Southern Economic Association is collaborating with JSTOR to digitize, preserve and extend access to Southern Economic Journal. http://www.jstor.org Estimating Local Welfare Generated by an NFL Team under Credible Threat of Relocation Author(s): Aju J. Fenn and John R. Crooker Source: Southern Economic Journal, Vol. 76, No. 1 (Jul., 2009), pp. 198-223 Published by: Southern Economic Association Stable URL: http://www.jstor.org/stable/27751460 Accessed: 29-06-2015 08:14 UTC Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://www.jstor.org/page/ info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. This content downloaded from 147.251.189.14 on Mon, 29 Jun 2015 08:14:34 UTC All use subject to JSTOR Terms and Conditions Southern Economic Journal 2009. 76(1). 198-223 Estimating Local Welfare Generated by an NFL Team under Credible Threat ofRelocation Aju J.Fenn* and JohnR. Crookerf This study offers the opportunity to examine the welfare contribution of theMinnesota Vikings toMinnesota households in the context of a credible threat of team relocation. We find the credibility of the threat of relocation is essential to providing unbiased estimates of welfare. This study utilizes contingent valuation methodology (CVM) and a random utility model (RUM) to analyze Minnesotans' decision-making mechanisms for supporting a new stadium initiative. While previous studies have attempted to measure the welfare associated with a sports franchise, we develop and discuss bias that may be imparted to estimates when the researcher fails to calculate a "choke price." Further, we develop an unbiased approach to identify welfare when respondents perceive a risk of losing the franchise. The range of welfare contribution by the Vikings to households inMinnesota is $445.3 million to $1,571.3 million according to a 95% confidence interval based on our study. JEL Classification: H41, L83 1. Introduction "The Minnesota Vikings face a very serious challenge with theMetrodome that threatens our ability to survive.The Metrodome seriously limitstheVikings' revenue opportunities and will soon cause the team to be uncompetitive or losemillions ofDollars?or both."1 The Minnesota Vikings are seeking a new stadium.Minnesotans know that the threatof relocation is a credible one, given theirexperience with the relocation of theMinnesota North Stars (a National Hockey League team that relocated toDallas) and their awareness of the circumstances surrounding the relocations of the Cleveland Browns (now the Baltimore Ravens) and theHouston Oilers (now theTennessee Titans). The Minnesota Vikings were sold by Red McCombs to Zygmund Wilf for $600 million. This paper is based on a survey conducted during theperiod thatMcCombs had the team up for sale. "In a written statement, Vikings owner Red McCombs expresses his frustration that theLegislature thisyear (2002) did not do more to help the football team realize its stadium dreams. In his statement,McCombs says he's engaged JPMorgan Securities to explore sale or relocation options for the team." * Department of Economics & Business, 14 E. Cache La Poudre St., Colorado College, Colorado Springs, CO 80903, USA; E-mail aju.fenn@coloradocollege.edu; corresponding author. f Department of Economics & Finance, Dockery 300-G, University of Central Missouri, Warrensburg, MO 64093, USA; E-mail crooker@ucmo.edu. The authors wish to acknowledge suggestions from Ann Simpson. Professor Allen Sanderson, Professor John Whitehead, and two anonymous referees. Received August 2005; accepted April 2008. 1 Quoted from theMinnesota Vikings Official Team Website (http://www.vikings.com/Stadium/; accessed June 1,2002). 198 This content downloaded from 147.251.189.14 on Mon, 29 Jun 2015 08:14:34 UTC All use subject to JSTOR Terms and Conditions Estimating Local Welfare of an NFL Team 199 (SOURCE: Minnesota Public Radio, May 21, 2002, Minnesota Public Radio) This circumstance provided us with a unique opportunity to examine thewillingness to pay (WTP) for a new stadium when the threatof relocation is real. Here we undertake an analysis of the determinants of credibilityand WTP under threatof relocation. This is a contingent valuation methodology (CVM) issuefaced by allCVM practitioners.Using a sample selectionmodel we find that respondentswho thinkthat theVikings may leave give differentanswers than thosewho do not.2 The key to any reliable survey is the credibility of the scenario. Using a situation with serendipitous timing,we are able to examine theWTP of respondentswho believe that the team would relocate.We contrast these findingswith those of respondentswho do not believe that the teamwill relocate. The estimateshelp us to shed some lighton thebroader CVM question of the divergence inWTP estimatesdue to credibilityof thepayment scenario.The purpose of thispaper is todevelop and estimatean unbiased estimatorof a respondent's household welfare generated by a professional sports franchisewhen the respondent perceives a riskof losing the franchise. There is copious economic literature on the costs and benefits of sports teams to communities. Some of the reasons cited for keeping or attracting a major league team are boosting the local economy and a heightened sense of civic pride (Siegfriedand Zimbalist 2000). The majority of studies (Baade and Dye 1990; Noll and Zimbalist 1997; Rappaport and Wilkerson 2001; Baade, Bauman, and Matheson 2008) suggest that stadiums do not generate a large enough increase in income to be viable solely on the grounds of boosting the economy. A direct attempt tomeasure the fanaticism of team supporters using consumer surplus concluded that formost teams the consumers' surplus from attending games alone might be insufficientto justifybuilding a publicly funded stadium (Alexander, Kern, andNeil 2000). However, for teams thathave sell-out seasons, not all fansmay be able to attend games.Moreover, National Football League (NFL) games for teams that sell out demonstrate public-good characteristics. These games are aired on television,and thus theperformances are nonrival and nonexcludable for the local television audience. An analogous surplusmay exist for fans who watch the games on television.The issue comes down to thevalue of thepublic-good aspects of the franchise to the residents of the area. Most studies in the literature (Baade and Dye 1990;Noll and Zimbalist 1997; Sanderson 2000; Siegfriedand Zimbalist 2000) acknowledge that thepublic-good aspects of a teamneed tobe valued. The public-good aspects forfans thatare generated fromdiscussing the team's fortunes,a sense of civic pride fromhaving a major league team in town, and so forth, need to be valued. However, as is the case with all public goods, directmarket valuation isnot possible. Proponents ofCVM, includingArrow et al. (1993) and Hanemann (1994), claim that if themethodology isproperly applied, the results fromCVM surveyscan be trusted. Johnson,Mondello andWhitehead (2007) have examined theWTP for a stadium in the context of keeping the Jacksonville Jaguars in Jacksonville, Florida. They find that theWTP estimates of $36.5 million lie far below the subsidies paid to attract the Jaguars to the city of Jacksonville. Johnson,Groothius, and Whitehead (2001) investigate the positive externalities associated with building a new hockey arena for thePittsburgh Penguins. They use CVM and model the survey respondents' WTP as a function of the suggested tax, the survey respondents' income, the number of games attended, public-good characteristics of the team, and other variables. They find that,while the team does display public-good characteristics, the public good value generated by the team does not justify the cost of a new arena. They point out the need for additional studies on other teams in other cities. 2 The authors are grateful to the anonymous refereewho suggested thatwe study this issue. This content downloaded from 147.251.189.14 on Mon, 29 Jun 2015 08:14:34 UTC All use subject to JSTOR Terms and Conditions 200 Aju J. Fenn and John R. Croaker Unfortunately, Johnson, Groothius, and Whitehead (2001) conducted their survey in 2000, just after a consortium of investorshad bought the team in 1999, and the credible threat of relocation or contraction had passed. In addition, the survey was conducted in February, during thehockey season. One might argue that responses by fansmay be biased by the current performance of the team. While in-season surveys may bias the WFP upward, out-of-season surveys (although they are free from current team performance) may represent a lowerWFP because the respondents are not currentlyderiving utility fromwatching the team. The out-of season WFP estimates may be viewed as a lower bound on the WTP, and the fans' in-season WFP (contained inAppendix A) may be viewed as an upper bound on theWTP. A similar approach was employed by Johnson and Whitehead (2000) to investigate the public-good aspects associated with building a new basketball stadium for theUniversity of Kentucky Wildcats and a minor league baseball stadium inLexington, Kentucky. One might argue thatcollege teams are not capable of relocating. Thus the threatof losing the team isnot as credible as in the case of a professional team that is for sale. This phenomenon may have impacted the WTP valuation. The Johnson and Whitehead paper uses the payment card format,which typically results inamore conservative estimate ofWTP. We use a dichotomous choice elicitation format thatmay result ina largerWTP value than ifwe had used thepayment card format.We use thedichotomous choice formatbecause ithas been shown to be incentive compatible and easier to answer (Boyle and Bishop 1988).3 We hope to learnmore about theWTP for a stadium when the threat of relocation is credible, as itwas with theMinnesota Vikings at the timeof our survey.We also conducted our survey during the off-season tomitigate the biases thatmay come from the latest victory or defeat. We draw upon the recreational demand literature from environmental economics to include travelcostmeasures of expenditures by respondentswho watch games at the stadium or on television. Finally, the scope of this survey ismuch larger than previous studies,with about half of the surveysbeing sent to nonmetropolitan households. We begin with a brief description of the literature addressing the connection between credibility and WTP. Following that, we present our survey methodology and sample characteristics. Then we proceed to a description of theCVM methodology and the "naive" empiricalmodel not treating theuncertainty in team relocation. Next, we present the empirical results for thisnaive model. After that,we update ourmodel to account foruncertainty in team relocation and include a section thatmodels the respondents' credibility beliefs. Finally, we empirically estimate our revised random utilitymodel with prior-determined relocation beliefs and develop our conclusions from this study.Appendix A contains a description and analysis of a data setgathered by on-site interviewswith Vikings fans outside the stadium. These results are provided for comparison inAppendix B. 2. Credible Threat of Relocation and WTP One of the biggest criticisms of CVM surveys is that if respondents do not find the scenario to be credible, then the responses lackmeaningful information about the resource being studied (Diamond and Hausman 1994). This is a keymethodological issue faced by all 3 We are grateful to an anonymous referee for pointing this out. This content downloaded from 147.251.189.14 on Mon, 29 Jun 2015 08:14:34 UTC All use subject to JSTOR Terms and Conditions Estimating Local Welfare of an NFL Team 201 practitioners ofCVM. In our survey,more than 50% of the respondents state that theybelieve theVikings would move if the team did not get a new stadium. Our WTP estimates are also much higher than those obtained for similar scenarios. The lessons from this surveymay be used to benefitother CVM surveyswhere timing iscritical, as well as tomodel the respondent decision-making mechanism under uncertainty. This idea is separate from the nomenclature of biases described at length in thework of Mitchell and Carson (1989) and in pieces like the recommendations of theNational Oceanic and Atmospheric Administration (NOAA) panel (Arrow et al. 1993). Our ideas deal mainly with the timingof a survey as itpertains to the information about the issue that is currently available. Early scholars have pointed out that it is important for respondents to understand the choices in the scenario exactly as the investigators intended them (Mitchell and Carson 1989). Our contribution to the literature is much more fundamental than "scenario misspecification." Basically, we deal with timing issues that speak to the heart of scenario credibility. If the respondent did not believe that theVikings would move, then thevaluation of the team would be substantially different from the one obtained. Given the relatively recent move of theirhockey team, theMinnesota North Stars, toDallas and themoves of otherNFL teams fromCleveland to Baltimore and fromHouston toTennessee, fanswere more likely to believe thepayment scenarios posed in thispaper than at any other time in recent history. Carson, Groves, and Machina (2000) point out that unless the surveymatters to the individual, and he believes that his response matters, there is no way to consider the survey question "consequential." Our ideas are perhaps closer to their paper than to any other strand in the literature. We pose our question in an "incentive compatible" framework as per their guidelines. The value added by our paper is thatwe spell out some of the details of how to execute a credible scenario in a situation where the public's perception is altered daily by reports from thenews media on a popular topic.We believe that the issue is connected to the "cheap talk design" idea introduced by Cummings and Taylor (1999). If individuals do not perceive that the teamwill move, then there is not likely to be a difference in their responses from, say, the responses of the fans of the Pittsburgh Penguins who answered their questionnaire shortlyafter the team had been sold and whose teamwas believed to be staying in Pittsburgh. If the threat to move is not a credible one, then the question reduces to a hypothetical scenario, which may undermine the perception that payment will indeed be collected. That, however, was clearly not the case with the Vikings. In face-to-face interviews during thefan questionnaire, several fans pulled out theircheckbooks and were willing towrite a check on the spot. Cummings and Taylor (1999) also address the issue of "realism" ina CVM survey.They state thatCVM researchers have previously acknowledged that the realism of the survey is directly connected to theaccuracy of the responses. They evaluate the relationship between the accuracy of responses and the probability that survey responses will result in real consequences. Their results support thenotion that there isa significantrelationship between the"realness" of a survey and theaccuracy of the results. In our case, themajority of the sample did believe that theVikings would move out of thearea ifthe team did not get a new stadium. The question, of course, is,when does one know that the threat is credible in theminds of respondents? If the survey is administered too soon, then respondents may not believe that the team is likely to leave. If it is administered too late, the teammay already have moved or the perception of relocation may have been tempered by the statements of a new owner towork thingsout in the area. This content downloaded from 147.251.189.14 on Mon, 29 Jun 2015 08:14:34 UTC All use subject to JSTOR Terms and Conditions 202 Aju J. Fenn and John R. Crooker There is an entire body of work on the idea of a credible threat in game theory.The essential idea has been incorporated by CVM practitioners. The gist is that, if the scenario is not believable to the respondent, then the results of the survey do not allow us to infervalue. We will estimate separate samples forbelievers and nonbelievers and contrast the estimates in the empirical results, ignoring relocation uncertainty. 3. Survey Methodology and Sample Characteristics A random sample of 1400 households was purchased from a professional sampling firm. The socioeconomic and demographic characteristics of the sample are designed to reflectthose of the state of Minnesota. Half of these households are located in the seven-county metropolitan area of theTwin Cities ofMinneapolis and St. Paul. The other half of the sample comes from the rest of the state. The contact procedures follow themethods outlined in Dillman (1978). Initially, a random subsample (whichwe call thepresample) of 200 households, with a 50/ 50 split between urban and other households, was mailed to respondents. This was done to ensure readability of the questions and to obtain feedback on the various bid amounts. The remaining 1200 surveyswere thenmailed. Forty-six of the surveyswere undeliverable, and 565 surveys were returned. The response rate was 42%. For comparison, Johnson and Whitehead (2000) had a response rate of about 36% based on a smaller sample size of 293 mail surveys. Table 1 summarizes thedescriptive statisticsof thekey variables. This section of thepaper addresses some of theadditional details about thedata. The survey isavailable upon request. It comprises 33 questions and is divided into three sections. The first section deals with games viewed and fan interestquestions. The second section outlines a payment scenario and solicits payment amounts using a yes/no format in response to a specific amount. The last section of the survey solicits demographic information. The firstfewquestions pertain togames attended at theVikings' stadium (theMetrodome) and/or viewed on television by the respondent. This section also solicits information about money spenton teammerchandise, travel time to the stadium from the respondent's home, and the number ofMinnesota sports teams that the respondent follows. The average number of games attended by respondents was 0.33, and the average number of games watched on television was 8.2. The median number of games watched on television was 10. The next few questions pertain to thepublic-good characteristics of the team. Forty-one percent of the respondents claim to read about Viking football on a daily basis, either in the paper, inmagazines, or online. Fifty-four percent of the respondents discuss theVikings' fortuneswith friends, co-workers, or familymembers on a daily or weekly basis. Eighteen percent describe themselves as die-hard fanswho "live and die with theVikings." About 13% of the respondents feltthat in theabsence ofVikings football, their levelof funwould decrease by "a great deal." This number climbs to 35% when we add the respondents who felt that in the absence of theVikings the level of funwould fall "slightly." The next section elicits theWTP fora new stadium. Itquotes theVikings' Website for the total cost of a new stadium, which is $450 million to $500 million. The survey goes on to say thatprivate and university economists have estimated the individuals' cost of this stadium tobe the amount quoted below. This amount is a one-time payment of $5, $10, $25, or $100, This content downloaded from 147.251.189.14 on Mon, 29 Jun 2015 08:14:34 UTC All use subject to JSTOR Terms and Conditions Estimating Local Welfare of an NFL Team 203 Table 1. Summary Statistics Variable Definition Mean Standard Deviation Maximum Minimum AMOUNT READ INTEREST DISCUSS FUN PUBGOOD SPEND PRESTGE WINS UP ER LEAVE TWINS UOFM NONWHT COLGRD INCOME SINGLE MALE KIDS TIM INST URBAN N = 565 Bid amount $5, $10, $25 or $100 37.26 1 if"A few days per week" or "Daily" 0.41 1 if"I am a die-hard fan" 0.18 1 if"A few days per week" or "Daily" 0.54 1 if"Fall slightly" or "Fall a great deal" 0.35 Public good (sum of READ, 1.48 INTEREST, DISCUSS, FUN) Money spent on tickets,merchandise, 323.80 and travel costs 1 if"A new stadium will bring 0.44 more prestige to the area" 1 if"A new stadium will help 0.11 theVikings win a Super Bowl" 1 if"The Vikings will leave 0.55 if theydo not get a new stadium" 1 if"Support theTwins over the 0.16 Vikings for a new stadium" 1 if"Support joint stadium 0.47 with University ofMN football" 1 ifrace isnonwhite 0.07 1 ifcollege or graduate school 0.51 education Annual income 56,766.24 1 if single 0.19 1 ifmale 0.73 Number of kids 2.01 1 ifrespondent has been in the state for 0.82 over 20 years 1 ifrespondent is from seven-county 0.50 metropolitan area 36.71 0.49 0.39 0.50 0.48 1.47 100 1 1 1 1 4 325.57 1879.14 0.50 0.31 0.50 0. 37 0.50 0.26 0.50 27,781.22 100,000 0.39 0.45 1.72 0.38 0.50 0 0 0 0 0 0 7500 0 0 0 0 0 depending upon the survey.4The next few questions allow the respondent to explain their reasons for agreeing or disagreeing to finance a new stadium. At the$5 level, 51.5% agreed to pay for a new stadium, and at the $15 level, 50.8% agreed to pay. At the $25 level, 50% agreed to pay that amount, and at the $100 level, 33.33% were willing to pay. On thewhole, at all bid amounts, 25% of the respondents who were willing to pay claimed that theywould do so because theyeither liked to attendVikings games or liked to watch them on television. The other 75% claimed that theywould be willing to pay for other reasons. The last section solicited demographic data from the respondent. About 73% of the respondentswere male, 19%were single, 93% were white, and 82% have lived inMinnesota for 20 ormore years. Fifty-one percent of the surveyparticipants had some college and/or graduate school education, and the average annual income was about $57,000. 4 Lower bid amounts ranging from SI to $5 demonstrated a very high acceptance rate during pretesting of the survey. This content downloaded from 147.251.189.14 on Mon, 29 Jun 2015 08:14:34 UTC All use subject to JSTOR Terms and Conditions 204 Aju J. Fenn and John R. Croaker 4. The Contingent Valuation Model This section illustrates the theoretical methodology of CVM. We are interested in estimating the respondents' WTP fora new stadium. To consider values estimated with CVM, the following question was proposed to a random sample of respondents: "Would you be willing to pay $B out of your own household budget for thenext year tomake a new stadium possible?1' The respondent may answer with either a "yes" or "no" response. The researcher models the response according to the following: Ri is respondent /"sresponse to the contingent question, WTP,- is the respondent's WTP for the stadium, and Bt is the bid level put forth by the interviewer to this particular respondent. Subscripting the bid amount with /allows us to offerdifferentbids to various respondents.5 Another issue thatwe must resolve in this investigation is the specification of the bid levels. Bid design has receivedmuch attention in theCVM literature (Cameron and Huppert 1991; Duffield and Patterson 1991; Nyquist 1992; Alberini and Carson 1993; Cooper 1993; Kanninen 1993a, b; Alberini 1995). A thorough discussion of this literature is found in Hanemann and Kanninen (1998). In this application, we wish to choose the bid levels that result in thegreatest precision inestimatingWTP. Our approach to selectingbid design was the sequential design procedure. To estimate WTP for the population of Minnesota precisely using the sequential bid design procedure, we used several sources of information. First, we interviewed Minnesotans and discussed their interest in theVikings and asked for their thoughts on a new stadium. On thebasis of this information,we created initial surveyquestions thatwe posed to students on a campus nearMinneapolis and toVikings fans on game day outside the stadium (intercept and in-person interviews). The interviews at the stadium included bid amounts of $500 (see Appendix A). Using these results as prior information,we formulated statisticallyoptimal bid levels (that is, thebid levels thatgenerate themost precise estimate ofmean WTP). For thenext iteration,we conducted a pretest ofMinnesota residents. Upon receiving the results of this pretest,we again formulated statisticallyoptimal bid levels thatwe used in the full sample. In termsof the range of bids used, we point out that thegeneral rulediscussed in theCVM literature is to avoid using bid levels in the outer 12% tails. This is because those bids are considered to be uninformative (Hanemann and Kanninen 1998).Our bids are somewhat tight, as threeof the four bid amounts were less than $30. Respondents seem to have rejected each of the threebid levels less than $30 at about the same rate.Distributing bids more evenly up to the top bid amount of $100 may have provided more information on the sensitivityof respondents to the bid amount. Also, more evenly dispersed bid levels would likely have improved the Yes WTPi > Bi No otherwise. (i) 5 There isa strand in theCVM literature exploring the timing of payments; Johnson. Mondello, andWhitehead (2006) address thisquestion. (In particular, itwould seem ifcapital markets are not perfect, the ability tomake payments over timewould enable respondents to contribute more to the resource.) However. Kahneman and Knetsch (1992) find that a one-time payment and an annual payment design generate equivalent results. Stevens. DeCoteau, and Willis (1997) and Stumborg, Baerenklau. and Bishop (2001) find the implicit discount rate in the annual payment design is unrealistically high. As there are concerns regarding themultiple-period design, and there is some empirical support for the one-time payment, the latter is the design we have adopted in this investigation. This content downloaded from 147.251.189.14 on Mon, 29 Jun 2015 08:14:34 UTC All use subject to JSTOR Terms and Conditions Estimating Local Welfare of an NFL Team 205 performance of theTurnbull nonparametric technique. Later, we reconsider thebid design after controlling for relocation credibility beliefs. 5. The Naive Empirical Model?Ignoring Relocation Uncertainty This section listsand explains the determinants of theWTP for a new Vikings stadium. The dependent variable, WTP, takes on the value of 1 ifthe fan responds with a "yes" to the bid amount on the survey and a value of 0 ifthe fan responds with a "no" to the bid amount. Equation 2 tests the hypothesis that theWTP for a new stadium depends on the following variables: the dollar value of the bid amount (AMOUNT), the respondent's income (INCOME), the extent to which theVikings are a public good (PUBGOOD), the prestige associated with having a new stadium (PRESTGE), the explicit and implicit costs incurred in the previous seasons by respondents who watch games either at the stadium or on television (SPEND), the belief that a new stadium will help the team win a Super Bowl (WINSUPER), the belief that the team will relocate ifnot given a new stadium (LEAVE), theMinnesota Twins baseball stadium drive (TWINS), a joint stadium with theUniversity ofMinnesota (UOFM), and a vector of demographic variables (Z). 8 is the error term in the model. Each respondent received a bid AMOUNF of $5, $15, $25, or $100 on his particular survey. The respondent then answered "yes" or "no" as to whether he would pay the particular bid amount on the survey.The overall "yes" response rate is47%. This suggests that the bid amounts have not been set too high or too low. INCOME corresponds to themidpoint of the income range that respondents circled. Some respondents did not answer the income question.6 In keeping with Johnson and Whitehead (2000), the index PUBGOOD is the sum of four dummy variables: READ, DISCUSS, INFERESF, and FUN. These variables are coded as either 0 or 1.READ is equal to 1 ifthe survey respondent answered "daily" or "weekly" when asked about how often he reads about the Vikings in newspapers, magazines, or online. DISCUSS was coded as 1 ifthe respondent claimed thathe discussed the team's fortuneswith friends, family, or co-workers on a daily or weekly basis and was coded as 0 otherwise. INTEREST was coded as 1 ifthe respondent claimed to be a die-hard fan and was coded as 0 otherwise.FUN measures thechange in thequality of lifeof the respondent iftheVikings were to leave town. If the respondent answered "fall slightly11 or "fall a great deal," this variable was coded as l and was coded as 0 otherwise. We create a variable called SPEND to account for the explicit and implicitcosts incurred in past seasons by people who purchase team merchandise and watch games either at the stadium or on television. SPEND isdefined as follows: 6 We replaced themissing values with the sample mean inmodel l and with predicted values of income from a semi logarithmic regression of income on various demographic variables inmodels 2 and 3. WFP = f (AMOUNF, INCOME, PUBGOOD, SPEND, PRESFGE, WINSUPER, LEAVE, FWINS, UOFM, Z, e) (2) SPEND = EXPLICIT COSTS + IMPLICIT COSTS, (3) This content downloaded from 147.251.189.14 on Mon, 29 Jun 2015 08:14:34 UTC All use subject to JSTOR Terms and Conditions 206 Aju J. Fenn and John R. Crooker where EXPLICIT COSTS are the dollars spent on tickets for the total number of games that the respondent attends plus the value of team merchandise that the respondent purchases. IMPLICIT COSTS are the travel costs (in termsof forgonewages) of attending games or the opportunity costs (again in terms of forgone wages) of watching games on television. These costs are calculated in accordance with the recreational demand literature from environmental economics (Freeman 1993). IMPLICIT COSTS can be furtherbroken down into the implicit costs of attending games at the stadium and the implicitcosts ofwatching games on television. Implicit costs of attending stadium games (ICSG) are given specifically by Equation 4: ICSG = ^{Hourly Wage Proxy) * [{Travel Time) + {Game Length)] * {Games Attended). (4) The hourly wage proxy is discounted by a factor of one-third, in keeping with the recreation demand literature.7The hourly wage proxy itself is calculated by dividing the respondent's annual income by thenumber ofworking hours in the year, assuming a 40-hour workweek. For each game that the respondent attends, she gives up the round trip travel time {Travel Time) to and from the stadium in addition to the lengthof the game {Game Length). The lengthof the average NFL game is assumed to be threeand a half hours. Implicit costs of watching games on television {ICTV) are calculated along the same lines as ICSG. This is described by Equation 5. ICTV = I: {HourlyWage Proxy)[Game Length] * {Games Watched on TV). (5) Notice that theSPEND variable isonly concerned with variables thatwere determined in previous seasons; hence, it is exogenous at the time of the survey. PRESTGE is a dummy variable that is coded as 1 if the respondent believes that a new stadium will "bring greater prestige to theTwin Cities area." LEAVE is a dummy variable coded as 1 if the respondent believes that "The Vikings will leave town iftheydo not get a new stadiumwithin thenext few years." Fifty-fivepercent of respondents believe that theVikings will relocate iftheydo not get a new stadium. WINSUPER is a dummy variable that is coded as 1 ifthe respondent believes that a new stadium will "help theVikings win the Super Bowl." TWINS is a dummy variable that is coded as 1 ifthe respondent chose theTwins when she indicated that shewould not pay for a Vikings stadium because shewould ratherpay for a Twins stadium. UOFM isa dummy variable that is coded as 1 if the respondent indicated that shewould be willing to pay for a Vikings stadium because of thepossibility of a joint stadiumwith theUniversity ofMinnesota football team.The two teams currently share the same facility.Furthermore, at the timeof the survey, theVikings were in talkswith theUniversity ofMinnesota about a joint facility.We also include a vector of demographic variables, Z, to pick up the impact of race, gender, education, etc. The entire list of these variables along with their definitions is displayed in Table 1. We use probit to estimateWTP fora new stadium. The resultsof thisfirstmodel (model 1) are contained inTable 2. Probit is a common technique in theCVM literatureand has good 7 There is a long strand of literature concerning the appropriate opportunity cost of time in recreational valuation studies. Seminal works include Knetsch (1963), Scott (1965), and Cesario and Knetsch (1970). However, there is no general consensus on what the appropriate opportunity cost should be. Cesario (1976) estimated the opportunity cost of time to be one-third thewage rate in an investigation of transportation and community studies. McConnell and Strand (1981) estimated the opportunity cost of time to be 0.6 of thewage rate. In our study,we use one-third thewage rate. This content downloaded from 147.251.189.14 on Mon, 29 Jun 2015 08:14:34 UTC All use subject to JSTOR Terms and Conditions Estimating Local Welfare of an NFL Team 207 Table 2. Model 1 Variable Regression Coefficient r-Statistic Marginal Impact on WTP CONSTANT AMOUNT PUBGOOD SPEND PRESTGE WIN SUP ER LEAVE TWINS UOFM NONWHT COLGRD INCOME SINGLE MALE KIDS TIMINST URBAN Log-likelihood function -1.60 -0.01 0.29 0.00 0.60 0.57 0.39 0.34 0.87 0.07 0.20 -0.00 0.02 0.10 -0.03 -0.00 -0.01 -227.84 -5.033 -3.73 4.49 2.17 4.18 2.11 2.77 1.97 6.29 0.23 1.35 -0.55 0.13 0.60 -0.65 -0.02 -0.06 -228.23 NA 41.15 0.10 83.90 79.85 55.51 48.20 123.01 10.25 27.52 -0.00 3.48 13.89 -3.80 -0.55 -1.23 performance relative to other techniques, even ifnormality is questioned (Creel and Loomis 1997). Though some concern arises regarding thepotential fornegative estimates ofWTP with probit, Creel and Loomis have found that theprobitmodel provides a better fitofmean WTP than other techniques that force WTP to be nonnegative. Explanatory variables that are missing values have been replaced by their respective sample means. We used a semi logarithmicmodel of income as a function of various demographic variables to predict the missing values of income. The use of thisproxy instead of themean value of income formissing values did not alter the results significantly.These results are presented inTable 3 under the "Model 2" heading. (The /-statisticsare reported in parentheses beneath the coefficient estimate in the table.) 6. Empirical Results from theNaive Model The results from our probit estimation ofmodel 1 are reported inTable 2.8,9We use the 1% significance level.We find that the bid amount {AMOUNT) is negative and significantly related to the respondents' WTP. The public-good aspect of the existence of a team {PUBGOOD) is also a positive and significant variable. These results are in keeping with Johnson and Whitehead's (2000) findings. In addition, we find that the explicit and implicit costs associated with watching games as captured by SPEND are positively and significantly related to theWTP for a new stadium. In termsofmagnitude of coefficients (apart from the constant term), PRESTGE, WINSUPER, UOFM, and LEAVE are the largest significant 8 The significance of variables and their signs remain unchanged for alternative limited dependent variable techniques, such as logistic or extreme valued distributions. 9 Additionally, we applied thedichotomous choice normality test specified inBera, Jarque, and Lee (1984). The results of the test suggest thatwe fail to reject the null hypothesis that the residuals are normally distributed. This content downloaded from 147.251.189.14 on Mon, 29 Jun 2015 08:14:34 UTC All use subject to JSTOR Terms and Conditions 208 Aju J. Fenn and John R. Crooker Table 3. Specification Sensitivity Variable Model 2 Model 3 CONSTANT -1.55146 -1.72193 (-4.9) (-5.4) AMOUNT -0.00728 -0.00737 (-3.8) (-3.8) PUBGOOD 0.28994 0.28445 (4.46) (4.11) SPEND 0.00066 ? (2.06) GAMES ? 0.02839 (1.89) PRESTGE 0.62459 0.65245 (4.39) (4.57) WINSUPER 0.55291 0.57423 (2.05) (2.12) LEAVE 0.38508 0.37059 (2.72) (2.61) TWINS 0.25443 0.27357 (0.92) (0.98) UOFM 0.85779 0.81279 (6.14) (5.80) NONWHF -0.00401 0.0624 (-0.0) (0.19) COLGRD 0.19355 0.21357 (1.31) (1.45) INCOME -1. 7E-06 1.6E-06 (-0.5) (0.61) SINGLE -0.00299 0.01511 (-0.0) (0.07) MALE 0.10678 0.08634 (0.64) (0.51) KIDS -0.02915 -0.02684 (-0.6) (-0.6) TIM INST -0.02404 -0.06338 (-0.1) (-0.3) URBAN 0.0322 0.03184 (0.23) (0.22) Log-likelihood function -229.225 -229.616 a /-statsare in parentheses. coefficients.These findings suggest that respondents aremore willing to pay for a new stadium because of theprestige itwill bring to the area, the threatof team relocation, and the increased chance ofwinning a Super Bowl. Approximately 47% of the respondents who were willing to pay for a new stadium indicated that theywould do so because of the possibility of a joint stadium with theUniversity ofMinnesota football team. The marginal effectsare obtained bymultiplying the regression coefficientsby thenegative of the reciprocal of the coefficient on the bid amount in keeping with Cameron (1988). The public-good value toMinnesotans, as indicated by themarginal effect in the fourth column of Table 2, is approximately $41. The sum of themarginal effects of team relocation, added prestige from a new stadium and a better chance at winning the Super Bowl, increase the This content downloaded from 147.251.189.14 on Mon, 29 Jun 2015 08:14:34 UTC All use subject to JSTOR Terms and Conditions Estimating Local Welfare of an NFL Team 209 Table 4. Marginal Impact Estimates inDollars by Variable forRural, Urban, and Pooled Samples Variable Rural Marginal Impact Urban Marginal Impact Pooled Marginal Impact AMOUNT CONSTANT PUBGOOD SPEND PRESTGE WINSUPER LEAVE TWINS UOFM NONWHT COLGRD INCOME SINGLE MALE KIDS TIM IN ST URBAN Log-likelihood NA (-1.983) -339.61 (-4.045) 25.83 (1.414) 0.31 (2.78) 123.14 (3.32) 127.22 (1.46) 89.00 (2.344) 17.93 (0.359) 154.61 (4.243) 142.41 (1.359) 58.27 (1.51) 0.00 (1.52) -24.58 (0.457) 48.20 (1.166) -9.12 (-0.867) 52.69 (0.931) 100.983 NA (-3.813) -122.10 (-2.734) 37.30 (4.247) 0.02 (0.435) 48.16 (2.433) 63.83 (1.875) 33.76 (1.702) 57.65 (2.589) 86.43 (4.562) -19.55 (0.522) 9.66 (0.49) 0.00 (0.091) 23.55 (0.93) -4.69 (-0.203) 2.98 (0.506) -31.86 (-1.244) 118.816 NA (-3.731) -228.23 (-5.033) 41.15 (4.489) 0.10 (2.169) 83.90 (4.175) 79.85 (2.111) 55.51 (2.769) 48.20 (1.970) 123.01 (6.294) 10.25 (0.227) 27.52 (1.347) 0.00 (0.584) 3.48 (0.128) 13.89 (0.598) -3.80 (-0.648) -0.55 (-0.021) -1.23 (-0.062) -227.839 respondents' WTP by about $219. The actual explicit and implicitcosts that respondents incur while watching games do little ($0.10) to boost theirWTP for a new stadium. The Minnesota Twins stadium drive (TWINS) affected the respondents' WTP for a Vikings stadium by $48. The possibility of a joint stadiumwith theUniversity ofMinnesota football team had a positive and significant effect,boosting WTP by $123.01. Approximately 5% of those who did not want to pay for a stadium claimed that itwas because they did not care about Vikings football. The model is re-estimatedwithout these observations. The results and significance of the variables are largely the same. These estimation resultsare available upon request. URBAN is insignificant,so themodel isestimated forurban, rural, and thepooled sample. These results are contained inTable 4. The r-statistics are reported inparentheses beneath thecoefficientestimate in the table. Statistically significant coefficients are indicated by the bold and italicized /-statistics. This content downloaded from 147.251.189.14 on Mon, 29 Jun 2015 08:14:34 UTC All use subject to JSTOR Terms and Conditions 210 Aju J. Fenn and John R. Crooker Another concern thatmay arise with models 1 and 2 is the potential multicollinearity between ticketprices and the number of games attended in theSPEND variable. In order to remedy this,we replace SPEND with thenumber of games attended inperson plus thenumber of games watched on television. The results of this thirdmodel are shown inTable 3 under the heading "Model 3." Once again, the results remainmore or less the same as those inmodels 1 and 2. 7. Credible Threat of Viking Relocation and the CVM If the respondent does not perceive theVikings relocation to be a credible threat, is he valuing theVikings? Johnson and Whitehead (2000) perform a valuation study for sports stadiums using a CVM format. They proposed to value a new basketball arena for the University ofKentucky. As theUniversity ofKentucky would not relocate ifa new stadium fails to be approved, Johnson andWhitehead (2000) point out that theirCVM studymay not be interpretedas a valuation of theUniversity ofKentucky basketball program. Analogously, inour survey,provided the respondent does not believe theVikings will move fromMinnesota without a new stadium, he is not necessarily valuing the Vikings franchise in our CVM question. Instead, the respondentmay solely be valuing thenew stadium. Ifwe wish to estimate value for the franchise,we may consider only thosewho perceive theVikings will leavewithout a new stadium. To examine how the individualswho felttheVikings will relocate without a new stadium value the franchise,we split the full sample into thosewho feltrelocation was credible and those who did not find the threat credible. We estimated thesemodel splits, and the estimated results are indicated inTable 5.As inTables 3 and 4, the /-statisticsare reported in parentheses beneath thecoefficient estimate in the table, and statistically significantcoefficients are indicated by the bold and italicized /-statistics. PUBGOOD, WINSUPER, and FWINS are statistically significant in the credible subsample and pooled sample but not in thenoncredible subsample. SPEND and PRESFGE are statistically significant in the noncredible subsample and pooled sample but not in the credible subsample. UOFM is statistically significant in all three sample splits.Also, in the credible pool, COLGRD ispositive and statistically significant. Interestingly, the coefficient on bid amount is insignificant in thenoncredible subsample model. This is troublesome for estimating WFP for at least two reasons. First, this suggests respondents are not strongly reacting to the bid amount in answering the CVM question. Second, the coefficient on bid amount is the negative reciprocal of the estimated standard deviation inWTP across the sample. This is empirically unsurprising, as we do see a large range in estimated WTP for this subsample (-$792.21 to $1,320.53). The noncredible subsample average value for theVikings is -$252.03. This empirical result for this sample split likely stems from at least two issues. First, this value does not necessarily reflecta low value for theVikings franchise, as this subsample does not perceive theVikings will leave without a new stadium. This implication is that the low value reflects a low value for constructing a new stadium. Second, we argue above that a negative WTP is theoretically plausible. The low acceptance rate of our CVM question by this subsample indicates that the precision in estimating the coefficient on the bid amount would have been assisted ifwe learned about theWTP distribution in the left tail (or leftof themean). This would have This content downloaded from 147.251.189.14 on Mon, 29 Jun 2015 08:14:34 UTC All use subject to JSTOR Terms and Conditions Estimating Local Welfare of an NFL Team 211 Table 5. Marginal Impact Estimates inDollars by Variable forCredible, Noncredible, and Pooled Samples Variable Credible Move Marginal Impact Noncredible Move Marginal Impact Pooled Marginal Impact AMOUNT CONSTANT PUBGOOD SPEND PRESTGE WINS UP ER LEAVE TWINS UOFM NONWHT COLGRD INCOME SINGLE MALE KIDS TIM IN ST URBAN Log-likelihood NA (-4.113) -81.68 (-1.882) 39.21 (4.719) 0.04 (0.966) 18.68 (1.000) 77.77 (2.498) 60.31 (2.624) 87.86 (4.943) -27.75 (0.622) 38.42 (2.081) 0.00 (0.840) -29.75 (1.167) -0.32 (0.014) -1.05 (0.186) -2.79 (0.115) -11.38 (-0.632) -135.299 NA (-0.953) -665.79 (-4.040) 36.61 (0.99) 0.48 (2.603) 408.15 (5.234) 308.46 (1.291) 42.18 (0.447) 311.03 (4.083) 151.12 (0.967) -41.15 (0.509) 0.00 (0.246) 98.03 (0.905) 86.36 (1.011) -11.91 (0.569) 23.21 (0.208) 13.03 (0.167) -77.513 NA (-3.731) -228.23 (-5.033) 41.15 (4.489) 0.10 (2.169) 83.90 (4.175) 79.85 (2.111) 55.51 (2.769) 48.20 (1.970) 123.01 (6.294) 10.25 (0.227) 27.52 (1.347) 0.00 (0.584) 3.48 (0.128) 13.89 (0.598) -3.80 (-0.648) -0.55 (-0.021) -1.23 (-0.062) -227.839 required negative bid amounts.10 We are not aware of a published CVM study that has investigated this phenomenon. This may be an interesting issue to consider in future investigations. The inability to estimate a statistically significant coefficient on the bid amount in the noncredible subsample isnot critical to our stated purpose of valuing theMinnesota Vikings franchise. It isnot clear that individuals who feel theVikings will remain inMinnesota without a new stadium are valuing the franchise in responding to our hypothetical stadium initiative. Hence, we do not consider the results of this subsample inprojecting a value for theVikings franchise. It is not trivial how researchers could propose a policy mechanism that proposes negative bid levels in a believable context. This content downloaded from 147.251.189.14 on Mon, 29 Jun 2015 08:14:34 UTC All use subject to JSTOR Terms and Conditions 212 Aju J. Fenn and John R. Crooker The individualswho feel theVikings will relocate without a new stadium are valuing the Vikings franchise in their response to theCVM question. The range of values in this credible subsample is?$158.85 to $322.68, with an average of $73.26.We toleratenegative estimatedWTP values out of convenience and to illustratethat themodel we have developed so farmay not be adequately assessing thewelfareMinnesotans place on theVikings. As these results indicate, the respondents'beliefsabout theVikings' relocation are criticalto theestimatedWTP. In thefollowing section,we extendourmodel toaccount forheterogeneous relocationbeliefs.We findthatthisricher model substantially improvesour analysis of theattitudeofMinnesotans toward theVikings. 8.Modeling theRespondents' Decision-Making Problem with Heterogeneous CredibilityBeliefs As noted in thepreceding section,CVM studies present a contingent scenario and ask the respondents'willingness to contribute at a specifiedbid to guarantee a specificoutcome. In our case,we ask respondents fortheirwillingness to contribute toconstruction of a new stadium forthe Minnesota Vikings. On the surface, thisquestion would allow us to infervalue fora new stadium for theVikings. However, previous researchershave noted that ifthere is a perception that the professional sports team will relocate without a new stadium, respondents' answers to this question may be used to infervalue that includes thewelfare receivedby respondents fromthe sports team. This is thefocus of our investigation: tomeasure thevalueMinnesotans place on theVikings. Reviewing the summary statistics inTable 1,we see that only 55% of the respondents indicated theybelieved theVikings would relocate without a stadium. As this suggests, our valuation estimate from the CVM question may not include a value for the sports team; ignoring the differences in credibility beliefs likely biases our valuation estimate. This is because a respondent who does not believe the Vikings will relocate does not perceive a potential loss of theVikings ifhe or she answers our CVM question with a "no." For this reason we find we must formally model the respondents' decision-making mechanism given theirperception of the likelihood theVikings would relocate without a new stadium.11 For notational convenience, we define respondent z's belief regarding relocation as 0,. Once we allow for heterogeneous credibility beliefs in our sample, we find the logical approach to modeling thisdecision-making process iswith a random utilitymodel (RUM), similar to the approaches ofHanemann (1984a, b), Smith and Desvousges (1990), Ott ,Huang, and Misra (1991), and Eom (1994). In these studies, the researchersmodel thediscrete selection of goods by consumers under uncertainty. As it is not clear that all respondents believe theVikings would definitely relocate or definitely remain inMinnesota without a stadium, we find this uncertainty of outcome is important to capture unbiased estimates of welfare generated by the sports franchise in Minnesota. Given the individual's belief regarding relocation, which we call 9,-,the individual's expected utility from answering our CVM question with a "no" is E[Ui\yi = 0} = Qi[V(Mh So, K0) + coo,]+ (1 - 0/)[K(M/, S0, K}) + e0i/], (6) 1 We thank an anonymous refereewho made this suggestion. This suggestion substantially improves thedevelopment of our paper. This content downloaded from 147.251.189.14 on Mon, 29 Jun 2015 08:14:34 UTC All use subject to JSTOR Terms and Conditions Estimating Local Welfare of an NFL Team 213 where y,-is the individual's response to theCVM question, with a 1 indicating a "yes" response and a 0 indicating a "no" response; V- + s0o/is individual is indirectutility function (with V being the respondent's nonstochastic portion of his or her indirect utility function);M, is individual z"sincome; and S\ indicates the stadium will be constructed,while S0 indicates the stadium will not be constructed. The variable K\ indicates theVikings remain inMinneapolis, while K0 indicates theVikings relocate outside ofMinnesota. We assume thenoise termss0o/,?01/ are normally distributed. The subscript 00 reflects that no stadium was constructed and the Vikings relocated. The subscript 01 reflects thatno stadiumwas constructed while theVikings remained inMinneapolis. Notice that the terms s0o/, ?01/are n?t stochastic from the respondent's perspective. The researcher, however, does not observe these terms, which drive differences in behavior across thepopulation. Given the respondent answers "no" and theVikings will leave Minnesota without a stadium, the indirect utility V(Mh 0, 0) + s0o/is realized. That is, the respondent receives the satisfaction level associated when no stadium is built and theVikings relocate. According to the respondent's estimated beliefs, thisoccurs with probability 0/.On the other hand, given theVikings will not relocatewithout a stadium and the respondent answers the CVM question with a "no," the indirectutilityV(Mh 0, 1)+ s0h isrealized. That is, the individual receives the satisfaction level from no stadium, and theVikings remain inMinnesota. This outcome occurs according to the respondent's estimated beliefswith probability 1 - 0Z. In keeping with Hanemann (1984a), we would expect the respondent to answer theCVM question with a "yes" when ?[?//|v/ = 1]> E[Ui\yf = 0] and a "no" otherwise.Notice that from the respondent's perspective, the level of indirectutility iscertain in the case of a "yes" answer. That is,E[Uj\yj = 1] = V(M, ? Bh 1, 1) + When a "yes" answer is given, the respondent pays the bid amount Bt but is certain that theVikings receive a new stadium and remain in Minnesota. Given this structure,we anticipate a "yes" response with probability Pr[en/ - 0,800, - (1 e/)e0i/> &iV(Mh s0, K0) (7) + (1 WViMi, So, Kx) - V(Mj - Bi9S{,Ki)}. For our purposes in this paper, we suppose that 0, is uncorrelated with each of the noise terms Sn? s0i/, and e0o/. Further, we model the noise terms zUh s0i/, and s0o, as being 0 mean normal processes for each individual. For convenience, we assume csl = Var(en/) = Var(e0i/) = Var(e0o/) and \|/ = Covfe u, s00/) = Cov(sn/, s0i/) = Cov(s0i/, e0o,) This allows us towrite Prlv, = 1 = 1-0) 0,K(M? So, K0) + (1 e,)K(A/,, S0, *i) - V(M, ~ Bh Su K{ CT8 (8) where we define 6 = sn/ - 6/800/ - (1 - 0/)?oi/> and the variance of 5 is a26 = 2[ 0) = Pr(e, > -y'x,-) = 1- 0(-y'v,), (9) given 8/isdistributedstandardnormal,L, takeson thevalue of 1 iftherespondentbelieves theVikings will leavewithout a new stadium and 0 iftheVikings remain inMinnesota without a new stadium, and y isan unknown vectorof coefficients.The estimatedmodel resultsappear inTable 6.To arrive at thevariables used in thiscredibilitybeliefmodel, we parsed thevariables that r-statisticsindicated did not add explanatorypower to themodel. Given 1 - 0(-y'x/) > 0.5 and L, = 1, we score a correct prediction for the model. Similarly, when 1 ? ( ? y'x,) < 0.5 and L, = 0, we score a correct prediction for the model. This content downloaded from 147.251.189.14 on Mon, 29 Jun 2015 08:14:34 UTC All use subject to JSTOR Terms and Conditions Estimating Local Welfare of an NFL Team 215 Table 6. Modeling theCredibility of theVikings Relocating Variable Coefficient r-Statistic Constant -1.6835 -12.2334 Past spending 0.0007 3.0124 Prestige 0.6754 4.9610 University ofMinnesota 0.8598 6.3523 Twins 0.3591 2.1471 Discuss 0.4447 2.8128 Win Super Bowl 0.6619 2.5992 Fun 1.5157 5.7724 Using this criterion for the observed sample, the fittedmodel accurately predicts the respondent's belief 79.3% of the time.One concern regarding the responses to our survey is the relatively uniform bid acceptance rate across bid levels. This information is presented in Table 7. Theory suggests that as the bid level increases, the respondents' willingness to contribute to the stadium initiative should wane. Though our bids are relatively tight,we see some undulating behavior regarding thebid acceptance rate as thebid level increases.Now that we have estimated the respondent's credibility belief, we reexamine this bid acceptance rate controlling for thepredicted credibilitybelief.This information ispresented inTable 8.Across the columns of Table 8,we report the respondents' credibility beliefs in five categories. These categories represent thosewho believe theVikings are 0-20%, 20-40%, 40-60%, 60-80%, and 80-100% likely to relocate without a new stadium, respectively.The rows of the table indicate thebid levels the respondent received.Generally, we see that inmoving across the columns ina particular row, the likelihood of the respondent accepting the stadium initiative increases. This suggests that as the respondent believes theVikings aremore likely to relocate without a new stadium, he or she becomes more willing to fund the stadium initiative.Moving down the rows in a given column indicates how respondents with similar credibility beliefs are impacted by higher bid levels.As we look down a column, we observe behavior consistent with economic theory.That is, the bid acceptance rate declines as the bid level increases. This suggests that controlling for the respondent's credibilityof relocation is important to understanding how he or shewill react to the stadium initiativeCVM question. For the RUM characterization of the decision-making process regarding the CVM question we developed in theproceeding section,we need an estimate of 0,.The predicted value 1 - 0(-y'x/) is a reasonable choice for thisbelief credibility.Now thatwe have an estimator for the respondent's belief regarding the likelihood of theVikings relocating in the event a new stadium isnot funded,we may return to the respondent's behavioral mechanism regarding the contingent valuation question. Table 7. Bid Levels and the Proportion of "Yes" Responses BidRural "Yes" Responses Urban "Yes" Responses $5 44%58% $15 53%48% $25 44%61% $100 32%36% This content downloaded from 147.251.189.14 on Mon, 29 Jun 2015 08:14:34 UTC All use subject to JSTOR Terms and Conditions 216 Aju J. Fenn and John R. Crooker Table 8. "Yes" Responses by Bid Level and Predicted Credibility Beliefs Relocation Belief Bid Level 0-20% 20-40% 40-60% 60-80% 80-100% $5 4.88% 40.00% 61.54% 88.24% 90.32% n = 41 n = 15 n = 26 n = \1 n = 31 $15 8.82% 43.75% 58.82% 60.87% 90.00% n = 34 n = 16 n = 17 w = 23 w = 30 $25 10.42% 36.36% 69.57% 90.91% 88.10% n = 48 ? = 22 n = 23 ?=11 w = 42 $37.2 0% 0% 66.67% 100%0% n ? 22 n ? 2 n = 3 n = 2 n = 2 $100 7.69% 16.67% 45.83% 40% 75.86% w = 52 ? = 18 n = 24 ? = 15 w = 29 10. RUM with Prior Credibility Belief Estimated With a consistent estimator of the respondent's credibilitybelief of theVikings relocating, we can return to the respondent's decision mechanism in theCVM setting. Specifically, we developed theprobability the respondent answers theCVM question with a "yes," as indicated in Equation 8. Using our prior estimator 0/ = 1 ? 0(-y'x/), our log-likelihood function becomes: ln(L) = ?>,-ln(l