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

Pricing Strategy under Reference-Dependent Preferences: Evidence from Sellers on StubHub Jian-Da Zhu National Taiwan University April 21, 2018 International Industrial Organization Conference (IIOC) Jian-Da Zhu (National Taiwan University) April 21, 2018 1 / 28

Motivation Features of StubHub: - The biggest secondary market for sports tickets in the United States - A fixed-price mechanism (not auction mechanism) - Sellers can change prices over time to impose dynamic pricing. - Sellers are unknown to buyers, so there is no reputation issues. - Buyers are guaranteed to receive the tickets. - StubHub provides the comprehensive transaction records for sellers to decide their listing prices. Jian-Da Zhu (National Taiwan University) April 21, 2018 2 / 28

Overview for StubHub Market 0 50 100 150 Median Listing Prices (Dollars) 0 50 100 Aggregate Transaction Quantities (Seats) 100 80 60 40 Days Prior to Game 20 0 Median Percentiles 0.1 and 0.9 Face Value Average Transaction Prices Transaction Quantities Jian-Da Zhu (National Taiwan University) April 21, 2018 3 / 28

Reference-Dependent Preferences Prospect Theory in Kahneman and Tversky (1979): a. Gain-loss utility relative to a reference point. b. Value function is concave in the gain domain and convex in the loss domain. c. The marginal effect is larger in the loss domain. What is the reference point? - One natural reference point is the starting point, such as the original purchase price. - It is called disposition effect in finance. (Barberis and Xiong, 2009) - It could be a combination of several prices. (Baucells et al, 2011) - It could be peoples rational expectations. (Kőszegi and Rabin, 2006) - Empirical research: taxi drivers (Crawford and Meng, 2011); housing prices (Genesove and Mayer, 2001). Jian-Da Zhu (National Taiwan University) April 21, 2018 4 / 28

Reference-Dependent Preferences Prospect Theory in Kahneman and Tversky (1979): a. Gain-loss utility relative to a reference point. b. Value function is concave in the gain domain and convex in the loss domain. c. The marginal effect is larger in the loss domain. What is the reference point? - One natural reference point is the starting point, such as the original purchase price. - It is called disposition effect in finance. (Barberis and Xiong, 2009) - It could be a combination of several prices. (Baucells et al, 2011) - It could be peoples rational expectations. (Kőszegi and Rabin, 2006) - Empirical research: taxi drivers (Crawford and Meng, 2011); housing prices (Genesove and Mayer, 2001). Jian-Da Zhu (National Taiwan University) April 21, 2018 4 / 28

Research Questions and Results 1. What s the reference point for seller? - Instead of original purchase price, the face value is more likely to be a reference point for sellers. - Round numbers are natural reference points. - Previous lowest prices could also serve as reference points for sellers. 2. How does this reference point affect a seller s behavior? - Based on theoretical prediction, sellers with reference-dependent preferences tend to set a lower price earlier, but a higher price in the last few days before the game. - They slow down the price adjustment as the listing price is close to the reference point. - The bunching evidence happens around the reference point for the distribution of listing prices. Jian-Da Zhu (National Taiwan University) April 21, 2018 5 / 28

Research Questions and Results 3. Who are affected more by the reference-dependent preference? - Sellers with less listings have larger loss aversion parameters. - Prices set by brokers are relative higher than those set by single sellers in the early days before the event, but the prices are inversely switched in the last few days before the game. Jian-Da Zhu (National Taiwan University) April 21, 2018 6 / 28

Outline - Motivation - Research Questions - Data - Theoretical Model and Predictions - Estimation Method and Results - Conclusion Jian-Da Zhu (National Taiwan University) April 21, 2018 7 / 28

Data The baseball tickets for one Major League Baseball franchise in 2011: 1. Listing data on StubHub Summary - Some part of the listings for those events. - Including all the listing information on the buying page. - Number of seats, section, row, prices, and fees. 2. Transaction data on StubHub - To identify the purchase time for listing data. 3. Transaction data in the primary market - Use the account ID to identify the sellers on StubHub. Summary - Understand the information of purchase for each seller on StubHub. - Understand the resale behavior for sellers on StubHub. Jian-Da Zhu (National Taiwan University) April 21, 2018 8 / 28

Listing Price Distribution First, focus on their initial listing prices. Definition: All price decisions - Listing prices relative to face value = Listing prices / Face value - Listing prices relative to original purchase price = Listing prices / original purchase price 0 2000 4000 6000 8000 0 2000 4000 6000 0 1 2 3 4 5 Listing Prices Relative to Face Value (N=82231) 0 1 2 3 4 5 Listing Prices Relative to Original Purchase Price (N=82231) Jian-Da Zhu (National Taiwan University) April 21, 2018 9 / 28

Listing Price Distribution Round numbers in face values can serve as reference points. Exclude the face values with round numbers: Evidence 0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000 0 1 2 3 4 5 Listing Prices Relative to Face Value (N=61343) 0 1 2 3 4 5 Listing Prices Relative to Face Value (N=61343) Jian-Da Zhu (National Taiwan University) April 21, 2018 10 / 28

Listing Price Distribution Over Time 0 1000 2000 3000 Within 7 Days Prior to Game 0 500 1000 1500 8 14 Days Prior to Game 0 1 2 3 4 5 Listing Prices Relative to Face Value (N=19195) 0 1 2 3 4 5 Listing Prices Relative to Face Value (N=10664) 0 500 1000 1500 15 30 Days Prior to Game 0 500 1000 1500 31 60 Days Prior to Game 0 1 2 3 4 5 Listing Prices Relative to Face Value (N=16321) 0 1 2 3 4 5 Listing Prices Relative to Face Value (N=13745) Jian-Da Zhu (National Taiwan University) April 21, 2018 11 / 28

Listing Price Adjustment Definition: Listing Price Change Percentage = P t+1 P t P t, where P t is the listing prices at time t. Average Price Change Percentage.35.3.25.2.15.1 0 1 2 3 4 Listing Prices Relative to Face Value Price Change Percentage.35.3.25.2.15.1 0 1 2 3 4 Prices Relative to Face Value Jian-Da Zhu (National Taiwan University) April 21, 2018 12 / 28

Different Types of Sellers on StubHub Number of Sellers Number of listings for one seller in whole season 1 4,403 41.92% 4,403 3.85% 2-5 2,768 26.35% 8,426 7.36% 6-10 1,167 11.11% 8,988 7.86% 11-15 576 5.48% 7,317 6.40% 16-22 442 4.21% 8,240 7.20% 23-50 658 6.26% 21,831 19.08% 51-79 274 2.61% 17,464 15.26% 80-109 96 0.91% 8,819 7.71% 110-149 45 0.43% 5,825 5.09% 150+ 75 0.71% 23,101 20.19% Total 10,504 100.00% 114,414 100.00% Summary 1 Summary 2 Jian-Da Zhu (National Taiwan University) April 21, 2018 13 / 28

Listing Price Distribution By Different Types of Sellers 0 100 200 300 Sellers with Only One Listing 0 2000 4000 6000 Sellers with 10+ Listings 0 1 2 3 4 5 Listing Prices Relative to Face Value (N=3167) 0 1 2 3 4 5 Listing Prices Relative to Face Value (N=65772) 0 1000 2000 3000 4000 Top 10% Sellers 0 200 400 600 800 1000 Top 1% Sellers 0 1 2 3 4 5 Listing Prices Relative to Face Value (N=47687) 0 1 2 3 4 5 Listing Prices Relative to Face Value (N=14308) Jian-Da Zhu (National Taiwan University) April 21, 2018 14 / 28

Listing Price Distribution in Two Weeks We focus on the period in two weeks prior to the game. Single sellers are likely to be affected by the face value. 0 50 100 150 200 Sellers with Only One Listing (in Two Weeks) 0 50 100 150 200 Top 1% Sellers (in Two Weeks) 0 1 2 3 4 Listing Prices Relative to Face Value (N=1381) 0 1 2 3 4 Listing Prices Relative to Face Value (N=2596) Jian-Da Zhu (National Taiwan University) April 21, 2018 15 / 28

Estimated Listing Prices for Single Sellers and Brokers Listing Prices (Dollars) 45 50 55 60 65 15 10 Days Prior to Game 5 0 Single sellers Brokers Jian-Da Zhu (National Taiwan University) April 21, 2018 16 / 28

Listing Price Distribution Listing Prices Relative to Previous Lowest Transaction Prices 0 500 1000 1500 0 1 2 3 4 5 Listing Prices Relative to Previous Lowest Transaction Prices (N=13429) Jian-Da Zhu (National Taiwan University) April 21, 2018 17 / 28

Theoretical Model For each seller i at time t, the profits maximization problem: 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, where Φ it (.) is the probability of sale. E t (V it +1 ) = u i (r i ), where r i is the remaining value after period T. F.O.C.: 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. Jian-Da Zhu (National Taiwan University) April 21, 2018 18 / 28

Theoretical Model If sellers are risk neutral without gain-loss utility, then u i (p it ) = p it. F.O.C. can be rewritten as p it = Φ it(p it ) Φ it (p it) + E t(v it+1 ) > E t (V it+1 ) If sellers are risk neutral with gain-loss utility, then the utility: u i (p it ) = p it + η[1(p it > RP i )(p it RP i ) α + ( λ)1(p it < RP i )(RP i p it ) α ], where λ > 1 and η > 0. Jian-Da Zhu (National Taiwan University) April 21, 2018 19 / 28

Theoretical Model If sellers are risk neutral without gain-loss utility, then u i (p it ) = p it. F.O.C. can be rewritten as p it = Φ it(p it ) Φ it (p it) + E t(v it+1 ) > E t (V it+1 ) If sellers are risk neutral with gain-loss utility, then the utility: u i (p it ) = p it + η[1(p it > RP i )(p it RP i ) α + ( λ)1(p it < RP i )(RP i p it ) α ], where λ > 1 and η > 0. Jian-Da Zhu (National Taiwan University) April 21, 2018 19 / 28

Theoretical Model To simply the problem, we assume that α = 1. There are three cases: - Case I: When p it > RP i: the optimal price p it should satisfy 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. - Case II: When p ijt < RP i: the optimal price p it should satisfy 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. - Case III: p it = RP i. The previous two cases are not satisfied. Jian-Da Zhu (National Taiwan University) April 21, 2018 20 / 28

Simulation Results from Model Assume Φ(1.5 0.05p), α = 0.8, η = 0.7, λ = 2.25, and RP = 50. 65 60 55 50 Listing Prices 45 40 35 30 Without RP 25 With RP=50 20 20 18 16 14 12 10 8 6 4 2 0 Day Prior to Game Jian-Da Zhu (National Taiwan University) April 21, 2018 21 / 28

Estimation Method Two-step estimation approach: First step: use a Probit model to estimate the probability of sale. Second step: estimate a structural parameters in utility function Model for the first step: s it = β 0 β 1 p it + X it γ + u it, p it = X it Π 1 + Z it Π 2 + v it, where s it = 1{s it 0} represents the sale of listings, and X it are listing characteristics and competition variables. Z it includes types of sellers and timing of listing. Error term distribution: ( ) (( ) ( )) u it 0 1 ρσ v N,, v it 0 ρσ v σ 2 v Jian-Da Zhu (National Taiwan University) April 21, 2018 22 / 28

Estimation Method From the first step, we know the function ˆΦ it (.) for each period. Given the parameters in the utility function, and the remaining value after the last day, the value function could be backward obtained by V it (p it; ψ) = u(p it; ψ)ˆφ it (p it) + [1 ˆΦ it (p it)]v it+1 (p it+1; ψ). where V it +1 = u(r i ), and r i = κrp i is the remaining value. The values of other alternative listing prices should be lower than the optimal one. V it (p it; ψ) V it ( p it ; ψ). Therefore, g it (ψ) = V it (p it; ψ) V it ( p it ; ψ) 0, Jian-Da Zhu (National Taiwan University) April 21, 2018 23 / 28

Estimation Method The estimator ˆψ is to minimize the objective function Q(ψ) = 1 NT (min {g it (ψ), 0}) 2, In the model, we assume that all the sellers share the same parameters in the utility function. Some other details for identification: it 250 alternative prices are used for each listing Focus on the last day, so α might not be identified. From the literature, it is also hard to identify η. λ could be identified based on the sharp bunching around the face value. Jian-Da Zhu (National Taiwan University) April 21, 2018 24 / 28

Empirical Results =1 15 110 220 Single Sellers Brokers Utility function α 0.0035 0.1186 0.0256 0.2361 [0.2964] [0.2664] [0.2683] [0.2838] η 8.32E-16 1.97E-14 4.72E-15 4.77E-15 [7.15E-15] [1.70E-14] [7.33E-15] [8.03E-15] λ 1.3997*** 1.1211*** 1.3911*** 1.0851*** [0.3778] [0.2787] [0.2820] [0.1380] Remaining value κ 0.6295*** 0.6081*** 0.6465*** 0.6853*** [0.0562] [0.0255] [0.0147] [0.0320] Q(ψ) 0.0585 0.0478 0.0516 0.0912 Number of listings 826 5506 3789 1894 Jian-Da Zhu (National Taiwan University) April 21, 2018 25 / 28

Empirical Results =1 15 110 220 Single Sellers Brokers Assume α = 0.8 Utility function η 7.21E-16 1.66E-16 7.21E-16 1.67E-16 [7.18E-16] [8.09E-16] [1.05E-15] [6.66E-16] λ 2.2537** 1.0542*** 1.0010*** 1.1013*** [0.8974] [0.0401] [0.0942] [0.0823] Remaining value κ 0.6295*** 0.6081*** 0.6465*** 0.6853*** [0.0514] [0.0164] [0.0220] [0.0252] Q(ψ) 0.0527 0.0595 0.0821 0.0813 Number of listings 826 5506 3789 1894 Jian-Da Zhu (National Taiwan University) April 21, 2018 26 / 28

Listing Prices Relative to Face Values on the Last Day 0 20 40 60 Sellers with One Listing 0 100 200 300 400 Sellers with <=15 Listings 0 1 2 3 4 Listing Prices Relative to Original Purchase Price (N=826) (Day 1) 0 1 2 3 4 5 Listing Prices Relative to Original Purchase Price (N=5506) (Day 1) 0 50 100 150 200 Sellers with >=110 Listings 0 20 40 60 80 100 Sellers with >=220 Listings 0 1 2 3 4 5 Listing Prices Relative to Original Purchase Price (N=3789) (Day 1) 0 1 2 3 4 5 Listing Prices Relative to Original Purchase Price (N=1894) (Day 1) Jian-Da Zhu (National Taiwan University) April 21, 2018 27 / 28

Conclusion Conclusion: - The reference points for sellers on StubHub are face values, instead of original purchase prices. - Sellers with reference-dependent preferences tend to set a lower price earlier, but a higher price in the last few days before the game. - The result shows that sellers with less listings (single sellers) have larger loss aversion parameters, and their listing prices are affected more by the reference-dependent preference. Future study: - Identification issue for parameters in the utility function. - Include all other periods into the estimation. Jian-Da Zhu (National Taiwan University) April 21, 2018 28 / 28

Thank you! Comments are welcome! Jian-Da Zhu (National Taiwan University) April 21, 2018 29 / 28

Summary Statistics for Listings on StubHub Back Obs. Mean Std. Dev. Min Median Max Average listing price ($) 159,223 70.40 44.46 2 60 677 Original purchase price in primary market ($) 114,387 34.52 16.79 0 31 99 Face value ($) 159,223 42.28 22.69 12 36 108 Number of seats 159,223 3.531 2.608 1 3 145 Front row dummy 156,204 0.105 0.307 0 0 1 Row quality 156,204 0.548 0.317 0 0.571 1 Distance from seat to home plate (feet) 159,223 253.3 93.24 72.81 243.1 439.3 Starting date for listing (days prior to game) 100 plus 159,223 0.224 0.417 0 0 1 30 to 100 159,223 0.358 0.479 0 0 1 14 to 30 159,223 0.180 0.384 0 0 1 0 to 14 159,223 0.238 0.426 0 0 1 With sellers information 159,223 0.719 0.450 0 1 1 Sold out or not 159,223 0.324 0.468 0 0 1 Jian-Da Zhu (National Taiwan University) April 21, 2018 0 / 9

Summary Statistics for Sellers on StubHub (I) Back Mean Std. Dev. Min Median Max Primary Market Purchase Information (N=10,541) Types of tickets Only single-game tickets 0.426 0.495 0 0 1 Only package tickets 0.359 0.480 0 0 1 Both single-game and package tickets 0.167 0.373 0 0 1 Purchase channel Only from box office 0.280 0.449 0 0 1 Only from internet 0.386 0.487 0 0 1 Both box office and internet 0.136 0.343 0 0 1 Renewed packages 0.545 0.498 0 1 1 Number of games purchased 29.50 31.44 1 20 81 Number of tickets purchased 140.0 486.8 1 42 33,064 Average number of tickets purchased in one game 6.199 29.83 1 3.200 1,889 Jian-Da Zhu (National Taiwan University) April 21, 2018 1 / 9

Summary Statistics for Sellers on StubHub (II) Back Mean Std. Dev. Min Median Max StubHub Resale Information (N=10,541) Number of tickets sold 15.53 88.03 0 2 5,519 Number of games listed 7.946 14.37 1 2 81 Number of tickets listed 33.65 159.6 1 7 8,308 Number of listings in the whole season 10.94 37.19 1 2 1,398 Average number of listings in one game 1.174 0.881 1 1 27 Average number of tickets listed in one game 3.890 5.842 1 2.500 142.5 Jian-Da Zhu (National Taiwan University) April 21, 2018 2 / 9

Summary Statistics by Types of Sellers (I) Back Single Sellers Middle Sellers Brokers Observations 8,914 1,470 120 Average Resale Information on StubHub Number of tickets sold 3.717 50.62 463.2 (6.326) (52.77) (647.2) Number of games listed 3.051 32.47 71.19 (3.223) (18.03) (13.58) Number of tickets listed 9.580 109.8 888.2 (11.18) (91.91) (1,133) Number of listings in 3.272 38.49 243.1 the whole season (3.416) (22.04) (216.9) Note: Standard deviations in parentheses. Jian-Da Zhu (National Taiwan University) April 21, 2018 3 / 9

Summary Statistics by Types of Sellers (II) Back Single Sellers Middle Sellers Brokers Observations 8,914 1,470 120 Average Purchase Information in Primary Market Number of games purchased 23.33 63.03 76.81 (28.37) (25.13) (12.40) Number of tickets purchased 94.74 301.5 1,520 (404.2) (379.1) (2,123) Types of tickets Proportion of only buying 0.491 0.0619 0.0667 single-game tickets (0.500) (0.241) (0.250) Proportion of only buying 0.328 0.547 0.342 package tickets (0.470) (0.498) (0.476) Proportion of buying both 0.140 0.315 0.400 single-game and package tickets (0.347) (0.465) (0.492) Note: Standard deviations in parentheses. Jian-Da Zhu (National Taiwan University) April 21, 2018 4 / 9

Summary Statistics by Types of Sellers (III) Back Single Sellers Middle Sellers Brokers Observations 8,914 1,470 120 Average Purchase Information in Primary Market Purchase channel Proportion of only buying 0.266 0.374 0.167 from box office (0.442) (0.484) (0.374) Proportion of only buying 0.396 0.340 0.167 from internet (0.489) (0.474) (0.374) Proportion of buying from 0.104 0.286 0.667 both box office and internet (0.306) (0.452) (0.473) Note: Standard deviations in parentheses. Jian-Da Zhu (National Taiwan University) April 21, 2018 5 / 9

Listings by Types of Sellers (I) Back Single Sellers Middle Sellers Brokers Observations 29,134 56,354 28,926 Average Ticket Information Average listing price ($) 56.51 66.11 72.19 (34.69) (37.40) (43.04) Face value 39.49 44.26 39.44 (20.14) (22.05) (22.71) Original purchase price 32.51 36.22 33.23 in the primary market (15.52) (16.75) (17.73) Number of seats 2.984 2.938 4.004 (1.973) (1.861) (3.195) Front row dummy 0.0567 0.0949 0.151 (0.231) (0.293) (0.358) Row quality 0.471 0.561 0.604 (0.297) (0.304) (0.319) Distance from seat 261.5 239.4 261.9 to home plate (feet) (83.30) (87.73) (96.87) Jian-Da Zhu (National Taiwan University) April 21, 2018 6 / 9

Listings by Types of Sellers (II) Back Single Sellers Middle Sellers Brokers Observations 29,134 56,354 28,926 Average Ticket Information Starting date for listing (days prior to game) 100 plus 0.126 0.202 0.263 (0.332) (0.402) (0.440) 30 to 100 0.239 0.325 0.399 (0.427) (0.468) (0.490) 14 to 30 0.199 0.193 0.202 (0.399) (0.394) (0.401) 0 to 14 0.435 0.280 0.137 (0.496) (0.449) (0.344) Sold out or not 0.349 0.423 0.442 (0.477) (0.494) (0.497) Jian-Da Zhu (National Taiwan University) April 21, 2018 7 / 9

Listing Price Distribution Back Consider all the price decisions by sellers: Number of Price Changes 0 5000 1.0e+04 1.5e+04 2.0e+04 Number of Price Changes 0 5000 1.0e+04 1.5e+04 0 1 2 3 4 5 Listing Prices Relative to Face Value (N=189815) 0 1 2 3 4 5 Listing Prices Relative to Original Purchase Price (N=189815) Jian-Da Zhu (National Taiwan University) April 21, 2018 8 / 9

Listing Price Distribution Back Evidence of round numbers as reference points: 0 1000 2000 3000 4000 0 20 40 60 80 100 Listing Prices Jian-Da Zhu (National Taiwan University) April 21, 2018 9 / 9