Pricing Strategy under Reference-Dependent Preferences: Evidence from Sellers on StubHub

Transcription

1 Pricing Strategy under Reference-Dependent Preferences: Evidence from Sellers on StubHub Jian-Da Zhu National Taiwan University April 2018 Abstract This paper uses both listing and transaction data on StubHub to study how different types of sellers price their tickets. Two types of sellers, single sellers and brokers, are identified from the data. The single sellers only post a few listings in the whole season, while the brokers sell lots of tickets in many listings. The results show that the listing prices set by the brokers are higher than those set by the single sellers in the early days before an event, but this reverses in the last few days before an event. This study also proposes a dynamic pricing model based on the reference-dependent preferences of sellers to support this finding. Both types of sellers tend to use the face values as reference points to determine the listing prices every day before an event. The estimation result further leads to the conclusion that single sellers have larger loss aversion parameters than those of brokers, which is consistent with the previous literature that market experience can eliminate the effect of reference points. Keywords: reference dependence, dynamic pricing Department of Economics, National Taiwan University. jdzhu@ntu.edu.tw 1

2 1 Introduction In the sports ticket market, official franchise websites are not the only marketplace for consumers to buy tickets. Secondary markets are even more popular places for fans to search for cheaper tickets, so many people tend to resell their sports tickets in a secondary market to earn money. For instance, StubHub is the most popular secondary market for sports tickets in the United States. A seller can post a listing with all the ticket information including a listing price, and then adjust this listing price at any time before the game day, so dynamic pricing becomes very common on StubHub. This paper uses data from StubHub, and aims to study how these heterogeneous sellers price their tickets dynamically over time. Compared with other secondary markets, StubHub is a quite professional platform for selling sports tickets. For each venue and game, StubHub has different web pages with detailed stadium maps to show where seating will be in relation to the field. This allows sellers to list their tickets easily and lets consumers search for tickets with a clear understanding of where their seats will be. In order to attract sellers and ensure they they can make a profit, StubHub provides comprehensive transaction records for the seller to set up the initial price, and the seller can easily change the listing price. Unlike some other secondary markets which reveal the rating of the sellers, no information about each seller is provided on StubHub. StubHub guarantees that buyers can certainly get the tickets from sellers. In addition, both sellers and buyers are charged a commission after the ticket is sold. Figure 1 shows an example of Major League Baseball tickets on Stub- Hub. For one particular area in different games with the same face value, the median listing price starts around $90 and decreases over time until the game day. The main reason is that the existing sellers adjust their listing prices downward over time, and new sellers tend to price lower in the market. Although the range of listing prices is quite large in the entire period, consumers purchase those listings with cheaper prices. The daily average transaction prices, as black dots, are mostly distributed lower than the median prices, especially in the last few days before a game. In addition to the listing prices, most transactions happen within one month before a game. 2

3 Figure 1: Overview for StubHub Market Median Listing Prices (Dollars) Aggregate Transaction Quantities (Seats) Days Prior to Game 20 0 Median Percentiles 0.1 and 0.9 Face Value Average Transaction Prices Transaction Quantities Not all the sellers have the same purpose in selling their tickets. Some might want to sell their tickets simply because they cannot attend the game, yet some sellers might want to make profits through the online secondary market. Therefore, heterogeneous sellers can have different pricing strategies. I have classified the sellers into two groups: single sellers and brokers. Those who sell tickets only in a few listings during the whole season are defined as single sellers, and those sellers who sell many tickets in many listings in the season are defined as brokers. Because transaction data in the primary market allow identification of how many tickets they buy in the primary market, the two types of sellers can be classified according to the detailed purchasing information. In addition, listing and transaction data on StubHub are used to trace their behavior. Comparing the price levels over time for the two types of sellers, I find that prices set by brokers are higher than those set by single sellers in the early days before an event, but this reverses in the last few days before the game. I propose a model in which sellers decide the optimal prices based on 3

4 their reference-dependent preference to illustrate this phenomenon. Reference-dependent preference comes from prospect theory, by Kahneman and Tversky (1979). According to a reference point, a seller has an additional gain from gain-loss utility when the transaction price is higher than the reference point, while the seller incurs a loss if the transaction price is lower than the reference point. Although the natural reference points for sellers are original purchase prices in the primary market, this study shows that face values of tickets serve as the reference points for sellers to determine the prices. To show evidence of a reference-dependent preference, I propose a dynamic pricing model, including two-step estimation procedure. In the first step, I use an econometric model to estimate the probability of sale for each listing on each day. In the second step, a set of structural parameters for different types of sellers are estimated by a simulated minimum distance method (Bajari, Benkard, and Levin, 2007) to rationalize that the observed listing prices are the optimal decisions. The result shows that single sellers have larger loss aversion parameters than those for brokers, which is consistent with the previous literature that market experience can eliminate the effect of reference points. Selling perishable goods in a limited time is related to the literature on dynamic pricing, which is also called revenue management in marketing literature. Monopolistic dynamic pricing models, starting with Gallego and Van Ryzin (1994), study how a monopoly firm decides a price over time under stochastic demand. The optimal pricing strategy can be characterized as a function of the inventory and time left in the horizon (Bitran and Mondschein, 1997). Zhao and Zheng (2000) extend the model by considering consumers whose reservation prices could change over time. In addition, an extensive literature focuses on a competitive model (Netessine and Shumsky, 2005; Xu and Hopp, 2006; Perakis and Sood, 2006; Lin and Sibdari, 2009). Recently, more literature further incorporates strategic consumers into a dynamic pricing framework (Levin, McGill, and Nediak, 2009; Deneckere and Peck, 2012). Dynamic pricing is also applied to price discrimination in airline markets (Escobari, 2012). Soysal and Krishnamurthi (2012) show that strategic consumers can lower retailers dynamic pricing revenues. Sweeting 4

5 (2012) finds that consumers in the sports ticket secondary market are not strategic. In the behavioral economics literature, reference-dependent preference starts from Kahneman and Tversky (1979) and Tversky and Kahneman (1991), and it is also related to the disposition effect in finance (Barberis and Xiong, 2009). A reference point could be exogenous, from the environment, or it could be based on people s rational expectations (Kőszegi and Rabin, 2006, 2007, 2009). Regardless of the types of reference points, both experimental and empirical literature find evidences to support this theory. Baucells, Weber, and Welfens (2011) use an experiment to demonstrate that reference price is a combination of the first and the last price of the time series. Crawford and Meng (2011) show that taxi drivers in New York target both hours and income for reference points. Genesove and Mayer (2001) find that sellers in the housing market tend to set higher asking prices to prevent losses, which is consistent with pricing behavior for single sellers in the last few days before a game. In addition, several previous studies combine dynamic pricing with reference point, and show how sellers impose dynamic pricing when consumers consider the previous listing prices as the reference points (Popescu and Wu, 2007; Bell and Lattin, 2000). Different from the previous literature, this paper focuses on how the reference-dependent preference of sellers affects their dynamic pricing behavior. The remainder of this paper is organized as follows. Section 2 summarizes the data in this study and shows the evidence of heterogeneous sellers. Section 3 presents a theoretical model to illustrate how reference-dependent preference affects pricing. Section 4 provides an empirical model to estimate the probability of sale to recover the opportunity costs, which serves as evidence of reference-dependent preference. Section 5 concludes this research. 2 Data The data in this study consist of three parts: the listing data on StubHub for one anonymous Major League Baseball franchise s home events in 2011, the transaction data for those home events on StubHub, and the purchasing information in the primary market. 5

6 On StubHub, sellers can post listings at any time before an event, and consumers browse those available listings to make a purchase. The listing data on StubHub contain all the information shown for consumers on the website, including listing price, section number, row number, seat number, and shipping options. To understand how sellers adjust the prices over time, the listing data were collected from the StubHub website daily during the period from March 25, 2011 to September 28, As StubHub hides the information of sellers but guarantees that consumers can get tickets sold by any sellers in the market, the listing data is not enough to identify the sellers. In addition, the disappearance of available listings is not equivalent to purchase, since sellers on StubHub can relist tickets with different listing identification numbers; therefore, the transaction data on StubHub are used to identify purchase for the listing data. 1 Most of the purchased listings in the sample can be matched with the detailed transaction information, such as transaction time. Purchasing data in the primary market can be used to identify the sellers because all the tickets are sold initially by the franchise. 2 Primary market transaction data include comprehensive purchase information, including types of tickets, purchase prices, ticket characteristics, purchasing dates, and identification number for buyers. Based on the buyers IDs, the amount of tickets bought in the whole season can be calculated. Besides the purchasing information, how many listings they have on StubHub can also be identified. However, not all the listings contain the detailed seat information, such as row number and seat number, so only around 71.9% of listings can be identified to know the information of sellers. 1 The transaction data only include the transaction price, quantity, section number, and row number. There is no seat number for each transaction, so I cannot match all the purchased listing data with their transaction data. Besides the defect of transaction data, I cannot guarantee that all the listings are collected during that periods because those listings with earlier starting date might not be included in the sample. 2 Assume that tickets are not resold or transferred in other secondary markets. 6

7 2.1 Summary Statistics Table 1 shows the summary statistics for the information of listings on Stub- Hub, including the listing price, starting date, original purchase price, face value, sold status, and other ticket characteristics. I exclude some of the listings with extremely high listing prices. 3 The remaining sample is 159,223 listings in 81 home events, around 2,000 listings for each game. Sellers on StubHub can adjust the listing prices easily at any time, so the observed daily listing prices might change over time for one listing. Table 1 reports summary statistics for maximum, minimum, and average prices of each listing. Because the seller tends to set a higher price in the beginning and lowers the price as the event date approaches, the average maximum prices of all the listings ($76.52) and the average minimum prices ($58.38) are all greater than the average face values ($42.28). Regarding the timing of listing, most sellers tend to list their tickets well in advance of the event. Around 58.2% of listings are listed more than one month prior to the event, while 23.8% of listings are listed two weeks ahead. The starting dates are strongly correlated with the starting listing prices because those listings listed at different times might be from different sellers with different opportunity costs. The original purchase prices can only be obtained when the sellers information is known. Because prices for season tickets or group tickets are cheaper than face values, the average original purchase price is $34.52, lower than the mean face value, $ Table 1 also presents quality characteristics for tickets, including the distance from seat to home plate, 4 front row dummy, and row quality. Row quality is the normalized measure to quantify the row number. The value one in row quality represents the first row in that section; the value zero shows the last row in that section. In addition, the listing period and number of price adjustments vary based on the observed periods for different events. The average listing period is about 35 days, and the sellers adjust their listing prices around 2 times for one listing. Since each 3 Those listings with prices exceeding $999 or 9 times larger than face value are excluded from the sample. 4 This variable does not vary within the same section. I only calculate the distance from seat to home plate by section. 7

8 Table 1: Summary Statistics for Listing on StubHub Obs. Mean Std. Dev. Min Median Max Price for each listing Maximum price ($) 159, Minimum price ($) 159, Average price ($) 159, Starting date for listing (days prior to game) 100 plus 159, to , to , to , Original purchase price in primary market ($) 114, Face value ($) 159, Number of seats 159, Front row dummy 156, Row quality 156, Distance from seat to home plate (feet) 159, With sellers information 159, Listing periods (days) 159, Number of price adjustment for each listing 159, Sold out or not 159, Sold partly 159, Note: The listing data are collected from March 25, 2011 to September 28, The data include the daily seat information on the buying page, such as price, quantity, row number, and seat number. The row quality is the measure to normalize the row number. The value one in row quality represents the first row in that section; the value zero shows the last row in that section. 8

9 listing has many tickets (seats), the seller can sell them separately in many ways. On average, 32.4% of listings are sold out before the event, and around 35.5% of listings are sold partly during the observed periods on StubHub. Based on the primary transaction data, the total number of identified sellers is 10,504. Table 2 shows the summary statistics for all the identified sellers. In the primary market, three different kinds of tickets can be purchased: single-game tickets, package tickets, and group tickets. 5 Prices for the single-game tickets and the package tickets are different. Consumers can buy the single-game tickets for any particular game, but the package tickets are designed for multiple games. Consumers with different needs can purchase different kinds of tickets. 42.6% of sellers only buy the single-game tickets in the primary market; 35.9% of sellers only buy the package tickets. Besides the types of tickets, consumers also have their usual channels to buy their tickets. Most sellers buy tickets from the website, but still around 28.0% of sellers buy tickets only from the box office. In addition to the purchase information in the primary market, listing and transaction data on StubHub indicate how many tickets those sellers tend to sell in the secondary market. The average number of listings in the whole season is 10.94, with around tickets per seller. Some sellers only have one listing in that year, but some sellers have lots of listings. The most active seller posted 8,308 tickets in 81 games by 1,398 listings. Table 3 shows the distribution of the number of listings among all the sellers. Among 10,504 sellers, 4,403 sellers (41.92 percent) only have one listing during the whole season, but 75 sellers (0.71 percent) post more than 150 listings. However, those 4,403 single-listing sellers only have 3.85% of all the listings, but those 75 top sellers have around 20.19% of all the listings (23,101 listings). According to the number of listings, I define two types of sellers: single sellers and brokers. The single sellers have fewer than 15 listings on StubHub in one season, while the brokers have more than 110 listings. 6 Under this definition, around 25% of listings are from the single 5 Table 2 does not show the summary statistics for the group tickets information because the proportion of the group tickets is relatively small in the sample. 6 The result in this research is robust based on different definitions for single sellers and brokers. The single sellers can also be defined as those either with fewer than 10 listings (around 20% of total listings) or with fewer than 22 listings (around 33% of total listings). 9

10 Table 2: Summary Statistics for Sellers on StubHub (N = 10, 504) Mean Std. Dev. Min Median Max Primary Market Purchase Information Types of tickets Only single-game tickets Only package tickets Both single-game and package tickets Purchase channel Only from box office Only from internet Both box office and internet Renewed packages Number of games purchased Number of tickets purchased ,064 Average number of tickets purchased in one game ,889 StubHub Resale Information Number of tickets sold ,519 Number of games listed Number of tickets listed ,308 Number of listings in the whole season ,398 Average number of listings in one game Average number of tickets listed in one game Note: The number of identified sellers is 10,541. The information can be separated as two parts: purchase information from the primary market and resale information on StubHub. Box office and internet are two biggest channels for selling tickets, but there are some other channels not listed. Single-game tickets and package tickets are two major ticket types in the primary market; other types of tickets are not listed. For the sellers, each listing might contain many tickets (seats), and those tickets could be partly sold. 10

11 Table 3: Types of Sellers Number of Sellers Number of Listings Number of listings for one seller in whole season 1 4, % 4, % 2-5 2, % 8, % , % 8, % % 7, % % 8, % % 21, % % 17, % % 8, % % 5, % % 23, % Total 10, % 114, % sellers, and around 25% of listings are from the brokers. The rest of the sellers are defined as the middle sellers with around 50% of listings in the market. Table 4 shows the summary statistics for single sellers, middle sellers, and brokers. Even though the single sellers and the brokers have similar numbers of listings in the market, the number of single sellers is 8,914, much greater than the number of brokers, 120. The first panel presents the average information for different types of sellers. For instance, the single sellers on average have 3.7 tickets sold, while the brokers on average have tickets sold in one season. In general, each broker has more listings than a single seller. Each broker has around listings in one season, but each single seller only has around 3.3 listings. The second panel in Table 4 shows the average purchase information for different types of sellers. As expected, the brokers buy more tickets than the single sellers in the primary market. Based on the types of tickets they The brokers can also be defined as those either with more than 150 listings (around 20% of total listings) or with more than 80 listings (around 33% of total listings). 11

12 Table 4: Summary Statistics by Single Sellers, Middle Sellers, and Brokers Single Sellers Middle Sellers Brokers Observations 8,914 1, Average Resale Information on StubHub Number of tickets sold (6.326) (52.77) (647.2) Number of games listed (3.223) (18.03) (13.58) Number of tickets listed (11.18) (91.91) (1,133) Number of listings in the whole season (3.416) (22.04) (216.9) Average Purchase Information in Primary Market Number of games purchased (28.37) (25.13) (12.40) Number of tickets purchased ,520 (404.2) (379.1) (2,123) Types of tickets Proportion only buying single-game tickets (0.500) (0.241) (0.250) Proportion only buying package tickets (0.470) (0.498) (0.476) Proportion buying both single-game and package tickets (0.347) (0.465) (0.492) Purchase channel Proportion only buying from box office (0.442) (0.484) (0.374) Proportion only buying from internet (0.489) (0.474) (0.374) Proportion buying from both box office and internet (0.306) (0.452) (0.473) Note: Standard deviations in parentheses. The single seller is defined as those with fewer than 15 listings on StubHub in one season, while the broker is defined as those with more than 110 listings. 12

13 have, the single sellers usually buy single-game tickets, but most brokers have package tickets. In addition, most of the single sellers use one particular way to buy tickets, either from the box office or from the internet, but the brokers often use multiple ways to buy tickets. Table 5 presents the summary statistics for all the listings by single sellers, middle sellers, and brokers. There are 29,134 listings (25.4 percent of all the listings) sold by the single sellers, and the number of brokers listings is 28,926 (25.2 percent). As to listing prices, the average price set by brokers is higher than that set by single sellers. There are two factors affecting the variation in listing prices. One is the quality of seats in different areas; the other is the listing day before the game. Tickets from the single sellers and the brokers are located in different areas, although the average face values for their listings are similar in the table. The brokers usually focus on those seats with higher markup, but single sellers have more uniform distribution over different areas. In addition to the location of seats, the row quality within the section is also different. Listings from brokers have higher row quality with more front row seats. Furthermore, listings with different starting dates have different listing prices. Table 5 shows that around 66.2% of brokers listings are posted more than one month prior to the game, but about 63.4% of single sellers listings are posted within one month of the game. Latecomer sellers tend to have lower prices than existing listing prices. Since brokers start the listing earlier, their listings have longer listing periods, with more frequent price adjustment. However, within a certain period, both types of sellers have a similar number of price adjustments. Also, compared with the sold listings by the single sellers, the brokers are likely to sell more listings with greater numbers of seats in each listing. To understand how the single sellers and the brokers price their tickets, all of the characteristics related to the listing prices should be controlled in the regression. For instance, the quality of listings by the brokers in the same section is better than that of single sellers, and the row quality should be considered the control variable as we compare their pricing strategies. In this way, the difference between two types of sellers is based on the same quality of tickets. I will discuss how to control those listing characteristics 13

14 to compare the pricing strategies for different types of sellers in the following subsection. 2.2 Price Dispersion In this subsection, I specify a linear model to discuss the price dispersion for all the listings: p ijt = X ijt γ + u ijt, (1) where p ijt is the listing prices for seller i in section j at period t, and X ijt includes four sets of variables: quality of seats in the field, characteristics of listings, game effects, and time effects. First, the quality of seats consists of the distance from seats to home plate for different sections, row quality, area effect, and area effect row quality. Listings with higher quality have higher prices in the market. Second, I control the number of seats in each listing and the starting date prior to the game. Most of the listings in the sample have two or four seats in one listing. Listings with more than five seats could be sold separately into several two-seat transactions or could be sold together as one transaction; therefore, those listings with more seats have higher value. Besides the number of seats in each listing, the starting date can affect the starting listing price. Sellers are likely to list lower prices when they come into the market late. Third, instead of using opponent dummies, I use all the game dummies to represent the effect of each game. In this way, I don t need to control the game day information, such as afternoon game or day of the week for game day. The last factor I control in the regression is the timing. Dummies for each day before the game and the day of the week effect for listing are included because sellers might have different strategies to adjust their listing prices on different days of the week. Table 6 shows the linear regression results for interpreting price dispersion. Columns (1)-(4) in Table 6 are the results for the whole sample. On average, the effect of distance on prices is around -$15.5 for every 100 feet from home plate. Compared with the listings with two seats, the listings with only one seat have lower value, but the listings with over two seats have 14

15 Table 5: Listings by Single Sellers, Middle Sellers, and Brokers Single Sellers Middle Sellers Brokers Observations 29,134 56,354 28,926 Average Ticket Information Average listing price ($) (34.69) (37.40) (43.04) Face value (20.14) (22.05) (22.71) Original purchase price in the primary market (15.52) (16.75) (17.73) Number of seats (1.973) (1.861) (3.195) Starting date for listing (days prior to game) 100 plus (0.332) (0.402) (0.440) 30 to (0.427) (0.468) (0.490) 14 to (0.399) (0.394) (0.401) 0 to (0.496) (0.449) (0.344) Front row dummy (0.231) (0.293) (0.358) Row quality (0.297) (0.304) (0.319) Distance from seat to home plate (feet) (83.30) (87.73) (96.87) Listing periods (days) (37.84) (43.84) (45.57) Number of price adjustments for each listing (2.179) (2.813) (2.300) Sold out or not (0.477) (0.494) (0.497) Sold partly (0.483) (0.497) (0.500) Note: Standard deviations in parentheses. The single seller is defined as those with fewer than 15 listings on StubHub in one season, while the broker is defined as those with more than 110 listings. 15

16 Table 6: Price Dispersion for Listings Price Relative Price log(price) to Face Value (1) (2) (3) (4) (5) (6) (7) Distance from seat to home plate *** *** *** *** *** *** *** [ ] [ ] [ ] [ ] [ ] [1.44e-05] [2.94e-05] Relative to number of seats = 2 Number of seats = *** *** *** *** *** *** [0.127] [0.127] [0.127] [0.120] [ ] [ ] Number of seats = *** 7.632*** 7.192*** 8.139*** 0.128*** 0.209*** [0.0931] [0.0931] [0.0918] [0.105] [ ] [ ] Number of seats = *** 5.687*** 5.834*** 4.698*** *** 0.113*** [0.0627] [0.0627] [0.0620] [0.0640] [ ] [ ] Number of seats *** 12.05*** 12.26*** 10.85*** 0.192*** 0.374*** [0.0978] [0.0978] [0.0969] [0.101] [ ] [ ] Relative to starting date 100+ days prior to game 0-2 days prior to game *** *** *** *** [0.191] [0.188] [ ] [ ] 3-5 days prior to game *** *** *** *** [0.135] [0.136] [ ] [ ] 6-9 days prior to game *** *** *** *** [0.114] [0.115] [ ] [ ] days prior to game *** *** *** *** [0.108] [0.111] [ ] [ ] days prior to game *** *** *** *** [0.0853] [0.0867] [ ] [ ] days prior to game *** *** *** *** [0.0856] [0.0878] [ ] [ ] Constant 190.9*** 190.8*** 191.7*** 200.6*** 195.7*** 5.656*** 3.271*** [0.606] [0.601] [0.604] [0.607] [0.650] [ ] [0.0113] Observations 880, , , , , , ,679 R-squared Area effect, Area effect row Yes Yes Yes Yes Yes Yes Yes Day prior to game, game effect Yes Yes Yes Yes Yes Yes Yes Day of the week effect No No Yes Yes Yes Yes Yes Note: Robust standard errors in brackets; *** p < 0.01, ** p < 0.05, * p < 0.1. Columns (5), (6), and (7) use the sample with information of sellers. 16

17 higher value. In addition, listing prices with starting date 0-2 days before the game are $10.34 less than those posted over 100 days prior to the game. R-squared in column 4 shows that around 67.1% of the variation for price dispersion could be interpreted by the model. Column (5) shows similar results when I focus on those listings with the information of sellers. Instead of measuring the price level, column (6) shows the regression with dependent variable, log(price). All the signs are the same, and the coefficients could be interpreted as the percentage change. The dependent variable in the last column is the price relative to face value. Only 43.8% of the total variation could be explained by the model. The reason why those variables X ijt cannot fully capture the variation of prices relative to face value is that the prices relative to face value could represent the markup of each ticket, which should depend on how the franchise underprices or overprices the tickets. To analyze the pricing strategies between the single sellers and the brokers, I extend the model in column (5) in Table 6 to add the dummies for different types of the sellers and interactions between sellers dummies and the day before the game. The result is shown in Figure 2. Controlled by all the potential factors to affect the listing prices, prices set by the brokers are higher than those set by the single sellers in the early days before the game, but this situation reverses in the last few days. In the last few days before the game, higher prices set by the single sellers could be interpreted as the remaining value, because the single sellers might be able to attend the game. However, the remaining value for the single sellers on the last day should also affect the pricing level in the early days before the game, but the listing prices set by the single sellers are not consistently higher than those set by the brokers in the early period. 2.3 Reference Points This subsection provides the evidence of reference points. Although listing prices can be adjusted at any time, I focus on the initial listing prices for each listing in this subsection. Three main possible reference points, face values, purchase prices from the primary market, and transaction prices on the previous day in the same section, are examined in the following analysis. 17

18 Figure 2: Estimated Listing Price Path for Single Sellers and Brokers Listing Prices (Dollars) Days Prior to Game 5 0 Single sellers Brokers Note: Dotted lines represent 95 percent confidence intervals. Each plotted value is the value of the time dummies estimated from the regression model plus the average listing price for brokers in the last day before the game. The dependent variable in the estimated regression is the listing price in dollars. On the last day, prices by single sellers is around 5 dollars higher than those decided by brokers; however, in the earlier day, prices by brokers is around 2 dollars higher than those by single sellers. 18

19 Figure 3: Listing Prices Relative to Face Values and Original Purchase Prices Number of Listings Number of Listings Listing Prices Relative to Face Value (N=82231) Listing Prices Relative to Original Purchase Price (N=82231) Note: Not all the listings can be observed from the beginning, so only 82,231 listings have the initial listing prices. Because all the sellers in the secondary market have bought the tickets in the primary market, the face values or the original purchase price could naturally be the reference points. Figure 3 presents the frequency distribution for two indices, listing prices relative to face values and original purchase prices in the primary market. The bunching evidence at one for listing prices relative to face values clearly shows that the seller tends to decide a listing price higher than the face value, instead of a listing price lower than the face value. However, this bunching evidence does not happen for listing prices relative to original purchase prices, which means that original purchase prices from the primary market might not serve as reference points for sellers to decide the listing prices. Many face values are round numbers, and round numbers could also be the reference points exogenously. Allen, Dechow, Pope, and Wu (2017) show that round numbers in finished time can serve as reference points for marathon runners. In the secondary market for sports tickets, Figure 4 also presents that listing prices at round numbers clearly have the bunching effect. To further understand whether face values are still the reference points or not, I focus on those listings with face values which are not round numbers, Figure 5 shows that the bunching evidence is still clearly shown at one. The other possible reference points are the previous transaction prices 19

20 Figure 4: Listing Price Distribution Number of Listings Listing Prices Note: This figure shows the initial listing prices between 0 and 100. The grey vertical lines show the value at 20, 25, 30,..., 100. because StubHub allows sellers to observe the previous transaction record. I focus on those listings with transaction in the same section on the previous day. Surprisingly, Figure 6 presents the distribution of the listing prices relative to the previous day lowest transaction prices, and it shows the bunching evidence at one. Although the transaction prices on each day might change over time, the result clearly shows that the seller tend to decide an initial listing price, higher than the lowest transaction price on previous day. To sum up, the face values and the previous day transaction prices might serve as important reference points to affect the pricing decision for sellers. In the next section, I will present a theoretical model with reference-dependent preference to a provide possible explanation for these pricing strategies. 20

21 Figure 5: Listing Prices Relative to Face Values and Original Purchase Prices (Excluding Face Values with Round Numbers) Number of Listings Number of Listings Listing Prices Relative to Face Value (N=61343) Listing Prices Relative to Face Value (N=61343) Note: I exclude those listings with face values ending at 0 or 5 in the last digit. number of observations is 61,343. The 3 Theoretical Model In this section, I present a dynamic pricing model in which sellers have a reference-dependent preference. For a given event g, there are T periods, indexed by t = {1, 2,...T }, for the sellers to sell their tickets, and the game starts after the period T. The sellers might come into the market at different times, but during each period in which the number of sellers is large, the market power for each seller is relatively small. Because of the heterogeneity of tickets, each seller can decide his or her own prices in each period to maximize expected profits. If a ticket is not sold in period t, the seller can decide the price again in period t + 1. In the model, each seller is assumed to have only one ticket when entering the market, and there is no switching cost for sellers to adjust the prices every day. To ignore the index g, the maximization problem for seller i at time t could be written as V it = max p it u i (p it )Φ it (p it ) + [1 Φ it (p it )]E t (V it+1 ), t = 1, 2,..., T, (2) where Φ it (.) is the probability of sale for listing i at time t, and E t (V it+1 ) is the expected value of holding the ticket at time t + 1. Because the quantity provided by each seller is relatively small in the market, the probability of 21

22 Figure 6: Listing Prices Relative to Previous Lowest Transaction Prices Number of Listings Listing Prices Relative to Previous Lowest Transaction Prices (N=13429) Note: This figure shows the frequency distribution of the listing prices divided by the previous lowest transaction prices in the same section, so the observations only include those with transaction on the previous day in the same section. sale Φ it (.) is assumed to be exogenous for each seller, which can be estimated based on all the listings in the market. Different sellers in the same section might decide different prices based on difference in expected value of the tickets. In the last period T, the expected value, E t (V it +1 ), could be explained as the remaining value of the ticket after the game starts. For those sellers who can attend the game even if they cannot resell their tickets, the remaining value should be positive. However, for those sellers with many tickets in one game, they might only have zero remaining value for most of the tickets. If the remaining value for seller i is assumed as r i dollars, then the expected value is u i (r i ). 22

23 The first-order condition for the profits maximization problem is u i(p it )Φ it (p it ) + Φ it(p it ) p it (u i (p it ) E t (V it+1 )) = 0, t = 1, 2,..., T. (3) Consider a risk-neutral seller without gain-loss utility, the utility is defined as u i (p it ) = p it. Then the first-order condition can be rewritten as p it = Φ it(p it ) Φ it (p it ) + E t (V it+1 ), t = 1, 2,..., T. (4) p it The intuition for equation (4) is that the optimal price in the current period is equal to the next period expected value plus the markup, which depends on the current period demand elasticity. This result is the same as the traditional dynamic pricing model. However, if the risk-neutral seller has gain-loss utility based on the exogenous reference point, RP i, the utility can be specified as u i (p it ) = p it + ηg(p it RP i ), (5) where G(p it RP i ) is the gain-loss utility, and η > 0 is the parameter to indicate how the gain-loss utility is relative to the consumption utility. Following the literature (Post, Van Den Assem, Baltussen, and Thaler, 2008), G(p it RP i ) can be defined as G(p it RP i ) = { (p it RP i ) α if p it RP i ( λ)(rp i p it ) α if p it < RP i, (6) where λ > 1 is the loss-aversion parameter, and α > 0 represents the curvature of the gain-loss utility. Based on the assumption α = 1, one of the following three cases should be satisfied: Case I. When p it RP i : the optimal price p it should satisfy the first-order condition under the gain domain: p it = Φ ( it(p it) η Φ it + (p it ) 1 + η RP i + 1 ) 1 + η E t(v it+1 ), t = 1, 2,..., T. (7) p it 23

24 Case II. When p ijt < RP i : the optimal price p it should satisfy the first-order condition under the loss domain: p it = Φ ( it(p it) ηλ Φ it + (p it ) 1 + ηλ RP i + 1 ) 1 + ηλ E t(v it+1 ), t = 1, 2,..., T. p it Case III. If the previous two cases are not satisfied, the optimal price is binding at the reference point, which p it = RP i. If the expected value E t (V it+1 ) in equation (4) is interpreted as opportunity cost, the last two terms in equations (7) and (8), the linear combination of the expected value and the reference point, can be treated as adjusted opportunity cost based on the gain-loss utility. In the case I, the adjusted opportunity cost could be affected upward or downward based on whether the expected value, E t (V it+1 ), is lower or higher than the reference point. As E t (V it+1 ) > RP i, the adjusted opportunity cost and the optimal price become lower, compared with the case without gain-loss utility. The seller with gain-loss utility tends to decide a lower price to ensure the sale of the ticket when she faces the gain domain. When E t (V it+1 ) < RP i, the adjusted opportunity cost and the optimal price become higher because seller tends to avoid the loss from selling the ticket. In the case II, the seller always faces the loss domain, so the optimal price becomes higher. Figure 7 shows the simulation result for the dynamic case. Based on the gain-loss utility, the seller tends to price lower under the domain of gains when the expected price is higher than the reference point. On the other hand, the seller is likely to price higher under the domain of losses if the reference point is higher than the expected value. 4 Empirical Estimation Results I use a two-step estimation approach to estimate the parameters in the utility function. In the first step, I estimate the probability of sale for each listing as a function of listing prices based on a probit model. The second step is to find a set of structural parameters to rationalize that the observed 24 (8)

25 Figure 7: Simulation Results Listing Prices Without RP 25 With RP= Day Prior to Game Note: The simulation result is based on a constant probability of sale over time Φ( p), gain-loss parameter η = 0.7, and loss-aversion parameter λ = 2.25, where Φ(.) is normal cumulative distribution function. The reference point is 50. listing prices are the optimal decisions, so I follow the second step in Bajari, Benkard, and Levin (2007) to obtain a simulated minimum distance estimator by considering a set of alternative listing prices and minimizing the violations of the optimal conditions. 4.1 First Step: Estimate the Probability of Sale In order to obtain the probability of sale for each listing, I specify a probit model as follows: s it = β 0 β 1 p it + X it γ + u it, (9) p it = X it Π 1 + Z it Π 2 + v it, (10) 25

26 where s it = 1{s it 0} represents the sale of listings, and X it includes the listing characteristics and competition variables to control the demand equation. However, prices set by sellers might be correlated with some unobserved demand shock u it, so equation (10) is needed to specify a cost-based shock to solve the endogeneity problem. The error terms u it and v it are jointly distributed according to a joint normal distribution: ( u it v it ) N (( 0 0 ), ( 1 ρσ v ρσ v σ 2 v )), (11) where ρ is the parameter to specify this endogeneity problem. If ρ = 0, there is no endogeneity problem. The demand estimation only needs to rely on the traditional probit model. However, if ρ 0, the endogeneity problem arises. I use the control function approach to first estimate equation (10), and then the estimated error term from the first stage is included into equation (9) to estimate the probit model. In order to flexibly estimate the demand equation, I estimate the coefficients on listing prices separately in two periods: 1-7 days prior to the game and 7-14 days prior to the game, so the 1-7 days prior to the game dummy listing prices should be included in equation (9). Furthermore, the variables Z it in equation (10) should also include the interactions between instrumental variables and the period dummy variable. Besides the endogenous listing prices variable in equation (9), the variables X it include two sets of variables: quality-based characteristics for listings and competition variables for demand estimation. Quality-based characteristics include the distance from seats to home plate, row quality, area dummies, row quality area dummies, game dummies, days prior to the game, and number of tickets in one listing. Those variables related to the quality of tickets not only can affect how the sellers decide the prices but also can influence the demand of consumers. The competition variables in X it should be controlled because they are correlated with the sellers decision on listing prices. I control the dummy to indicate whether there exists competing listings, 7 the number of competing 7 The definition of competing listings is those listings in the same event, in the same section, on the same date, and with the same number of tickets. 26

27 listings, mean and lowest prices for competing listings, and the proportion of listings with higher row quality. To solve the endogeneity problem, the instrumental variables in equation (10) should be correlated with the listing prices but not correlated with unobserved demand shock in u it. I use two sets of instruments: types of sellers and timing of listing. Different types of sellers might have different opportunity costs which affect the pricing decision. I use the different types of tickets they have and the number of listings they post in one season as the cost-based shift instruments, which should not be correlated with unobserved demand shock. The other set of instruments is the starting date for listings. Sellers with different opportunity costs would decide to post their listings on different days; however, it is better to assume that those timing decisions are not correlated with unobserved demand shock. Table 7 presents the regression on all the instruments and interactions between the instruments and period dummy. I also include all the characteristics X it in this equation. The overall F-statistic for all the instrumental variables is greater than 10, which indicates that there is no weak instrument problem in the first stage. Table 8 shows the estimates of demand. Column 1 presents the traditional probit model with exogenous listing prices; Column 2 shows the IV probit model estimated by control function approach. If the unobserved demand shock is ignored, the coefficients on listing prices from the probit model have slightly positive bias. Furthermore, the mean elasticities calculated by the IV probit model are around and for 7-14 days and 1-7 days prior to the game respectively. 4.2 Second Step: Estimate the Parameters in Utility Function The estimated probability of sale for each listing in each period is obtained as ˆΦ it (p it ) based on the coefficients in Table 8. If I assume that the remaining value is zero for each seller, equation (12) shows that the optimal value function can be backward calculated from the last period by the observed 27

28 Variables Table 7: Regression on Instruments Listing Prices Types of seller variables: Sellers buying single-game tickets 0.475*** (0.0459) 1-7 days prior to game *** (0.0632) Sellers buying package tickets 0.233*** (0.0606) 1-7 days prior to game *** (0.0766) Number of listings *** (7.46e-05) 1-7 days prior to game -5.99e-05 (9.63e-05) Starting date for listings (Days prior to game) 100 days plus 7.745*** (0.0665) 1-7 days prior to game 3.419*** (0.141) days 5.230*** (0.0540) 1-7 days prior to game 2.429*** (0.133) days *** (0.0905) 1-7 days prior to game 2.207*** (0.133) 7-10 days *** (0.0788) 1-7 days prior to game 0.548** (0.214) 4-7 days *** (0.0793) Observations 2,304,574 F-statistic on all the instruments p-value Note: Standard errors in parentheses; *** p < 0.01, ** p < 0.05, * p <

29 Table 8: Demand Estimation Variables Probit Model IV Probit Model Listing price coefficients *** *** [0.0002] [0.0005] 1-7 days prior to game *** *** [0.0001] [0.0001] Distance from seat to home plate (feet) *** *** [0.0001] [0.0001] Relative to number of seats = 2 Number of seats = *** *** [0.0145] [0.0156] Number of seats = *** *** [0.0070] [0.0072] Number of seats = *** *** [0.0045] [0.0046] Number of seats *** *** [0.0052] [0.0064] Competition coefficients: Dummy variable for competing listings *** *** [0.0088] [0.0108] Number of competing listings, log(n+1) *** *** [0.0045] [0.0047] Mean price for competing listings *** *** [0.0002] [0.0002] Lowest price for competing listings [0.0002] [0.0002] Proportion of higher row quality seats *** *** [0.0057] [0.0058] Coefficients on estimation error from first stage ** [0.0005] Constant *** *** [0.0301] [0.0795] Observations Log-likelihood Note: Standard errors in brackets; *** p < 0.01, ** p < 0.05, * p <