What factors determine the fans' willingness to pay for Bundesliga tickets? An analysis of ticket sales in the secondary market using data from ebay.de.

Kemper, Christoph ; Breuer, Christoph

Introduction

Ticket pricing of sporting events, a much-discussed topic in the business of sports, has intensified in recent years due to the development of dynamic ticket pricing systems in the sports industry (Drayer, Shapiro, & Lee, 2012b). Throughout the 20th century most sports managers employed either a one-size-fits-all approach, by which prices for every ticket and every game are exactly the same, or a seat-location approach, by which prices are set in correlation to proximity to the field (Drayer et al., 2012b). Due to the increasing costs of player salaries and the continuous improvement of stadiums, increased income is required (Drayer et al., 2012b). Two examples of coping strategies for generating additional income are the growth of sport sponsorships and the negotiation of stadium-naming rights (Howard & Crompton, 2005). Another source of revenues, examined in detail here, is the optimization of ticket pricing strategies.

For the 1999 season, the Colorado Rockies were the first team in professional sports to implement variable ticket pricing (VTP) (Drayer et al., 2012b; Rovell, 2002). By applying VTP prices are differentiated by factors such as opponent and day of the week (Drayer et al., 2012b). However, the prices are set long before the season starts and are not supposed to change during the season. This feature was modified as the San Francisco Giants introduced dynamic ticket pricing (DTP) to the sports industry in 2009. Now ticket prices varied on a daily basis and on several situational factors--such as team performance, player performance, and even weather conditions (Drayer et al., 2012b). The most recent development concerning dynamic ticket pricing was achieved when this pricing approach reached Europe as two English football clubs--Cardiff City and Derby County--adopted it in the 2012-13 season ("Demand based pricing," 2012; "Demand ticket pricing," 2012). However, to date no German sports club has implemented a dynamic pricing system.

Nevertheless, further optimization of ticket pricing strategies seems promising, with the very existence of ticket brokers indicating that the pricing strategy of many sports clubs is suboptimal (Volpano, 2003). Ticket brokers, although they contribute little to the production of a sporting event, benefit from pricing inefficiencies in the primary market (Drayer, Stotlar, & Irwin, 2008; Happel & Jennings, 2002; Rascher, McEvoy, Nagel, & Brown, 2007). Happel and Jennings (2002) estimated that more than 1,000 recognized ticket brokers exist in the United States alone, and Stecklow (2006) assumed that 20-30% of all tickets are resold. However, the knowledge of the secondary market price provides valuable information for price setting in the primary market (Drayer & Shapiro, 2009). Therefore, it seems plausible that an understanding of the determinants that influence ticket prices in the secondary market is essential for more efficiently pricing tickets in the primary market and for designing a dynamic pricing system for use in that market.

It appears that no study has ever investigated the factors that influence the fans' willingness to pay for the German football Bundesliga. Thus, the current paper extends previous research on secondary market ticket prices, all of which focused exclusively on the American sport leagues NFL and MLB (Drayer & Shapiro, 2009; Drayer, Rascher, & McEvoy, 2012a; Shapiro & Drayer, 2012; Shapiro & Drayer, 2014). Furthermore, it seems that only the study of Drayer and Shapiro (2009) actually analyzed auctions in a reselling setting. Based on pricing theory, auctions can be regarded as much more suitable for determining willingness to pay than posted price offerings, because prices can fluctuate freely and not the seller but the buyer of the product determines the price (Lusk & Shogren, 2007; Miller et al., 2011; Volkner, 2006a, 2006b). However, the study of Drayer and Shapiro (2009) seems limited in terms of the number of observations and the number of analyzed determinants. The authors only analyzed a data set of 10 NFL playoff games that preceded the Super Bowl. Therefore, the current study adds to the literature by analyzing a data set that is almost ninefold compared to the study of Drayer and Shapiro (2009) and that extends the number of observed games from 10 to 153. Additionally, several determinants that previously have not been analyzed in an auction-based setting are now being taken into account. Furthermore, the current study seems to be the first to evaluate a European soccer league, which can be distinguished from the American sport leagues as the Bundesliga is an open league, which incorporates promotion and relegation. In addition, the current study addresses the research question by applying a two stage least squares (2SLS) regression. Drayer and Shapiro (2009) simply applied a standard ordinary least squares (OLS) regression, which does not take into account the simultaneity problem in microeconomics.

Theoretical Framework

The current paper is based on the economic model of sports ticket demand developed by Swofford (1999), Spindler (2003), and Drayer et al. (2012a). The model adopts a neoclassical perspective. On this view the consumer, who is subject to a budget constraint, is assumed to choose a consumption bundle that maximizes utility based on the customer's preferences. Thus, the price has a negative effect on the demanded quantity (Andreff & Szymanski, 2009). Many studies on sport demand are in support of this theoretical assumption (e.g., Borland & MacDonald, 2003; Villar & Guerrero, 2009).

The Existence of a Secondary Ticket Market

Swofford (1999) discussed three reasons why secondary ticket markets might exist. First of all, the ticket broker in the secondary market might be less risk-averse than the producing firm in the primary market. The general concern of sports clubs is to sell out the stadium in order to enhance fan experience. Consequently, clubs set ticket prices below the optimal price. Another aspect is the selling of season tickets in order to yield a steady source of income prior to the season and to hedge against poor performances. Hence, sport clubs appear to trade off profit for certainty and, thereby, leave an opening for speculators who do not face these issues. Second, ticket resellers might have a lower cost-function due to lower information costs, lower transactions costs, or lower taxes. In this case, then, ticket resellers act like any other middleman, because they can get better information about the consumer market or can offer the product to the consumer at a lower price than that of the original producer. Third, resellers might face a different revenue function. Sports clubs are more interested in long-term relationships, whereas resellers can exploit the short-term revenue potential without worrying about their reputation. Therefore, sports clubs and ticket resellers are concerned with revenues over different time frames. Furthermore, ticket resellers might be better at price discrimination than sports clubs and able to charge different prices depending on a variety of determinants. Another point is that sport clubs generate income not only from ticket sales but also from ancillary revenue streams such as merchandise, concessions, and sponsors. Ticket resellers, however, optimize revenues based on a single product. Spindler (2003) extended the research of Swofford (1999) and developed a graphical representation, which was adapted and slightly adjusted by Drayer et al. (2012a). Figure 1 shows a combination of the illustrations of Spindler (2003) and Drayer et al. (2012a). The model assumes a fixed supply of tickets (the stadium capacity). Daon represents the demand if there is perfect price discrimination (i.e., if each person pays exactly in accordance with her/his willingness to pay). This demand curve is often known as the all-or-none demand curve. If the sports club were able to price discriminate perfectly, it would make [Q.sub.l] * [P.sub.h] in revenues. However, due to the club's inability to price discriminate perfectly, it faces a lower demand curve. The demand curve [D.sub.p] represents the average demand during the season for the primary market in the case that there exists no secondary market. In order to sell-out the stadium, the sports club would chose the price Pl and would yield revenues of [Q.sub.l] * [P.sub.y] Following Spindler (2003) and Drayer et al. (2012a), the existence of a secondary market would increase the demand for sports tickets and the sports club would face the demand curve [D.sub.ps]. The higher demand curve is mainly a result of two factors. First, ticket broker can enter the market, thus, creating additional demand in the primary market. Second, demand of fans increases as well, because the secondary market provides a form of insurance and mitigates the risk of losing money in the case that fans cannot attend the game (Rascher & Schwarz, 2012). As a result, the club would choose the price Pm in order to sell out the stadium. Due to reasons detailed by Swofford (1999) (e.g., having better skills in price discrimination) the ticket broker faces an average demand curve [D.sub.tb], which lies between the demand curve of the sports club and the all-or-none demand curve.

[FIGURE 1 OMITTED]

Now two scenarios can be considered. In the first, the ticket broker sells tickets in the secondary market at a higher average price than the sports club in the primary market. Spindler (2003) provides the example of a ticket broker buying [Q.sub.l] - [Q.sub.m] tickets from the sports club at a price of Pm, which he could then sell at a price [P.sub.tb] and for a profit of ([Q.sub.l] - [Q.sub.m]) x ([P.sub.tb] - [P.sub.m]) - K, where K represents additional selling costs apart from the ticket purchase price Pm. In this scenario, both the club and the ticket broker benefit from the existence of a secondary market. The sports club faces the higher demand curve [D.sub.ps] and the ticket broker generates profits. In the second scenario, the primary seller uses the ticket broker as a discounter. Suppose the sports club is able to differentiate between the regular customers and ticket brokers. It charges a price of [P.sub.h] and sells a quantity of [Q.sub.h] tickets to regular customers. Then the club dumps the rest of the tickets ([Q.sub.l] - [Q.sub.h]) to the ticket broker at a price of [P.sub.l]. Revenues of the sports club would account for ([Q.sub.h] * [P.sub.h]) + ([Q.sub.l] - [Q.sub.h]) * [P.sub.l]. The ticket broker could resell the tickets at a price of Ptb. Hence, he could make profits of ([Q.sub.l] - [Q.sub.h]) * ([P.sub.tb] - [P.sub.l]) - K. Again in this scenario, both the sports club and the ticket broker would be better off with a secondary ticket market than without it (Spindler, 2003; Drayer et al., 2012a).

The Principles of Price Discrimination

Drayer et al. (2012a) applied the presented economic model in order to analyze determinants of ticket prices in the secondary market. The current paper follows the same approach in order to analyze ticket price determinants in the secondary market for Bundesliga tickets. These determinants can be applied by sports clubs to further differentiate their ticket prices and increase producer surplus. Pricing theory distinguishes between three degrees of price discrimination. First-degree or perfect price discrimination is when a firm is able to charge each consumer his or her individual willingness to pay. This is more a theoretical concept. However, well-designed auctions can approximate first-degree price discrimination (Rascher & Schwarz, 2012). Therefore, the evaluation of eBay auctions offers a great learning potential concerning the fans' willingness to pay. Second-degree price discrimination refers to the concept of offering different menus of consumption options. Classical examples are volume discounts, multi-tiered pricing, bundled pricing, two-part tariffs, time, and quality discrimination. Examples of third-degree price discrimination include the offering of senior or student discounts. That means, discounts are granted for identifiable customer groups (Rascher & Schwarz, 2012).

Variable and dynamic ticket pricing--the focus of the current study--can be classified as forms of second-degree price discrimination (Rascher & Schwarz, 2012) (e.g., games against opponents of higher quality results in a shift of the demand curve to the right). Consequently, a higher price can be charged (Rascher et al., 2007). Dynamic ticket pricing is essentially the extreme version of VTP (Rascher & Schwarz, 2012). Its objective is to capitalize on the shifts of demand and the fans' willingness to pay by differentiating ticket prices by multiple factors, like opponent, day and time of the game, or even weather conditions. Therefore, the objective of the current study is to examine which factors might be applied by Bundesliga clubs to further differentiate their ticket pricing structure.

Literature Overview

The literature review is organized in four sections. First, the literature on sport demand in general is reviewed. Second, studies on ticket prices in the primary market are presented. Third, studies on the most recent development in sports ticket pricing, namely dynamic pricing, are illustrated. Fourth, studies on ticket prices in the secondary market are explored.

Sport Demand and the Role of Pricing Sport demand, in terms of stadium attendance, has long been a much discussed topic among sport economists. Overviews are provided by Borland and MacDonald (2003), Downward and Dawson (2000), and Villar and Guerrero (2009). Ticket prices of sporting events are generally negatively correlated with stadium attendance. Furthermore, ticket prices are usually found to be in the inelastic portion of the demand curve (Andreff & Szymanski, 2009; Borland & MacDonald, 2003; Villar & Guerrero, 2009) as a consequence of the ambiguous task for sports managers to maximize ticket revenues and attendance at the same time (Courty, 2003). In contrast to the vast amount of studies on stadium attendance, the research on sports ticket prices in the primary and secondary market is limited.

Ticket Pricing in the Primary Market

Studies concerning ticket pricing in the primary market were contributed by Reese and Mittelstaedt (2001), Rishe and Mondello (2003), and Rishe and Mondello (2004). While Reese and Mittelstaedt (2001) used a questionnaire format analyzing ticket price setting within the NFL, Rishe and Mondello (2003) analyzed a data set of the NFL for the seasons 1996-2001. Rishe and Mondello (2004) extended their 2003 study by analyzing NBA, NFL, NHL, and MLB ticket prices for a data set from 1996-2002. Generally, the price setting varied significantly from team to team and from league to league.

Dynamic Ticket Pricing in the Primary Market

It seems only five papers have addressed the topic of dynamic pricing in the field of sport so far. Two papers discussed the topic on a general level and three publications analyzed a data set of ticket prices in order to identify determinants of the dynamic pricing system.

An agenda for research and practice was developed by Drayer et al. (2012b). They discussed general issues from a management perspective concerning the specification of a dynamic ticket pricing system in the field of sport. Furthermore, they outlined potential areas for future studies and pointed out that more research is necessary in order to understand fans' willingness to pay and the determinants that influence such willingness. Nufer and Fischer (2013) analyzed the pricing strategies of European football leagues and came to the same conclusion--that dynamic pricing systems offer great revenue potentials for sport clubs.

Three empirical studies included Paul and Weinbach (2013) and Shapiro and Drayer (2012, 2014). Paul and Weinbach (2013) analyzed a data set of ticket prices for the 2011 season for the San Francisco Giants, St. Louis Cardinals, Chicago White Sox, and Houston Astros, the four American Major League Baseball baseball teams then using a dynamic ticket pricing system. However, results varied widely for the different teams. Shapiro and Drayer (2014) conducted another study about determinants of dynamic ticket pricing systems based on an analysis of ticket prices for 12 selected San Francisco Giants games of the 2010 season. Shapiro and Drayer (2012) compared ticket prices of the San Francisco Giants of the 2010 season in the secondary market with ticket prices in the primary market and could show that dynamic pricing is not yet capable of tapping the customer's whole willingness to pay. Customers were willing to pay nearly 50% more for tickets in the secondary market compared to the price of the dynamic pricing system. Therefore, it seems advisable to analyze ticket sales in the secondary market in order to identify and quantify the factors that influence the real customer's willingness to pay for tickets of sporting events.

Ticket Pricing in the Secondary Market

Despite the awareness of the lessons to be learned from the secondary market (Drayer et al., 2008), only four papers could be identified that used secondary market data in order to determine the factors that affect what fans are willing to pay for sports tickets. Drayer and Shapiro (2009) and Drayer et al. (2012a) analyzed data for the NFL, while Shapiro and Drayer (2012) and Shapiro and Drayer (2014) used data from the MLB in order to identify relevant determinants concerning the fan's willingness to pay. However, only Drayer and Shapiro (2009) used data from ebay.com, which applies an auction format as well as a direct sales format. The other three studies used data from StubHub, where prices are posted. By comparison and based on pricing theory, auctions on secondary market websites such as eBay can be regarded as more suitable for determining the fans' willingness to pay (Lusk & Shogren, 2007; Miller et al., 2011; Volkner, 2006a, 2006b). The results of these studies will be presented in the following section while specifying the data model of the current study.

Model Specification

Econometric Specification

In order to examine the factors that influence ticket prices in the secondary market, we apply a robust two stage least squares (2SLS) regression approach. Other studies on sport attendance and ticket pricing generally apply an ordinary least squares (OLS) approach, based on the assumption that supply is fixed. The secondary ticket market, however, can be regarded as a fluid market and supply as well as demand can change on a continual basis. The implication is the classic simultaneity problem in microeconomics (Greene, 2003). In order to resolve this issue, we first estimate the supply of secondary market tickets and use the forecasted quantity in a second stage in order to specify the regression of the transaction price. This is the standard use of 2SLS to solve simultaneity problems.

However, the validity of 2SLS relies on appropriate instrument variables in the first stage in order to estimate supply. Drayer et al. (2012a), in a study about posted ticket prices in the secondary market, as well as Garcia and Rodriguez (2002), in a study about sport attendance, used stadium capacity as an instrument variable in order to forecast ticket quantity. It seems reasonable that the overall number of available tickets in the primary market should be correlated with the offered tickets in the secondary market, while at the same time the stadium capacity should only indirectly influence the ticket price in the secondary market. From an econometric point of view, these are the two requirements of an instrument variable (Greene, 2003). In the opinion of the authors, the instrument variable might be improved by using the actual stadium attendance. This variable should be a better instrument to predict the number of transactions in the secondary market because it offers a detailed differentiation on game level, whereas the stadium capacity only represents a measure on team level. Nevertheless, both instrument variables were examined in order to find the best fit for the data. We specify the following two-equation system:

First Stage:

[Y.sub.1] = [[alpha].sub.1] + [[beta].sub.1][X.sub.1] + [[beta].sub.2][X.sub.2] + [[epsilon].sub.1] (1)

Quantity Regression

Second Stage:

[Y.sub.2] = [[alpha].sub.2] + [[beta].sub.3][X.sub.1] + [[gamma].sub.1][Y.sub.1] + [[epsilon].sub.2] (2)

Price Regression

[Y.sub.2] represents the secondary market ticket price, which is estimated in the second stage. Equation (1) is the first stage of the 2SLS regression model and represents the forecasted quantity that is an input into equation (2). [X.sub.1] is a vector of exogenous variables that affects both the quantity and the price regression. The vector [X.sub.2] represents the instrument in the first stage. The vectors [[beta].sub.i](i = 1,2,3) are to be estimated. The variables [[alpha].sub.1] and [[alpha].sub.2] represent the intercepts of the models. The variables [[epsilon].sub.1] and [[epsilon].sub.2] are error terms. Robust estimation is used to control for any possible heteroscedasticity. In this respect, heteroscedasticity-consistent standard errors are reported using White's correction.

Variable Selection

The variable selection of the econometric model is based on the literature review on determinants of ticket prices in the primary market, sport ticket prices through dynamic pricing, and ticket prices in the secondary market. An evaluation of factors that influence stadium attendance completed the theoretical foundation of the model. Due to the specific situation of the Bundesliga, and due to data availability, some variables which were previously used had to be adapted.

Dependent Variable

In the first stage of the 2SLS model the dependent variable is the number of transactions on ebay.de for each game (TRANS). As the dependent variable in the second stage of the 2SLS model, the final selling price in [euro] for one ticket of an eBay auction is used (TICKET_PRICE_AUC). Many auctions offered multiple tickets. Hence, the number of sold tickets per auction (NUMBER_OF_TICKETS) is used as a weighting variable.

Derivation of Explanatory Variables

The explanatory variables are grouped into eBay-related variables, game-related variables, time-related variables, ticket-related variables, team performance-related variables, economic-related variables, and weather-related variables. Table 1 provides a summary of the explanatory variables as well as a short description of these variables.

eBay-related variables.

Number of transactions. The economic model of sports ticket demand suggests a negative relationship between quantity and price. Hence, the number of transactions is included in the data model and a negative impact is expected. However, due to the simultaneity problem described above, the number of transactions first serves as the dependent variable in the first stage of the 2SLS and then the predicted values are used as an explanatory variable in the second stage.

Number of bids. The total number of bids is an auction-specific variable. It was only used in the study of Drayer and Shapiro (2009), who found that the secondary market ticket price increased with the number of bids for that auction.

Game-related variables.

Team-specific effects. Whether a game is of special interest is a classic variable applied in studies about sport demand. Shapiro and Drayer (2014) reported higher ticket prices in the secondary market when MLB teams played against an opponent of the same division. Contrary, Drayer and Shapiro (2009) as well as Drayer et al. (2012a) found no significant effect of such a variable. Consequently, the current study includes a variable to specify whether the game is a derby/rivalry game or not. Furthermore, Shapiro and Drayer (2014) included additional baseball-specific variables, like whether a certain player was scheduled to pitch. However, these variables can be neglected due to the specific focus of the current study. In European soccer the focus seems to be more on the team itself rather than on individual players like it may be the case in the American sports leagues MLB and NFL. Furthermore, Borland and MacDonald (2003) reported that a majority of studies did not find a significant effect of star players.

Match uncertainty. The impact of match uncertainty is a frequently discussed topic concerning stadium attendance (e.g., Borland & MacDonald, 2003; Villar & Guerrero, 2009). In the case of secondary market ticket prices Shapiro and Drayer (2009) found no effect of match uncertainty, while Drayer et al. (2012a) reported that ticket prices increase for games with opponents that are expected to be of equal quality. These two studies operationalized the concept of match uncertainty using betting odds. However, betting odds for games of the Bundesliga are only published prior to the game on quite short notice. Therefore, due to the focus of the study on tracking ticket prices over time, we use differences in league positions to measure the level of competitiveness. This measure was also used, for example, by Garcia and Rodriguez (2002).

Seasonal uncertainty. Shapiro and Drayer (2014) reported a significant negative effect of season uncertainty on the ticket price in the secondary market. As the Bundesliga incorporates promotion and relegation, two variables concerning seasonal uncertainty are included in the data model: a categorical variable identifying whether the championship is already decided or not and a categorical variable identifying whether the teams to be relegated are already determined. Studies on stadium attendance concerning soccer used similar operationalizations (e.g., Borland & MacDonald, 2003; Villar & Guerrero, 2009).

Time-related variables.

Number of days prior to the game that a specific auction ended. Drayer and Shapiro (2009), Shapiro and Drayer (2012), as well as Shapiro and Drayer (2014) analyzed the effect of time prior to the game. Drayer and Shapiro (2009) found that ticket prices in the secondary market decreased as the day of the match approached. Shapiro and Drayer (2014) did not include this variable in their final model concerning secondary market ticket prices. Shapiro and Drayer (2012) reported that prices first increased and then decreased. However, the study of Shapiro and Drayer (2012) seems limited, because the authors only evaluated four time points (20, 10, and 5 days prior to match day as well as the match day itself). The current study uses a continuous variable to analyze this effect.

Number of the match in the season. Drayer and Shapiro (2009), Drayer et al. (2012a) as well as Shapiro and Drayer (2014) reported a positive effect of the match number. That means, as the season progressed ticket prices increased in the secondary ticket market. The match number is also used in the current study to determine the part of the season.

Day and time of the week. Drayer and Shapiro (2009) reported a significant effect of the day of the week. Contrary, Drayer et al. (2012a) found no significant effect of the day of the week. Similarly, Shapiro and Drayer (2014) found no effect concerning whether the game took place on a weekend day or during the week. Shapiro and Drayer (2014) seemed to be the only study that incorporated the time of the match. The authors reported that games at 7 p.m. showed the highest ticket prices in the secondary market. The Bundesliga offers five primary time slots: Friday at 8:30 p.m., Saturday at 3:30 p.m., Saturday at 6:30 p.m., Sunday at 3:30 p.m., and Sunday at 5:30 p.m. Hence, the day and time of the match is specified using one categorical variable. Ticket-related variables.

Standing vs. seated place. Neither studies on dynamic ticket pricing nor studies on secondary market ticket prices have analyzed the impact of whether a ticket corresponds to a standing or seating place. However, studies on stadium attendance suggest that this factor should be accounted for. Consequently, a dummy variable is included in the current study.

Sold out status of the stadium. Drayer et al. (2012a) reported a positive effect of the sold stadium capacity on the ticket price in the secondary market. Shapiro and Drayer (2014) found no significant effect of the sellout status. The current study includes a dummy variable to evaluate this effect.

Original face value of the ticket. The original face value of the ticket is generally associated with a positive effect on the secondary market ticket price. This is supported by Drayer and Shapiro (2009), Drayer et al. (2012a), Shapiro and Drayer (2012), and Shapiro and Drayer (2014). Consequently, this variable is included in the data model as well and serves as a proxy for stadium category and quality of viewing.

Team performance-related variables.

Current season performance. The season performance is measured by the current winning percentage of the home and the away team. Drayer et al. (2012a) as well as Drayer and Shapiro (2009) found a positive effect of the home team's winning percentage on the ticket price in the secondary market. Shapiro and Drayer (2014) only reported a positive effect of the away team's winning percentage on the ticket price in the secondary market. In the study of Drayer et al. (2012a) the away team's winning percentage was not significant.

Current form of the competing teams. The current form of the competing teams is operationalized by the number of points in the last three matches of the home and away team prior to the game. In the study of Shapiro and Drayer (2014) neither the current form of the home team nor the current form of the away team showed significant effects. Drayer et al. (2012a) reported a positive effect of the current form of the home team measured by a variable called power rank (a covers.com ranking that incorporated factors such as strength of schedule, recent performance, and team-based offensive and defense statistics).

Team quality prior to the season. Drayer and Shapiro (2009) as well as Drayer et al. (2012a) reported a positive effect of the lagged home team's winning percentage on the ticket price in the secondary market. A significant effect of the lagged winning percentage of the away team was only found by Drayer et al. (2012a). The current study uses the league position of the home and away team at the end of last season as a proxy for team quality prior to the season. Rottmann and Seitz (2008) applied the same variables to predict attendance figures for the Bundesliga and found significant effects of the lagged league position of the home and away team. Furthermore, as the Bundesliga is an open league, Rottmann and Seitz (2008) evaluated the impact of promoted teams and found higher attendance figures for promoted home teams but not for promoted away teams of the Bundesliga. Therefore, two dummy variables are included to specify whether the home and away team was promoted at the end of last season. Economic-related variables of the home team.

Drayer and Shapiro (2009) reported a positive effect of the home team's per capita income and a negative effect of market size. Contrary, in the study of Drayer et al. (2012a) neither of these two variables was reported to be significant. In order to evaluate the impact of these to variables, the home team's per capita income and the population of the home team are included in the current study.

Weather-related variables.

Based on stadium attendance studies, good weather conditions generally are associated with higher stadium attendance rates (Villar & Guerrero, 2009). However, the study of Shapiro and Drayer (2014) reported no effect of forecasted temperatures. Other studies on secondary market ticket prices did not include weather variables in their study design. Only Paul and Weinbach (2013) found mixed effects concerning weather conditions on the dynamic ticket price in the primary market. Hence, the current study incorporates the temperature on the day of the game as well as precipitation on the day of the game. Due to data availability and for greater accuracy, we use actual weather data for the day of the match rather than forecasted data. Furthermore, the current study also analyzes the effect of the temperature and precipitation at the end of the auction. These variables have not been taken into account thus far. Hence, the existing literature is extended in this respect.

Data Collection

The data set in the current study covers the whole second half of the Bundesliga season 2013-14. Every day the words Fussball Bundesliga Tickets, followed by the names of the competing teams, were used to search for tickets on ebay.de. Based on the transaction code, all relevant auctions could be tracked and the final selling price could be evaluated. Starting date of the data collection was January 1, 2014, because the first game of the second half of the season took place on January 24, 2014. End of the data collection period was May 10, 2014, which was the last match day of the season. This period of time was chosen because it offered a broad variety of games. Unfortunately, ebay.de was not willing to provide researchers with the necessary information, so data had to be collected manually. No VIP tickets were taken into account because those tickets included additional services like food, beverages, and parking. Tickets for selected customer groups such as students, pensioners, and disabled people were also not considered due to the reduced price and the possibility for upgrading tickets on match day in the stadium. The final data set accounted in total for 6,510 eBay auctions in which 11,637 tickets were sold. Many auctions offered the sale of more than one ticket. In this case the final price was divided by the number of tickets sold to calculate the price per ticket.

Apart from data that were directly collected on ebay.de, several other sources were used to build up an extensive database. Data concerning the date and time of each match were gathered from the official homepage of the first German Bundesliga (http://www.bundesliga.de). The outcome of the games and data concerning league positions were tracked on http://www.ergebnisselive.com. The original face value of each individual ticket was collected from the homepage of the respective football team. Relevant information about derby/rival games were taken from http://www.derbysieg.com/derby-termine. Attendance data was gathered from the homepage http://fussballdaten.sport.de/bundesliga/2014. Data concerning population and income per capita were taken from MB-Research (2013). Weather data were collected from the German Weather Service (http://www.dwd.de).

Results

The results are illustrated in two steps. First, the descriptive results are presented. Second, the results of the regression model are shown.

Descriptive Results

The descriptive results for the continuous variables are illustrated in Table 2.

The observed prices for tickets of Bundesliga football games on ebay.de varied widely and ranged between 0.75 [euro] and 633.50 [euro] with an average selling price of 69.40 [euro]. The average face value amounted to 34.73 [euro]. That means the average fan participating in an online auction is willing to pay roughly twice as much as the current face value. Also the number of auctions per match differed significantly. Depending on the scheduled teams, between 1 and 323 auctions per match could be tracked.

The descriptive results concerning the categorical variables are presented in Table 3. The primary time slot for games of the Bundesliga is Saturday at 3:30 p.m., which is also reflected by the descriptive statistics. The percentage of ticket sales for games on Saturday at 3:30 p.m. amounted to 70.6% of all transactions. Auctions for derby games accounted for 11.2% and roughly half of the transactions occurred when the championship was already decided. The variable that identified whether the teams to be relegated were already determined showed no variation, because in the season 2013-14 this decision took place on the last match day. Consequently, this variable was not considered in the regression model.

Regression Model

The results of the regression model are reported in Tables 4 and 5. Table 4 shows the results of the first stage and Table 5 provides the results of the second stage of the 2SLS regression. To account for any heteroskedasticity issue, robust standard errors (HCSE) are reported using White's correction (White, 1982). A Wu-Hausman test was applied to test for endogeneity. The significant test results, F(1, 6480) = 25.08, p < .001), support the application of a 2SLS regression. A test for weak instruments showed significant results, F(1, 6481) = 737.78, p < .001), suggesting a strong instrument variable.

In the final model attendance at game level was used as an instrument variable in the first stage, because this variable showed a strong significant effect and provided a better fit than stadium capacity. Furthermore, the weak instrument test for the model with attendance showed a higher F-statistic compared to the model with stadium capacity. However, using stadium capacity as an instrument variable did not change the general results in the second stage. Multicollinearity was no issue in the first stage. All variance inflator factors (VIF) were below 10, which is the most commonly recommended maximum level of the VIF (e.g., Hair, Anderson, Tatham, & Black, 1995; Kennedy, 1992; Neter, Wasserman, & Kutner, 1989; O'Brian, 2007). In the second stage the predicted values of the number of transactions showed a VIF above 10. This is not surprising because the number of transactions was predicted by all exogenous variables and the instrument variable in the first stage. However, the large sample size disintegrates any large bias effect on standard errors. Consequently, a lower VIF would only strengthen the already existing significant effect of the number of transactions in the second stage. By applying a log-transformation to the number of transactions in the first stage the issue of multicollinearity vanished completely and all VIF in the first and second stage were below 10. The log-transformation did not change the overall results in the second stage.

The second stage of the 2SLS regression model explained 59.6% of the variance in the data set and most of the variables showed significant effects on a 0.1% level. The number of points in the last three matches of the away team and the temperature at the end of the auction were significant on a 1% level. The number of transactions and whether the game was scheduled on Sunday at 5:30 p.m. compared to the reference category Saturday at 3:30 p.m. showed significant effects on a 5% level. The league position of the home team in the last season was only significant on a 10% level. No significant effects were observed for the number of points in the last three matches of the home team and for the precipitation at the end of the auction.

All variables--except for the temperature on match day--showed the expected signs. Tickets for more successful teams were prices higher. The current winning percentage of the home and away team, as well as the number of points in the last three matches of the away team showed a positive impact. The coefficients for the league position of the home and away team at the end of the previous season are both negative. This means that a more successful team in the previous season caused higher secondary market ticket prices in the current season. Tickets for a sold-out game were traded with a mark-up of 18.10 [euro] and tickets for derby games were valued with a mark-up of 12.41 [euro]. The variable match number had a positive effect, which implies that as the season proceeded, ticket prices increased each match day by 2.40 [euro]. The temperature on match day showed a negative effect. This was surprising because generally good weather conditions are associated with higher ticket prices. The precipitation on the day of the match as well as the temperature at the end of the auction, however, showed the expected signs.

The variables concerning match and seasonal uncertainty showed the expected signs, too. If the difference in league positions of the competing teams was reduced by 1, ticket prices increased by 0.70 [euro] and tickets for games after the championship was decided were sold with a mark-down of 6.92 [euro]. Also the general microeconomic relationship held true--if the number of eBay auctions increased by 1 the average ticket price decreased by 0.04 [euro].

Discussion

The second stage of the 2SLS regression explained 59.6% of the variance in the data set. Drayer and Shapiro (2009) reported a [R.sup.2] of 63.6%, Drayer et al. (2012a) 56.0%, and Shapiro and Drayer (2014) 79.7%. Hence, the explained variance of the data model is comparable to previous studies about determinants of ticket prices in the secondary market. Drayer and Shapiro (2009) published the only study so far that used eBay data, analyzing 750 auctions. In comparison, the number of observations in the current study, which analyzed a data set of 6,510 eBay auctions, was almost ninefold. From an econometric point of view, however, the study of Drayer and Shapiro (2009) can be criticized, because it applied a standard OLS approach, whereas the current study made use of a 2SLS regression in order to address the simultaneity problem in microeconomics. The determinants by which sports clubs could further differentiate their ticket prices are discussed in the following.

Both eBay-related variables showed significant effects. As expected, the number of eBay auctions per game had a negative impact on ticket prices. Interestingly, Drayer and Shapiro (2009) as well as Shapiro and Drayer (2014) found a positive effect of the number of available tickets on the secondary market ticket price. Both studies argued that as ticket holders realize that fans are willing to pay high prices for tickets in the secondary market, they become more likely to sell their own tickets. However, while this is more a supply argument, the result of the current study seems more plausible as it corresponds to the general relationship between quantity and price in the economic model of sports ticket demand. The second eBay-related variable showed a positive impact. If the number of bids increased by 1, the ticket price increased by 1.06 [euro]. Drayer and Shapiro (2009) reported similar results in which the ticket price increased by $1.65 with each additional bid.

Game-related variables included the variables whether the game was a derby game or not, match uncertainty, and seasonal uncertainty. Derby games had a positive effect on the ticket price. A similar result was reported by Shapiro and Drayer (2014). Games of MLB teams playing against an opponent of the same division were traded at a higher price. However, in the studies of Drayer and Shapiro (2009) and Drayer et al. (2012a) the variable division was not significant. Both uncertainty-related variables, the difference in league position of the competing teams and whether the championship was already decided or not, had a negative effect on the ticket price in the secondary market. While Shapiro and Drayer (2009) found no effect of match uncertainty, Drayer et al. (2012a) reported a significant negative effect, as is the case in the current study. That implies, the closer fans expect the game to be, the higher the price fans are willing to pay. Similar to the study at hand, a significant negative effect of season uncertainty was found by Shapiro and Drayer (2014). As relevant decisions in the season are already made, ticket prices dropped significantly.

Time related variables included the number of days prior to match day, match number, and day and time of the match. As the day of the match approached the ticket price decreased continuously. Similar effects were found by Drayer and Shapiro (2009) and Shapiro and Drayer (2012). Shapiro and Drayer (2014) did not include this variable in their final model. Drayer and Shapiro (2009) reported an effect of $4.89 per day compared to 0.54 [euro] per day in the current study. The study of Shapiro and Drayer (2012) can be generalized, because the authors evaluated only four time points (20, 10, and 5 days prior to match day as well as the match day itself). In their study, ticket prices increased from 20 days prior to the game to five days before the game and dropped on game day. Dwyer, Drayer, and Shapiro (2013) analyzed the impact of time in advanced ticket purchase decisions based on an online questionnaire. The authors found that as time before the event decreased the consumer expected a lower ticket price. This result corresponds to the finding of the current study. The variable match number had a positive effect. Drayer and Shapiro (2009), Drayer et al. (2012a), and Shapiro and Drayer (2014) reported similar findings. Drayer and Shapiro (2009) found that the greatest price inefficiency occurred with regard to the round of the playoffs, and that teams are leaving substantial revenues on the table by inadequately raising prices between each round of the playoffs. This finding is also supported by the current study. On each successive match day customers were willing to pay an increase of 2.40 [euro]. Significant effects were also found for the combined variable day and time of the day. Drayer and Shapiro (2009) reported a significant effect of the day of the week, while Shapiro and Drayer (2014) found a significant effect of the time of the day. Whether the game took place on a weekend day or during the week showed no significant effect in the previously mentioned study. Drayer et al. (2012a) analyzed the impact of the day of the week and found no significant effect. Based on the results of the current study, the most valuable time slots for games of the Bundesliga are Saturday at 6:30 p.m. and Sunday at 3:30 p.m., which showed significant mark-ups compared to games on Saturday at 3:30 p.m.

Ticket-related variables included whether a standing or seating place was sold, whether the game was sold out at the time of observation, and the original face value of the ticket. The willingness to pay for standing places was 17.26 [euro] higher than for seated places. This is not surprising, because the original face value for tickets in the stands is quite low. This result implies that it seems more important for fans to attend a game rather than to savor high quality seats. Other studies on ticket prices in the secondary market or on dynamic pricing in the primary market did not analyze this variable. Hence, the current study does extend the literature in this respect. Tickets for sold out games were traded with a mark-up of 18.10 [euro]. Although Shapiro and Drayer (2014) found no significant effect of the sellout status, Drayer et al. (2012a) reported a positive effect of the sold stadium capacity. Thus, the results of the regression model confirmed the expectations. The original face value of the ticket had a positive effect on the ticket price in the secondary market. This result is consistent with the other four studies in the field of ticket prices in the secondary market, all of which found a positive effect.

All performance-related variables support the conclusion that fans want to see a successful team. The current season winning percentage of the home and away team, and the number of points of the away team in the last three matches were found to have a positive impact on ticket prices in the secondary market. The league position of the home and away team at the end of last season showed a negative effect. That means, tickets for better teams in the last season were priced higher. These results are consistent with results from previous studies. Drayer et al. (2012a) as well as Drayer and Shapiro (2009) reported a positive effect of the home team's current winning percentage, and Shapiro and Drayer (2014) reported a positive effect of the away team's current winning percentage. Drayer et al. (2012a) found no significant effect of the away team's winning percentage. Concerning the current form of the competing team, Drayer et al. (2012a) found a positive effect for the home team, whereas Shapiro and Drayer (2014) reported no significant effect. A positive effect of the lagged home team's winning percentage was reported by Drayer and Shapiro (2009) as well as Drayer et al. (2012a), while a significant effect of the lagged winning percentage of the away team was only found by Drayer et al. (2012a). These results also correspond to the findings of Rottmann and Seitz (2008), which analyzed attendance figures of the Bundesliga. Since the current study is the first to evaluate ticket price determinants for an open league, the variables whether the home or away team was promoted at the end of last season could be evaluated as well. Both variables showed a positive effect on ticket prices in the secondary market. Therefore, it seems that fans of promoted teams are willing to pay significant higher ticket prices in order to see the new club of the Bundesliga. Similarly, Rottmann and Seitz (2008) reported higher attendance figures when the home team was promoted at the end of last season.

The included economic-related variables showed the expected signs as well. Like in the study of Drayer and Shapiro (2009) the home team's per capita income showed a positive effect and market size showed a negative impact on ticket prices in the secondary market. These findings are also consistent with studies about stadium attendance. It seems plausible that a higher income level provokes higher ticket prices. The negative effect of market size can be interpreted in the way that a smaller market provides less competitive offerings for leisure activities, resulting in higher ticket prices.

Significant weather-related variables included the temperature on the day of the game, precipitation on the day of the game, and temperature at the end of the auction. Temperature on the day of the game was used as a proxy for the forecasted temperature and showed a negative effect. Only Shapiro and Drayer (2014) took forecasted temperature into account but reported no significant effect. However, generally good weather conditions are associated with higher stadium attendance (Villar & Guerrero, 2009). Hence, it appears that it would have been more likely to find a positive effect in this case. Precipitation on the day of the game showed the expected negative effect. Yet, Shapiro and Drayer (2014) found no significant effect of the variable forecasted precipitation. A variable that has not been evaluated in similar studies is the temperature at the end of the auction. Higher temperatures on the day the ticket was sold on eBay increased the selling price. Therefore, the current study does extend the determinants of ticket prices in the secondary market in this respect, too.

The identified determinants can be applied by sports clubs of the Bundesliga to further differentiate their current variable ticket pricing strategy or to implement a dynamic pricing approach. As a consequence, the sports club would be able to capitalize on the fans' willingness to pay, which varies from game to game. In other words, the sports club could take advantage of the different demand functions of games with different characteristics and, thus, would face a higher average demand curve over the whole season. The former demand curve [D.sub.ps] would shift upwards in the direction of the demand curve of the ticket broker [D.sub.tb]. The amount of the upward shift, however, would depend on the level of further price discrimination. Therefore, by applying a more detailed pricing approach the sports club would reduce the consumer surplus and gain additional producer surplus. The ticket broker, on the other hand, would lose producer surplus. Consequently, the resale activity of ticket brokers should be expected to decline because their competitive advantage, like better skills at price discrimination (Swofford, 1999), would be diminished.

In summary, the conducted analysis lays the foundation for sports clubs of the Bundesliga to increase their ticket revenues and, therefore, to cope with increasing financial obligations like rising player salaries, transfer fees, or stadium maintenance costs (Drayer et al., 2012).

Conclusion and Limitations

The present study is the first to examine by means of analyzing auctions on ebay.de the determinants of fan's willingness to pay for football tickets of the Bundesliga. This study thus extends previous research by Drayer and Shapiro (2009), Drayer et al. (2012a), Drayer and Shapiro (2012), and Shapiro and Drayer (2014), which investigated ticket sales in the secondary market of the American sports leagues NFL and MLB. However, only the first of these four studies used actual auctions from ebay.com, whereas the other three used posted price data from stubhub.com. The auction based format of eBay can be regarded as a data source offering a much higher level of validity concerning the evaluating of the fans' willingness to pay than stubhub.com, which uses a posted price format.

Ticket prices in the secondary market were found to be roughly twice as much as the actual face value of the ticket. Interestingly, Drayer and Shapiro (2009) reported the same ratio in their study about ticket prices on eBay for NFL playoff games. Hence, the current study draws the same conclusion as Drayer and Shapiro (2009)--that tickets in the primary market are clearly priced inefficiently. This study found 23 determinants to significantly influence the ticket price in the secondary market for tickets of the Bundesliga. Although overall results of the current study are comparable to those of the four studies previously published about ticket prices in the secondary market, the current study adds several previously unanalyzed determinants to the literature.

The identified determinants would be applicable if Bundesliga football clubs chose to further differentiate their ticket prices or decided to develop a more sophisticated dynamic pricing approach. Although major sports clubs in Europe may be more resistant to innovative pricing methods than teams of American sports leagues (Nufer & Fischer, 2013), increasing financial obligations (Bundesliga Report 2014) might force the football clubs of the Bundesliga to reconsider their current pricing strategies. As the present study shows, fans are willing to pay prices for football tickets via online auction that are much higher than the current face value. Therefore, if the football clubs want to benefit from at least a part of fans' willingness to pay higher prices, adopting a dynamic pricing approach could yield a substantial revenue increase.

Due to its innovative approach of analyzing eBay auctions, the current study is not free from limitations. First, future studies should repeat the current study in order to test for reliability. Because of the phenomenon of ticket sales in an online market being relatively new, there should be investigation regarding the question of whether and how significant determinants change over time. Second, this study covered only games of the second half the 2013-14 Bundesliga season. Although this period of time was sufficient for the purpose of the current study, the factors that influence the fan's willingness to pay might vary compared to the first half of the season. Therefore, a future study should extend the data collection period. Furthermore, roughly 20% of the transactions in the data set could be assigned to home games of Bayern Munich. This might have led to a bias of the results. Third, as this study only covered ticket sales for football games, a future study should investigate other sports leagues. Fourth, the perceived value of tickets might change due to cultural differences. Therefore, the approach of this study should also be applied in other countries. In addition to the limitations mentioned above, it has to be pointed out that the current study only included auctions on ebay.de. Other popular secondary market websites like viagogo.de might reveal different effects. However, it has to be noted that viagogo.de applies a posted price format compared to an auction format of ebay.de. Hence, future studies could also examine the determinants that influence ticket prices in the secondary market for different distribution channels.

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Christoph Kemper, DPhil, is a researcher in the Department of Sport Economics and Sport Management at German Sport University Cologne. His research interests include pricing strategies, willingness to pay, and statistical modeling.

Christoph Breuer, PhD, is a professor in the Department of Sport Economics and Sport Management at German Sport University Cologne. His research interests include sport organizational economics and economics of sponsoring. Table 1 Variable Description Category Subcategory Variable Name Description eBay-related TICKET_PRICE The final selling price variables _AUC TRANS in [euro] for one ticket of an eBay auction. The total number of transactions on ebay.de for each game. NUMBER_ OF_ The number of sold TICKETS BIDS tickets per auction. The number of bids that were made for a ticket in a specific auction. Game-related Opponent DERBY A dichotomous variable variables specifying whether the match is of special interest. Match DELTALP A continuous variable uncertainty measuring the level of competitiveness of the game by the absolute difference in league positions. Seasonal CHAMP_ A categorical variable uncertainty DECISION identifying whether the championship is already decided or not. RELE_ A categorical variable DECISION identifying whether the teams to be relegated are already determined. Time-related DAYSBEFORE The number of days variables prior to the game that a specific auction ended. MATCH_ The number of games NUMBER already played during the season plus 1. DAY_TIME_ The time slot of the MATCH game/day and time the specific game was held. Ticket- TICKET_CAT A categorical variable related specifying whether the variables place within the stadium was a standing or seated place SOLD_OUT A dichotomous variable, which specified whether a game was sold out or not at the time of ticket purchase. TICKET_ The price of the ticket FACE_VALUE in the primary market. This variable serves as a proxy for stadium category and quality of viewing. Team Season CUR_WIN_HOME A continuous variable performance- performance measuring the home related team's current season variables winning percentage at the time the ticket was sold. CUR_WIN_ AWAY A continuous variable measuring the away team's current season winning percentage at the time the ticket was sold. Current POINTS_ A continuous variable form of the 3GAMES_ HOME measuring the current competing competitiveness of the teams home team by the number of obtained points in the last 3 matches. POINTS _ A continuous variable 3GAMES_ AWAY measuring the current competitiveness of the away team by the number of obtained points in the last 3 matches. Team LAGGED_ A continuous variable quality LP_HOME measuring the home prior to team's league position the season at the end of the previous season. LAGGED_ A continuous variable LP_AWAY measuring the away team's league position at the end of the previous season. PROM_TEAM_ A dichotomous variable, HOME which specified whether the home team was promoted in the previous season. PROM_TEAM_ A dichotomous variable, AWAY which specified whether the away team was promoted in the previous season. Economic- INCOME A continuous variable related measuring the per variables capita income of the home team (in thousand). POP A continuous variable measuring the population of the home team (in thousand). Weather TEMP_ M_ A continuous variable DAY measuring the temperature on the day of the match. PRECIP_M_ A continuous variable DAY measuring the precipitation on the day of the match. TEMP_ A continuous variable END_AUC measuring the temperature on the day the ticket was sold on eBay. PRECIP_ A continuous variable END_AUC measuring the precipitation on the day the ticket was sold on eBay. Instrument STADIUM_ A continuous variable variables CAPACITY measuring the stadium capacity of the home team. ATTENDANCE A continuous variable measuring the actual stadium attendance on game level. Table 2 Descriptive Results for the Continuous Variables Variable N Min Max Mean SD TICKET_PRICE_AUC in [euro] 6510 0.75 633.50 69.41 50.15 NUMBER_OF_TICKETS 6510 1 6 1.79 0.61 TRANS 6510 1 323 123.81 92.55 BIDS 6510 1 89 17.46 9.75 DELTALP 6510 1 17 7.58 4.54 DAYSBEFORE 6510 0 93 9.25 8.08 MATCH_NUMBER 6510 18 34 28.09 4.60 TICKET_FACEV 6510 10 94 34.73 17.45 CUR_WIN_HOME in % 6510 20.0 95.06 52.44 23.74 CUR_WIN_AWAY in % 6510 20.0 95.06 52.34 19.47 POINTS_3GAMES_HOME 6510 0 9 4.68 2.76 POINTS_3GAMES_AWAY 6510 0 9 4.71 2.54 LP_HOME_LS 6510 1 16 8.19 5.72 LP_AWAY_LS 6510 1 16 7.83 5.35 INCOME (thousand) 6510 17.9 28.3 23.14 3.19 POP (thousand) 6510 34.8 3,330.4 839.24 748.25 TEMP_CURRENT in [degrees]C 6510 -10.3 16.5 9.18 3.58 PRECIP_CURRENT in mm 6510 0.0 20.9 1.52 2.80 TEMP_ M_DAY in [degrees]C 6510 -11.3 18.9 8.44 4.11 PRECIP_M_DAY in mm 6510 0.0 24.8 1.08 2.48 STADIUM_CAPACITY (thousand) 6510 23.4 80.7 55.08 17.86 ATTENDANCE (thousand) 6510 22.0 80.6 53.96 18.04 Table 3 Descriptive Results for the Categorical Variables Variable Categories N Percentage in % DERBY Yes 732 11.2 No 5778 88.8 CHAMP_ DECISION Yes 3265 50.2 No 3245 49.8 RELE_DECISION No 6510 100.0 DAY_TIME_MATCH Saturday 3:30 p.m. 4599 70.6 Saturday 6:30 p.m. 804 12.4 Sunday 3:30 p.m. 331 5.1 Sunday 5:30 p.m. 501 7.7 Friday 8:30 p.m. 275 4.2 TICKET_CAT Standing 1967 30.2 Seating 4543 69.8 SOLD_OUT Yes 4701 72.2 No 1809 27.8 PROM_TEAM_ HOME Yes 886 13.6 No 5624 86.4 PROM_TEAM_ AWAY Yes 398 6.1 No 6112 93.9 Table 4 2SLS Regression Results--First Stage--and HCSE Variable Beta HCSE t-statistic Constant -589.74 14.075 -41.900 BIDS -0.039 0.068 -0.580 DERBY 17.723 2.618 6.769 DELTALP 2.892 0.214 13.485 CHAMP_DECISION -7.430 2.611 -2.846 DAYSBEFORE 0.652 0.082 7.998 MATCH_NUMBER 4.202 0.377 11.135 DAY_TIME_MATCH Sat 3:30pm vs. Sat 6:30 p.m. 21.361 3.181 6.716 Sat 3:30pm vs. Sun 3:30 p.m. 24.983 4.200 5.948 Sat 3:30pm vs. Sun 5:30 p.m. 40.827 3.734 10.934 Sat 3:30pm vs. Fri 8:30 p.m. -10.951 2.396 -0.046 TICKET_CAT (Seating) -9.506 2.046 -4.647 SOLD_OUT 40.520 2.385 16.991 TICKET_FACE_VALUE 0.155 0.060 2.575 CUR_WIN_HOME 0.938 0.067 14.000 CUR_WIN_AWAY 0.700 0.061 11.423 POINTS_3GAMES_HOME -3.191 0.319 -10.004 POINTS_3GAMES_AWAY 2.207 0.271 8.141 LP_HOME_LS 6.247 0.281 22.248 LP_AWAY_LS 1.622 0.244 6.6550 PROM_TEAM_ HOME -4.192 3.320 -1.263 PROM_TEAM_ AWAY -15.597 3.284 -4.749 INCOME (thousand) 9.533 0.345 27.657 POP (thousand) 0.015 0.002 7.211 TEMP_ M_DAY 5.497 0.327 16.792 PRECIP_M_DAY -0.247 0.313 -0.789 TEMP_END_AUC -0.209 0.228 -0.919 PRECIP_ END_AUC -0.045 0.269 -0.169 ATTENDANCE (thousand) 2.024 0.083 24.458 DF 6481 [R.sup.2] 0.734 [R.sup.2]adj 0.733 F-statistic 962.53*** Variable p-value Sig. Constant < .001 *** BIDS 0.562 DERBY < .001 *** DELTALP < .001 *** CHAMP_DECISION 0.004 ** DAYSBEFORE < .001 *** MATCH_NUMBER < .001 *** DAY_TIME_MATCH Sat 3:30pm vs. Sat 6:30 p.m. < .001 *** Sat 3:30pm vs. Sun 3:30 p.m. < .001 *** Sat 3:30pm vs. Sun 5:30 p.m. < .001 *** Sat 3:30pm vs. Fri 8:30 p.m. 0.964 TICKET_CAT (Seating) < .001 *** SOLD_OUT < .001 *** TICKET_FACE_VALUE 0.010 * CUR_WIN_HOME < .001 *** CUR_WIN_AWAY < .001 *** POINTS_3GAMES_HOME < .001 *** POINTS_3GAMES_AWAY < .001 *** LP_HOME_LS < .001 *** LP_AWAY_LS < .001 *** PROM_TEAM_ HOME 0.207 PROM_TEAM_ AWAY < .001 *** INCOME (thousand) < .001 *** POP (thousand) < .001 *** TEMP_ M_DAY < .001 *** PRECIP_M_DAY 0.430 TEMP_END_AUC 0.358 PRECIP_ END_AUC 0.866 ATTENDANCE (thousand) < .001 *** DF [R.sup.2] [R.sup.2]adj F-statistic . Significance: 10% level * Significance: 5% level ** Significance: 1% level *** Significance: 0.1% level Table 5 2SLS Regression Results--Second Stage--and HCSE Variable Beta HCSE t-statistic Constant -160.28 10.756 -14.902 TRANS -0.041 0.019 -2.195 BIDS 1.061 0.059 17.972 DERBY 12.411 1.344 9.236 DELTALP -0.700 0.148 -4.734 CHAMP_DECISION -6.917 1.867 -3.706 DAYSBEFORE 0.537 0.075 7.141 MATCH_NUMBER 2.404 0.258 9.333 DAY_TIME_MATCH Sat 3:30pm vs. Sat 6:30 p.m. 11.799 2.055 5.742 Sat 3:30pm vs. Sun 3:30 p.m. 10.893 1.563 6.968 Sat 3:30pm vs. Sun 5:30 p.m. 1.171 1.424 0.823 Sat 3:30pm vs. Fri 8:30 p.m. -3.341 1.554 -2.150 TICKET_CAT (Seating) -17.261 1.552 -11.119 SOLD_OUT 18.102 1.408 12.854 TICKET_FACE_VALUE 1.063 0.059 17.894 CUR_WIN_HOME 0.756 0.041 18.313 CUR_WIN_AWAY 0.217 0.036 6.079 POINTS_3GAMES_HOME -0.233 0.226 -1.031 POINTS_3GAMES_AWAY 0.685 0.213 3.218 LP_HOME_LS -0.257 0.140 -1.834 LP_AWAY_LS -0.836 0.129 -6.486 PROM_TEAM_ HOME 28.677 2.071 13.848 PROM_TEAM_ AWAY 6.003 1.354 4.435 INCOME (thousand) 3.257 0.203 16.080 POP (thousand) -0.009 0.001 -8.972 TEMP_ M_DAY -0.712 0.203 -3.511 PRECIP_M_DAY -1.517 0.146 -10.372 TEMP_END_AUC 0.438 0.147 2.969 PRECIP_ END_AUC 0.0271 0.183 0.149 DF 6481 [R.sup.2] 0.598 [R.sup.2]adj 0.596 F-statistic 349.20 *** Variable p-value Sig. Constant < .001 *** TRANS 0.028 * BIDS < .001 *** DERBY < .001 *** DELTALP < .001 *** CHAMP_DECISION < .001 *** DAYSBEFORE < .001 *** MATCH_NUMBER < .001 *** DAY_TIME_MATCH Sat 3:30pm vs. Sat 6:30 p.m. < .001 *** Sat 3:30pm vs. Sun 3:30 p.m. < .001 *** Sat 3:30pm vs. Sun 5:30 p.m. 0.411 Sat 3:30pm vs. Fri 8:30 p.m. 0.032 * TICKET_CAT (Seating) < .001 *** SOLD_OUT < .001 *** TICKET_FACE_VALUE < .001 *** CUR_WIN_HOME < .001 *** CUR_WIN_AWAY < .001 *** POINTS_3GAMES_HOME 0.302 POINTS_3GAMES_AWAY 0.001 ** LP_HOME_LS 0.067 LP_AWAY_LS < .001 *** PROM_TEAM_ HOME < .001 *** PROM_TEAM_ AWAY < .001 *** INCOME (thousand) < .001 *** POP (thousand) < .001 *** TEMP_ M_DAY < .001 *** PRECIP_M_DAY < .001 *** TEMP_END_AUC 0.003 ** PRECIP_ END_AUC 0.882 DF [R.sup.2] [R.sup.2]adj F-statistic . Significance: 10% level * Significance: 5% level ** Significance: 1% level *** Significance: 0.1% level