable for selecting finonefl (the opt -out choic e) is significant and negative, and this is not surprising because this option was not chosen very often. The variable for choosing an area when it is outside the elk range (i.e. 0% likelihood for all elk -related attributes) is significant and positive. Table 2.3 : Overall Mixed Logit Estimates Variables Parameter Estimates SD Estimates % with Parameter >0 Seeing One Elk 0.0222** 0 .0004 100% (0.00871) (0.04231) Hearing an Elk Bugle 0.0318*** 0.0611*** 70% (0.00893) (0.01533) Seeing a Bull Elk 0.0203* 0.0549*** 64% (0.0108) (0.0158) Seeing 10 Elk 0.0420*** 0.1094*** 65% (0.0155) (0.0271) Distance 20 -0.0226*** (0.00359) Outside of Elk Range 0.896** (0.404) None -2.414*** (0.340) Respondents Choice Sets 309 913 309 913 309 913 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 In order to get a better sense of coefficient estimate variation, it is worthwhile to examine a mixed logit estimation model as well. As stated previously, the mixed logit is more flexible than a conditional logit, allows for heterogeneous preferences, and works well with panel data. 20 The distance parameter is not given a distr ibution because it could lead to an undefined marginal rate of substitution. 62 Table 2.3 presents the results from the mixed logit model estimated with full correlation in the random parameters and with panel data structure for preferences and error terms. The results show significant variation in the parameter estimates for three of the four elk viewing attributes. The exception is seeing at least one elk, which does not have a standard deviation significantly different than zero. Additionally, the seeing one elk parameter also has a smaller MRS (close to 1) than what was estimated using a conditional logit model. The second parameter, hearing an elk bugle, also has a smaller estimated MRS (1.41) than estimate found using a conditional logit mo del. Regarding the hearing an elk bugle attribute, the mixed logit model estimates a mean parameter of 0.032 and an estimated standard deviation of 0.061. This indicates that roughly 30% of respondents have a zero (or negative) value for elk bugling . The p arameter for seeing a bull elk exhibits a similar pattern, though the estimated mean coefficient is not significant at the 5 percent level. The biggest change, when compared to the conditional logit estimate, comes from the attribute seeing 10 or more elk. In the conditional logit model, the estimated parameter was not even significant. With a mixed logit model, the MRS (1.86) is higher than a ny of the other parameters. One reason this may have not shown up in the earlier conditional logit estimation is because of the large variation. The estimated standard deviation of seeing 10 or more elk is over 2.5 times as large as the mean parameter esti mate itself. This means about 65% of respondents prefer seeing 10 or more elk, and the remaining 35% do not. The parameter estimate for seeing a bull elk is significant at the 10% level, and the MRS value is 0.90. Our mixed logit model assumes a n ormal mixing distribution with infinite support. Because of this, we have to be cautious about interpreting the results. Taken literally, these results imply that someone, somewhere has an infinitely negative value for hearing an elk bugle. 63 While it is po ssible that someone could have slightly negative values for some of these elk -related attributes, the more likely scenario is that a portion of respondents simply do not care about the attributes. The key takeaway from the mixed logit approach to estimatio n is that there is significant variation in how respondents value the various elk -related attributes that was otherwise masked in the conditional logit model . While the mixed logit approach is helpful insomuch as it revealed the extent of the variation in the parameter estimates, it does not provide much in the way of explanations as to which visitors to the Michigan Elk Range would have either a positive or zero value for an elk -related attribute. The follow section will attempt to explain where this varia tion is occurring. The first step will be to return to a conditional logit model. However, this time it will be run using separate models for each of the different activity groups identified in each respondent™s choice scenarios. Then, we will explore a la tent class logit approach, which uses respondent characteristics to explain the variation in the estimated elk - related attribute parameters. 64 VII. Identifying and Exploring Classes of Elk Range Visitors Table 2.4 : Primary Activities ( per respondent ) in Choice Experiment Scenarios Activity (Activity Group in Bold) Frequency Percent Water Activities 71 22.9% Fishing at a Lake 29 9.4% Fishing at a Stream 27 8.7% Kayaking, Canoeing, or Boating 9 2.9% Swimming or Wading in Water 6 1.9% Hunting 56 18.1% Hunting 56 18.1% Path Activities 64 20.8% Hiking, Trail Running, or Backpacking 45 14.6% Bicycling 11 3.6% Horseback Riding 8 2.6% Wildlife Activities 47 15.2% Viewing Elk 35 11.3% Viewing/Photographing Wildlife or Scenery 11 3.6% Mushroom Picking 1 0.3% Camping 71 23.0% Camping 70 22.7% Picnicking or Family Day Gatherings 1 0.3% Total 309 100% 65 Table 2.5 : Conditional Logit Estimates by Primary Activity Group Variables Path Activities Wildlife Viewing Hunting Camping Water Activities See One Elk 0.0202** 0.0697*** 0.0158 0.0299*** 0.0309*** (0.00957) (0.0248) (0.0140) (0.00957) (0.00944) Hear Elk Bugle 0.0225 0.0660*** 0.00304 0.0271** 0.0350*** (0.0117) (0.0141) (0.0131) (0.0117) (0.0126) See Bull Elk -0.000437 -0.00276 0.0315*** 0.00224 -0.000158 (0.00973) (0.0217) (0.00951) (0.00928) (0.00787) See 10 Elk -0.0110 0.00480 0.0241* 0.00532 0.0117 (0.0126) (0.0129) (0.0141) (0.0111) (0.0110) Distance -0.00907* -0.0170** -0.0138** -0.0142*** -0.0185*** (0.00512) (0.00664) (0.00638) (0.00521) (0.00577) Outside of Elk Range 0.647 1.768 0.688 1.004 1.931*** (0.627) (1.319) (0.631) (0.590) (0.652) None -3.024*** -0.491 -1.715** -1.982** -0.993 (0.886) (0.963) (0.831) (0.773) (0.701) Respondents Choice Sets 64 191 47 139 56 164 71 211 71 208 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 66 The choice scenario was set up so that respondents chose between two hypothetical recreational areas for a specified recreational activity . Table 2.4 lists these primary activities and organizes them into similar groups. Table 2.5 shows the results from running individual conditional logit models for each of the primary activity groups. The rationale behind run ning separate conditional logit models for each activity group is that the approach may reveal insights into secondary elk viewing effects (e.g. fi how much do hunters value seeing elk?fl ). Another benefit from separating the models is that it could improve t he parameter estimates for elk -related attributes. As was stated earlier, the strict assumptions of the conditional logit are more likely to be realized when using separate models because there is likely to be more homogeneity between respondents of the sa me activity group than across activity groups. That being said, the cost to splitting up the overall sample is that these models lose statistical power. Despite this concern about statistical power, each activity group has a significant distance attribute as well as at least one significant elk -related attribute. This suggests the presence of incidental elk viewing value (i.e. value from elk viewing that occurs simultaneously with or as a subordinate component of other forms of recreation). Path activities (hiking, biking, and horseback riding) have an MRS of 2.23 for seeing at least one elk (significant at the 10% level). Path activity respondents are also the least likely of any activity group to select the opt -out option. Respondents whose primary activi ty was some sort of water activity have MRS estimates of 1.67 for seeing at least one elk and 1.89 for hearing an elk bugle. The fiNonefl (opt -out choice) variable is not significant, but the fiOutside of Elk Rangefl variable is significant and positive. Respo ndents in this activity group were the most likely to choose areas outside of the elk range, and a comparison between the significant estimates shows that it takes, on average, a 30% chance of seeing at least one elk and hearing an elk bugle before water a ctivity respondents 67 change their choice from an area outside of the elk range to an area inside of the elk range. This is not entirely surprising given that water activities are ostensibly the most removed from elk viewing. 21 Camping has significant coeffic ients for seeing at least one elk, hearing an elk bugle, and a significantly negative coefficient on the none (opt -out choice) variable. The MRS values for campers are 2.11 for seeing at least one elk and 1.91 for hearing an elk bugle. The hunting activity group presents an interesting case because it is one of the only places in the entire study where we see a significant parameter estimate for seeing a bull elk. The MRS of seeing a bull elk for hunters is 2.29, meaning that a hunter would be willing to dr ive an additional 23 minutes to see a bull elk. As one would expect, the wildlife viewing group places the highest value on the elk -related attributes. Wildlife viewers would be willing to drive around 40 additional minutes for either a 10% increase in the chance of seeing at least one elk or a 10% increase in hearing an elk bugle. Neither the fiNonefl (opt -out choice) nor are fiOutside of Elk Rangefl variables are significant for wildlife viewers. 21 Although rare, a few respondents to the intercept survey did report seeing elk at Cornwall Flooding, one of the lakes in the Michigan Elk Range. 68 Table 2.6 : Summary of Elk Experience Variables used in Laten t Class Logit Apart from running separate conditional logit models, another way to explain the variation in the elk -related attr ibute parameter estimates is with a latent class logit approach that segments respondents into classes using explanatory variables of our choice. There is no hard and fast rule for selecting class membership variables, as it depends on the specific researc h question and the available data. We chose to use information on respondents™ elk viewing experience in order to explain class membership. The idea behind this choice was to see whether past elk viewing experience affects future recreational decisions. If there is a novelty effect (similar to filistingfl in the birding community), we would expect those with lower elk viewing experience to be willing to drive farther in order to experience the elk -related attributes. Additionally, a novelty effect would likel y result in higher values for the relatively rare attributes (e.g. seeing a bull elk) as opposed to the relatively common attributes (e.g. seeing at least one elk). Conversely, results indicating that those with more elk viewing experience are willing to drive farther to experience the elk -related attributes could indicate a type of habit formation or Question or Variable Description Choices Percentage Question 24 (follow -up survey) Have you ever gone elk viewing in Michigan? 1=Yes 0=No 80.83% 19.17% Question 28 (follow -up survey) Have you ever seen wild elk outside of Michigan? 1=Yes 0=No 60.35% 39.65% Question 17 (intercept survey) What role did the chance of seeing elk play in your decision to visit? 1=Primary Reason 2=Played Some Role 3=No Role 16.48% 38.79% 44.73% Mean SD Approximate Driving time to MI Elk Range An approximate driving time to the Michigan Elk Range was given to each respondent based on their home zip -code (in minutes). 151.19 87.24 69 enthusiasm informed by past experience. Class membership explanatory variables include whether the respondent has ever gone elk viewing in Michigan, whether t he respondent has ever seen elk outside of Michigan, whether elk viewing was the primary reason for their intercepted visit, and their approximate distance from the Michigan Elk Range. These explanatory variables are described in Table 2.6. 22 Table 2.7 : Class Membership for Latent Class Logit Model for Two Classes when using Elk Experience as Explanatory Variables ( Class 2=Reference Class) Variables Class 1 Have you ever gone elk viewing in Michigan? (Q24 Follow -Up) -0.709** (0.351) Have you ever seen elk outside of Michigan? (Q28 Follow -Up) -0.553* (0.298) Was seeing elk the primary reason for visiting on the intercepted visit? (Q15 Intercept) -2.55*** (0.801) Approximate Driving Time (in minutes) -0.00602*** (0.0018) Constant 1.668*** (0.473) Class Share 41% Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 22 In addition to the explanat ory variables found in table 2.6, we checked for other significant elk viewing experience variables from follow -up survey questions . We also checked demographic variables (age, income, gender, and education level), but only age was significant, and its sig nificance went away when combined with the elk viewing experience variables. 70 Table 2.8 : Preferences for Latent Class Logit Model for Two Classes Explained by Elk Experience Variables Class 1 Class 2 See One Elk 0.0163* 0.0281** (0.00979) (0.0124) Hear Elk Bugle -0.0137 0.0536*** (0.00927) (0.00949) See Bull Elk 0.0084 0.0170 (0.0107) (0.0114) See 10 Elk -0.0164 0.0310** (0.0120) (0.0145) Distance -0.022*** -0.0163*** (0.00556) (0.00397) Outside of Elk Range 0.702* -0.553 (0.406) (0.914) None -2.468*** -0.626 (0.395) (0.548) Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 The latent class logit model results in two sets of estimates for two classes of respondents. We chose to use two classes because this choice minimizes the consistent Akaike information criterion (CAIC) and the Bayesian information criterion (BIC) suggesti ng two classes are preferred to more classes (Pacifico and Yoo 2013). Table 2.7 displays the class membership composition, where class 2 is the reference class. On average, members of class 1 are likely to be closer to the Michigan Elk Range and are less l ikely to have ever gone elk viewing (inside or outside of Michigan). They are also less likely to have reported that their intercepted visit was primarily related to seeing elk. Broadly speaking, we can think of class one as having less elk experience and/ or enthusiasm and class 2 as having more elk viewing experience and/or enthusiasm. Table 2.8 shows parameter estimates for each group. Members of class 1, made up of those with less elk experience, have an MRS estimate of 0.74 (at the 10% level) for the s eeing at 71 least one elk, and none of the other elk -related attributes are significant. Class 1 is also less likely to opt -out and select neither area but more likely to select an area that is outside the elk range. On the contrary, members of class 2, the f arther class and those more likely to have gone elk viewing before, value seeing at least one elk, hearing an elk bugle, and seeing 10 or more elk. The MRS values for class 2 are 1.72 for seeing at least one elk, 3.29 for hearing an elk bugle, and 1.90 for seeing 10 or more elk. About 40% of respondents fall into class 1, and about 60% of respondents fall in class 2. These results suggest a type of habit formation when it comes to elk viewing, but a word of caution is in order. Class membership is defined by both elk viewing experience and approximate driving time to the Michigan Elk Range. It™s possible that the reason local visitors place a lower value on elk -related attributes is because they may have seen them unintentionally in the past and thus have l ittle interest in seeing again in the future. This kind of attitude toward elk would suggest a type of novelty effect. We tried to get at this possible attitude by asking respondents to the follow -up survey about their experience with unintentional elk sig htings (i.e. seeing elk while doing something else), and this the resulting variable was not significant in explaining class membership. It is possible that respondents did not understand what this question was asking, in which case we would expect to see an undercount in that category. VIII. Reflections on the Results using Auxiliary Data Perhaps the most surprising finding from this study was that visitors to the Michigan Elk Range seemingly have little or no value for viewing bull elk. The only times we saw significant parameter estimates for this attribute was with hunters, when we ran individual conditional logit models for each of the primary activity groups, and with the overall mixed logit model. 23 This 23Both estimates are significant at the 10% level. 72 general lack of interest in bull elk is surprising b ecause bull elk are rarer than female elk. Besides that, they are larger, have antlers, and engage in sparring during the rutting season. Another puzzling related aspect is that elk bugling, a sound that bull elk make during the fall, is generally a signif icant attribute throughout this study, so this would suggest that people enjoy hearing but not seeing bull elk. There are several reasons why this finding could be wrong. As was discussed earlier, we imposed several feasibility constraints to make all pos sible choice sets realistic. Chiefly, we required that the chances of seeing a bull elk and chances of seeing 10 or more elk be less than the chances of seeing at least one elk. This constraint reduced the amount of independent variation for these two attr ibutes, and this necessarily made the attribute parameters harder to identify (Appendix V I presents the correlation matrix that shows that the feasibility constraints resulted in a design with high correlation among the attributes). Still, we seemed to hav e had better luck in estimating the fisee 10 or more elkfl parameter (i.e. the other constrained attribute), as it has a higher significance level in both the mixed logit model as well as the latent class logit model. Another possible problem could stem from the fact that we did not provide a detailed definition of what a bull elk is Šnor did we provide a detailed definition of any of the elk -related attributes. 24 Accordingly, if respondents did not associate antlers with the term fibull elkfl, this lack of conte xt could have caused the low valuation. Lastly, there could have been unintentional problems that resulted from splitting the attribute for seeing a bull elk from the attribute for hearing a bull elk. 24 In the auxiliary question preceding the choice experiment, we used the term fiseeing a bull (male) elkfl 73 Table 2.9 : Cross Tabulation for questions on experie nce with elk -related attributes and importance of elk -related attributes for future recreation Not Important (%) Somewhat Important (%) Very Important (%) Seeing at least One Elk Attribute Has not seen at least one elk (n=58) 51.72% 29.31% 18.97% Has seen at least one elk (n=255)*** 32.55% 49.80% 17.65% Seeing 10 or more Elk Attribute Has not seen 10 or more elk (at one time ) (n=137) 72.26% 22.63% 5.11% Has seen 10 or more elk ( at one time ) (n=175)* 59.43% 33.71% 6.86% Seeing a Bull Elk Attribute Has not seen a bull elk (n=82) 71.95% 15.85% 12.20% Has seen a bull elk (n=230)*** 43.48% 43.91% 12.61% Hear an Elk Bugle Attribute Has not heard an elk bugle (n=94) 62.77% 27.66% 9.57% Has heard an elk bugle (n=218)*** 37.16% 47.35% 13.78% One way to check the validity of the models is to compare these findings to additional data collected elsewhere in the follow -up survey. Table 2.9 compares respondent™s experience with each elk viewing attribute (seeing a bull elk, hearing an elk bugle, an d seeing 10 or more elk) with a rating of how important that same attribute is in the context of future recreation. The results in Table 2.9 seem to confirm our intuition about the problem with the bull elk parameter. About one -half of respondents say that seeing a bull elk is not important when considering future recreation in the Michigan Elk Range. This is 15 percentage points lower than the seeing 10 or more elk attribute (where 65% of respondents rated it as not important) and only about 5 74 percentage p oints higher than the hearing an elk bugle attribute (where 45% of respondents rated it as not important). It is not clear why there appears to be a discrepancy between what respondents told us in these auxiliary questions with what respondents told us in the choice experiment, but it does confirm our suspicion that the value of elk viewing may be understated by the choice experiment. The results from Table 2.9 also seem to give credence to the lesson we took from the latent class logit models. Remember t hat Class 2, the class that lives farther away and has more elk experience, exhibited significant parameter estimates for the seeing at least one elk, hearing an elk bugle, and seeing 10 or more elk attributes. Class 1, on the other hand, only had a signif icant parameter estimate for seeing at least one elk. These results suggested that those with more elk viewing experience are more likely to show future interest in elk. This finding does not suggest that interest in elk viewing is driven by a type of novelty effect. Table 2.9 provides further support for this idea. For all four elk -related attributes shown, those who had not previously experienced the elk -related attribute were more likely to say that the attribute was unimportant in future recreational de cisions and less likely to say that the attribute was somewhat or very important in future recreational decisions. IX. Discussion Overall, the results of this study suggest that the best way to think about the values of elk -related attributes is to bifurcate v isitors into two groups -those who value elk -related attributes and those who do not. One of the assumptions underlying recreation demand modelling is that recreation site choice is, in part, a function of a visitor™s distance to that site. All else being e qual, we expect those living closer to a given recreational site will take more trips than those living farther away. One way to think about the results of this study, then, is that the class that doesn™t 75 value elk -related attributes (Class 1) is made up o f local visitors whose site demand function is driven primarily by distance. There are many substitute sites in the region for fishing, hunting, hiking, etc., so if they found themselves farther away from the Michigan Elk Range it is conceivable that they would select another recreational site. The class that does value the elk -related attributes, on the other hand, exhibit a site demand model that is driven by both the value of elk viewing and distance. In other words, they are willing to bypass substitute sites for the opportunity to experience some form of elk viewing. The visitors that value elk -related attributes have, on average, more experience viewing elk. This finding suggests that novelty (or variety -seeking) is not a major factor in visitors™ dec isions to go elk viewing. In this sense, our finding is closer to the findings of Brock et al. (2017) than to that of Kolstoe and Cameron (2017). Brock et al. found that the people who hold the highest value for backyard bird -feeding are those with more ex perience, and they find no evidence that species rarity is an important attribute for backyard bird -feeding. Kolstoe and Cameron find that birders (who travel away from home) place a premium on sites they have not visited before (indicating novelty) as wel l as sites that feature an endangered species. Our results are limited in the sense that elk experience was determined using a few general questions in the follow -up survey. Future studies could provide greater clarity in this area by using a dynamic choic e model to estimate recreation demand (Smith 2005). One of the unique contributions of this study was to separate elk viewing into four component attributes and to define the attribute levels as the chance of experiencing these attributes. One advantage o f this approach is that it adds precision to the results when compared to qualitative attribute levels often found in the literature. With the quantitative attributes, we were able to present MRS values that express the trade -off between the number of minu tes a 76 visitor would be willing to drive in exchange for a 1% increase in the chance of experiencing an elk -related attribute. While intuitively useful, this approach made it difficult to econometrically identify the separate elk -related attributes. The att ributes feature a high level of correlation (principally due to the feasibility constraints we imposed), and this made it especially difficult to estimate respondents™ WTP for seeing a bull elk and seeing 10 or more elk. Appendix V I explores this multicollinearity issue in more detail. In it, we show the correlation between each of the elk -related attributes and re -run the models from this paper with a single elk -related attribute made up of the sum of all four elk -related attributes . While this aggregated approach cannot identify the separate effects of the elk attributes, it demonstrates the same general pattern of results: namely, across all visitors, there is a preference for elk but this preference exhibits significant heterogene ity; among user groups, elk viewers care the most about elk, but some activity groups also have preferences for incidental elk viewing; and there is a class of visitors that are indifferent to elk. 77 REFERENCES 78 REFERENCES Boxall, P.C., & Adamowicz, W.L. (2002). Understanding Heterogeneous Preferences in Random Utility Models: A Latent Class Approach. Environmental and Resource Economics , 23(4), 421-446. doi-org.proxy1.cl.msu.edu/10.1023/A:1021351721619 Boxall, P. C., & Macnab, B. (2000). 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U.S. Department of the Interior, U.S. Fish and Wildlife Service, and U.S. Department of Commerce, U.S. Census Bureau. 2016 National Survey of Fishing, Hunting, and Wildlife -Associated Recreation. 81 APPENDICES 82 Appendix I: Survey Disposition Tables Intercept Survey Table A1.1 : Intercept Survey Method of Contact Method Frequency Percent In-person Interview 367 17.9% (if group completed in-person interview) Paper Survey 1,365 66.7% (if a paper survey was left at a vacant vehicle or campsite) Already Surveyed 305 14.9% (groups were not given surveys if they already completed an interview or paper survey in the previous month) Refuse 11 0.5% (if group refused to complete an interview or accept a paper survey) Total 2048 This table indicates how groups were contacted during the intercept survey In total, we counted 2,463 vehicles in the Pigeon River Country State Forest in the summer (June 7 -September 1) and fall (September 9 - November 24). 2,048 vehicle groups were invited to participate in this survey. The number of vehicle groups (2,048) is le ss than the total vehicle count (2,463) because we only surveyed one person from groups that contained more than one vehicle. We treated unoccupied campsites (i.e. tent with no people or vehicles) the same as an unoccupied vehicle and left a paper survey. Each of the vehicle groups fits into one survey method category, and the breakdown of these categories is shown in Table A1.1. 367 vehicle groups (about 18% of total) were interviewed. 1,365 (about two thirds) vehicle groups were provided with a mail -bac k paper survey. 305 (about 15%) vehicle groups were already surveyed. This is a flexible category, but it 83 generally means that the visitor either told us that they had already completed the survey or that we recognized the visitor/vehicle/campsite and did not leave an additional paper survey. Only 11 vehicle groups directly refused to participate in the study. These refusals were all in -person, as no visitors sent in a refusal via mail. Table A1. 2: Response Rate for Paper Surveys ( by season ) Overall Summer Fall Did not Return 972 454 518 (71.2%) (71.7%) (70.8%) Returned 393 179 214 (28.8%) (28.3%) (29.2%) Total 1,365 633 732 Table A1.3 : Response Rate for Paper Surveys ( by select sites ) Overall Elk Sites Campgrounds Pigeon Bridge Cornwall Flooding Did not Return 972 94 162 88 110 (71.2%) (62.25%) (71.05%) (64.23%) (75.86%) Returned 393 57 66 49 35 (28.8%) (37.75%) (28.95%) (35.77%) (24.14%) Total 1,365 151 228 137 145 Table A1.2 reports paper survey response rate. Out of the 1,365 paper surveys we distributed, 393 or 28.8% of them were returned. The response rate did not vary much from summer to fall, as is shown in Tables A1.2.In addition, the response rate for the 151 paper 84 surveys left at elk sites was 37.75%, and the response rate for the 228 paper surveys left at state forest campgrounds was 29%. In the end, the intercept survey resulted in 756 usable intercept surveys. Follow -Up Survey The final question on the i ntercept survey asked respondents to provide an email address for a follow -up online survey. Of the 756 usable intercept surveys, we collected 580 email addresses (77%) and 102 mail addresses (13.5%). Table A1.4 shows the disposition of the 580 email invit ations, and Table A1.5 provides a schedule of when survey invites were sent to our sample. Table A1.4 : Follow up Survey Email Distribution Survey Invitations Sent Out 580 Undeliverable Emails 24 4.14% Surveys Started but not Completed 39 6.72% Refused 1 0.17% Completed Surveys 316 54.48% Table A1.5 : Distribution of Follow -Up Survey Invitations 1st Invitation March 29, 2019 2nd Invitation April 2, 2019 3rd Invitation April 5, 2019 4th Invitation April 10, 2019 5th Invitation April 13, 2019 6th Invitation April 20, 2019 85 Appendix II: Intercept Survey The survey below was left on the windshields of parked cars in the Michigan Elk Range when no visitors were around. The survey was placed an envelope, along with a map of the PRC, a map of entrance points, and a postage paid return envelope. If weather conditions warranted, the materials were placed in a clear plastic sleeve. Images of the envelope and maps follow the survey images. 86 Figure A2.1 : Intercept Survey (Pape r Version) 87 Figure A2.1: (cont™d) 88 Figure A2.1: (cont™d) 89 Figure A2.1: (cont™d) 90 Figure A2.2 : Map of Recreation Sites and Map of Entrance/Exit Roads 91 Figure A2.2: (cont™d) 92 Figure A2.3: Intercept Survey Outer Envelope 93 Appendix III : Follow -Up Online Survey Figure A3.1: Screen Shot of Online Follow -Up Survey 94 Figure A3.1 : (cont™d) 95 Figure A3.1 : (cont™d) 96 Figure A3.1 : (cont™d) 97 Figure A3.1 : (cont™d) 98 Figure A3.1 : (cont™d) 99 Figure A3.1 : (cont™d) 100 Figure A3.1 : (cont™d) 101 Figure A3.1 : (cont™d) 102 Figure A3.1 : (cont™d) 103 Figure A3.1 : (cont™d) 104 Figure A3.1 : (cont™d) 105 Figure A3.1 : (cont™d) 106 Figure A3.1 : (cont™d) 107 Figure A3.1 : (cont™d) 108 Figure A3.1 : (cont™d) 109 Figure A3.1 : (cont™d) 110 Figure A3.1 : (cont™d) 111 Figure A3.1 : (cont™d) 112 Appendix IV: Strategies for Defining a Target Population Previous sections have alluded to the idea that the target population of Michigan Elk Range visitors is difficult to define. In some recreation demand contexts, it is possible to simply define the target population of recreationists as the total population of a state or region or as some easily identifiable percentage of the total population. In our case , however, the target population is likely quite distinct from total Michigan adults . This is because the main recreational activities in the area (e.g., hu nting, fishing, elk viewing , horseback riding, etc.) are relatively specialized and have low participation rates among people in certain Michigan regions and/or demographic groups. Therefore, it would be helpful to know about how many people visit the Mich igan Elk Range for recreation in a year. Additionally, this essay segments respondents by their primary activity (or activities) , and we can think of these different activity groups as sub -populations of the total population. The welfare estimates shown in this paper should be thought of as individual, per -trip consumer surplus values. There is much we can learn from this, but it would also be useful to know the relative size s of the se sub -population s in order to estimate aggregate consumer surplus values b y activity groups. The principal reason for aggregating these consumer surplus values is to aid forest managers as they inevitably deal with user conflicts. We have previously shown that wildlife viewers have the highest individual consumer surplus values, but this could differ when looking at aggregate measures depending on the relative size of wildlife viewers among all Michigan Elk Range visitors. This section will identify some strategies that could be used in future research to identify the total Mich igan Elk Range visitor population and their total trips as well as activity group sub -populations. The most promising way to identify total visitation to the Michigan Elk Range is through the use of traffic counters located at key entrance roads into the Pigeon River Country 113 State Forest (the largest surveyed area in the Michigan Elk Range). The PRCSF is large and dispersed, so there are many possible entrances into the forest. That being said, PRCSF forest management has identified seven roads that they believe to be the principal entrance points to the forest. These traffic counts are useful for determining total visitation, but there are several limitations. The first limitation is that some non -recreationists are included in the counts. The counts include people who work in the forest ŠMDNR employees, logging vehicles, and oil company vehicles. They also include traffic to several cabins and homes dispersed within the forest area as well as a yoga r etreat also located in the area . Another limitation is that certain survey areas are not covered by traffic counters. This includes the portion of the Atlanta State Forest included in our intercept survey routes as well as the Green Timbers portion of the PRCSF (west of the E Sturgeon Valley Rd. traffic counter). A third limitation is that visitors frequently leave and reenter the forest during a single trip . In order to address this, we included a question in the intercept survey that asks how many times the visitor left and reentered the forest on the intercepted visit. The traffic counts can be combined with the vehicle counts we generated during the roving intercept survey. These intercept surveys provided us with a count of parked vehicles along predete rmined routes. One way to estimate some of the activity sub -populations is through the use of cameras we placed at key locations in the Michigan Elk Range. 25 We set up several Bushnell game cameras in the PRCSF and ASF in the summer and fall of 2018 as wel l as the spring/summer of 2019. The places with cameras tended to be parking areas for trailheads, lakes, and elk viewing areas . The sub -populations that we can estimate using these camera counts include hikers and/or bicyclists, lake users (mainly swimmi ng, boating, and fishing), and elk viewers. Estimating 25 A total of 19 locations had cameras at some point during 2018 and 2019. 14 locations were consistently monitored. There are some gaps in the images due to malfunctions and camera theft. 114 vehicle counts at these parking areas will not provide us with an all -encompassing count for these sub -populations (e.g. some elk viewers do not park at elk viewing areas), but it does provide some add itional information. We have developed a system for processing the images using a software called TIMELAPSE (Greenberg and Godin 2015), and we hope that this method will not only provide vehicle counts but vehicle duration as well. According to our interce pt survey, 46% of the respondents on an overnight trip stayed in one of the seven state forest campgrounds located in the PRCSF. Anyone camping in a Michigan state forest campground is required to fill out a paper registration form and pay a campground use r fee. The PRCSF campgrounds are administered by Otsego Lake State Park in Gaylord, MI , and they compile these registration forms and maintain statistics on the yearly campsite use nights by campground .26 In order to convert this into a visitor count estima te, we would need to know the average number of occupants at a PRCSF campsite. We included a question in an online follow -up survey of the intercept survey visitors asking how many people occupied the ir campsite on the intercepted visit, and the average re sponse was 2.7 .27 The equestrian campground , Elk Hill Equestrian Campground, uses a separate, online reservation (managed by the MDNR). Given that we know that 46% of intercepted visitors (on an overnight trip) stayed in a state forest campground, we should be able to match the traffic count estima tes with the campground estimates. Hunters are a particularly challenging sub -population to estimate because hunting is the most dispersed activity in the forest. Hunters do not park in a single area, so it would not be possible 26 The following is an example of how this count is calculated. Say that on Day 1 seven campsites in a campground were occupied. Say that on Day 2 three campsites in the same campground were occupied. The two -day total number of nights for this campground would be 10. 27 Only 126 people answered this question. However, this number is c onsistent with interviewer survey experience in the campgrounds. 115 to monitor them with camer as at parking areas. In light of this, one way to estimate the sub -population of hunters is through the use of MDNR hunter surveys. Among other statistics, the deer hunting survey report includes estimates for the total number of hunters as well as the tot al number of days spent hunting for the three counties that make up the Michigan Elk Range ŠOtsego, Cheboygan, and Montmorency. By making some assumptions and simple calculations, we can convert these county -level estimates into Michigan Elk Range estimates . For example, from these surveys we can get the share of hunting days that occur on private land versus public land. We would then estimate what percentage of total public land is in the elk range. This would give us the total hunting days in the Michigan Elk Range. In order to check for validity, we would then compare these estimates to what we know from the intercept survey as well as the traffic counts. 116 Appendix V: Robustness Checks The following tables are made up of four columns. The first three co lumns show marginal rate of substitution (MRS) values for the elk -related attributes and driving time. In this context, the MRS values can be interpreted as the additional minutes a visitor would be willing to drive for a 1% increase in the chance of exper iencing the elk -related attribute. The first column, fiAll Responsesfl, includes both intransitive choice sets and an opt -out option (i.e. None). The second column, fiDrop Intransitive Responsesfl, shows the MRS values when we drop intransitive choice sets. Th e third column, fiBinary Responsesfl, shows the MRS values when we only include binary choices (i.e. no opt -out option). The fourth column uses the same responses as the fiAll Responsesfl column (i.e. keeps intransitive choice sets and an opt -out option), but it differs in that the cost (i.e. additional time driving) is converted from time to a monetary travel cost. In this context, the MRS values can be interpreted as the monetary costs ($) a visitor would be willing to incur for an additional 1% increase in t he chance of experiencing the elk -related attribute. To make this conversion, we assume that visitors travel in the Michigan Elk Range at an average of 25 mph. 25 mph was chosen because road conditions in the Michigan Elk Range are poor, so travel can be s low. We assume that direct expenses for operating a vehicle are $0.285 per mile. Lastly, we assume that visitors value their time at 1/3 of their hourly wage rate. 117 Table A5.1 : MRS using Conditional Logit Models All Responses Drop Intransitive Responses Binary Responses MRS using Monetary Conversion Conditional Logit (No Interactions) See at least One Elk 2.38*** 2.23*** 2.45*** 2.06*** Hear an Elk Bugle 2.55*** 2.59*** 2.39*** 2.29*** See a Bull Elk 0.37 0.29 0.29 0.29 See 10 or more Elk 0.55 0.59 0.34 0.52 Conditional Logit (Demographic Interactions with fiNonefl) See at least One Elk 2.39*** 2.24*** N/A 2.06*** Hear an Elk Bugle 2.56*** 2.59*** N/A 2.29*** See a Bull Elk 0.37 0.29 N/A 0.29 See 10 or more Elk 0.55 0.59 N/A 0.51 Conditional Logit (Demographic Interactions with fiOutside Elk Rangefl) See at least One Elk 2.30*** 2.14*** 2.37*** 1.95*** Hear an Elk Bugle 2.58*** 2.61*** 2.42*** 2.28*** See a Bull Elk 0.39 0.30 0.32 0.29 See 10 or more Elk 0.60 0.64* 0.38 0.54 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 118 Table A5.2 : MRS using Conditional Logit separated by Activity Group All Responses Drop Intransitive Responses Binary Responses MRS using Monetary Conversion Path Activities See at least One Elk 2.22* 1.97* 2.09* 2.06 Hear an Elk Bugle 2.48 2.99* 2.28 2.35 See a Bull Elk -0.05 -0.19 -0.15 -0.27 See 10 or more Elk -1.21 -0.60 -1.29 -1.32 Wildlife Activities See at least One Elk 4.10*** 3.84*** 4.04*** 2.90*** Hear an Elk Bugle 3.88*** 3.85*** 3.84*** 2.70*** See a Bull Elk -0.16 -0.16 0.03 -0.10 See 10 or more Elk 0.28 0.44 0.15 0.53 Hunting Activities See at least One Elk 1.15 1.01 1.30 1.09 Hear an Elk Bugle 0.22 0.32 -0.04 -0.29 See a Bull Elk 2.29* 2.06* 2.27* 3.78 See 10 or more Elk 1.75* 1.78** 1.69* 2.33 Camping Activities See at least One Elk 2.11*** 1.93*** 2.20*** 1.63** Hear an Elk Bugle 1.92** 1.88** 1.62* 1.51* See a Bull Elk 0.16 0.25 -0.02 -0.03 See 10 or more Elk 0.38 0.10 0.18 0.33 Water Activities See at least One Elk 1.67*** 1.83*** 1.72*** 1.39** Hear an Elk Bugle 1.89*** 1.91*** 1.84*** 1.60** See a Bull Elk -0.01 -0.06 -0.003 0.01 See 10 or more Elk 0.64 0.58 0.34 0.54 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 119 Table A5.3 : MRS using Mixed Logit All Responses Drop Intransitive Responses Binary Responses MRS using Monetary Conversion See at least One Elk 0.98*** 1.04*** 1.26*** 0.65* Hear an Elk Bugle 1.40*** 1.53*** 1.40*** 1.13*** See a Bull Elk 0.90* 0.53 0.71 0.69 See 10 or more Elk 1.86*** 1.38** 1.08 1.76** Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Table A5.4 : SD of Elk -Related Attributes using Mixed Logit All Responses Drop Intransitive Responses Binary Responses Monetary Conversion See at least One Elk 0.0004 0.045** 0.013 0.001 Hear an Elk Bugle 0.061*** 0.062*** 0.072*** 0.052*** See a Bull Elk 0.055*** 0.047** 0.070*** 0.053*** See 10 or more Elk 0.110*** 0.101*** 0.102*** 0.121*** Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Table A5.5 : MRS using Latent Class Logit (Elk Experience Class Membership) All Responses Drop Intransitive Responses Binary Responses 28 MRS using Monetary Conversion Class 1 See at least One Elk 0.74* 0.61 0.51* Hear an Elk Bugle -0.62 -0.35 -0.55 See a Bull Elk 0.38 0.37 0.15 See 10 or more Elk -0.75 -0.45 -0.33 Class 2 See at least One Elk 1.72*** 1.60*** 1.27** Hear an Elk Bugle 3.29*** 3.08*** 3.32*** See a Bull Elk 1.04 0.84 0.89 See 10 or more Elk 1.90** 1.99** 1.61** Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 28 Does not converge. 120 Appendix VI: Robustness Check using a Single Elk Attribute Variable The elk -related attributes are highly correlated (Table A 6.1), and this makes them difficult to separately identify. This appendix re -runs the models presented in Essay 2 with one elk -related attribute (the sum of seeing at least one elk, hearing an elk bugle, seeing a bull elk, and seeing 10 or more elk). We use principal component analysis to look for a way to combine the elk -related attribute variables (Table A 6.2). The results suggest that adding up the elk -related attribute variables is a valid approach. This variable will be referred to as fiAll Elk Attribute sfl in the analysis below. The results for all the fiAll Elk Attributefl models accord with those presented in the body of the chapter. Namely, for the population average based on conditional logits, there is evidence of a significant preference for elk. Based on mixed logit, there is evidence of significant heterogeneity in the preference for elk. Distinguishing preferences by activity groups reveal wildlife viewers place the highest value on elk, and there is evidence of incidental value of elk viewing s ince groups focused on hunting, camping or water activities also prefer elk attributes, but less so that wildlife viewers. Finally, the latent class analysis similarly finds that there is a class that significantly prefers elk and one that does not. Table A6.1 : Overall Correlation of Elk -Related Attributes Seeing at least One Elk Hearing an Elk Bugle Seeing a Bull Elk Seeing 10 or more Elk Seeing at least One Elk 1.000 Hearing an Elk Bugle 0.753 1.000 Seeing a Bull Elk 0.846 0.637 1.000 Seeing 10 or more Elk 0.835 0.623 0.698 1.000 121 Table A6.2 : Principal Component Analysis of Elk -Related Attributes Comp 1 Comp 2 Comp 3 Comp 4 Seeing at least One Elk 0.538 -0.108 -0.026 -0.836 Hearing an Elk Bugle 0.467 0.077 0.077 0.187 Seeing a Bull Elk 0.498 -0.724 -0.724 0.380 Seeing 10 or more Elk 0.494 0.685 0.685 0.350 Eigenvalue 3.20 0.40 0.30 0.10 122 Table A6.3 : Overall Conditional Logit Estimates with fiNonefl and fiOutside of Elk Rangefl Interactions Variables (1) (2) (3) All Elk Attributes 0.0166*** 0.0166*** 0.0166*** (0.00228) (0.00227) (0.00226) Distance -0.0103*** -0.0102*** -0.0103*** (0.00223) (0.00222) (0.00220) Outside of Elk Range 1.100*** 1.103*** 2.872* (0.273) (0.274) (1.466) None -1.926*** 0.666 -1.939*** (0.335) (2.318) (0.336) None x Driving Time -0.00378 (0.00417) None x Male -0.0130 (0.583) None x Education Level -0.154 (0.131) None x Income 0.00301 (0.00666) Outside of Elk Range x Driving Time -0.00718*** (0.00257) Outside of Elk Range x Male -0.554 (0.431) Outside of Elk Range x Education Level -0.0454 (0.0946) Outside of Elk Range x Income 0.00345 (0.00401) Respondents Choice Sets 309 913 309 913 309 913 Standard errors clustered by respondent reported in parentheses *** p<0.01, ** p<0.05, * p<0.1 123 Table A6.4 : Overall Mixed Logit Estimates Variables Parameter Estimates SD Estimates % with Parameter >0 All Elk Attributes 0.0240*** 0.0294*** 79% (0.00333) (0.00336) Distance -0.0208*** (0.00309) Outside of Elk Range 0.622* (0.333) None -2.523*** (0.303) Respondents Choice Sets 309 913 309 913 309 913 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 124 Table A6.5 : Conditional Logit Estimates by Primary Activity Group Variables Path Activities Wildlife Viewing Hunting Camping Water Activities All Elk Attributes 0.00667 0.0357*** 0.0192*** 0.0162*** 0.0177*** (0.00458) (0.00659) (0.00566) (0.00477) (0.00514) Distance -0.00703 -0.0140** -0.0147** -0.0131*** -0.0163*** (0.00504) (0.00559) (0.00611) (0.00501) (0.00539) Outside of Elk Range 0.233 1.015 0.860 0.663 1.475** (0.582) (1.319) (0.605) (0.538) (0.583) None -3.418*** -1.112 -1.540* -2.285*** -1.413** (0.850) (0.803) (0.816) (0.768) (0.661) Respondents Choice Sets 64 191 47 139 56 164 71 211 71 208 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 125 Table A6.6 : Class Membership for Latent Class Logit Model for Two Classes when using Elk Experience as Explanatory Variables ( Class 2=Reference Class) Variables Class 1 Have you ever gone elk viewing in Michigan? (Q24 Follow -Up) -0.676* (0.345) Have you ever seen elk outside of Michigan? (Q28 Follow -Up) -0.519* (0.289) Was seeing elk the primary reason for visiting on the intercepted visit? (Q15 Intercept) -2.189*** (0.658) Approximate Driving Time (in minutes) -0.00577*** (0.00173) Constant 1.678*** (0.459) Class Share 43% Standard errors in parentheses *** p<0.01, ** p <0.05, * p<0.1 Table A6.7 : Preferences for Latent Class Logit Model for Two Classes Explained by Elk Experience Variables Class 1 Class 2 All Elk Attributes 0.00281 (0.00318) 0.0349*** (0.00522) Distance -0.0222*** -0.0177** * (0.00570) (0.00427) Outside of Elk Range 0.782** -1.005 (0.362) (0.933) None -2.298*** -0.809 (0.353) (0.572) Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1