University of Southern California Dissertations and Theses

Behavioral approaches to industrial organization

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Behavioral approaches to industrial organization

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Content Behavioral Approaches to Industrial Organization by Michele Fioretti A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY (Economics) May 2019 Copyright 2019 Michele Fioretti Acknowledgments I am grateful to several people for their help and support. Thank you, Geert Ridder, for the time and dedication you invested in my research. You taught me that thinking without rigor is equal to not thinking at all. I have learned immensely under your guid- ance. My sincere gratitude goes to Giorgio Coricelli, who at different times played the roles of a mentor, a brother, and a friend. You constantly challenged me to look beyond the surface of economic models and sustained me at the time of need. Thank you. Many thanks to my other dissertation committee members, Roger Moon, and Sha Yang. I would like to thank Giovanni Gardelli for many helpful discussions and for inadvertently push- ing me towards graduate studies. I greatly appreciate the efforts and friendship of my coauthors, Jorge Tamayo, Sean Marden, Hongming Wang, Kenneth Chuk, Simon Smith, Alexander Vostroknutov, Petra Thiemann, Olga Namen, Elena Manresa, and Alejandro Robinson-Cortés. I could not have made it this far without my friends, especially Ali Abboud, Andreas Aristidou, Vittorio Bassi, Francesco Benigni, Andrea Beretta, Ambuj Dewan, Raffaella Ghittoni, Roberto Grilli, Jinhui Liang, Veronica Mancini, Monica Mor- lacco, Andrea Nocera, Samuele Pigliapoco, Fabrizio Piasini, Silvia Romagnoli, Mahrad Sharifvaghefi, Lena Smith, Andrea Tafuro, and Elisa Toccaceli. A warm thank to the USC faculty and staff, primarily to Chad Kendall, Yilmaz Kocer, Michael Leung, and Young Miller. Finally, to my family for their unwavering support of my pursuit of higher educa- tion, and especially to Simone Fioretti for being so close despite being so far. i Abstract This dissertation explores different topics in Industrial Organization under the lenses of Behavioral Economics. The first chapter examines the rationale for investing in Cor- porate Social Responsibility (CSR). CSR includes all those programs that allow firms to better engage with their stakeholders. It has a vast array of applications, ranging from charitable donations to fair trade. To address this question, the chapter focuses on the optimal donation of an existing internet company which purchases celebrity belongings to subsequently auction them. In each auction, a fraction of the transaction price is do- nated to a charity. The data have been collected from the website of the company. After structurally estimating consumer preferences for charity and goods, as well as the cost of purchasing the items for the firm, the analysis shows that most of the gains from do- nating come from cost savings rather than an increase in consumers’ willingness to pay. This result suggests that consumers may not provide enough incentives for firms to be- have prosocially. Further, the model indicates that the firm’s donations largely exceeds the donation level that maximizes profits. This result suggests that firms may engage in CSR not just to maximize profits, but also to give back to society, a finding that is in line with the recent growth of benefit corporations and social entrepreneurship. The second chapter studies a dynamic environment where subjects are endowed with an asset and profit from selling it. An experiment is conducted to understand how sub- jects form reference points and how these reference points affect sale decisions. Partici- pants know beforehand whether they will observe future prices after they sell the asset or not. Without future prices participants are affected only by regret about previously observed high prices (past regret), but, when future prices are available, they also avoid regret about expected after-sale high prices (future regret). Moreover, as the relative sizes of past and future regret change, participants dynamically switch between them. This demonstrates how multiple reference points dynamically influence sales. The third chapter investigates a value-added policy reform in the US Medicare Ad- vantage, which tied subsidies to Medicare insurers with quality of service. The chapter focuses on the supply-side reaction of the insurers and finds that the introduction of the policy is associated with a greater (lower) premium in high (low) risk counties for higher quality plans. At the same time, the risk pool improved significantly for high-quality in- surance plans. The chapter shows evidence that enrollee’s baseline health status enters in the computation of the quality measure, which created incentives for high-quality plans to select away from riskier counties. The selection response calls into question the distri- butional implication of quality payments and, more broadly, highlights the difficulty of implementing value-added policies. iii Contents List of Tables ix List of Figures xi 1 Giving For Profit or Giving to Give: the Profitability of Corporate Social Re- sponsibility 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Auctions on Charitystars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Intensive and Extensive Margin of Donations . . . . . . . . . . . . . . 8 1.3 Charitable Motives, Auctions and Percentage Donated . . . . . . . . . . . . 13 1.3.1 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.2 Comparative Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.3.3 Consumer Utility and Revenues to the Producer . . . . . . . . . . . . 20 1.4 Nonparametric Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.5 Estimation Method and Results . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.5.1 Structural Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.5.2 Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.5.3 Tests to Estimation and Identification . . . . . . . . . . . . . . . . . . 29 1.6 Counterfactual Experiments on the Demand Side . . . . . . . . . . . . . . . 32 1.6.1 Net Revenues in Charity Auctions . . . . . . . . . . . . . . . . . . . . 34 1.7 The Supply Side and the Profit-Maximizing Donation . . . . . . . . . . . . . 35 1.8 Giving for Profit and Giving to Give . . . . . . . . . . . . . . . . . . . . . . . 40 1.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2 Dynamic Regret Avoidance 45 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.2 The Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.3 Evidence of Regret Avoidance . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.4 Regret-Averse Utiltiy Function . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.5 A Structural Model of Dynamic Regret Avoidance . . . . . . . . . . . . . . . 55 2.6 Estimation of the Structural Model . . . . . . . . . . . . . . . . . . . . . . . . 58 2.6.1 Estimation of the Conditional Choice Probabilities . . . . . . . . . . . 58 2.6.2 Estimation of the Parameters . . . . . . . . . . . . . . . . . . . . . . . 60 2.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 v 3 Quality, Quality Payments, and Risk Selection in Private Medicare 69 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.2 Medicare Advantage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.2.1 Plan Bidding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.2.2 Quality Rating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.2.3 Quality Bonus Payment . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.3 Data Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.4 Contract-Level Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.4.1 Risk Score . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.4.2 Market Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 3.4.3 Bid, Rebate, and Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . 82 3.5 Within-Contract Cross-County Evidence . . . . . . . . . . . . . . . . . . . . . 85 3.6 Why Does QBP Induce Risk Selection? . . . . . . . . . . . . . . . . . . . . . . 87 3.6.1 A Model of Risk, Quality, and Insurer Profit . . . . . . . . . . . . . . 88 3.6.2 Difference-In-Difference Evidence on the Risk-Quality Mechanism . 90 3.6.3 Characterizing the Risk-Outcome Correlation . . . . . . . . . . . . . 94 3.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 A Appendix to Chapter 1 99 A.1 Auction Webpage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 A.2 Data Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 A.2.1 Description of the Variables . . . . . . . . . . . . . . . . . . . . . . . . 100 A.2.2 Prices and Revenues . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 A.3 Omitted Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 A.3.1 Lemma 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 A.3.2 Proof of Lemma 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 A.3.3 Reserve Price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 A.3.4 Lemma 2 and Lemma 3 . . . . . . . . . . . . . . . . . . . . . . . . . . 106 A.3.5 Proof of Lemma 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 A.3.6 Proof of Lemma 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 A.3.7 Proof of Proposition 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 A.3.8 Proof of Proposition 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 A.3.9 Proof of Lemma 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 A.3.10 Proof of Proposition 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 A.3.11 Proof of Proposition 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 A.3.12 Proof of Corollary 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 A.4 Bargaining with Celebrities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 A.5 Additional Tables and Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 A.5.1 The Nationality of the Bidders . . . . . . . . . . . . . . . . . . . . . . 129 A.5.2 Asymmetric Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 A.5.3 Additional Tables from the Structural Model . . . . . . . . . . . . . . 132 A.5.4 Robustness Checks for the Structural Estimations . . . . . . . . . . . 134 A.5.5 Different Set of Covariates . . . . . . . . . . . . . . . . . . . . . . . . . 136 A.5.6 Out-of-Sample and Overidentification Test . . . . . . . . . . . . . . . 138 vi A.5.7 Estimation of q by Type of Provider of the Object . . . . . . . . . . . 138 A.5.8 Estimation of q with Different Heterogeneity . . . . . . . . . . . . . 139 A.5.9 Estimation of q on a Subset of Auctions . . . . . . . . . . . . . . . . 141 A.5.10 Estimation of q Using IVs for the Reserve Price and q . . . . . . . . 141 A.5.11 Additional Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 A.6 Counterfactual Scenario with Different Altruistic Parameters . . . . . . . . . 144 A.7 Revenue Comparison Across Auction Formats . . . . . . . . . . . . . . . . . 145 A.8 Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 B Appendix to Chapter 2 153 B.1 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 B.1.1 Market Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 B.1.2 Price Dynamics and Training . . . . . . . . . . . . . . . . . . . . . . . 155 B.1.3 Overall Design Details . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 B.1.4 Additional Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 B.1.5 Market Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 B.2 Behavior of Regret-Free Agent . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 B.3 Supplementary Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 B.4 Description of the Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 B.5 Additional Regressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 B.6 The Computation of Future Regret . . . . . . . . . . . . . . . . . . . . . . . . 166 B.6.1 Normal Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . 167 B.7 Discretization of the State Space and Transition Matrix . . . . . . . . . . . . 169 B.8 Full Derivation of the Dynamic Discrete Choice Model . . . . . . . . . . . . 170 B.9 Nonparametric Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 B.10 Additional Estimations of the Structural Model . . . . . . . . . . . . . . . . . 175 B.10.1 Different Regret Functions . . . . . . . . . . . . . . . . . . . . . . . . . 175 B.10.2 Loss Aversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 B.11 Instructions (English) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 B.11.1 Market Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 B.12 Instructions (Italian) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 B.12.1 Market Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 B.12.2 Holt and Laury Task (Italian) . . . . . . . . . . . . . . . . . . . . . . . 192 C Appendix to Chapter 3 195 C.1 Additional Figures and Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 D Bibliography 205 vii List of Tables 1.1 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Relation between log(Price) and percentage donated . . . . . . . . . . . . . 10 1.3 Linearity of the relation between log(Price) and percentage donated . . . . 11 1.4 Relation between the rate of daily bidders and percentage donated . . . . . 12 1.5 Overview of the most common models of giving . . . . . . . . . . . . . . . . 14 1.6 Estimation ofa andb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.7 Estimated revenues vs realized revenues . . . . . . . . . . . . . . . . . . . . 30 1.8 Evidence of bargaining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1.9 Cost estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.1 Random effects logit regression of the choice to keep the asset . . . . . . . . 53 2.2 The estimation of past and future regret . . . . . . . . . . . . . . . . . . . . . 62 2.3 The estimation of past and future regret in both conditions . . . . . . . . . . 64 3.1 Bonus and rebates by quality scores for the period 2009-2014 . . . . . . . . . 76 3.2 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.3 Effect of QBP on the risk score . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.4 Effect of QBP on risk score, by service area risk and competition . . . . . . . 81 3.5 Effect of QBP on market characteristics . . . . . . . . . . . . . . . . . . . . . . 83 3.6 Effect of QBP on bidding and rebate . . . . . . . . . . . . . . . . . . . . . . . 84 3.7 Effect of QBP on premium and drug deductible . . . . . . . . . . . . . . . . . 84 3.8 Effect of QBP on premium, within-contract cross-county variation . . . . . . 86 3.9 Effect of QBP on drug deductible, within-contract cross-county variation . . 88 3.10 Weight increase of outcome measures in quality rating . . . . . . . . . . . . 91 3.11 Risk score and outcome rating . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.12 Quality, risk and outcome rating . . . . . . . . . . . . . . . . . . . . . . . . . 93 3.13 Risk-outcome correlation across periods . . . . . . . . . . . . . . . . . . . . . 96 3.14 Risk-quality correlation across periods . . . . . . . . . . . . . . . . . . . . . . 97 A.1 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 A.2 Relation between log(Price) and percentage donated (small dataset) . . . . 122 A.3 Linearity of the relation between log(Price) and percentage donated (small dataset) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 A.4 Relation between the rate of daily bidders and percentage donated . . . . . 125 A.5 OLS and IV regressions for the transaction price. . . . . . . . . . . . . . . . 126 ix A.6 OLS and IV regressions for the number of daily bidders. . . . . . . . . . . . 127 A.7 Evidence of bargaining: IV regressions . . . . . . . . . . . . . . . . . . . . . . 128 A.8 Nationalities of the bidders . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 A.9 Regression of log(Price) on bidder nationality . . . . . . . . . . . . . . . . . 130 A.10 Regression of log(Price) on recurrent winners . . . . . . . . . . . . . . . . . 131 A.11 First step of the structural estimation . . . . . . . . . . . . . . . . . . . . . . 132 A.12 Logit regression of q on covariates. . . . . . . . . . . . . . . . . . . . . . . . . 133 A.13 Structural estimation when q2f10%, 85%g and pricee 100 ande 400 . . . 134 A.14 Structural estimation when q2f10%, 78%g and pricee 100 ande 1000 . . 135 A.15 Structural estimation when q2f10%, 78%g and pricee 100 ande 400 . . . 135 A.16 Structural estimation when q2f10%, 85%g and pricee 100 ande 1000 . . 136 A.17 Structural estimation when q2f10%, 85%g and pricee 100 ande 400 . . . 137 A.18 Distance between q A and q B – Monte Carlo simulations . . . . . . . . . . . . 149 A.19 Monte Carlo simulation 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 A.20 Monte Carlo simulation 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 B.1 Overview of variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 B.2 Random effects logit regression of the choice to keep the asset with risk preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 B.3 Early sales in the two conditions . . . . . . . . . . . . . . . . . . . . . . . . . 164 B.4 The correlation between sale price and future regret for sales happening at different times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 B.5 Estimation of Model 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 B.6 Estimation of Model 2 and Model 3 . . . . . . . . . . . . . . . . . . . . . . . 176 B.7 Estimation of (2.5.3) with the regret terms as in (2.6.4) . . . . . . . . . . . . . 177 B.8 Estimation of (2.5.3) with the regret terms as as in Model 4 and 5 . . . . . . 177 B.9 Estimation of regret and loss-aversion parameter in the risk-neutral case . . 178 B.10 Estimation of models 1 and 2 with loss aversion parameter . . . . . . . . . . 179 C.1 Part C measures in the quality rating, 2013 . . . . . . . . . . . . . . . . . . . 203 C.2 Part D measures in the quality rating, 2013 . . . . . . . . . . . . . . . . . . . 204 x List of Figures 1.1 Number of auctions by percentage donated . . . . . . . . . . . . . . . . . . . 7 1.2 Comparative statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.3 Comparing the bids and private values under different models of giving . . 19 1.4 The revenue maximizing donation (q ) . . . . . . . . . . . . . . . . . . . . . 21 1.5 Model fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 1.6 The extent of overbidding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 1.7 Expected prices in charity vs non-charity auctions . . . . . . . . . . . . . . . 33 1.8 Expected net revenues decrease in the donation . . . . . . . . . . . . . . . . 34 1.9 The revenue maximizing q is zero . . . . . . . . . . . . . . . . . . . . . . . . 35 1.10 Optimal donation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.1 Screenshots of two markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.2 The optimal selling price threshold for different risk preferences . . . . . . 49 2.3 Proportion of missed sales when selling is optimal . . . . . . . . . . . . . . 49 2.4 Past and Future regret avoidance . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.5 The effect of the past peak on the probability of selling the asset in the No Info condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.6 The effect of the past peak and the expected future peak in the Info condi- tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.7 Substitution between Past and Future regret . . . . . . . . . . . . . . . . . . 65 3.1 Effect on risk score, event study . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.2 Weight increase of outcome measures in quality rating . . . . . . . . . . . . 92 A.1 A screenshot of the webpage for a listing at the time of data collection . . . 99 A.2 Density of key variables by percentage donated . . . . . . . . . . . . . . . . 103 A.3 Illustration of the proofs of Lemma 3 and Lemma 2 . . . . . . . . . . . . . . 112 A.4 Illustration of the results in Propositions 1 and 2 . . . . . . . . . . . . . . . . 117 A.5 Optimal fraction donated (q) - accounting for more covariates . . . . . . . . 121 A.6 Number of bidders and number of auctions over time . . . . . . . . . . . . 122 A.7 Plot of the coefficient for q from a quantile regression . . . . . . . . . . . . . 123 A.8 Plot of the coefficient for q from a quantile regression (small dataset) . . . . 124 A.9 Robustness checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 A.10 Optimal fraction donated for jerseys provided by footballers and charities . 139 A.11 Optimal donation and profits for different levels of heterogeneity . . . . . . 140 xi A.12 Optimal fraction donated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 A.13 Optimal donation with instruments for reserve price and q . . . . . . . . . . 142 A.14 Density of the homogenized transaction prices by returning winners . . . . 143 A.15 Counterfactual scenario with different charity parameters . . . . . . . . . . . 144 A.16 Expected gross revenues per auction . . . . . . . . . . . . . . . . . . . . . . . 145 A.17 Expected revenues across different auction formats . . . . . . . . . . . . . . 146 A.18 Variance of the revenues across different auction formats . . . . . . . . . . . 147 B.1 The screen presented to the participants . . . . . . . . . . . . . . . . . . . . . 154 B.2 The screen in the two conditions . . . . . . . . . . . . . . . . . . . . . . . . . 155 B.3 Prices in 48 markets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 B.4 The effect of a new price peak on the sale probability . . . . . . . . . . . . . 161 B.5 The propensity to sell the asset in the two conditions over time . . . . . . . 161 B.6 pdf, sum of 3 uniform RVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 B.7 pdf, sum of 13 uniform RVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 B.8 CDF, sum of 3 uniform RVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 B.9 CDF, sum of 13 uniform RVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 C.1 Effect on risk score, by service area risk, event study . . . . . . . . . . . . . . 196 C.2 Effect on risk score, by market competition, event study . . . . . . . . . . . . 197 C.3 Effect on premium and drug deductible, event study . . . . . . . . . . . . . 198 C.4 Effect on premium, within-contract cross county variation, event study . . . 199 C.5 Effect on drug deductible, within-contract cross county variation, event study200 C.6 Risk score and outcome rating, event study . . . . . . . . . . . . . . . . . . . 201 C.7 Quality, risk and outcome rating, event study . . . . . . . . . . . . . . . . . . 202 xii Chapter 1 Giving For Profit or Giving to Give: the Profitability of Corporate Social Responsibility 1.1 Introduction Rising inequality and environmental hazard have placed firms under increasing scrutiny to take responsible actions towards their stakeholders and the safeguard of the environ- ment. These actions fall within the so-called corporate social responsibility, or CSR. 1 In the past, CSR mainly consisted of charitable donations. Today, it has become more collab- orative, as businesses connect with non-profit organizations, and integrate their money- making activities with their social goals. Although social impact is a commendable pur- suit, it is unclear whether it leads to greater profits, and thus, the motivation to engage in these programs could fall outside profitability. Many inquiries into CSR have focused on its benefits by comparing the performances of socially responsible and non-socially responsible firms. The most notable studies in this literature found that the presence of CSR investments is associated with high prof- its (Cheng et al., 2014; Eccles et al., 2014). Yet, it might be the case that the size of CSR spending matters. While some CSR investment can be fruitful (e.g., energy saving), exces- sive investments can curtail profits (e.g., superfluous pollution abatement technologies). Large investments in CSR could also indicate a company’s genuine desire to contribute to society at the expense of profit maximization. Thus, failing to account for the size of CSR investments may incorrectly capture the relationship between CSR and profits as well as lead to a misinterpretation of firms’ objectives. This paper fills this gap by investigating the profit-maximizing amount of CSR in a rare case of a firm whose CSR programs are easily quantifiable and by providing evidence that "giving to give," in addition to "giving for profit," might be a driving force behind firm’s behavior. I study the strategic decisions of Charitystars, an international for-profit firm that offers 1 For example, by 2017, virtually all the 250 largest corporations worldwide yearly report some mea- sure of CSR in their accounts. https://home.kpmg.com/content/dam/kpmg/campaigns/csr/pdf/CSR_ Reporting_2017.pdf. 1 online auctions of celebrities’ belongings for charity. 2 Charitystars’ CSR policy consists in donating a fraction of the final price paid for the auctioned items to charities. I exploit variation in this fraction to estimate the impact of CSR on consumer demand and on the cost of procuring the items. To estimate demand, I build a structural auction model where bidders’ utility is a function of their private values for the item and their prosocial prefer- ences. In counterfactual analysis, I find that consumers’ willingness to pay is somewhat unresponsive even to large changes in the percentage donated, showing how consumers may not provide sufficient monetary incentives for firms to behave prosocially. 3 Providers of the items (mostly charities and celebrities) can require a fee for each item. To estimate Charitystars’ procurement costs, I exploit the fact that the firm sets the reserve price to break even. Thus, variation in the fraction donated provides information about how procurement costs vary with the donations. I find that procurement costs decrease as the fraction donated increases. Donating affects Charitystars’ profits mostly through cost-savings rather than larger revenues, suggesting that synergies between firm’s goals and CSR are crucial for CSR’s success. 4 By comparing Charitystars’ marginal revenues and marginal costs, my analysis shows that the firm’s median fraction donated (85%) is significantly higher than the profit-maximizing donation (30%), on average. Adopting the profit-maximizing strategy would raise profits by a factor of four. This could indicate that Charitystars’ objective is not only to maximize profits but also to consider its social impact. Thus, the case of Charitystars provides novel evidence that even for-profit firms can forego a portion of their profits to contribute to social welfare. Many for-profits firms may have social impact as one of their objectives as well, which is reflected in the fact that several US states have recently passed dedicated corporate leg- islation reforms ("Benefit Corporation") to support for-profit social impact firms (Finfrock and Talley, 2014; Battilana and Lee, 2014). 5 Nevertheless, evidence that social responsibil- ity is conducive to higher economic or financial return is sparse. Although Eichholtz et al. (2010) find a large price premium (16%) for energy-efficient buildings, a meta-analysis of over 160 papers found only a small positive correlation between CSR and profits, and suggested that causation may well flow from profits to CSR (Margolis et al., 2007). Sev- eral other issues beyond the endogeneity between CSR and profitability plague causal inference in this domain (Bénabou and Tirole, 2010). One of these issues is the large het- 2 With offices in London, Milan and Los Angeles, Charitystars is a for-profit start-up with almost $4m in equity. Since its foundation in 2013, the company generated over $10 million for charities and non- profit organizations. For more information, see www.charitystars.com and on www.crunchbase.com/ organization/charitystars. 3 Likewise, there is evidence for limited or even harmful effects of CSR on employees’ productivity (List and Momeni, 2017; Cassar and Meier, 2017, 2018) and on social welfare (Kotchen, 2006). Competition across firms (Bagnoli and Watts, 2003; Shleifer, 2004) and social norms (Bartling et al., 2014) can curtail CSR’s positive impacts. 4 This conclusion can be extended to other firms as well. For example, in a treatment of a recent experi- mental study (Gosnell et al., 2016), Virgin Atlantic would donate to charities if pilots in the treatment group met their fuel-saving targets. The treatment resulted in important cost savings for Virgin Atlantic. 5 Benefit Corporation firms (or B Corp) differ from other limited liability companies because they have a legally binding fiduciary responsibility to take into account also the interests of the workers, the com- munity and the environment. Patagonia, Kickstarter and many subsidiaries of Danone are examples of B Corp. For additional information on B Corp legislation see www.economist.com/business/2012/01/07/ firms-with-benefits. 2 erogeneity of CSR activities, which complicates comparison across firms (Chatterji et al., 2009). Moreover, this variation may interact in surprising ways, sometimes reducing the perceived social impact of the firm, which could actually lower consumers’ willingness to pay. This happens, for example, by disseminating misleading information of envi- ronmental friendliness (Lyon and Maxwell, 2011) and by giving to charities to influence connected congressmen (Bertrand et al., 2018). 6 This paper contributes to this literature in several ways. Charitystars’ data provide various advantages to assess the returns of giving. For most firms, the benefits from donating are not limited to a single charity-linked good, but rather they are spread across the entire product line of the firm. 7 To judge the optimality of giving, a researcher would require exogenous variation in the amount donated for each good. This problem does not emerge for Charitystars, as each charity auction can be thought of as a single market. Another critical feature of these data is that the reserve price is set so that the firm breaks even. Thus, the cost of procuring the items can be inferred. Finally, on Charitystars the percentage donated is clearly shown on each listing, and the credibility of donations is supported by certificates issued by Charitystars and the recipient charity. Therefore, these data are particularly suited to address the profitability of giving. 8 The other contribution of the paper is related to the endogeneity between CSR and profitability, which I solve by focusing on the profit-optimal level of CSR. I tackle this question both theoretically and empirically. Thereotically, I build a charity auction model to investigate the intensive margin of giving. This theoretical model extends the literature on charity auctions to explicitly account for the structure of the donation in the data (Go- eree et al., 2005; Engers and McManus, 2007). In charity auctions, bidders are compelled by two forces. First, they have a taste for winning the auction and donating (Andreoni, 1989). As a result, winning the auction carries additional utility, incentivizing bidders to raise their bids. Second, losing the auction does not leave bidders with zero payoff. Instead, they are gratified by participating in the social contest and helping to drive up the price. The last effect is an externality from the winner to the other bidders, who ex- tract surplus from the former. I use the model to investigate how changes in the fraction donated affect bidding and thus, revenues to the auctioneer and consumer surplus. Empirically, estimation of the model requires the nonparametric identification of the distribution of values and two charitable parameters that determine the weights of the two forces. To gain intuition, imagine two auctions for the same item that have a differ- ent fraction of the final price donated, and think of the bids placed in each auction by the same bidder. The difference between the donations implied by the two bids reflects 6 Some attributes of a product are not observable and consumers may use CSR to update their beliefs about the product (e.g., Kitzmueller and Shimshack, 2012; Elfenbein et al., 2012). In this case, researchers would mistakenly attribute the additional willingness to pay to CSR. 7 For example, Apple has donated $160 m since 2006 to a charity fighting HIV in Africa through its Red branded products. To understand Apple’s giving, a researcher should identify its effect not only on the Red branded products, but also on all the other ones. 8 This paper is also related to a line of work on the existence of a premium for products linked to char- ities. Several papers are dedicated to the analysis of eBay’s Giving Works data. (e.g., Elfenbein and Mc- Manus, 2010; Elfenbein et al., 2012). The question I address diverges from these analyses as it concerns profits rather than revenues. For this reason, the data is collected from Charitystars instead of eBay, as Charitystars’ listings have only one seller (Charitystars itself). 3 the benefit from winning and donating. Comparing marginal donations across auctions identifies the externality parameter. Identification relies on the restriction that the distri- bution of values for the item does not depend on how much is donated. This exclusion restriction means that the consumption value of the item does not change as the auc- tioneer changes the fraction donated. The exclusion restriction is formally tested and not rejected by the data. This identification strategy is reminiscent of that for risk-aversion in first-price auctions (Guerre et al., 2009; Lu and Perrigne, 2008). The resulting fit of the model is satisfactory with estimated expected revenues within 10% of the realized ones. Prices on Charitystars command a small premium as bidders’ willingness to pay increases based on how much the firm donates. However, donations have a large direct cost in terms of foregone revenues. A counterfactual scenario where the firm does not donate estimates the loss in net revenues to be as large ase 260 per listing, or about 70% of the average transaction price. Thus, the firm would be better-off if it ran regular non-charity auctions. Given the large revenues lost due to the donations, why is Charitystars for-profit? Why is the company still offering only charity auctions? It might be the case that do- nations affect procurement costs. Charitystars operates like a platform, procuring items from providers, such as celebrities, charities or private individuals and selling them to consumers. The cost of procuring the jerseys are estimated using a price shifter, the varia- tion in the portion of the reserve price kept by the firm. The estimated costs are decreasing in the percentage donated, indicating that providers prefer more generous auctions. As an example, celebrities may be eager to exchange their belongings for inexpensive pub- licity. Intersecting the estimated marginal net revenues from the demand side with the marginal cost curve yields an interior solution for the optimal donation. Thus, to under- stand the full extent of giving on Charitystars’ decisions, both sides of the market must be investigated because donations impact both revenues and costs. CSR programs in other industries function similarly (e.g., Cheng et al., 2014). For instance, socially responsible mutual funds invest in less profitable firms with social impact (Barber et al., 2018; Hong and Kacperczyk, 2009), but they also face lower costs of financing as socially responsible investors forego higher returns (Riedl and Smeets, 2017). 9 The estimation shows that the optimal donation percentage is 30%, yet the median percentage donated in the data is 85% (mean 70%). Charitystars would increase its prof- its per jersey frome 25 toe 100 on average if it were to adopt the optimal policy. 10 A possible explanation for this suboptimal outcome is that Charitystars may overestimate the elasticity of prices to the amount donated. Such a bias could encourage the firm to donate a larger share of revenues. Although such a behavioral bias cannot be ruled out, it is unlikely that the firm holds biased estimates of how prices react to the sharing rule given the number of external investors and the large number of auctions hosted by the 9 Other examples include green technologies, whose diffusion does not only depend on the willingness to pay of consumers for environmentally friendly products, but also on their cost of production (Kok et al., 2011). 10 In this paper the term “profits” refers to a positive cash flow balance. Though many successful firms had negative financial profits in their early years (for example eBay and Amazon), their success critically depended on large cash flows in order to pay for their daily operations without recurring to external fund- ing. This further shows the importance of the choice of the fraction donated for Charitystars’ shareholders. 4 firm (over a thousand per year). 11 An alternative explanation is that the firm may donate more to increase participation in future auctions. However, this margin does not convinc- ingly explain the data. Another possibility is that high donation fractions may discourage other firms from entering the market. Nevertheless, Charitystars is a de facto monopolist in the market I study (official soccer jerseys signed by professional players during official matches). 12 Considering all these possible explanations, the fact that Charitystars’ median dona- tion is 55% higher than the profit-maximizing level could indicate that the firm also cares about the size of its contributions. Charitystars’ money-making ability and ethical con- cerns are clearly not separable. Quoting Hart et al. (2017), if consumers and investors value social donations, why “would they not want the companies they invest in to do the same?” Socially responsible shareholders may see this company as an opportunity to sustain their donations over time, while even receiving dividends. Under this logic, Charitystars cares not only about its profitability but also its total giving. Although there is some evidence that firms do not maximize profits, an empirical as- sessment is challenging because costs are often not observed but only inferred by invert- ing the equilibrium mapping resulting from this very assumption. For example, Ellison et al. (2016) and DellaVigna and Gentzkow (2017) show suboptimal pricing strategies for computer component firms and US retail stores, and attribute them to managerial costs. 13 Suboptimal choices are also observed in the NFL, as certain plays called by coaches do not maximize the probability of victory (Romer, 2006), and teams often waste their top picks at the annual draft (Massey and Thaler, 2013). These papers speculate that influence from shareholders and fans could sway decisions away from optimality. Yet, empirical research providing similar evidence with business data is lacking. 14 Socially responsible firms provide a fruitful context to analyze profit maximization because these firms aim to persuade concerned consumers by engaging in costly activities that benefit a third party (the charity). The results in this paper strongly suggest that socially responsible firms have social motives as they derive utility from contributing to the greater good more than is profit-maximizing. This demonstrates that firms’ decision can be influenced by concerns that are external to profits, a finding that could apply to firms in other industries as well. The remainder of the paper is organized as follows. Charitystars’ auctions are in- troduced in Section 3.3. Sections 2.5, 1.4 and 1.5 study the charity auction model first 11 Bloom et al. (2015) show that private equity owned firms (like Charitystars) are well managed and have better management practices than comparable firms – especially with respect to data collection and data analysis. 12 Entering this market requires a very large investment in establishing relations with celebrities and their agents. Charitystars has dealt with more than 1,000 celebrities and 450 charities since 2013, and is currently gaining traction in US and Asia. More information at https://techcrunch.com/2016/08/08/charitystars/. 13 Principal-agent problems between shareholders and management are another reason why firms may fail to maximize profits (e.g., Hart, 1995; Liljeblom et al., 2011). Managerial quality is also related to higher profits (e.g., Bloom and Van Reenen, 2007; Goldfarb and Xiao, 2011; Hortaçsu et al., 2017; Adhvaryu et al., 2018). 14 In a related paper, Kolstad (2013) shows that surgeons respond more to intrinsic incentives (quality report cards) than to monetary ones. Despite analyzing the decision of people rather than firms, the author also finds that objectives can extend beyond profitability. See also Besley and Ghatak (2007, 2017). 5 theoretically, and then empirically, by discussing identification and estimation. Coun- terfactuals on revenues are in Section 1.6. Section 1.7 analyzes how donating influences procurement costs and finds the optimal fraction donated. The results are discussed in Section 2.7. Section 2.8 concludes. 1.2 Auctions on Charitystars Charitystars is a for-profit internet platform helping charities do fundraising, by offer- ing charity auctions of celebrities’ memorabilia. Charitystars auctions a very broad spec- trum of items, from VIP tickets to the Monaco Gran Prix to famous photographs and arts collectibles. 15 Soccer is one of the most popular item categories with over 4,000 auctions held in 3 years. Moreover, Charitystars is a de facto monopolist in the market for actually worn soccer jerseys. The firm is a monopolist Given that the firm’s only operation con- sists of providing charity auctions, Charitystars’ auctions for soccer jerseys represents a good environment in which to investigate the profitability of a firm’s social responsibility (e.g., Gneezy et al., 2010). All Charitystars’ auctions employ an open, ascending-bid format analogous to eBay. Auctions involve a single item. Bidders can submit a cutoff price (this tool is called proxy bidding on eBay) instead of a bid. Once a cutoff is set, Charitystars.com will issue a bid equal to the smallest of the standing price (or the reserve price if there is no bid yet) and the highest submitted cutoff price, plus the minimum increment. Thus, the winner pays the second highest valuation, plus a minimum increment. 16 The charity receiving the donation, as well as the fraction of the transaction price being donated are common knowledge before each auction. The donations are guaranteed by issuing certificates. Charitystars procures the memorabilia either from footballers, teams and charities or from third party sellers. The fraction donated is chosen by the firm and the provider of the item, who may also require a payment for procuring the item. A unique feature of this data is that the firm sets the reserve price such that the portion of the reserve price that is kept by the firm equates costs, on average. 17 Thus, procurement costs can be easily inferred from the reserve price. A particularity of Charitystars’ auctions is the secrecy of the reserve price: at any point in time bidders only know whether the reserve price is met or not. Although the reserve price is never disclosed, not even after the end of an auction, it can be found in the source code (HTML) behind each listing. 18 In addition, on Charitystars after each unsold auction there is an additional step where the highest bidder is given the option 15 Charitystars is owned by its funding members, who also are managers in the company, and by insti- tutional investors such as private equity firms and angel investors. 16 The auction countdown is automatically extended by 4 minutes anytime a bid is placed in the last 4 minutes of the auction. This impedes sniping (i.e. the practice of bidding in the very last seconds of an auction), which is common in eBay and is associated with lower transaction prices and less users (Backus et al., 2017). 17 This information was revealed by advisors of the firm. 18 Secret reserve prices are not uncommon in online auctions. The empirical auction literature have treated these occurrences by simply adding an additional bidder who keeps the object in case no one bids above the reserve price (e.g., Bajari and Hortaçsu, 2003). 6 to purchase the object by paying the reserve price (7% of the cases). To avoid possible concerns the following analysis is restricted to listings counting at least two bidders that concluded in a direct sale. I use publicly available data from Charitystars.com. The dataset was collected directly from the website and contains auctions of authentic soccer jerseys sold between July 1, 2015 and June 12, 2017. 19 These dates were chosen as they mark the beginning and the end (after the Champions League final) of two consecutive football seasons. The dataset includes 1,583 auctions. There is wide variation in the percentage that is donated, though for most auctions the fundraising corresponds to either 10%, 78% or 85% of the final price. Throughout the paper, I let q denote the percentage donated. Figure 1.1 shows this variation for two subsets of the data. Charitystars keeps the whole portion that is not donated to a charity as net revenues. For example, if a percentage q is donated, the firm keeps 1 q of the price paid. Charitys- tars’ standard minimum fee is 15%. If the provider of the item requires a large payment, the percentage donated is smaller. Overall, the jerseys are quite similar across different fraction donated, and q does not depend on the quality of the player. 20 All auctions where the fraction donated is greater than 85% are disregarded as they coincide with special events (black bars in Figure 1.1). Figure 1.1: Number of auctions by percentage donated (a) Transaction price2(100, 1000) 1 171 1 15 1 2 53 195 110 559 3 24 2 50 1 0 100 200 300 400 500 600 0 10 15 20 30 70 72 78 80 85 86 88 90 93 100 Percentage donated % (q) Number of auctions (b) Transaction price2(100, 400) 114 7 1 37 144 54 356 2 23 2 21 1 0 100 200 300 400 500 600 10 20 70 72 78 80 85 86 88 90 93 100 Percentage donated % (q) Number of auctions Notes: Number of auctions available in the dataset by percentage donated. The plots include only auctions that ended in a transaction and for which the reserve price was greater than 0, the number of bidders was at least 2 and the minimum increment is not greater thane 25. Panel (a) shows the number of auctions avail- able for each percentage donated when the dataset is restricted to auctions whose price is ine(100, 1, 000). There are 1,188 auctions in total. Panel (b) restricts the dataset to more homogeneous auctions (762 auc- tions). Charitystars generally withholds at least 15% of the final price and therefore all auctions whose percentage donated is above 85% are excluded from the analysis as these are special one-off charitable events (black columns). 19 All other soccer related auctions not involving jerseys (such as shin guards, footballs and shorts) are excluded from the database. 20 To check whether q is influenced by the quality of the player, I downloaded data on player quality by the FIFA videogame on the previous 5 years and checked the correlation between q and the overall player quality in the videogame. The correlation is very low and varies over the years between -0.07 and 0. 7 All items are posted online on the firm’s website and advertised on the social media of the firm in a similar fashion. The listing webpage shows pictures of the item on the left of the screen, and bidders find a short description on the bottom of the page, together with the information on the recipient charity. A picture of a typical webpage at the time of the data collection is reported in Appendix A.1 (Figure A.1). The website layout did not change during the time period under analysis. For each auction, all bids placed, the date and time of the bid, the bidder nationality and the charity receiving the money are observed. Unfortunately, auctions start dates are not available online, but the average length of Charitystars’ auctions is usually between 1 and 2 weeks. Length is therefore proxied using the distance in days between the first bid posted and the closing day. 21 Table 1.1 gives an overview of the main characteristics of the auctions for listings with transaction prices larger thane 100 and smaller thane 1,000, with at least 2 different bidders and whose minimum increment is withine 25. The final price is greater than the reserve price in more than 95% of the listings. On average (me- dian) the winning bid is 2.9 (2) times larger than the reserve price. This database consists of 1,108 auctions and will be used throughout. The analysis in the next section is also replicated on a smaller dataset, with more ho- mogeneous auctions. This dataset includes only jerseys that were sold at prices below e 400. This upper limit (e 400) was chosen because in the summer of 2017 Charitystars decided to set ae 50 minimum raise anytime the standing price reachese 400 (i.e. the minimum increment changes during the auction depending on the standing price). This is a high value which may suggest that the company believes that items reaching such a high price may differ under some characteristics. 22 1.2.1 Intensive and Extensive Margin of Donations Effect on transaction prices. The hypothesis that bids and donations are positively re- lated implies that higher bids are associated with greater portions of the final price do- nated (q). To test this hypothesis, I run a series of regressions focusing only on the winning bid (i.e. the transaction price). In fact, none of the other bids provide useful information in an environment where bidders can update their bids multiple times. Table 1.2 performs the following OLS regression log(price t )= g 0 + x t g+g q q t +# t , (1.2.1) where t indexes the auctions. The vector of covariates, x, includes all variables other than the fraction donated, q. The columns of the table vary based on the definition of x, which is given in the bottom panel of the table. The variables are defined in detail in 21 A larger list of auction variables which will be used in most regression tables is available in Table A.1 in Appendix A.2. Figure A.2a in Appendix A.2 plots the pdf of the transaction price for the three most frequent auction formats (q2f10%, 78%, 85%g). 22 Note also that such a high minimum increment undermines the identification of the structural model in Section 1.4 (e.g., Haile and Tamer, 2003; Chesher and Rosen, 2017). For this reason, auctions with large minimum increments are removed from the dataset. Table 1.1 shows that the mean of the Minimum incre- ment variable is close toe 1, which is also the value at the 90th quantile. 8 Table 1.1: Summary statistics Variable Mean St.Dev. Q(25%) Q(50%) Q(75%) Q(95%) Auction characteristics Fraction donated (q) 0.70 0.27 0.78 0.85 0.85 0.85 Transaction price ine 364.25 187.50 222.00 315.00 452.50 760.00 Reserve price ine 179.03 132.02 100.00 145.00 210.00 500 Minimum increment ine 1.71 3.15 1.00 1.00 1.00 5.68 Number of bidders 7.83 3.27 5.00 7.00 10.00 14 Sold at reserve price (b) 0.04 0.20 0.00 0.00 0.00 0.00 Length (days) 8.08 3.07 7.00 7.00 7.00 14.00 Extended time (b) 0.43 0.50 0.00 0.00 1.00 1.00 Charity’s activity Helping disables individuals (b) 0.35 0.48 0.00 0.00 1.00 1.00 Infrustructures in dev. count. (b) 0.09 0.29 0.00 0.00 0.00 1.00 Healthcare (b) 0.23 0.42 0.00 0.00 0.00 1.00 Humanit. scopes in dev. count. (b) 0.14 0.34 0.00 0.00 0.00 1.00 Children’s wellbeing (b) 0.84 0.36 1.00 1.00 1.00 1.00 Neurodegenerative disorders (b) 0.06 0.23 0.00 0.00 0.00 1.00 Charity belongs to a soccer team (b) 0.10 0.29 0.00 0.00 0.00 1.00 Improving access to sport (d) 0.63 0.48 0.00 1.00 1.00 1.00 Notes: Overview of the main covariates used in all specifications in the reduced form analysis and in the struc- tural model. A (b) singals that the variable is binary (0/1). Only auctions with price betweene 100 ande 1000. Prices are in Euro. If the listing was in GBP the final price was converted in euro using the exchange rate of the last day of auction. Appendix A.2. The main finding is that g q is above 20% and significant (at 1% level) in most columns, suggesting that higher bids are correlated with greater donations. Two additional observations are of interest. First, the transaction price and the num- ber of bidders are positively correlated. This provides a simple test in favor of a model where bidders draw private values. If instead valuations were common, bidders would optimally shade their bids in order to escape from the winner’s curse. Because the size of the curse grows with the number of bidders, lower bids are expected when an additional bidders joins an auction (Bajari and Hortaçsu, 2003). A private value model for Chari- tystars’ auctions is also consistent with bidders having different tastes for teams, players and causes. Second, the inclusion of the reserve price in Table 1.2 is responsible for a jump in the Adjusted R 2 from 32% to 46%. According to Roberts (2013), this increase suggests that the reserve price carries information that is unobservable to the researcher but observable to the bidders and auctioneer. For example, bidders’ willingness to pay may be higher if a player receives an important prize while one of his jerseys is up for auction with a high q. If no regressor in the data reflect such a prize, the estimated coefficient for q may be biased. Moreover, omission of the reserve price signals an omitted variable bias, as the percentage donated is not significant in Column (I). Given that the auctioneer anticipates that bidders are affected by the size of q, one would expect the correlation between the reserve price and the fraction donated to be 9 Table 1.2: Relation between log(Price) and percentage donated (I) (II) (III) (IV) (V) log(Bidders) 0.291 0.298 0.300 0.285 0.280 (0.032) (0.029) (0.029) (0.029) (0.029) Fraction Donated (q) 0.037 0.234 0.235 0.230 0.258 (0.057) (0.048) (0.049) (0.052) (0.055) log(Reserve Price) 0.353 0.356 0.341 0.342 (0.023) (0.023) (0.025) (0.026) Main Variables Y Y Y Y Y Add. Charity Dummies Y Y Y League/Match Dummies Y Y Time Dummies Y Adjusted R-squared 0.323 0.459 0.459 0.472 0.492 BIC 1,404 1,162 1,191 1,269 1,333 N 1,108 1,108 1,108 1,108 1,108 * – p< 0.1; ** – p< 0.05; *** – p< 0.01 Notes: OLS regression of log of the transaction price on covariates. Only auctions with price betweene 100 ande 1000. Control variables are defined in Appendix A.2. Robust standard errors in parenthesis. high and positive if the reserve price were not correlated with unobservables (see Ap- pendix A.3.3). However this correlation is close to zero in the data. 23 This evidence supports correlation between reserve prices and unobserved heterogeneity, and it will be exploited in the structural model. 24 Given that q is not exogenous, I additionally control for possible endogeneity using instrumental variables. For example, endogeneity arises if bidders bid based on some variables that are not controlled for in Table 1.2, and the bargaining outcome depends on these variables. I propose the average q and the average reserve price across the auctions ending within 5 days of each auction as an instrument (Hausman, 1996). The instruments are valid if, after controlling for covariates, the concurrent auctions are not correlated. Notice that the covariates include the number of listings of jerseys from the same team in the previous 3 weeks and for the same player in the previous 2 weeks. The results in Table A.5 in Appendix A.5 report the OLS and the IV regressions for a regression equation 23 Appendix A.3.3 shows that if a bidder who is indifferent between bidding a positive value and not bidding at all bids exactly the reserve price, then the optimal reserve price increases with q. However, the data does not find support for the optimal selection of the reserve price given that the linear correlation is -0.2646 in the large sample and -0.2103 in the small sample. As a robustness check, the estimated cost in Section 1.7 divided by(1 q) (i.e., \ reserve price = cost /(1 q)) are a decreasing function of q. 24 The correlation between the reserve price and the transaction price is 0.5175, implying that the reserve price can explain a large portion of the variance of the price. Table A.2 in Appendix A.5 estimates (1.2.1) on the restricted sample, including only items sold for less thane 400. Although the table reports a smaller coefficient for q (g q ' 0.13), prices and donations are still positively correlated. 10 similar to (1.2.1). The IV regressions have a valid first stage and the Hausman test for the endogeneity of the instrumented regressors cannot reject the null that the regressors are exogenous. In addition, the estimates confirm that prices are increasing in the fraction donated. Table 1.3: Linearity of the relation between log(Price) and percentage donated (I) (II) (III) (IV) OLS Q(0.25) Q(0.50) Q(0.75) log(Reserve Price) 0.353 0.521 0.370 0.298 (0.023) (0.037) (0.030) (0.032) log(Bidders) 0.298 0.254 0.302 0.354 (0.029) (0.034) (0.037) (0.051) Fraction Donated (q) 0.234 0.255 0.274 0.308 (0.048) (0.058) (0.070) (0.085) Main Variables Y Y Y Y Adjusted R-squared 0.459 0.319 0.303 0.288 N 1,108 1,108 1,108 1,108 * – p< 0.1; ** – p< 0.05; *** – p< 0.01 Notes: OLS Regression and quantile regressions of the logarithm of the trans- action price on covariates. Only auctions with price betweene 400 ande 1000. Boostrapped standard errors with 400 repetitions. The null hypothesis that q is the same in column (II), (III) and (IV) is not rejected at common levels. Control variables are defined in Appendix A.2. Robust standard errors in parenthesis. Overall, this suggests that bidders react to giving incentives. Related papers found qualitatively comparable results. For example, Elfenbein and McManus (2010) estimated that prices in eBay charitable listings are on average 6% larger than comparable non- charity ones, while Leszczyc and Rothkopf (2010), using a controlled experiment, deter- mined that a 40% donation leads to a 40% price increase. In their investigation on char- itable giving as a reputational device, Elfenbein et al. (2012) find similar returns to those estimated in Table 1.2 for eBay Benefit sellers with poor feedback history (e.g., 25% higher prices when q= 1), but much smaller returns for virtuous sellers. The charity auctions literature has also investigated the shape of the relation between q and prices (e.g., Elfenbein and McManus, 2010). Quantile regressions are a commonly used approach to test linearity. Table 1.3 reports three quantile regressions in the same spirit of regression (1.2.1). 25 All the coefficients of q are similar across the four columns, and in particular, we cannot reject the null hypothesis that the coefficients computed at the first, second and third quartiles are equal (F test p-value 0.82). The same result can be observed graphically in Figure A.7 in Appendix A.5 which plots these coefficients, and can also be replicated in the smaller sample (Table A.3 and Figure A.8). This evidence 25 Another way to test linearity of the relation between log(Price) and q is to add a squared term for q to the regressions in Table 1.2. The null hypothesis that the coefficient of q 2 is 0 cannot be rejected for all columns. 11 suggests a linear relation between the q and the logarithm of the price. Effect on the number of bidders. Moving from the intensive to the extensive margin of giving, a total of 2,247 bidders compete on average in 5.34 different auctions. This mean increases to 8.51 different auctions when excluding bidders who bid in only one auction. Most bidders take part in different auction formats (varying over the amount donated): excluding bidders who placed fewer than 2 bids, more than 80% of the bidders bid at least on two auctions with different amount donated. This is a very large number given that q = 85% for half of the auctions in the data (559 out of 1108). Also, note that the participation decision of Charitystars users is not correlated with the percentage donated. 26 Therefore bidders seem to participate in all auctions and do not select on the basis of the amount donated. This is confirmed in Table 1.4 using Poisson regressions of the form (Table A.4 in Appendix A.5 performs the same regression on auctions with final price in[100, 400]) log(E[bidders t jx t , q t ])= g 0 + x t g+g q q t + log(length t )+# t , where the variable Length is the length of the auction (in days) and is used as the exposure variable (the results are to be interpreted in terms of daily bidders). The first two columns refer to the larger dataset, whereas the second two are for the smaller dataset. The even columns in the table suggest that the weak relation between q and the number of bidders holds also when conditioning on other covariates. This result is also confirmed if q and the reserve price are instrumented as previously shown (see Table A.6 in Appendix A.5). Table 1.4: Relation between the rate of daily bidders and percentage donated (I) (II) (III) Fraction Donated (q) 0.032 0.050 –0.000 (0.055) (0.057) (0.059) Main Variables Y Y Y Charity Dummies Y Y League/Match Dummies Y Pseudo R-squared 0.125 0.127 0.139 N 1,108 1,108 1,108 * – p< 0.1; ** – p< 0.05; *** – p< 0.01 Notes: Poisson regression of the number of bidders on co- variates. The length of the auction is used as exposure vari- able and is not included among the covariates. Control vari- ables are defined in Appendix A.2. Robust standard errors in parenthesis. 26 The Spearman rank-order correlation test reveals that the correlation between q and the number of bidders is only 0.0855 in the large sample and 0.0650 in the small sample. In addition, the correlations between q and the other covariates are small(0.25, 0.25). 12 A final consideration can be made concerning symmetric bidding. Given the data availability, there are two main sources of asymmetry that can be tested in a reduced form fashion. First, as most jerseys belong to Italian teams (63% of the auctions) and most charities are Italian (90% of the auctions), one may ask whether bidders from different na- tionalities employ different strategies. Table A.9 in Appendix A.5.2 reports the coefficients from three regressions similar to (1.2.1) where the dummies for each winner’s nationality are added to the vector of covariates, x. Thus, prices do not differ by nationality after controlling for covariates and q. Asymmetry may also come from recurrent winners as these bidders may be more interested in collecting soccer jerseys than in contributing to a public good. Recurrent winners are not unusual: in fact, the median number of auctions won by each winner in the sample is three. Table A.10 in Appendix A.5.2 investigates whether recurrent winners are willing to pay more on average. This is captured by the dummy variable Recurrent Winner that takes value 1 if the winner won more than 3 auctions. The correlation in Col- umn (I) between Recurrent Winner and the transaction price is not present in the other columns. In fact, it vanishes when adding another covariate accounting for the level of competition in the auction (the total number of bids placed). Moreover, the same corre- lation is also not significant in the smaller dataset, where observations are more homoge- neous. 1.3 Charitable Motives, Auctions and Percentage Donated This section builds and investigates the property of the charity auction model that will be estimated in Section 1.5.1. In the model, bidders’ willingness to pay depends both on their valuation of the auctioned item, as well as their prosocial motives (e.g., Bénabou and Tirole, 2006). Understanding what motivates bidders to pay higher prices when Charitystars donates more is a necessary step towards assessing the profitability of donations. In an ascending auction, like those on Charitystars.com, the final price is equal to the second-highest bid, denoted by b II , and in equilibrium, a bidder will stay in the auction as long as the standing price is smaller than his or her willingness to pay. Charity auctions differ from standard auctions in that a bidder’s utility depends also on the funds raised, as charitable motives provide bidders with additional satisfaction in proportion of the funds raised. The additional utility from being the donor is modelled by the termb q b II , whereb transforms the pecuniary contribution, q b II , in utils and indicates the satisfaction from winning and being the donor. Though losing bidders do not consume the item, and so receive no consumption utility, they receive a positive satisfaction from the winner’s do- nation. The reward to the losing bidders is modeled by the term a q b II . As bidders could value their own donations differently from those of the others,a and b can be dif- ferent from each other. Therefore, the realized utility to a bidder who values the private 13 good v can be summarized by u(v;a,b, q)= ( v b II +b q b II , if i wins a q b II , otherwise. (1.3.1) This model extends the seminal works on price-proportional auctions and on charity auctions by Engelbrecht-Wiggans (1994) and Engers and McManus (2007) to fit the main characteristics of Charitystars.com (i.e., a fraction q of the final price is donated). As charitable motives cannot explain the full amount of one’s bid, the literature assumes that a,b2[0, 1). Table 1.5 summarizes the most common theories of altruism, which are briefly re- vealed here. The null hypothesis, rejected by the structural estimation in Section 1.5, is that bidders are not interested in giving. This corresponds to a = b = 0. In this case, the classic textbook equilibrium applies, and bidding is in no way shaped by altruistic behaviors. Table 1.5: Overview of the most common models of giving Model Overview Noncharity (a= b= 0) Bidders do not pay a premium in charity auctions. Pure altruism (a= b> 0) Bidders obtain extra utility from donating, and are willing to pay a premium. They do not distinguish across sources of donation. Warm glow (b> a> 0) Bidders derive greater satisfaction from their own donation (impure altruism). See-and-be- seen (b> a= 0) Bidders derive utility only from their own donation. Limiting case of warm glow (a= 0). Volunteer shill (a> b> 0) Bidders obtain greater utility from giving by others. Notes: a and b are defined in equation (1.3.1). The source of this table is Leszczyc and Rothkopf (2010). Although a and b can be different from each other, this does not have to be the case: purely altruistic bidders (a = b > 0) receives the same utility in either situation. They are moved by their compassionate concern for others, and they receive a psychological benefit that is independent from the identity of the donor (Ottoni-Wilhelm et al., 2017). 27 Although donating is an altruistic behavior, it may be the result of selfish motives due to the pride inherent in prosocial behaviors (Fisher et al., 2008). This is examined in the 27 A theoretical treatment of these auctions first appeared in Engelbrecht-Wiggans (1994), who analyzed auctions with price-proportional benefits to bidders (all bidders receive an equal share of the final price). 14 impure altruism literature, championed by Andreoni (1989) who proposed a model of warm glow where utility flows from the mere act of being the giver (b > a > 0). An extreme case of impure altruism is the see-and-be-seen model, whereb> 0 buta= 0 where bidders have no intrinsic motivation. This model captures the role of social status or prestige in donation (e.g., Harbaugh, 1998). Situations where the names of the donors are available to the public belong to this category. 28 A model with a > b > 0 was found to have good fit in a field experiment (Leszczyc and Rothkopf, 2010) where researchers manipulated the auction to understand the extent of overbidding in charity auctions. This model, called volunteer shill, is characterized by bidders with larger intrinsic valuation, as the largea indicates that bidders are more inter- ested in the fundraise (pure altruism) than in the identity of the donor (impure altruism). Therefore, despite its simplicity and reduced form style, the utility function is flexible enough to accommodate different models of giving. The way charitable motives affect outcomes to the auctioneer will become evident in the next sections which investigates bids and surplus. 1.3.1 Equilibrium Turning to the bidders’ optimal strategy in a charity auction, the following assump- tions are made. Assumption 1. Optimality: 1. The values are private and independent; 2. All n> 1 bidders draw their values for the private item from a continuous distribution F() with probability density f() on a compact support[v, v]; 3. The hazard rate of F() is increasing. The first condition requires that bidders have independent and private valuations for the soccer jerseys. The estimation will relax this assumption by including unobserved het- erogeneity, effectively making private values affiliated. Private values are also supported by the discussion of the results in Table 1.2, which excluded common values. Points two and three of Assumption 1 are regularity conditions common to most auction models. In particular, condition three is key in order to establish that the equilibrium bidding function is a global optimum. This condition will also play a central role in proving iden- tification of the primitives in Section 1.4. 28 Outside of the fundraising literature, a model where b is the sole positive parameter is similar to a setting where bidders receive subsidies from the auctioneer for each dollar spent. Set-asides and subsi- dies are commonly used in procurement auctions for natural resources. For example, in their analyses of Californian timber auctions, Athey et al. (2013) found that policies such as subsidies and entry restrictions are welfare improving over set-asides. In this case, the government would promote a b > 0 by instituting subsidies. 15 Due to the strategic equivalence between English and second-price charity auctions, the theoretical treatment will be based on the second-price auction (Engers and McManus, 2007). 29 The expected utility to bidder i with valuation v in a charity auction with n bidders is E[u(v;a,b, q)]=E v(1 qb)b II , i wins | {z } i wins and pays b II + qa b II Pr i’s bid is 2 nd | {z } i loses and bids b i = b II + qaE b II , i’s bid is< 2 nd | {z } i loses and price p= b II > b i . (1.3.2) The expected utility is taken over three mutually exclusive events. In the first line of (1.3.2) i places the highest bid and wins. This provides the bidder with private consumption v and altruistic satisfaction by b q b II . In the second line, i loses the auction and either sets the price by bidding the second-highest bid, or bids a price below the second-highest bid. In either case i gains the expected value of a q b II . The next proposition provides the bidding function in a symmetric Bayesian Nash equilibrium. Lemma 1. The equilibrium bid for a bidder with private valuation v and charitable parametersa andb in a symmetric second-price charity auction where the auctioneer donates q is: b (v;a,b, q)= 8 > > < > > : 1 1+q(ab) ( v+ R v v 1F(x) 1F(v) 1qb qa +1 dx ) , ifa> 0^ q> 0 v 1qb , ifa= 0_ q= 0. (1.3.3) Proof. See Appendix A.3.2. This bid function is also optimal in an ascending auction. In this case, b (v;a,b, q) de- scribes the highest value at which winning is worthwhile. In equilibrium a bidder stays in the auction as long as the standing price, p, is below her willingness to pay, b(v;a,b, q), and the winner pays the second-highest bid, b II . When bidders are not charitable, a = b = 0, or when the proceeds of the auction are not used to finance any public good, q = 0, bidders bid their valuation b (v; 0, 0, q) = b (v;a,b, 0)= v. The limit of the function in the top row of (1.3.3) converges to that in the bottom row asa goes to 0. Finally, Proposition 8 in Engers and McManus (2007) demon- strates that revenues in charity auctions are bounded (if the auctioneer cannot shut down the auction), meaning that under no combination of a and b bidders make unlimited transfers to the auctioneer. Their proof holds also in this scenario where q< 1. 29 Engers and McManus (2007) demonstrate that the optimal strategy in a second-price charity auction is also optimal in the analogous button auction version. They also note that the observation of bidders’ exiting times is not required for the result to hold. Therefore the equivalence can be extended to more general ascending auctions, like online auctions. In such an auction, the FOC are required to hold only for the second highest bidder at the price at which he or she drops out. 16 1.3.2 Comparative Statics This section assesses how bids react to changes in bidders’ altruism (a change in taste), and in the auctioneers’ generosity (a change in q). Bids are unambiguosly increasing in the one’s own donation, b. The greater the glow from the act of donating, the more bidders are willing to pay for the item. Figure 1.2a illustrates how bidders change their bids after a marginal increase ina. The x-axis displays all bidders’ private values, while the deriva- tive of the bid at each value is presented on the y-axis. Bidders can be separated in two groups based on whether they revise their bids up or down. Low-value bidders increase their bids, and high-value bidders decrease their bids. The following proposition formal- izes the findings from the figure, proving conditions on the existence and uniqueness of the private value that separates the bidders who increase their bids from the others. Figure 1.2: Comparative statics (a) Derivative of the bid with respect toa 0 line −100 −75 −50 −25 0 25 50 0 25 50 75 100 Private values Derivative of bid w.r.t. α α = 19 %, β = 46 %, σ = 20 α = 19 %, β = 10 %, σ = 20 α = 19 %, β = 10 %, σ = 80 (b) Derivative of the bid with respect to q 0 line −30 −10 10 30 50 0 25 50 75 100 Private values Derivative of bid w.r.t. q α = 19 %, β = 46 %, σ = 20 α = 19 %, β = 10 %, σ = 20 α = 19 %, β = 10 %, σ = 80 Notes: a and b are defined in equation (1.3.1). Panel (a). The effect of a marginal increase in a. Panel (b). The effect of a marginal increase in q. In both graphs q= 85% and F() is a truncated normal in[0, 100] with mean 50 and standard deviations (see the legend). Lemma 2. If a > 0, there exists a value v such that all bidders with private values in (v , v] decrease their bids after a marginal change ina. Proof. See Appendix A.3.5. 30 An interpretation of Lemma 2 views bids as strategic complements or substitutes (Bén- abou and Tirole, 2006). Due to the monotonic bidding strategies, bidders with high values are possible winners. A marginal change ina has two effects. It intensifies the degree of 30 If the bid of the lowest value bidder is greater than v/(1 qb), the private value separating the two groups is unique. Otherwise either the derivative is always negative, or there are two cutoffs such that bidders at the two extremes (below the first cutoff and above the second cutoff) decrease their bids, and the bidders between the two cutoffs increase their bids. In this case, the lowest value bidders do not increase their bids because they know they cannot affect the transaction price. 17 substitutability between the bid of a high-value bidder and that of the others: this makes a possible winner willing to trade a larger payoff from losing with some probability of winning. Thus, possible winners decrease their bids. A similar change ina also changes how low-value bidders perceive their bids vis-à-vis those of the other bidders. Given that such a bidder will likely lose the auction, he or she can affect the payoff only by placing the second-highest bid. Thus, in order to extract surplus from the possible winners, the bidder raises his or her bid; this higher bid is complementary to that of a greater win- ning bidder. A comparison of the dotted and dashed lines in Figure 1.2a corroborates this idea: more low value bidders increase their bids when they believe they are pivotal, which happens when the variance of F(v) is larger (dotted line). An immediate extension of Lemma 2 is that the expected prices are generally decreas- ing ina. In fact, given a large enough number of bidders and keepingb and F(v) constant, an increase ina is associated with more bidders shedding their bids. A sufficient number of bidders or a sufficiently skewed distribution of values is required so that low-value bidders – those who increase their bids after a marginal change ina – are price takers. To provide an insight into how bids are affected bya andb, Figure 1.3 plots the distribution of bids and private values. In Panel (a), b > a and all bidders overbid relative to their private values as they enjoy greater returns from winning and donating. Of course in this case the auctioneer earns gross revenues beyond the non-charity auction. However, charity auctions cannot always guarantee revenues beyond non-charity ones. Panel (b) shows that the auctioneer would improve his or her records by announcing a non-charity auction instead when a is much larger than b. 31 The figure shows that high value bid- ders shade their bids more than the others. When this happens the effect on revenues is uncertain. This discussion partially extends to the relation between b and q. Excluding the trivial case a = 0 which is equivalent to an increase in b, the sign of the derivative of the bid with respect to q depends on the model of giving. Bids rise after a marginal change in q for all bidders under warm glow (b a). This is depicted by the solid line in Figure 1.2b. In the same figure, the bid derivatives for the voluntary shill model (b < a) are strikingly similar to those in Figure 1.2a, where bidders either post higher or lower bids (dotted and dashed lines). 32 Lemma 3. Ifb a, bids are increasing in q for all bidders. Ifa> b, there exists a private value ˜ v such that bidders with private values in( ˜ v, v] decrease their bids after a marginal increase in q. Proof. See Appendix A.3.6. 31 See Figure A.17 in Appendix A.5.11 for a revenue comparison across different charity and non-charity auctions using the primitives in Figure 1.3b. See Engers and McManus (2007) for the bidding functions for first-price and all-pay auctions. 32 Similarly to Lemma 2, in the case a > b there is only one bidder separating those who increase their bids from those who decrease their bids if the lowest value bidder bid more than her private value (e.g., b(v) v). Otherwise, there can be either no cutoff or two cutoffs. In the last case, only the bidders with the lowest and the highest valuation will decrease their bids. However, while the high-value bidders decrease their bids because a marginal increase in q is associated with a marginally greater payoff from losing, the low value bidders decrease their bids because they cannot affect the transaction price. 18 Figure 1.3: Comparing the bids and private values under different models of giving (a) Warm glow (b> a> 0) 0.0 0.2 0.4 0.6 0.8 1.0 0 50 100 150 Private Value / Bid CDF Private Value Bid α = 0.1 , β = 0.5 (b) Volunteer shill (a> b> 0) 0.0 0.2 0.4 0.6 0.8 1.0 0 25 50 75 100 Private Value / Bid CDF Private Value Bid α = 0.5 , β = 0.1 Notes: a and b are defined in equation (1.3.1). The plots show the distributions of private values (solid line) and bids (dotted line). 50 simulations, 12 bidders. While bidders bid more than their private values in Panel (a), most of the bidders bid below their private values in Panel (b). The primitives are q = 85%, F()N(50, 25) on[0, 100]. When the glow from winning and donating is greater than the externality from some- body else’s contribution, all bidders increase their bids as the auctioneer becomes more generous. In this case, bids are strategic complements (Bénabou and Tirole, 2006), lead- ing to higher prices in expectation. Under voluntary shill instead, bidders already have large intrinsic motives, as represented by the high a. In these circumstances, bidders find harder to signal themselves as genuinely prosocial by winning the auction before the society (as everyone shares high intrinsic altruism). This phenomenon drains bids by high-value bidders (Gneezy and Rustichini, 2000); their behavior is related to the classic free-riding in public good games as they exchange a higher probability to win the auction with the consumption of the public good funded by others. This discussion should be read in light of the lack of agreement in the empirical lit- erature assessing the effect of donations on prices and revenues in charity auctions (e.g., Carpenter et al., 2008; Schram and Onderstal, 2009; Isaac et al., 2010; Elfenbein and Mc- Manus, 2010; Leszczyc and Rothkopf, 2010; Elfenbein et al., 2012). For example, Leszczyc and Rothkopf (2010) attributed the widespread overbidding over the non-charity auction that emerged in a series of field experiments to large externalities. They concluded that thea> b case is conducive to higher revenues. However, this conclusion is only partially true. Higher revenues are only possible if the number of bidders is low, as in this case low value bidders are more likely to set the price – a suspicion confirmed by their data as the average number of bidders is only between 2 and 4 per auction. In contrast, an- other field experiment found charitable prices to sink below non-charity ones at a school charity auction (Carpenter et al., 2008). Once again this can be explained in terms of high externalities as bidders who are likely to win shed their bid in this case, dumping the price. 19 1.3.3 Consumer Utility and Revenues to the Producer How do bidders fare in charity auctions? Despite the possibly higher prices in charity auctions, the consumer surplus is at least as large as that in a similar standard auction. Proposition 1. Whena = 0, the expected consumer surplus in a charity auction is equal to the consumer surplus in a non-charity auction. It is greater whena> 0. Proof. See Appendix A.3.7. The proof is constructive and reflects the fact that the boost in utility from losing the auction (through the public good) is greater than the (possible) higher price paid when winning it. In fact, in thea = 0 case bidders extract the same utility as in the non-charity case – the donation acts as a discount, and bidders bid more until they fully exhaust their discount. When a > 0, the positive externality flowing from the winner to the losers increases bidders’ expected utility further, making bidders in charity auctions better-off. Finally, does supplying charity-linked goods boosts a firm’s net revenues? If a = 0, the higher bid paid does not result in higher net revenues to the auctioneer. The discount passes-through to the bidders, while net revenues to the auctioneer decrease by a factor q(1b)/(1 qb) compared to standard non-charity auctions. Firms should not hold charity in this case. Cross-bidders externalities (a > 0) can improve net revenues to a charitable auction- eer. This happens when there is enough uncertainty in the auction so that low value bid- ders are price-makers, as displayed in Figure 1.2a. However, the externality cannot be too large in order to prevent high-value bidders from excessively shedding their bids. This highlights the peculiar way charity-linked goods affect markets creating complex strate- gic interactions across agents. In a charity auction, prices balance not only the intensive margin (an agent’s surplus) with the extensive margin (the probability of winning), but also an additional margin represented by free-riding. When the latter is kept at bay firms may find donations profitable. 33 Proposition 2. Defineh(p e ) = ¶p e ¶q q p e as the elasticity of the expected price, p e , to the donation, q. When a = 0, the auctioneer should not donate. When a > 0, the revenue optimal donation solvesh(p e )= q 1q . Proof. See Appendix A.3.8. Intuitively, net revenues first increase as the auctioneer increases q, reach a maximum, before decreasing to zero, as when q = 1 the auctioneer donates all he or she makes. Net revenues have an inverted-U shape which is maximized at q . This holds not only in the auction setting, but also generally for any revenue-dependent CSR activities. The ratio q/(1 q) is the ratio of what is given versus what is kept, and it is convex in q. The 33 The discussion of the producer surplus assumes that costs do not depend on the fraction donated. This assumption is relaxed in Section 1.7, as decreasing costs in q are important to explain why Charitystars donates. 20 firm will increase its donation rate until the marginal benefit from higher bids ((1 q)h) equates the marginal cost from donating an extra euro (q). This is evident from Figure 1.4, where net revenues (right axis) are optimized at the q that setsh = q/(1 q). Figure 1.4: The revenue maximizing donation (q ) 0 0.1 0.2 0.3 0.4 0 10 20 30 40 0.00 0.25 0.50 0.75 1.00 Percentage donated (q) Elasticity, q/(1−q) Net Revenues Elasticity q / (1−q) Net Revenues Notes: a and b are defined in equation (1.3.1). The figure reports the optimal percentage donated (q ) obtained at the intersection of the elasticity of the expected winning bid with respect to q and the curve q/(1 q). The elasticities (solid and dotted curves) are reported on the left vertical axis. The right axis shows the net revenues (dashed curve) as(1 q) R v b(v)dF (2) (n) (v). The distribution of values F(v) is uniform on[0, 100],a= 0.7,b= 0.9 and there are two bidders. Figure A.4 in Appendix A.3 illustrates the results in these propositions. The analysis so far indicates that if two second-price auctions are observed and if they differ only for the proportion donated, simply comparing changes in the final price across auctions could lead the researcher to believe that bids are decreasing in the amount donated. In reality, it could be that high-value bidders are shedding their bids in the auction with the greater q (see Figure 1.2b and Proposition 3). This could lead observers to mistakenly conclude that bidders do not react to charitable incentives, or that unobservables play a major role in the estimation. In conclusion, charitable incentives may affect bids and profits in different ways. These comments highlight the importance of properly understanding bidders’ preferences in markets of charity-linked goods in order to design mechanisms to simultaneously in- crease profits while raising funds. 21 1.4 Nonparametric Identification This section establishes the identification of the primitives, a,b and F(v), given the observed bids, b(v;a,b, q), and the percentage donated, q. Let G(b(v;a,b, q); q) be the observed distribution of bids, and l G (b(v;a,b, q); q) be its inverse hazard rate. 34 Fol- lowing the seminal work of Guerre et al. (2000), the bids can be inverted, which implies that the distribution of bids is equal to the distribution of private values. 35 Therefore, G(b(v;a,b, q); q) = F(v). Identification of the primitives relies on the FOCs from the bidding problem. The unknown variables in the FOCs (equation A.3.1 in Appendix A.3.2) include not only the primitives of the model, but also each bidder’s realized pri- vate value, v. If all bids are observed, then the distribution and density of equilibrium bids, G(b(v;a,b, q); q) and g(b(v;a,b, q); q) are observed too. It follows that the number of unknowns in the FOCs can be reduced by using the identity between G() and F(), v= x(b;a,b, q)= (1b q) b(v;a,b, q)+a q b(v;a,b, q)l G (b(v;a,b, q); q) . (1.4.1) The LHS features only a bidder’s private value, v, while the RHS is a function of the bids, q, the inverse hazard rate, l G and the parameters a and b. The term in parentheses on the RHS can be seen as a sort of “virtual valuations” from classic auction theory and, in this setting, it has a similar intuition as marginal donation. 36 To see this, assume that the auctioneer makes a take it or leave it offer to a single bidder at a price p. The bidder’s demand is the probability that that the offer is accepted, or D := 1 G(p), with inverse demand p(D) = G 1 (1 D). The amount donated is q p(D) D = q G 1 (1 D). Taking derivative w.r.t. D gives q MR(p) = pl G (p), where MR(p) = ¶p(D) D/¶D is the marginal revenue to the auctioneer. Therefore the term in parentheses can be seen as a marginal donation and tells how the amount donated changes when the bid increases marginally. The following Lemma shows that without additional restrictions, the parameters and the distribution can be combined in different ways yielding the same bids distributions. In particular, the proof demonstrates that two different sets of parameters (e.g.,fa,bg and f˜ a, ˜ bg) are observationally equivalent. Lemma 4. a,b and F(v) are not identified without additional restrictions. Proof. See Appendix A.3.9. A similar nonidentification result holds in the estimation of risk aversion in first-price auctions, in which case the econometrician relies on quantile restrictions and on cross- auction variation on the number of bidders to identify the risk parameters (e.g., Guerre 34 The inverse hazard rate of the bid distribution isl G (b(v;a,b, q); q)= 1G(b(v;a,b,q);q) g(b(v;a,b,q);q) , while the inverse hazard rate of the distribution of private values isl F (v)= 1F(v) f(v) . 35 Under Assumption 1 the following relations hold: G(B) = Pr(b(v) < B) Pr(v < b 1 (B)) = F(b 1 (B)). An analogous relation holds for the pdf g(b(v))b 0 (v)= f(v). 36 A bidder’s virtual valuation is defined by v 1F(v) f(v) . 22 et al., 2009; Campo et al., 2011). These restrictions are of no use in English charity auctions as, for example, the number of bidders do not show up in the FOCs. Let’s turn to (1.4.1) to figure out the most opportune restriction leading to identifica- tion of the primitives. x(b,a,b, q) is strictly increasing and differentiable in b(v;a,b, q). 37 Thus, there are no two different combinations of a and b yielding the same vector of pseudo-private values v. These two observations are key because they ensure that every distribution F(.jˆ a, ˆ b, q) (one for each ˆ a, ˆ b combination, given q) is unique by Theorem 1 in Guerre et al. (2000). 38 Therefore, using variation in the percentage donated across auctions, the primitives are identified by distribution equality F(.jˆ a, ˆ b, q A )= F(.jˆ a, ˆ b, q B ), with q A 6= q B . This strategy fails if, for example, higher valued bidders self-select in auctions with higher (or lower) fractions donated. An additional assumption is required: Assumption 2. Identification: F() does not depend on q. The identification restriction states that bidders’ consumption utility does not depend on the amount donated. It holds if bidders do no select into different auctions (e.g., auc- tions with different amount donated) based on their valuations. The model shown in Section 2.5 automatically satisfies this assumption, because it defines F(v) as the uncon- ditional distribution of private values. In the model, q modulates the net utility to a bidder through the origination of a public good: in no way does it affect v. Moreover, Section 1.2.1 finds that Charitystars’ bidders do in fact bid in multiple auctions without regard for q. Also, the same section shows no correlation between the number of bidders and q. These stylized facts support the idea that q does not affect the values bidders hold for the private good (the auctioned item), but only the composite valuation for the impure good. Upon estimation of the model, the validity of these conditions can be tested (see Section 1.5.3). The following Proposition provides identification of the primitives if all bids (and thus all bidders’ willingness to pay) are observed, as is common in a second-price sealed-bid auction. Proposition 3. If all bids are observed, under Assumptions 1 and 2, the parametersa andb and the distribution of values F(v) are identified by variation in q across auctions. Proof. See Appendix A.3.10. 37 The term in parentheses of (1.4.1) is increasing in b if f 0 (v) > f(v) 2 1F(v) + g(b;)b 00 (v;), where I used ¶ 2 G(b(v;);) ¶v 2 = ¶ 2 F(v) ¶v 2 . The claim follows from Assumption 1 as f 0 (v) > f(v) 2 1F(v) and b 00 < 0. The relation hold in the data. 38 Theorem 1 in Guerre et al. (2000) is based on a set of regularity conditions: values v are private and in- dependent, the bidding function b(v;) is increasing andx() is strictly increasing in[b, b] and differentiable. These properties follow from Assumption 1. 23 The intuition behind this proposition is rather simple. Assume that the econometrician observes two auctions, A and B, conforming to the assumption of Proposition 3. In a symmetric equilibrium, two bidders with equal valuations (e.g., v A = v B ) taking part in two auctions that differ only with regard to the percentage donated (i.e., q A 6= q B ) will place different bids (i.e., b(v;, q A )6= b(v;, q B )) according to the bid function (1.3.3). Because of the monotonicity of bids in v, the ranking of their bids on their respective bid distribution will be the same (i.e., G A (b(v;, q A )) = G B (b(v;, q B ))). This is because, for bidders whose private value is at thet-quantile of the distribution of private values, their bids will also be at the t-quantile of the bid distribution. Thus, the FOCs (1.4.1) can be simplified further by taking difference across the FOCs for the two auctions along the quantiles of the bid distributions. The parameters a and b are identified under the full-rank condition of the resulting matrix, whereas F(v) is identified by plugging the identified parameters in the RHS of (1.4.1). However, Proposition 3 does not cover Charitystars’ auctions for two reasons. First, to win an English auction bidders bid the second-highest bid plus an increment. Although minimum increments on Charitystars are negligible and thus constitute no harm for iden- tification (Haile and Tamer, 2003; Chesher and Rosen, 2017), this statement means that the winner’s bid does not solve the FOC in (1.4.1). Second, the equivalence between English auctions and button auctions may not hold for most bidders. Thus, the willingness to pay for all bidders but the second-highest one is not identified. As a result, most bids do not reflect the private valuations, and one cannot use the monotonicity of the bidding fuction to determine the distribution of private values from the observed distribution of bids. 39 The next proposition amends Proposition 3 and ensures identification of the primitives under these circumstances. Proposition 4. If only the winning bid is observed,a,b and F(v) are nonparametrically identified by first deriving the distribution of bids that would have been observed in parallel second-price auctions, and then by applying Proposition 3. Proof. See Appendix A.3.11. The precise meaning of “parallel second-price auction“ is a second price auction with the same primitives as those in the English auction. The distribution of values in a par- allel auction can be derived by the sole observation of the winning bids. In fact, this bid identifies the price at which the second-highest bidder opts-out of the auction. Therefore, the FOCs (1.4.1) must hold at this price for this bidder. 40 In addition, the existence of a one-to-one mapping between the distribution of bids and the distribution of the second- highest bids (following the theory of order statistics) ensures that the former is identified. This would be equal to the distribution of bids observed in a parallel second-price auction. 41 39 Formally, from the observed bids one cannot guarantee that b 1 (v) = v, and thus that F(V) = Pr(v V)= Pr(b(v) b(V))= G(b(V)). 40 Note that the minimum increment in Charitystars ise 1 for most auctions. 41 Denote with a subscript w the winning bid and its distribution. The distribution of bids from a “parallel second-price auction”, G(B) = Pr(b(v) B), is found by a reparametrization in n of the distribution of the winning bid G w (b) which is obtained from the data. Because of the equilibrium condition, the latter is 24 At this point, all the ingredients to identify the primitives following Proposition 3 are present. Proposition 3 can also be extended to include a finite number of auction types (e.g., q2fq 1 , q 2 , ..., q K g), as shown in the following corollary. The proof uses the panel structure of the data to create a projection matrix that cancels out the left-hand side of (1.4.1) as in Proposition 3. Corollary 1. a,b and F(v) are also nonparametrically identified when the dataset includes more than 2 types of auctions. Proof. See Appendix A.3.12. This approach is related to that in Guerre et al. (2009) who identify risk-averse utility functions nonparametrically using variation in the number of bidders across auctions. Lu and Perrigne (2008) instead used a combination of first-price and English auction to iden- tify risk-aversion. Because risk-aversion does not affect equilibrium bidding in ascending auctions, they first recovered the distribution of values from the open auctions, and then plugged its quantiles in the FOC for the bidders in first-price auctions. This is equiva- lent to solving (1.4.1) knowing the private value on the left-hand side. Shifters similar to q have also been used to study correlated private values in English auctions (Aradillas- López et al., 2013), interdependent costs in procurement auctions (Somaini, 2015) and selective entry (Gentry and Li, 2014). Symmetric bidding is a crucial assumption. Theorem 6 in Athey and Haile (2002) shows that the primitives of an asymmetric auction model are identified from the win- ning bids if the identity of the bidders is known. Lamy (2012) discussed asymmetry with anonymous bidders (as in Charitystars’ case), his result does not extend to ascending auctions. Still, the assumption of symmetric bidding in charity auctions may not be so restrictive. First, there does not seem to be strong evidence suggesting asymmetric be- havior in Charitystars (see Section 3.3). Second, Elfenbein and McManus (2010) provide empirical evidence of symmetric bidding for the highest bidders in a study of eBay char- ity auctions. 42 1.5 Estimation Method and Results The estimation closely follows the identification procedure in Proposition 4. However, additional difficulties come from the need to deal with auction heterogeneity. Controlling for observable and unobservable heterogeneity is important. The estimation procedure includes three steps and is described in the next section. Sections 1.5.2 reports the results and 1.5.3 performs out-of sample validation using additional data and simulations. equal to the distribution of the second highest bid among n bidders G (2) (n) (b). This gives G w (b) = G (2) (n) (b) = n G(b) n1 +(n 1) G(b) n which has a unique solution in(0, 1). 42 Furthermore, the notion of symmetry adopted in this paper does not imply that bidders cannot bid asymmetrically across auctions. For example, given a large dataset, symmetry can be relaxed by allowing the giving parameters to change across charity characteristics (each auction is linked to a given charity), or other observables, using a flexible functional form for the parametersa andb. 25 1.5.1 Structural Estimation The estimation is based on comparing two types of auctions with different q. Figure 1.1 indicates that in most auctions the auctioneer donates either 85%, 78% or 10%. Clearly, as q A ! q B the necessary rank condition fails to hold and the model is not identified (see the Monte Carlo experiments in Table A.18 in Appendix A.8). Thus, the primitives are estimated using the sample of auctions with q2f10%, 85%g. The remaining auctions (q= 78%) will be helpful to test the model. Given that the samples are not random, an important empirical issue is whether auc- tions at 10% systematically differ from the others. This would complicate the comparison between the two sets of auctions. A logistic regression in Appedix A.5.3 explores this further by analyzing the probability that a listing is chosen to be at 10% or at 85%. Table A.12 tabulates the results. The most important regressors to be accounted for are the re- serve price, the number of bidders and some charity dummy variables. It will therefore be necessary to account for these observables in the estimation. The first step of the estimation procedure deals with auction heterogeneity. A common approach to deal with observables is to perform a hedonic regression of the bids on co- variates, and use the error terms as pseudo-winning bids (Haile et al., 2003). The advantage is that it pools all the data together by homogenizing bids into residuals (e = b x 0 g), ultimately offering a very tractable way to analyze the data. One of the major shortcomings of this approach is that it fails to properly account for unobservables. However, if unobservables and reserve prices are correlated, Roberts (2013) shows how a control function approach can be used to account for them. Since the reserve price is the lowest price that the firm is willing to accept, oscillations in the reserve price may reflect different market conditions (e.g., news or charitable events) or object characteristics that affect bids but are not explicitly accounted for in the data (e.g., the jersey was worn and sold right after the player won a particular individual award which is not captured by the covariates). First step. Due to the way the reserve price is set, I model the reserve price in auction t by reserve price t = R(x t , UH, cost 1q ), and the transaction price by price t = W(x t , UH, cost 1q , b w,t ). The functions R() and W() are invertible and include the observable and unobservable heterogeneity, as well as the lowest price available if goods were homogeneous ( cost 1q ). 43 b w,t is the homogeneous price. For simplicity, I assume that R() and W() are exponen- tial functions. b w,t is estimated by first running an OLS regression of the logarithm of the reserve price on the covariates (i.e., log(reserve price t ) = d 0 + x t d). Denote the gener- ated regressor by b y (i.e., ˆ y t = log(reserve price t ) b d 0 x t b d). Successively, the following hedonic regression yields the homogenized pseudo-winning bids, ˆ b w , as log(price t )= g 0 + x t g+g UH ˆ y t + b w,t , (1.5.1) where t indexes the auctions. The error term in (1.5.1) are the homogenized pseudo- winning bids, b w,t , which will be used in the next two steps of the estimation. 44 Table 43 On average, the net reserve price is set to cover costs (e.g.,(1 q) reserve price= cost. 44 x includes all the variables labelled Main Variables in Appendix A.2. This set of covariates corresponds 26 A.11 in Appendix A.5.3 displays the estimated coefficients from (1.5.1). Section 3.3 entertained the possibility of asymmetry among bidders who won multiple auctions and the other bidders. As an additional check, the distributions of the pseudo- winning bids from (1.5.1) conditional on the winner being a collector should be more skewed to the right compared to that of the other bidders, as collectors bid higher values on average. The data fail to support this thesis. Instead, the Kolmogorov-Smirnov test does not reject equality of the distributions at 0.1422 in the large sample and 0.1520 in the small sample. 45 This result further confirms that the alleged weak asymmetry vanishes once unobserved heterogeneity has been accounted for, either by using a more homoge- neous sample (as in the last two columns of Table A.10) or by a control function approach (as in equation 1.5.1). Second step. To derive the distribution of bids in a “parallel second-price auction” as by Proposition 4, separate the pseudo-winning bids for the two auction types. Let the superscript a2f10%, 85%g indicate whether the variable belongs to the 10% auctions or the 85% auctions. Following the proof, the distribution of bids, G a (b), is obtained by observation of the winning bids b a w . Denote the (observed) distribution of the winning bids by G a w (). Then G a (b) is found as the solution in[0, 1] of G a w (b)= nG a (b) n1 (n 1)G a (b) n , (1.5.2) where the second term in brackets is the distribution of the second-highest order statistic expressed in terms of the distribution G a (b). Solving this equation gives the distribution of bids that would have been observed in the parallel sealed-bid auction. The density g a (b) is found similarly. The derivative with respect to b a of equation (1.5.2) is: g a w (b)= n(n 1)G a (b) n2 [1 G a (b)]g a (b), (1.5.3) which uniquely pinpoints the density of the bids, g a (b). Solution of (1.5.2) and (1.5.3) requires the computation of G a w (b) and g a w (b). This is done by a Gaussian kernel whose bandwidths are chosen according to Li et al. (2002). 46 Third step. In the last step, G a (b) and g a (b) form the inverse hazard rates,l a G (b), for each auction format a. The objective is to match the FOCs for the two types of auctions for each quantile of the bid distribution. According to the identification, at the true param- eters the LHS of the FOC (1.4.1) computed for the 85% auctions at the t-quantile, ˆ v 85% t , is equal to the LHS of the FOC for the 10% auctions at the same t-quantile, ˆ v 10% t . This delivers the moment condition ˆ v 10% t ˆ v 85% t = 0. to column (II) in Table 1.2, which has the lowest BIC. Note that the percentage donated (and the reserve price which is used in the control function approach) is not used in either OLS regressions, as variation over q is key for identification. 45 Figure A.14 in Appendix A.5.11 plots the pdfs. Adding more covariates further increase the p-value of the test statistics. 46 The bandwidth of the kernel estimators are h a g = c a T 1/5 a for each pdf and h a G = c a T 1/4 a for each CDF, where c a = 1.06 minfs a , IQR a /1.349g, T a is the number of auctions of type a 2 fl, hg, s a is the standard deviation and IQR a is the interquantile range of the transaction prices of auction a. Trimming is used to account for the bias at the extreme of the support of the bids. 27 The number of possible moment conditions is theoretically infinite. This issue is solved by matching the quantiles of the bid data for the 10% auctions with the smoothed version of the 85% auction data, for which more observations are available. DefineQ =fa,bg; the criterion function to be minimized is: Q = arg min Q 1 T T å t ˆ v 10% t (Q) ˆ v 85% t (Q) 2 , (1.5.4) where T is the number of 10% auctions. The minimization algorithm searches for the values ofa andb minimizing the criterion function in the admissible region (a,b2[0, 1]). The distribution of private values F(v) is found as the empirical distribution of the left- hand side of (1.4.1). The performance of the estimator is good even in small samples as shown by the Monte Carlo simulations reported in Table A.19 in Appendix A.8. 47 The simulations sug- gest asymptotic normality of the estimator as the RMSE decreases at a rate close to p n, where n is the number of auctions. 1.5.2 Estimation Results As a requirement of the second step of the structural estimation, the number of poten- tial bidders must be fixed in order to compute the distributions of the pseudo-bids from the pseudo-winning bids (as shown in equation 1.5.2). Setting the number of bidders at the 99th-quantile of the distribution of bidders is a good choice as it avoids concerns with outliers. In fact, extremely high number of bidders may depend more on the item charac- teristics rather than on the distribution of values and parameters. Additional estimations ofa andb for lower quantiles of n are considered as robustness checks. Table 1.6 reveals thatb> a, coherent with the warm glow model of altruism (Andreoni, 1989). The estimates hardly vary with the number of potential bidders and are always significant. The 95% confidence interval are also reported in square brackets and are obtained by bootstrap. The same exercise is reported in Table A.13 in Appendix A.5.3, where the dataset is restricted to observations with prices greater thane 100 and smaller thane 400. The a parameter stays roughly unchanged, while its counterpart b has slightly dropped (ca. 38% instead of 46%), but still greater than a. The confidence intervals are much larger than in the previous estimates. This does not rule out a greater b than that estimated in the smaller sample. This is probably due to the smaller number of observations, which is only about 60% of those in the larger database (470 auctions in total). Overall, the smaller sample confirms that bidders account for the charitable gifts according to warm glow theory. 48 Finally, Tables A.14 and A.15 in Appendix A.5.3 report estimation results when the three steps of the estimation routine are applied to the auctions with q = 10% and q = 47 Comparing the columns referring to the median estimates shows that the Gaussian kernel outperforms the Triweigth kernel in small samples, while the RMSE is very close in the two cases. Using a triweight kernel does not affect the estimates. 48 Adding more covariates does not qualitatively affect these estimates. 28 Table 1.6: Estimation ofa andb Number of bidders a b Quantile n [95% CI] [95% CI] 99% 16 19.5% 46.2% [10.0%, 29.1%] [25.5% 59.9%] 95% 14 19.3% 46.2% [10.3%, 28.6%] [26.4% 62.9%] 90% 12 19.0% 46.1% [10.4%, 27.1%] [28.1% 62.0%] 75% 10 18.6% 46.1% [9.2%, 27.3%] [27.4% 62.6%] 50% 7 17.4% 45.9% [7.9%, 27.1%] [26.1% 62.6%] Notes: a and b are defined in equation (1.3.1). Re- sults from the structural estimation of a and b for se- lected quantiles of the distribution of the number of bidders. The 95% confidence intervals are reported in square brackets. The CI are found by bootstrap with re- placement (401 times). Dataset restricted to all auctions such that q2f10%, 85%g and price betweene 100 and e 1000. 731 observations in total. 78%. The estimated a and b are close to those in Tables 1.6 and A.13 and the confidence intervals largely overlap. 1.5.3 Tests to Estimation and Identification The model predicted expected gross revenues are close to the realized revenues. Ta- ble 1.7 compares the simulated and realized median and average revenues. These prices are computed as the expectation of the second-highest bid using the estimated primi- tives. To account for auction heterogeneity, these quantities are transformed in euro by adding back either the average or the median fitted prices from the first step estimation in (1.5.1). The table displays a good fit of the estimates with values within 10% of the realized ones. 49 49 The computation of the expected revenues is standard. First, to find the expected (or median) revenues from the homogenized auctions I integrate the bidding function (equation 1.3.3) with respect to the distri- bution of the second highest-bid, yielding p e = R v b(t; ˆ a, ˆ b)dF (2) (n) (t). Second, I evaluate the entity of the cross-auctions heterogeneity as ¯ X = \ log(Price)b g log(bidders), where ˆ x indicates the fitted (or estimated in case ofg) value of each covariate x in (1.5.1). Finally, the expected (or median) revenues is the sum of p e and the average (or median) value of ¯ X. In the second step, the effect of the number of bidders is subtracted from the fitted prices because this variable already affects the first step through the distribution of the sec- ond highest bid. Since the number of bidders may correlate with other unobservables, the results reported in Table 1.7 are obtained by including also the log(Total Number of Bids Placed) among the covariates in the first step of the estimation routine (equation 1.5.1). Additional robustness checks in the appendix show 29 Table 1.7: Estimated revenues vs realized revenues q= 85% q= 10% Estimated Realized Estimated Realized Median revenues 353.58 347.50 299.27 300.50 (+1.74%) (-0.41%) Average revenues 355.78 374.09 301.14 334.92 (-4.89%) (-10.09%) Notes: Estimated median and average unitary revenues for Charitystars. Rev- enues in euro are computed in multiple steps. (i) Subtract the median num- ber of bidders times its estimated coefficient in the OLS regression (1.5.1) from the fitted values of the same regression. (ii) Compute the expected revenues obtained as the expectation of the second-highest bid using the primitives es- timated in Section 1.5.1 (F(),a,b). (iii) Sum the fitted values in (i) with the homogenized expected price in (ii) and apply the log-level transformation. Re- alized revenues are determined at the median number of bidders for each auc- tion type. The covariates used in (1.5.1) include the total number of bids as in Appendix A.5.5. Another way to validate the estimates in Table 1.6 is to simulate bids and try to match them with some stylized facts highlighted in Section 3.3. A striking result from that sec- tion was the linearity between prices and donations. Figure 1.5b replicates this finding by plotting the simulated bids (y axis) for different percentages donated (x axis). Remark- ably, the three curves (corresponding to the bids placed by bidders with values at the first three quartiles of the estimated F()) are linear and increasing in q (compare with Table 1.3 and Figure A.7) A direct test to identification is to apply the estimates to the 78% auctions and check whether the implied distribution of values differ from that estimated in Section 1.5.2. This can be done in multiple ways. The most challenging one is to apply the estimated param- eters to recover F() for the 78% data. This consists of (i) manipulating the winning bids and covariates with the coefficients estimated in the two regressions at the first-step of the estimation procedure (using the coefficient in equation 1.5.1). Then, (ii) the distribution of bids are computed following (1.5.2) (and (1.5.3) for the density). Finally, (iii) the private values are determined assuming the same ˆ a and ˆ b exposed in Table 1.6. Figure 1.5a plots the densities from auctions at 10% (solid line) and those at 78% (dot- ted line) for n = 16. The two pdfs have similar shapes, displaying a slight bimodality at the same values. The Kolmogorov-Smirnov test does not reject the null hypothesis that the two distributions are equal at 0.1154 level. 50 The outcome would not change by replacing the first step with a regression on all observations with q2f10%, 78%, 85%g. The same exercise can also be repeated on a different set of covariates. For example, Appendix A.5.6 report estimates of a and b when the “Total Number Of Bids Placed” is added as an independent variable. First, the estimates do not vary substantially from that adding this variable does not qualitatively change the estimated ˆ a and ˆ b (see Appendix A.5.5). 50 An analogous plot is found for other values of n and the KS test always fails to reject identity of the distributions. 30 Figure 1.5: Model fit (a) Out-of-sample validation n= 16 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 −1.0 −0.5 0.0 0.5 1.0 Private Value pdf q = 10% q = 78% (b) Linearity of the bids 1 st , 2 nd , 3 rd quartile of F(v) 150 200 250 300 350 0.1 0.25 0.4 0.55 0.7 0.85 1 Percentage donated Bid (EUR) Private value at Q(25%) Private value at Q(50%) Private value at Q(75%) Notes: Panel (a). Comparison of the density of the private values estimated from the structural model employing data from auctions with q =f10%, 85%g and the density of the private values estimated by projecting the three-step estimation on the q = 78% auctions. The null hypothesis (equality) cannot be rejected at standard level. The computation assumes n = 16, but the same result can be replicated with different n. The plotted densities are computed using a Gaussian kernel and Silverman’s rule-of-thumb bandwidth (Silverman, 1986). Panel (b). Simulated bids computed at the first, second and third quartiles of the estimated value distribution. The density f(v) is approximated using a cubic spline. Only auctions with price betweene 100 ande 1000. those in Table 1.6. Second, Figure A.17 shows that the pdf from a similar out-of-sample analysis does not reject the null hypothesis of equality of densities. 51 In addition, Figure A.9b in Appendix A.5.5 I propose an overidentification test: I separate the moments in (1.5.4) between those referring to a realized G(b) above or below 50%, and estimate the densities in the two samples. The result supports the identification procedure. This is a remarkable result: the distribution of private values computed using the auxiliary data cannot be distinguished from that found by matching the FOCs from other two auction datasets. This is a direct test of Assumption 2 because dependence between q and F() would immediately return an incongruence in the estimates. A similar result would be expected in case of heterogeneous a and b. Furthermore, this test is clearly conservative as the way covariates impact prices in the auctions at 78% does not need to be the same as for the other auctions (f10%, 85%g). This is because auctions vary both in terms of timing (e.g., period of the year) and the object characteristics (both observable and unobservable). These checks confirm the goodness of fit of the model. These tests provide indirect support for the way nonpecuniary motives are modelled in the theoretical literature of 51 The p-value of the Kolmogorov-Smirnov test is 0.1874. Adding even more covariates further increases the p-value of the test statistics with no affect on the estimateda andb. 31 auctions with externalities (e.g., Jehiel et al., 1999; Lu, 2012) and, more generally, revenue- dependent profits: constant marginal return to charity revenues. 52 1.6 Counterfactual Experiments on the Demand Side With the estimated primitives, the model can be used to gauge the effectiveness of CSR strategies under different consumers’ willingness to pay. The first question to ask is whether bids are greater than private values. To address this, I simulate private values (solid line) and bids (dotted line) and plot them in Figure 1.6a. The plot suggests stochas- tic dominance of bids on values. Thus all bidders increase their bids beyond their private values. This means that (for any given number of bidders) the expected second-highest bid from the second-price auction is larger than the second-highest private value. Hence, gross revenues to Charitystars are greater than those to a comparable non-charity auction. Figure 1.6: The extent of overbidding (a) Estimated scenario 0.0 0.2 0.4 0.6 0.8 1.0 117 175 261 389 580 865 Private Value / Bid CDF Private Value Bid: true α , β (b) Counterfactual scenario withb= 0.8 0.0 0.2 0.4 0.6 0.8 1.0 117 175 261 389 580 865 Private Value / Bid CDF Private Value Bid: true α , β = 0.8 Notes: a and b are defined in equation (1.3.1). Bids are computed drawing 200 values from the estimated distribution of private values F(v) and the selecteda andb; q= 1. Prices are converted in euro by summing the median of the fitted prices in the first step of the estimation (1.5.1). The first step of the estimation also includes log(Total Number of Bids Placed) as a covariate. Panel (a) uses the estimated primitives. Panel (b) uses the estimated F(v) anda and assumesb= 0.8. Only auctions with price betweene 100 ande 1000. The price price premium is not constant. The distance between values and bids is quite large, especially for higher quantiles, as donations increase willingness to pay by a little less thane 100 for a bidder at the 80 th -percentile of the distribution (about 1/4 of the bidder’s valuation). This distance widens further were consumers to receive an additional glow from winning the auction. This is evident from Figure 1.6b, which plots 52 For example, Goeree et al. (2005) at page 906 state to “keep the constant marginal benefit assumption because it provides a tractable model [...]” despite believing that a model with diminishing returns would mirror reality better. 32 simulated bids withb= 0.8 instead of the estimated ˆ b. 53 Figure 1.7: Expected prices in charity vs non-charity auctions (a) Estimated scenario 250 300 350 400 450 500 550 0.00 0.25 0.50 0.75 1.00 Percentage donated (q) Gross Revenues Charity auction: true α , β Standard auction (b) Counterfactual scenario withb= 0.8 250 300 350 400 450 500 550 0.00 0.25 0.50 0.75 1.00 Percentage donated (q) Gross Revenues Charity auction: true α , β = 0.8 Standard auction Notes: a andb are defined in equation (1.3.1). The two panels report the expected gross revenues to Chari- tystars at the estimated parameters (solid line), and from a standard auction with no donation (dotted line). The density f(v) and the distribution F(v) are approximated using a cubic spline. Only auctions with price betweene 100 ande 1000. Revenues in euro are computed in multiple steps. (i) Subtract the median num- ber of bidders times its estimated coefficient in the OLS regression (1.5.1) from the fitted values of the same regression. (ii) Compute the expected revenues obtained as the expectation of the second-highest bid using the primitives estimated in Section 1.5.1 (F(),a,b). (iii) Sum the fitted values in (i) with the homogenized expected price in (ii) and apply the log-level transformation. The covariates used in (1.5.1) include the total number of bids as in Appendix A.5.5. The charity premium is increasing in q and is about 11.3% when the auctioneer do- nates 85% (see Figure 1.7a). This is close to the estimates in Elfenbein and McManus (2010) who estimated a premium of 12% when the auctioneer donates 100% using eBay’s Giving Works data. There’s almost no charity premium when the auctioneer donates lit- tle (the estimated premium when q = 0.10 in Elfenbein et al. (2012) is much larger at 6%). Obviously this analysis assumes that the number of bidders is constant across auctions (in this case 8). The premium increases slightly with the number of bidders, reaching about 14% when there are 16 bidders and the auctioneer donates 85%. Figure 1.7b shows that a greater glow would lead to much larger premiums at the right end of the distribution of the amount donated. 53 The way the distribution of private values and the charitable parameters interact in shaping bids is further investigated in Appendix A.6. The discussion shows that bids in charity auctions would still dom- inate bids in standard auction even when sharply increasing the externality parameter. This is because the distribution of values determines the probability of winning the auction which control overbidding (see Lemma 2). 33 1.6.1 Net Revenues in Charity Auctions Despite the positive gross return to donating, the demand side analysis so far per- formed does not justify positive donations. In fact net revenues are decreasing almost lin- early in the percentage donated (Figure 1.8a). If Charitystars were to sell its items without donating, it would make overe 300 in net revenues, whereas it only brings homee 53 when it donates 85%. Interestingly, while bidders are much more aggressive when the glow is greater, as indicated by Figure 1.7b, these higher revenues should not induce the auctioneer to donate (compare the solid and dotted lines in Figure 1.8a). Even increasing the number of bidders does not make charity auctions more appealing than non-charity auctions for any positive q (Figure 1.8b). Figure 1.8: Expected net revenues decrease in the donation (a) n = 7 bidders 0 50 100 150 200 250 300 350 400 0.00 0.25 0.50 0.75 1.00 Percentage donated (q) Net Revenues True α , β True α , β = 0.8 (b) n = 16 bidders 0 50 100 150 200 250 300 350 400 0.00 0.25 0.50 0.75 1.00 Percentage donated (q) Net Revenues True α , β True α , β = 0.8 Notes: a and b are defined in equation (1.3.1). The two panels report the expected net revenues to Char- itystars (solid line) at the estimated parameters, for different number of bidders (7 in Panel (a) and 16 in Panel (b)), and the marginal cost reduction due to a marginal increase in the percentage donated in terms of the expected bid (dotted line). The density f(v) and the distribution F(v) are approximated using a cubic spline. Only auctions with price betweene 100 ande 1000. Revenues in euro are computed in multiple steps. (i) Subtract the median number of bidders times its estimated coefficient in the OLS regression (1.5.1) from the fitted values of the same regression. (ii) Compute the expected revenues obtained as the expec- tation of the second-highest bid using the primitives estimated in Section 1.5.1 (F(),a,b). (iii) Sum the fitted values in (i) with the homogenized expected price in (ii) and apply the log-level transformation. The covariates used in (1.5.1) include the total number of bids as in Appendix A.5.5. The suboptimality of charity auctions at creating revenues is due to the rigidity of the elasticity of prices to giving, h. Given the estimated parameters, h can be computed Proposition 2 states that the revenue optimal percentage donated, q , sets the elasticity equal to the donation-ratio q/(1 q). Figure 1.9a shows that these two curves intersect only at the origin. The same is true for theb= 0.8 case (Figure 1.9b). Charitystars faces a possible deviation ofe 250 in terms of higher revenues by inter- rupting the donations (Appen dix A.4 discusses profits when the firm keep a fixed per- centage in any auction). Moreover, as investigated in Appendix A.7, the firm has already 34 adopted the best mechanism to maximize its revenues across standard charity auction mechanisms (aside from a standard noncharity auction). To understand why Charitys- tars donates at all, the next section explores possible decreasing marginal costs in the donation as a result of bargaining between celebrities and charities. Figure 1.9: The revenue maximizing q is zero (a) n = 7 bidders 0 0.05 0.1 0.15 0.2 0.00 0.25 0.50 0.75 1.00 Percentage donated (q) Elasticity True α , β q / (1−q) (b) n = 16 bidders 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 0.00 0.25 0.50 0.75 1.00 Percentage donated (q) Elasticity True α , β = 0.8 q / (1−q) Notes: a andb are defined in equation (1.3.1). The elasticity of the bid as the percentage donated increases. The number of bidders is assumed to be 7. The density f(v) and the distribution F(v) are approximated using a cubic spline. Only auctions with price betweene 100 ande 1000. Revenues in euro are computed in multiple steps. (i) Subtract the median number of bidders times its estimated coefficient in the OLS regres- sion (1.5.1) from the fitted values of the same regression. (ii) Compute the expected revenues obtained as the expectation of the second-highest bid using the primitives estimated in Section 1.5.1 (F(),a,b). (iii) Sum the fitted values in (i) with the homogenized expected price in (ii) and apply the log-level transformation. The covariates used in (1.5.1) include the total number of bids as in Appendix A.5.5. 1.7 The Supply Side and the Profit-Maximizing Donation One reason for Charitystars to donate is that if the provider of the object is charitable, he could be more willing to provide items when the firm is more generous. In addition, providing an item could create more positive awareness of the social responsibility of the provider (especially for a football team or a footballer) and this form of advertisement could benefit them more if the objects they deliver to Charitystars are associated with greater q. In this view, Charitystars works like a platform as it matches consumers with providers of the items. Charitystars incurs transaction costs in terms of organization and dealing with the pro- curers of the items. To explain how costs are affected by the fraction donated, I consider a possible bargaining problem between the firm and a celebrity. The selection of q could depend on each agent’s bargaining powers. To provide evidence of bargaining, I exploit 35 a period of the year where the relevant bargaining power is tilted toward the providers. 54 I compare the donations in the inactive summer months of July and August with those in the other months. The hypothesis is that providers have greater bargaining power in these months because, due to the inactivity of the major European leagues, there are fewer objects available at this time. In fact, Charitystars sold only 24.5 objects on average in these months, versus an average of 50.6 objects in the other months. Thus, Charitystars should be more generous in this period on average. This hypothesis is first confirmed by testing the difference between the average q for August and that for the other months in the sample (Welch test: ¯ q other = 0.698, ¯ q Aug = 0.775, one-sided p-value 0.030) and for July and August vs the other months in the sample (Welch test: ¯ q other = 0.693, ¯ q Jul&Aug = 0.770, one-sided p-value< 0.001). To control for the number of bidders, the jersey’s value and a number of other variables I perform the following OLS regressions q t = g 0 + x t g+g m month t +# t , (1.7.1) where “month” refers to either the month of August only, or July and August. Table 1.8 reports the results, confirming the presence of bargaining between parties, as Charitystars is more generous when it has less bargaining power. The results are robust to the inclu- sion of more covariates (even columns). Arguably the same result could originate from Charitystars’ reacting to the expectation of fewer bidders in the Summer by increasing q (to increase the number of bidders). Table A.7 in Appendix A.5 instruments the number of bidders and the reserve price using the mean of these variables for auctions happening within five days of each auctions. The results confirm the estimates presented in Table 1.8. The Hausman Test does not reject the null hypothesis that q and the number of bidders are exogenous. In Appendix A.4, I build a Nash bargaining model to show that, under the mild con- dition that the net expected price is larger than costs, the marginal cost (c 0 = ¶c(q)/¶q) is decreasing in q. This empirical and theoretical evidence suggests that the firm donates to decrease its costs. In this section, instead of exploring a full bargaining problem between Charitystars and the provider, I focus on a simpler monopolist problem: the firm opti- mizes its profits by choosing the optimal percentage donated considering that costs are a generic function of q. Given knowledge of the number of bidders, a,b and F(v), a profit-maximizing plat- form would donate the profit-maximizing q defined as q = arg max q2[0,1] Z v (1 q)b(v,a,b, q) c(q), dF (2) (n) (v) where F (2) (n) (v) is the distribution of the second highest private value out of the n bidders. Denoting the expected price by p e and by the dominated convergence theorem (as in the 54 The provider of the item is known only in 70% of the auctions. Dividing the sample between auctions where the fraction donated is small (< 0.5) and large ( 0.5) reveals that beyond 70% of those who provided an object in the first group, also provied an item in the second group, showing homogeneity in the way the goods are provided across auctions. 36 Table 1.8: Evidence of bargaining (I) (II) (III) (IV) August 0.070 0.074 (0.029) (0.030) July & August 0.077 0.068 (0.022) (0.024) Main Variables Y Y Y Y Add. Charity Dummies Y Y League/Match Dummies Y Y Adjusted R-squared 0.311 0.354 0.316 0.357 N 1,109 1,109 1,109 1,109 * – p< 0.1; ** – p< 0.05; *** – p< 0.01 Notes: The table presents the OLS estimate for the dummy variables August (1 if the month is August, 0 otherwise) and July and August (1 if the month is either July or August, 0 otherwise) in equation (1.7.1). Only auctions with price betweene 100 ande 1000. Robust standard errors in parentheses. proof of Proposition 2) the equation can be written in terms of the donation-elasticity (h) c 0 (q)= 1 q q hp e p e . (1.7.2) The expression on the RHS is the difference between the updated price after a marginal in- crease in q (i.e., 1q q hp e ) and the original price (p e ). The optimal donation sets the marginal cost reduction from a marginal increase in q equal to the reduction in marginal benefits. Equation 1.7.2 can be manipulated to show that if c 0 is negative, q > 0. Denote the revenue optimal donation by q R as the solution of q R /(1 q R ) = h(q R ) (see Proposi- tion 2). The demand analysis in the previous section states that to maximize net rev- enues Charitystars should set q R = 0. The profit-maximizing donation is such that c 0 (q ) p e (q ) + 1 q 1q = h(q ). Comparing the last two equations, because the ratio in paren- theses is negative, it must be that q > q R . How much should the firm donate? Unfortunately, costs are not observable from the website, but they can be inferred from variation in the net reserve price. In order to avoid losses, Charitystars’ managers ensure that the smallest net revenue covers costs. This is equivalent to setting the reserve price such that (1 q) reserve price = c(q). I exploit this key information and focus on the average marginal costs across auctions, by following a procedure analogous to that in the first step of the demand estimation. First, I homogenize the reserve prices by regressing them on the same covariates previously used in the estimation procedure log(reserve price t )= x t g+# t , (1.7.3) 37 where t indexes each one of the 1,108 auctions in the dataset (not just a subset of the auctions based on q as in the structural estimation). I exponentiate the sum of the median fitted reserve price ( \ reserve price t ) and the error terms (ˆ # t ), so that the homogenized reserve price (r t ) is expressed in terms of the median auction in euro (as done in the structural model). 55 Then, costs are equal to the net homogenized reserve price (nr t = (1 q)r t ). Average marginal costs are derived by regressing nr t over q2 (0, 1) using a polynomial expansion for q (i.e.,å J j=0 p j q j ). Identification of the marginal cost fails if there is an omitted variable that depends on q and that affects the way the reserve price is set. Therefore, the reserve price will be associated with q not only through the cost channel, but also through this omitted channel– despite this, the correlation between q and the other variables is small. However, in this case the “Number of Bidders” include information on this additional variable: a greater reserve price due to this omitted variable will be reflected in a change in the number of bidders, everything else equals. 56 In addition, also the variable “Number Of Total Bids Placed” may account for unobservables, if, for example, each bidders bid more aggressively within the auction because the item is particularly valuable (either due to better quality or greater q). Thus, it is important to include these variables in order to consistently estimate the marginal cost. Table 1.9 gives the estimated coefficients using either a quadratic or a cubic functional form for costs. Comparing the two columns, the estimated intercept (p 0 ) and linear coef- ficient (p 1 ) are similar, while the introduction of the cubic term (p 3 ) expands the size of the quadratic coefficient (p 2 ) in the second column. Although the coefficients are similar across columns, adding the cubic term inflates the standard errors in column (II). This depends on a small number of auctions for q in the neighborhood of 50% (Figure 1.1a). Nevertheless, both specifications seem to fit the data fairly well as they explain a large portion of the variance of the net reserve price (Adjusted R 2 60%). Figure 1.10a plots marginal costs and marginal benefits, demonstrating that Chari- tystars should indeed donate a share of its revenues in order to maximize profits. The estimated marginal costs are negative across both specifications for all q, empirically ver- ifying the intuition of decreasing costs. In addition, a marginal increase in q seems to decrease costs less when q is high, so that the cost reduction follows the logic of decreas- ing returns. Thus, even accounting for costs, large donations cannot be justified: q is 30%, not 85%. 57 By setting the donation optimally, Charitystars would almost quadruple 55 To test the impact of auction heterogeneity on q , I replicate the analysis in Appendix A.5.8 where I consider the 1 st and 3 rd quartiles instead of the median auction. 56 To assess the relation between unobserved heterogeneity and q in the data, I study how the residual from the control function approach in the first step of the estimation in Section 1.5.1 vary with q. The Spear- man’s rank correlation coefficient between the estimated unobserved heterogeneity and q is only -0.0666 (Pearson: -0.0714). Had the choice of q depended on unobservables, a much larger correlation coefficient would have been expected. As a robustness check, running a similar analysis after including more re- gressors to better account for cross-auction heterogeneity does not affect the conclusions (see Figure A.5 in Appendix A.4). 57 To test the significance of this estimate I sample with replacement all the auctions in the dataset. I use the sampled data to estimate marginal costs and the 10% and 85% sampled auctions to estimate marginal revenues. This process is repeated 400 times. The 99% confidence interval for q is [0.035, 0.45], while the 38 Table 1.9: Cost estimation Quadratic Cost Cubic Cost (I) (II) p 0 237.58 249.01 (15.10) (90.73) p 1 -432.35 -572.24 (80.31) (1059.12) p 2 214.86 521.43 (78.75) (2235.97) p 3 -186.06 (1312.63) Adjusted R 2 0.582 0.582 BIC 11,966.43 11,973.14 N 1,108 1,108 * – p< 0.1; ** – p< 0.05; *** – p< 0.01 Notes: OLS regression of the homogenized reserve price on a quadratic (Column I) and a cubic (Col- umn II) polynomial expansion of q. p 0 is the in- tercept, whilep 1 ,p 2 andp 3 refers to the linear (q), quadratic (q 2 ) and cubic term (q 3 ). Only auctions with price betweene 100 ande 1000. Control vari- ables are defined in Appendix A.2. Robust stan- dard errors in parentheses. its profits. The median amount pocketed by Charitystars is only 15% for each object sold, yielding an expectation ofe 25 of profit for each auction, as displayed in Figure 1.10b. The figure shows that profits would jump toe 95 per auction on average with the opti- mal policy. In addition, profits almost double when the optimal donation is compared to the average donation (70%). 58 A limit of the analysis is that it does not consider the probability of striking each deal with the providers. Assuming that the probability of a certain deal depends on the provider of the jersey, I replicate the analysis separating the auctions based on the type of the provider. I distinguish between (i) private providers and (ii) footballers and charities. The analysis shows that in the first case, there is no cost savings, and the firm should set q= 0. In the second case, the optimal donation is similar to that in Figure 1.10a. In partic- ular, when the charity is the provider of the item, charities may be better-off at receiving a larger fixed fee and a smaller fraction of the price, rather than receiving a large fraction of the final price. In particular, small charities could be averse at taking risk, and this strategy could increase their utility. The details of the analysis are in Section A.5.7. median boostrapped q is 0.295. The standard deviation is 0.102. 58 In the appendix, I replicate the same analysis while accounting for unobserved heterogeneity in a dif- ferent way. First, in Appendix A.5.9 I estimate costs on a subset of the data excluding all auction formats with less than 15 auctions. In Appendix A.5.10, I use instrumental variables to take care of possible endo- geneity in the reserve price and in q. The results in the both appendices confirm those in Figure 1.10. 39 Figure 1.10: Optimal donation (a) Optimal fraction donated −600 −500 −400 −300 −200 −100 0 0.00 0.25 0.50 0.75 1.00 Percentage donated (q) MB, MC (EUR) M Net Benefits MC − Quadratic MC − Cubic (b) Optimal profits median donation −25 0 25 50 75 100 0.00 0.25 0.50 0.75 1.00 Percentage donated (q) Profits Notes: Panel (a) shows the optimal percentage donated as the intersection of marginal costs (dotted and dashed lines) and marginal net benefit (solid line). Panel (b) displays how profits change with q. The vertical line at 85% indicate the median donation by Charitystars. The number of bidders is assumed to be 7. The density f(v) and the distribution F(v) are approximated using a cubic spline. Only auctions with price betweene 100 ande 1000. Marginal revenues in euro are computed in multiple steps. (i) Subtract the median number of bidders times its estimated coefficient in the OLS regression (1.5.1) from the fitted values of the same regression. (ii) Compute the expected revenues obtained as the expectation of the second- highest bid using the primitives estimated in Section 1.5.1 (F(),a,b). (iii) Sum the fitted values in (i) with the homogenized expected price in (ii) and apply the log-level transformation. The covariates used in (1.5.1) and (1.7.3) include the total number of bids as in Appendix A.5.5. 1.8 Giving for Profit and Giving to Give The main finding in Section 1.7 is that Charitystars is not maximizing profits (Figure 1.10a). On average, the firm donates more than twice the optimal percentage, leaving 3/4 of the value of its optimal profits to charities and consumers (Figure 1.10b). The analysis focuses on an unconstrained problem. In reality, Charitystars may not be able to set the fraction donated as freely as it likes. In this section, I argue that Charitystars has enough bargaining power to influence the way the fraction donated is set, and thus, such large generosity suggests that Charitystars has prosocial preference. There are also more classic explanations for Charitistars’s suboptimal behavior. For instance, the firm could be more generous to invest in reputation in order to attract more bidders or to increase the number of auctions. Yet, higher fraction donated are not corre- lated with more bidders in Charitystars’ auctions (Table 1.4). The median number of auc- tions and median number of bidders from 2015 to 2019 display no trend in either variable, suggesting that auctions and number of bidders do not respond to earlier investments in reputation (Figure A.6 in Appendix A.5). 59 In addition, excessive donations reduce cash 59 As an additional robustness check, regressing the monthly number of auctions and monthly median number of bidders on the average q in each month and its lags display no correlation between donations 40 flows, which are crucial for young firms to grow without resorting to external capital. Moreover, Charitystars is a de facto monopolist in the e-commerce of celebrities’ belong- ings for charity because of the large number and variety of auctions it offers. 60 There are also large barriers to entry in Charitystars’ business due to the need for a sizable network of contacts with celebrities, and for a large number of users. Failure to properly assess the elasticity of prices to the fraction donated is another possible explanation to Charitystars’ large donations. However, this explanation seems unlikely for multiple reasons. First, the firm hosts thousands of auctions yearly, and there- fore it has sufficient data to establish how prices change with the fraction donated. Sec- ond, a portion of Charitystars’ equity is hold by private equity funds. These investors are interested in quickly setting the firm on a path for profitability in order to resell its shares for a capital gain, and are generally well-equipped in terms of data analysis tools (Bloom et al., 2015). A more likely reason for Charitystars’ large donations could be that such large do- nations are optimal for other areas of the business, such as selling a painting, or a din- ner with a CEO. The presence of managerial costs to set multiple donation percentages for different business areas (DellaVigna and Gentzkow, 2017) could explain Charitystars’ suboptimal behavior. Nevertheless, selling soccer jerseys is the most active area of the Charitystars’ business and should probably have priority over the other products sold by Charitystars. While none of these hypothesis can be ruled out with the data at hand, the intuition that Charitystars cares also for how much it donates, as its bidders do, seems to be more plausible. Thus, Charitystars’ objective function may extend beyond profits to include the amount it donates. The increasing interest for charitable donations and environmentally friendly technologies (Bénabou and Tirole, 2010; Kitzmueller and Shimshack, 2012) may imply that social impact is important for other firms as well. The recent introduction of new le- gal corporate forms designed for for-profit entities also wishing to serve a broader social purpose is a point in case (Talley, 2012). This novel legal status shelters the managers of responsible firms in case of poor financial performances. This paradigm opens interesting scenarios on the economic limits of this fiduciary duty. In addition, a greater social impact may be required by socially responsible share- holders who also demand the company they invest in to behave accordingly (Riedl and Smeets, 2017). Firms with greater social impact could have easier access to capital. 61 Pre- vious research documents this for socially responsible private equity funds (Barber et al., 2018) and for firms dedicated to long-term sustainability (Cheng et al., 2014). Easier access to funds could protect responsible firms from market forces. This analysis could be extended to other socially responsible firms. For example, both Charitystars and Toms Shoes, a large for-profit firm that donates a pair of shoes for each pair it sells, face a rigid elasticity of demand. 62 However, unlike Toms, Charitystars’ pro- and future outcomes. 60 Charitybuzz, a large American charity auction website, is not present in Europe, which is Charitystars’ main market, and does not offer charity auctions of soccer jerseys. 61 For example, (Dyck et al., 2018) shows that social responsible firms are more likely to be owned by institutional investors than other firms. 62 Reports show that in 2014, Toms Shoes Founder Blake Mycoskie sold 50% of Toms to the ven- 41 duction technology enjoys lower costs when it donates, whereas Toms must produce two pairs of shoes for each pair it sells. 63 Given the poor recent profitability of Toms Shoes, this example shows the importance of correctly assessing how much to donate. Accord- ing to Hart et al. (2017), if donations and money-making activities are non-separable, firms should place shareholders’ welfare maximization before the firm’s market value. Dona- tions and money-making activities are clearly non-separable for Charitystars. If Charitys- tars were to interrupt its donations to charities, the firm would bear higher procurement costs– or even be unable to obtain the celebrities’ belongings it would like to sell. CSR and money-making activities would be separable if, instead, Charitystars’ donations had no impact on the production technology (e.g., celebrities were indifferent to the donations). This is the case of Toms Shoes: if the firm were not to donate shoes, its shareholders could still do so, demonstrating that not all firms should behave prosocially. 64 1.9 Conclusion CSR is pervasive. In January 2018, the CEO of BlackRock, a fund with $6 tn in as- sets, stated that “society is demanding that companies [...] serve a social purpose,” and thretened to liquidate BlackRock’s position from non-socially responsible firms. 65 Yet, evidence that CSR leads to greater profits is still mixed. To shed some light on the mechanisms that make CSR profitable, this paper examines Charitystars’ decisions to donate a portion of its revenues. Charitystars is an international for-profit firm offering charity auctions of celebrities’ belongings. Because Charitystars’ donations are salient for consumers and are easy to measure, this setting is suitable to investigate how the intensity of CSR programs affects profits, an issue that is understud- ied in the literature. In particular, failing to account for the fact that profitability may not increase monotonically in CSR expenditure may distort our understanding of how CSR impacts profits and on the reasons firms invest in CSR. This analysis also allows the exploration of Charitystars’ objectives, as excessive CSR may signal an interest in social impact in addition to profitability. Charitable donations affect both Charitystars’ revenues and costs. First, I show that transaction prices increase as the fraction donated increases. To study the elasticity of demand to changes in the fraction donated, I build a structural model of a charity auction and investigate its properties theoretically. I also estimate bidders’ prosocial inclinations ture capital firm Bain Capital for $625m (more information at https://dealbook.nytimes.com/2014/08/ 20/toms-sells-half-of-itself-to-bain-capital/?_php=true&_type=blogs&_r=0). Financial perfor- mance has not met the expectations since the sale, as the company shoulders a huge debt and has trou- bles attracting new customers. More information at www.bloomberg.com/news/articles/2018-05-03/ even-wall-street-couldn-t-protect-toms-shoes-from-retail-s-storm. 63 Consumer demand is not inelastic in all situations. In a natural experiment at an amusement park, Gneezy et al. (2010) find no significant impact of donations with fixed prices. Instead, the adoption of a pay-what-you-want pricing policy in connection with 50% donation increases revenues. 64 Hart et al. (2017) argues in favor of shareholders’ value maximization if either the two activies are not separable, if governments do not fully internalize all externalities generated by the production or if shareholders are not prosocial. 65 Source: https://www.blackrock.com/corporate/investor-relations/larry-fink-ceo-letter. 42 and distribution of their private values from first order conditions. Counterfactuals show that willingness to pay is quite unresponsive to changes in the donation. As a result, the increase in transaction prices due to the donations does not cover the donation itself. Thus, even in cases where CSR is especially salient for consumers, consumer demand may fail to provide firms with enough incentives to behave prosocially. Thus, the benefits of CSR should come from other areas, which range from less expensive financing (Riedl and Smeets, 2017; Barber et al., 2018) to better stakeholder engagement and accounting standard (Cheng et al., 2014). Second, donations also affect the cost of procuring celebrities’ belongings. I estimate costs by exploiting the fact that the firm sets the reserve price to cover costs. I find that costs are decreasing in the fraction donated, which is consistent with the supposition that Charitystars and item providers bargain over how much to donate. In addition, I provide support for the existence of bargaining by showing that the percentage donated is higher when the providers have more bargaining power. To determine whether donating is profitable for Charitystars, I compare how marginal revenues from the demand analysis, and marginal costs vary with the fraction donated. The results indicate that donating is profitable for Charitystars, but also that most of the benefits from donating come from lower costs rather than greater revenues. CSR is prof- itable because money-making activities and donations are non-separable for Charitystars (Hart et al., 2017). Although Charitystars’ median fraction donated is 85%, I demonstrate that the profit-optimal fraction donated is 30% on average. Charitystars’ profits would increase four-fold if the firm were to maximize profits. After rejecting several possible explanations, I argue that the firm not only “gives for profit,” but also “gives to give.” This paper fills gaps in several literatures. First, it solves the long-lasting problem of measuring CSR by introducing a new dataset, which allows employing structural meth- ods to identify a clear mechanism describing how CSR affects consumers’ willingness to pay and the firm’s profits. I also contribute to the industrial organization literature by providing methods to identify and estimate auctions with cross-bidders externalities and by examining how consumers bid in these auctions. Finally, I contribute to the literature on firms’ objectives by showing that Charitystars does not only maximize profits. While most of the inquiries on why firms fail to maximize profits have focused on either princi- pal agent problems between shareholders and managers or managerial costs, my findings introduce a novel channel, namely that firms can behave prosocially. This finding is sup- ported by recent legal developments such as the introduction of the “Benefit Corporation” status, which defends the mission of for-profit social impact firms. Due to the role played by firms in today’s economy, my results can potentially have important implications for analyzing market competition and, more generally, industrial policy. An interesting di- rection for future research could investigate empirically if social responsibility increases market shares in an oligopolistic market by intensifying product differentiation. 43 Chapter 2 Dynamic Regret Avoidance 1 2.1 Introduction Regret is a negative emotion, associated with an action or inaction, which is experi- enced when one wishes that another choice would have been made. Regret avoidance was found to be an important factor in many empirical studies on topics ranging from heart disease prevention in health economics (Boeri et al., 2013) to auctions (Filiz-Ozbay and Ozbay, 2007; Hayashi and Yoshimoto, 2016), financial markets (Fogel and Berry, 2006; Frydman et al., 2017; Frydman and Camerer, 2016), portfolio and pension scheme selec- tion (Muermann et al., 2006; Hazan and Kale, 2015), and currency hedging (Michenaud and Solnik, 2008). Apart from the empirical applications, regret avoidance has been studied both the- oretically (Bell, 1982; Loomes and Sugden, 1982; Skiadas, 1997; Sarver, 2008; Hayashi, 2008; Bikhchandani and Segal, 2014; Leung and Halpern, 2015; Qin, 2015; Buturak and Evren, 2017) and experimentally (Coricelli et al., 2005; Camille et al., 2004; Zeelenberg, 1999; Bleichrodt et al., 2010; Strack and Viefers, 2017). Even though many aspects of re- gret avoidance were considered in these studies, their focus is mainly on static problems where a single decision is made that can be affected by the information about possible counterfactual outcomes. Such problems are important since many real life decisions, like buying a house or a pension plan, fit into this setting. Nevertheless, many interesting phenomena that involve regret have a dynamic nature, the stock market being one impor- tant example. These situations are characterized by the presence of the time dimension: a decision or decisions should be made given some past information and/or expectations of the future, both of which change as time unfolds. Regret in this case also becomes a dynamic variable that is reevaluated in each time period. More importantly, there emerge the concepts of past and future regret. A choice is influenced by past regret when an action taken today brings about a desirable outcome that was foregone in the past. Future re- gret involves taking actions that prevent missing the opportunity of achieving a desirable expected future outcome. For example, in financial markets the decision to sell an asset might depend on the highest observed price in the past (past regret), but traders might 1 The work in this chapter is joint with Alexander Vostroknutov (University of Maastricht) and Giorgio Coricelli (University of Southern California). 45 also think about the hypothetical counterfactual situation in which they sell an asset today and regret doing it later (future regret), and adjust their behavior accordingly. In this paper we investigate how past and future regret influence choices in a con- trolled experimental setting, similar to a stock market. Our main interest is to understand how different elements of the dynamic situation interact and influence behavior: in our case, the decision to sell an asset. In particular, we are interested in the following ques- tions: (i) How strongly does the avoidance of past and future regret influence the choice to sell? and (ii) Is there an interaction between past and future regret? Does one become stronger or weaker in the presence of the other? In our experiment, reminiscent of those reported in Oprea et al. (2009), Oprea (2014), and Strack and Viefers (2017), participants take part in a series of “stock markets”: they observe how the price changes in real time and choose when to sell an asset that they own. Participants make choices in two types of markets. In some markets they do not see the future price of the asset after they made their selling decision. In other markets they do see the future price. Participants are always informed beforehand about the type of the market they are in. This setup allows us to analyze past and future regret, and their interaction. In both conditions past regret can potentially influence participants’ decisions to sell the asset since the price history is observable. At the same time, we are able to see if access to the prices after selling has an effect on the decision making (future regret). More importantly, our design makes it possible to use structural modelling and estimate the parameters of a utility specification that includes past and future regret components in a dynamic discrete choice setting (e.g., Rust, 1987; Hotz and Miller, 1993). We find that participants are influenced by the observable past prices and do behave differently depending on whether they know that the future prices will or will not be observed after they sell the asset. Our evidence that participants sell the asset to make the effect of past regret smaller or absent confirms the results of the recent studies which focus on past regret only (Gneezy, 2005; Strack and Viefers, 2017). We go further and consider the possibility that agents keep the asset longer when they know that they can observe future price and expect it to be high, as compared to the case when they know they will not observe future prices. Our data show that information about the availability of the prices after selling, indeed, has this expected effect on the decision to sell. More importantly, when the participants know that they will not observe future prices, their choices to sell are not affected by future regret avoidance. In addition, we find that indi- vidual risk preferences also play a role in the selling decisions. However, their effect on choice is secondary to regret avoidance and does not influence the estimates of the regret parameters. Estimates of the parameters of a regret-averse utility function obtained from a dy- namic discrete choice model suggest that the effects of the past and future regret are not simply additive. We demonstrate that there is an interaction between past and future re- gret in the utility, which would not be possible to identify with simple regression analysis. Past and future regret are not complements, but rather lessen the effects of one another. This happens because, while both regret components of the utility function are negative, the interaction term offsets the effect of the smaller one. We call this phenomenon a sub- stitution effect between past and future regret. At each point in time participants’ selling choices are not influenced by both types of regret at once but are rather guided by the one 46 which is stronger. This also implies that, depending on the circumstances, the behavior on the market can be either past or future oriented. Our findings demonstrate that individuals incorporate past and future regret into the utility function in dynamic settings, and that they are able to extract and update com- plex counterfactual information about the changing environment and integrate it into the decision process. 2.2 The Experiment The data were collected in a behavioral experiment in which participants were pre- sented with a series of mini stock markets. Each participant observed the graph of a market price as it gradually changed in time in 0.8 seconds intervals and had to decide when to sell an “asset” (see Figure 2.1). For the first 15 periods participants could only observe the price. Then, in period 15, they were forced to buy an asset at the current price. The point of entry was marked with a vertical red line. The market price kept changing until participants decided to sell the asset (marked with a blue line on the graph). In case no selling decision was made the market continued until its closure in period 50, at which point participants were forced to sell. The profit was equal to the selling price minus the entry price (price in period 15), so that participants could actually lose money (each participant received ae 10 fee that covered her in the case of a loss). In each market the price followed a stochastic mean reverting process defined by y t+1 = ay t +(1a)#, wherea= 0.6, y t is the price in period t, and# is an identically and independently distributed random variable (uniform betweene 0 ande 10). Participants were informed about the process that generated the price and made selling decisions in six training markets without payment which allowed them to see the examples of the price dynamics and get used to the interface (the market prices used in the experiment are graphed in Appendix B.1.5). Each participant made selling decisions in 48 different markets, which could be of two types. In some markets (No Info condition, left picture in Figure 2.1) participants knew from the beginning that after they sell the asset they will not see the future price. In the Info condition (right picture in Figure 2.1) participants knew from the beginning that after selling the asset they will observe the evolution of the price until the market closure in period 50. This information was shown in the upper-left corner of the graph from period 1 onwards (INFO DOPO means “info after”). The markets were presented in random order that was generated independently for each participant. Half of the markets were presented in the No Info and half in the Info condition. The sequence of conditions was also randomized. After the markets, the participants were presented with an incentivized Holt-Laury task (Holt and Laury, 2002) and a questionnaire. Overall, 154 participants took part in the experiment in 9 sessions. The average earnings in the main task were e 11.46. The experiment was programmed in z-Tree (Fischbacher, 2007). Further details of the design can be found in Appendix B.1. 47 Figure 2.1: Screenshots of two markets Notes: Above the graph participants could see the entry price (Valore di entrata), current price (Valore corrente), selling price (Valore di uscita), and profit (Guadagno), which was green for positive and red for negative profit. In the No Info condition the future price was not shown (left picture). In the Info condition the price evolution was shown after the selling decision (right picture). The sentence at the bottom of the left picture says: “Please wait until the market is closed.” 2.3 Evidence of Regret Avoidance In this section we look at some summary statistics, in order to compare the selling behavior to the no regret benchmark, and report a regression analysis that shows the effects of past and future regret. This analysis can provide only crude estimates of how the current market state influences the choices to sell, since it is static in nature and does not take into account the dynamic structure of the markets. Nevertheless, it does demonstrate how the participants react to past and expected future prices. We start with a comparison of the behavior of our participants with the optimal choice of a risk-neutral regret-free agent who should sell the asset whenever the price rises above a certain threshold that depends on the number of periods left in the market. The dynamic stopping problem that describes optimal choices is formulated in Appendix B.2. We focus on the class of CRRA utilities U(y) = y 1r 1 1r , where y is a selling price, and numerically evaluate the optimal policy prescribed by the dynamic program from Ap- pendix B.2. Figure 2.2 illustrates the optimal policies for five values of the risk parameter r (both risk-loving and risk-averse). It is optimal for the agent to sell the asset if the price is above the shown thresholds. The figure demonstrates that risk-loving agents (with r < 0) optimally sell the asset at higher prices than risk-averse agents (r > 0). Notice, however, that the effect of risk preferences on the optimal threshold is rather small. The threshold is virtually the same in period 16 for risk-loving and risk-averse agents, and in period 49 the threshold changes frome 4.7 (r = 0.7) toe 5.3 (r =1). This implies that we should not expect any strong behavioral effects to stem from the heterogeneity in risk preferences. In order to compare the behavior of participants with this benchmark we consider sell- ing decisions at relatively high prices, since participants’ choices coincide with the model 48 Figure 2.2: The optimal selling price threshold for different risk preferences Optimal sale price threshold ρ = -1.0 ρ = -0.3 ρ = 0.0 ρ = 0.3 ρ = 0.7 8 7 6 5 Period 16 19 22 25 37 28 34 46 49 43 40 31 Notes: The figure plots the optimal sale prices for a CRRA utility agent who is regret neutral. Figure 2.3: Proportion of missed sales when selling is optimal [5 ,6.3) [6.3, 6.7) Proportion of missed optimal sales Deciles of price [6.7, 7) [7, 7.2) [7.2, 7.3) [7.3, 7.4) [7.4, 7.5) [7.5, 7.6) [7.6, 8] > 8 0.8 0.6 0.4 0.2 0.0 1 2 3 4 8 5 7 10 9 6 Optimal proportion Notes: The proportion of times the participants decided to keep the asset despite the current price being greater than the optimal selling threshold of the risk-neutral regret-free agent. Observations are grouped by deciles. The solid line at zero shows the proportion of missed sales expected from the rational no regret agent. The spikes are1SE. 49 prediction to keep the asset when the prices are low. Figure 2.3 summarizes selling de- cisions in situations when the participants had a choice to sell, and the price was above the optimal selling threshold (of a risk-neutral agent). If our participants chose in accor- dance with the predictions of the no regret utility model, they would have sold the asset in all these cases. We observe that even at the 10th decile of the price distribution there is a large deviation from the optimal strategy: participants do not sell the asset in 34% of the cases. When we look at the prices belowe 6.3 (first decile), we see that the asset is kept in 80% of the cases when it actually should have been sold, a huge discrepancy with the predictions of the standard model. Still, the deviations from the standard model can, in principle, be noise artifacts. To falsify this idea we run a logit and an OLS regression where the dependent variable is the decision to keep the asset and the independent one is the current price (conditional on being above the optimal threshold). We find a signif- icant negative trend in the probability to keep the asset (logit coefficient0.71 ; OLS coefficient0.16 ). This shows that the differences in proportions are not random and are higher for lower prices. This evidence suggests that the participants mostly keep the asset in situations when the standard model predicts it should be sold. One potential explanation of this effect is loss aversion. Suppose that participants suffer some additional fixed disutility from having negative profit (selling the asset at a price lower than the entry price). This can, in principle, make them keep the asset longer in order to make a positive profit. However, in our data the correlation between the entry and selling prices is very small (Spearman’s r = 0.058, p < 0.001). This suggests that loss aversion is not a good candidate for ex- plaining the data. Moreover, it does not predict any difference between the Info and No Info conditions which we report below. We hypothesize that the observed behavior is driven by the desire to minimize regret, which is proportional to the distance between the current price and the highest price in the past (past regret) or the expected highest price in the future (future regret). The highest price in the past, or past peak, is calculated as the highest price achieved up to the current period. 2 The future expected highest price (future peak) is the expectation over the maximum price that can be achieved in all future paths (see Section 2.4 for details). To test the idea that the past peak influences the decision to sell, we examine the selling rates. Overall, participants sell the asset in 51% of the situations when the price goes above the past peak (i.e., it is a new peak). If we look only at the cases when the price is above the optimal threshold of the risk-neutral agent without regret, then the selling rate becomes 71% at the new peak and 34% when the price is not the new peak. This provides evidence that the past peak has an influence on the decisions to sell even when the standard model unambiguously predicts only sales. To see the importance of the past peak for the decision to sell consider Figure 2.4A. We group the new past peaks by how high they are and find that, when the new past peak is abovee 8, selling happens in 71% of the cases, in the range[7, 8] – in 63%; in the range[6, 7] – in 30%; and in the range[5, 6] – in 2.6%. Notice that the percentages of selling, when the price is in the same intervals, but is not a new peak, are 46%, 32%, 14%, and 3.4% respectively, much lower values. Figure 2 Gneezy (2005) shows in a setting similar to ours that the past peak is a more plausible reference point than the purchase price. 50 Figure 2.4: Past and Future regret avoidance Ratio of sales in No Info to Info A Price is below the past peak Price is the new peak Asset sold within €0.5 of past peak Asset sold within €1.0 of past peak B Period 16 19 22 25 37 28 34 46 49 43 40 31 Price range (5, 6] (6, 7] (7, 8] > 8 0.8 0.6 0.4 0.2 0.0 Selling rate 1.3 1.2 1.1 1.0 0.9 Notes: Panel A: The percentage of sales when the price reaches a new peak (dark grey) and when the price is below the current past peak (light grey). The error bars are1SE. Panel B: The ratio of the number of sales up to period t in the No Info condition to the number of sales up to period t in the Info condition. The dashed line includes sales withine 0.5 of the past peak and the solid line withine 1 of the past peak. B.4 in Appendix B.3 shows the same graph restricted to observations above the optimal threshold in the standard model. The influence of the past peak is unchanged. Thus, the difference in sale rates cannot be explained by the standard theory, we need to consider past peaks in order to explain our data. To show the influence of the future peak on the decisions to sell, we notice that the fu- ture expected highest price is decreasing in time, since early in the market there is plenty of opportunities for the price to rise, whereas, when there are only few periods left, the price cannot go much higher than its current level. Therefore, future regret, which is pro- portional to the future peak, should be highest in early periods and decrease later on. If our participants are sensitive to future regret, we should observe a difference in sell- ing behavior between the No Info and Info conditions in early periods. The two lines on Figure 2.4B represent the cumulative ratio of the number of sales in the two conditions which are withine 0.5 ande 1 of the past peak. For each time period this ratio exceeds one which implies that there are more decisions to sell in the No Info than in the Info con- dition. This effect is especially evident in the early periods. In the late periods the number of selling decisions becomes approximately the same. 3 This provides first evidence that participants sell less often early on in the Info condition because of the possibility of future regret, which makes them keep the asset longer in order to reduce the disutility associated with it. Moreover, the ratio is higher for the sales which aree 0.5 close to the past peak than for the sales which aree 1 close. This is the case since in the No Info condition being closer to the past peak implies higher probability of selling, whereas in the Info condition the past peak is less salient due to the possibility of observing high prices after selling. To investigate the influence of a larger set of variables on the decisions to sell we run a series of logit regressions shown in Table 2.1 with the dependent variable equal to 1 if a participant keeps the asset and 0 if she sells it. Notice that these regressions can 3 Figure B.5 in Appendix B.3 shows that the ratios starting from period 33 oscillate in the vicinity of one. 51 provide only a simplified picture of the relationships in our data since they do not account for the time dependencies due to the Markovian nature of the price evolution and the optimizing behavior of the participants. The main variables of interest are the market condition (info), the past peak, the future expected peak, and their interactions. 4 We see that both past and future peaks significantly influence the probability to keep the asset (columns II and III): the higher they are, the longer the participants hold the asset. More importantly, in the Info condition we see that the influence of the past peak decreases and the influence of the future expected peak increases (interactions with the variable info, column III). This is consistent with our hypothesis that the possibility to observe future prices makes participants more focused on the future. 5 We further investigate the decision to keep the asset by introducing more variables. The regressions reported in Table B.2, Appendix B.5, show a small but significant effect of the risk preferences, as estimated by the Holt and Laury task (Holt and Laury, 2002), on the probability to keep the asset (variable hl). As risk aversion increases, the prob- ability of keeping the asset goes down, which is consistent with the predictions of the no regret model (Appendix B.2). Nevertheless, risk preferences alone cannot account for the dependency of the selling choices on the market condition, the past price history, or future expected prices since all the interactions of the corresponding variables with hl are insignificant (regressions in columns V and VI). Finally, the regressions in Table B.3, Appendix B.5, show a significant effect of the market condition (Info vs. No Info) in early periods. The probability of keeping the asset is higher in theInfo condition (variable infoearly, columns I and II), which is in line with future regret avoidance as we explained above (Figure 2.4B). To summarize, we find some evidence that the decisions to sell are influenced by past regret avoidance (Figure 2.4A and Table 2.1). We also find that in theInfo condition future peaks become more and past peaks less salient for the decision to keep the asset (Table 2.1), which is consistent with future regret avoidance. Finally, participants keep the asset longer in the early periods of theInfo condition when future regret is the strongest (Figure 2.4A and Table B.3 in Appendix B.5) suggesting an interaction between the two types of regret. These results, however, should be treated with caution. While the presence of past regret avoidance is unambiguous, given that past peaks are always observed by partic- ipants and are, in a sense, “tangible,” we cannot reliably conclude from the regression analysis that participants exhibit future regret avoidance since the significant effect of the variable future expected peak can have other sources. Regressions do not account for the dynamic structure of the optimization problem and, essentially, just reveal correlations between the selling events and the corresponding states of the market. Therefore, the effect of the future expected peak can come from the attempts of participants to act upon some kind of future expectations, which does not at all imply that they try to avoid future 4 See Appendix B.4 for the description of the variables used in the regressions and Appendix B.6 for the computation of highest expected future price. 5 We also make several observations about the control variables. The probability of selling increases with time (coefficient on period is negative). The negative coefficient on price 2 suggests non-linearity in response to price changes and increase in probability of selling as price increases. The positive coefficient on the future expected price shows that the selling behavior is modulated by future considerations, in particular, a higher expected price in the future makes participants keep the asset longer. 52 Table 2.1: Random effects logit regression of the choice to keep the asset Pr[choice= keep] (I) (II) (III) Price –0.497 –0.319 –0.326 (0.146) (0.133) (0.134) Price 2 –0.102 –0.125 –0.125 (0.013) (0.012) (0.012) Time –0.088 –0.082 –0.082 (0.004) (0.004) (0.004) Future Expected Price 1.423 1.401 1.381 (0.230) (0.190) (0.188) Past Peak 0.506 0.600 (0.035) (0.045) Future Expected Peak 0.309 0.210 (0.071) (0.084) Past Peakinfo –0.209 (0.065) Future Expected Peak info 0.183 (0.066) Info 0.129 (0.675) Constant 4.525 –1.955 –1.746 (1.161) (0.966) (1.099) N 112,137 112,137 112,137 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: choice is zero at the time the participant sells the asset and one otherwise. Observations are all periods in all markets for all participants in which they made a choice (periods 16 to 49). Errors are clustered by participant. The descriptions of all variables can be found in Appendix B.4. regret. The same can be said about the possible interaction between past and future re- gret, the presence of which our data suggest: it can simply be an artifact of optimization with some considerations of the future. In order to resolve this issue, in the following sections we formulate and provide estimates of the structural model, which allows us to explicitly separate the role of past and future regret from that of future expectations while taking into account the dynamic nature of the task. 2.4 Regret-Averse Utiltiy Function We start with defining the regret-averse utility function that is further used in the structural model. We hypothesize that the highest price in the past is a reference point, that our participants use to measure how well they are doing (as shown in Figure 2.4A). This 53 is a dynamic variable that changes when the price gets above the observed highest peak. 6 We conjecture that the higher the past peak the more negative the feeling of past regret should be given the current price (which is always less than or equal to the highest past peak). This implies that the past peak should exert influence on the decision to keep the asset (past regret). Our modelling choice is motivated by recent work (e.g., Gneezy, 2005; Strack and Viefers, 2017) which leverages on the saliency of the highest past price as the key measure of regret, allowing us to disregard other functions of past prices that could be used as reference points for past regret. Highest past prices were found to be important in trading decision on financial markets. For example, in their analysis of the decision to exercise stock options, Heath et al. (1999) found that exercising activity doubles when the current price attains the maximum level over the past year. Denote the maximum past price by s p,t = max tt fy t g. Under past regret (only), or situations when the agent knows that future prices after selling are not observable, the utility function is u(y t , s p,t )= py t ws p,t (2.4.1) if the asset is sold in period t. The consumption part of the utility is given by py t while the disutility from regret is captured by the second term with parameter w. The results in the previous section show a limited role of risk aversion and therefore we assume risk neutrality in this section, though we also estimate the model assuming CRRA preferences. This utility function offers a simple testable hypothesis: when w = 0 the decision of the agent does not depend on the past peak. This means that the less the agent cares about past regret, the less his selling price is influenced by the past peak. 7 If participants are aware that they will observe prices even after selling the asset, they can anticipate a situation when the future price will exceed the selling price, which would lead to negative emotions (future regret). In this case participants’ decisions to sell should be sensitive to the future expected highest price, which is a dynamic variable that depends on the current price and the number of periods left before the market closure. When this information is not available, the future regret should not play any role in the selling decisions since participants do not anticipate any negative emotions from observing high prices after selling. 8 The expectation of the highest future peak at time t, denoted by s f ,t = E[max t<tT y t jy t ], is a function of the price today and the number of periods left until the market closure. s f ,t is the expectation of the maximum price achievable in T t periods given the 6 Notice that without regret the optimal policy is to sell the asset whenever the price rises above the threshold in Figure 2.2 which depends only on the number of periods left. Thus, in the no regret case the selling decision is independent of any reference points. 7 It should also be acknowledged that this is not a standard regret aversion function which has one reference point and two parameters like in Bell (1982) and Loomes and Sugden (1982). Since we eventually focus on two reference points (past and future regret) such a function would complicate both the estimation and the interpretation of the results across conditions. 8 A similar negative response was found in Cooke et al. (2001), where reported satisfaction scores were negatively correlated with the prices after the sale decision. 54 current price y t . In the future regret case the agent’s utility is captured by u(y t , s p,t , s f ,t )= py t ws p,t as f ,t . (2.4.2) We operationalize regret over future foregone outcomes as the disutility of “observing” the expected highest future price at time t. 9 As an additional observation, notice that s f ,t is increasing in y t and decreasing in t because of the presence of a terminating period (see Appendix B.6 for the details). Con- versely, notice that s p,t is a weakly increasing function of time, since it is defined as a maximum of the past prices. This suggests that future regret should be dominant in early periods while past regret in late periods. In order to make the utility specification more flexible and to be able to infer whether the current reference point is the highest price observed in the past, the expected highest price in the future, or a combination of these two variables, we add an interaction term to the utility function. The utility now becomes u(y t , s p,t , s f ,t )= py t ws p,t as f ,t ls p,t s f ,t . (2.4.3) Estimating the three regret parameters will make it possible to tell how the reference point changes in time depending on the relative sizes of the past and future regret. Our definition of the future regret is a major departure from the analysis in Strack and Viefers (2017), who focus only on the regret over past decisions. The novelty of our approach is that we consider a decision maker who takes into account both the endoge- nously changing past reference point (the past peak) and the exogenously given infor- mation about the possibility of future regret which shares features with the classical static regret. Thus, our decision maker is affected by both the past price shocks, as in Strack and Viefers (2017), and by the knowledge of the availability of price information after selling the asset, which comes at a cost, since the decision maker may be future regret averse. We model these two forces with separate reference points, one in the past and one in the future, and investigate empirically whether they subdue or reinforce each other. 2.5 A Structural Model of Dynamic Regret Avoidance To asses the role of dynamic regret avoidance in decision making we interpret the distance between the optimal policy and the actual choice in terms of consumption utility and regret. We estimate a dynamic discrete choice model (e.g., Rust, 1987, 1994) where the value from selling the asset is directly compared with the continuation value: participants sell when the former is larger than the latter. This section sketches the model that will be taken to the data in Section 2.6. Appendix B.8 provides the full derivation. In a dynamic environment participants choose their best action taking into account the 9 When allowing for risk preferences (Appendix B.10.1) we define the future regret as the disutility at the future highest peak,aU(s f ,t ;r), where U(;r) is a CRRA utility with risk aversion coefficient r. An alternative approach would be to define it as the expectation of a regret function over possible draws of the future price, e.g. E[U(max t<tT (y t ))jy t ]. This, however, would entail significant estimation difficulties. Our definition is in line with the idea that participants have a “target income” at any point in time (see, e.g., Camerer et al., 1997; Crawford and Meng, 2011). 55 Markovian nature of the prices and optimal future decisions. In each period t one of two choices is made: to sell the asset (d= 0) or to keep it (d= 1). u d (x t ) denotes the per period regret-averse utility from choosing action d when the current state is x t = (y t , s p,t , s f ,t ). According to this notation u 0 (x t ) may refer to either (2.4.1), (2.4.2), or (2.4.3) depending on whether the subject is in the No Info or Info condition, respectively. A participant’s intertemporal utility is E T å t=1 b t1 u d (x t )+# d t where the expectation is taken over the future values of the independent variables. b2 (0, 1) is the discount factor. Similarly to most of the binary static discrete choice models, it is assumed that the value of each choice includes an additive logit error (# 1 t ,# 0 t ), which accounts for unobserved state variables that may affect choices. The dynamic environment can be summarized using a value function v d which repre- sents the discounted sum of the future payoffs and is defined by the Bellman equation v d (x t )= ( 0+bEfv(x t+1 )jx t , d= 1g if d= 1 (keep) u 0 (x t )+ 0 if d= 0 (sell). (2.5.1) Notice that the deterministic part of the per period payoff of continuing, u 1 (x t ), and the continuation value of selling the asset are zero. In fact, participants are only paid the price at which they sell the asset at the time when they sell it. Therefore, the expected value function before a choice is taken is the expectation (over the error term) of the utility from the optimal choice in (2.5.1) and can be written as v(x t ) = R # maxfv 0 (x t )+# 0 t , v 1 (x t )+ # 1 t )gdL(#). To solve the Bellman equation we show that the distribution of the observed choices uniquely identifies the utility function. However, the large size of the state space (x t 2 X t ) and the large number of periods make a solution by backward induction (the classic method when periods are finite) a daunting task. Yet, leveraging on the stationarity of the utility function and a contraction mapping argument we can transform (2.5.1) into a set of equations that can be solved by least squares method (e.g., Pesendorfer and Schmidt- Dengler, 2008; Aguirregabiria and Mira, 2010). Intuitively, the participant will choose to keep or sell the asset depending on which action provides the higher value conditional on any given realization of the state variable (x t ). Therefore, we expect this relation to be reflected in the probability of choosing each action conditional on the state and period. For this case Hotz and Miller (1993) show the existence of an invertible mapping between the value functions and the related probabil- ity of choosing each action given x t . This probability is known as the Conditional Choice Probability (CCP) and is denoted by p 1 (x t ) = Pr(d = 1jx t ) for the probability of continu- ing and p 0 (x t ) = Pr(d = 0jx t ) for the probability of selling. Importantly, the CCP can be estimated directly from the data. We therefore treat p d (x t ) as a known object for all t and x t . The identification procedure uses the CCP , together with the properties of the logit distribution, to simplify the Bellman equation in terms of known variables. The logit assumption gives an analytical solution for the probability of choosing each 56 action. For example, the probability of choosing action 0 is p 0 (x t )= 1/ 1+ exp(v 1 (x t ) v 0 (x t )) which depends on the difference of the two alternative specific value functions (in equation 2.5.1). This difference is v 1 (x t ) v 0 (x t )=u 0 (x t ) +b Z X t+1 Z # maxfv 0 (x t+1 )+# 0 t+1 , v 1 (x t+1 )+# 1 t+1 )gdL(#)dF(x t+1 jx t ) (2.5.2) where the inner integral is over the error term, and the outer one is over the state space in the next period. The law of motion of x t across periods is characterized by the transition matrix F(x t+1 jx t ) which describes the probability of moving from x t to x t+1 . Note that, since the only random variable is the current price, the transition matrix depends only on the distribution of y t . The last equation can be simplified further. As noted by Hotz and Miller (1993) the CCP can be inverted resulting in v 1 (x t ) v 0 (x t ) = ln(1 p 0 (x t )) ln(p 0 (x t )). 10 The difference between the value of keeping and selling the asset can, thus, be thought of in terms of changes in the probability of selling the asset. This means that the left hand side of (2.5.2) is a known function of the data, the CCP . Let us denote it byf(p 0 (x t )) and rewrite (2.5.2) as f(p 0 (x t ))=u 0 (x t )+b å X t+1 u 0 (x t+1 ) ln(p 0 (x t+1 )) f(x t+1 jx t ) (2.5.3) where the summation substitutes the integration as the state space needs to be discrete (a technical requirement). 11 Note also that in passing from (2.5.2) to (2.5.3) the expectation of the optimal choice in period t+ 1 is rewritten in terms of the utility from the terminating action (sale) and the probability of selling the asset in the next period. Appendix B.8 shows all the steps of this derivation which is based on the properties of the logit error. Several observations about the equation (2.5.3) should be made. First, it summa- rizes intertemporal choices by only comparing the utility from selling at two consecu- tive periods with the expected (log) probability of selling in the next period given by å X t+1 ln(p 0 (x t+1 )) f(x t+1 jx t ). This term is important because it incorporates the contin- uation value and can be thought of as the utility from waiting for a better price. In fact, this expectation is proportional to the continuation value at t+ 1 through the definition of the CCP . 12 Hence, we know that the RHS of (2.5.3) increases when agents expect high returns from keeping the asset in the following periods. Because the LHS of (2.5.3) corre- 10 The CCP of selling the asset is p 0 (x t ) = 1/(1+ exp(v 1 (x t ) v 0 (x t ))). This can be transformed into v 1 (x t ) v 0 (x t )= ln(1 p 0 (x t )) ln(p 0 (x t )). 11 The discretization of the state space is necessary to estimate the model. For our experiment this is not a problem, the participants face a discrete state space anyway as y t was rounded to cents. The discretization is implemented according to the approach proposed by Tauchen (1986) to approximate a vector autoregres- sion model with a finite state Markov chain. All variables (current price, past peak and future peak) are discretized on the same support in [0.59, 9.32]. The distance between the 400 bins ise 0.02. This method is described in detail in Appendix B.7. 12 From the derivations above we have ln(p 0 (x t+1 )) = ln(1+ exp(v 1 (x t+1 ) v 0 (x t+1 ))) which is ap- proximately equal to v 1 (x t+1 ) v 0 (x t+1 ). 57 sponds to the difference between the value function from keeping and selling the asset, a greater continuation value implies that the agent is more likely to keep the asset in period t. Second, given the same continuation value, ifw> 0 the model predicts that the agent will be less likely to sell in period t if the distance between the past peak and the current price is larger than the expectation of the same difference in the following period. To see this, notice that RHS of (2.5.3) increases if the difference between the past peak and the current price goes up, which in turn should increase the LHS, or decrease the probability of selling. This reasoning can be also applied to the future expected peak. In the Info condition, an agent will be less likely to sell the asset in period t if s f ,t > E[s f ,t+1 ] and a> 0, other things equal. This follows again from the increase in RHS of (2.5.3) when the expectation of the future peak changes marginally. We have constructed a simple two-step estimator. The first step involves recovering the CCP and the transition matrix directly from the data. In the second step these objects are plugged into (2.5.2) (e.g., Hotz and Miller, 1993; Pesendorfer and Schmidt-Dengler, 2008). This gives us the objective function (equation 2.5.3) used to estimate a param- eterized version of the utility of selling the asset u 0 (x t ), which includes regret-averse components for the two conditions (Info and No Info). In conclusion, the procedure just described relies on the common logit assumption in the binary choice literature, the pres- ence of a terminating action (selling the asset) and on the Markovian structure of the state variables. 2.6 Estimation of the Structural Model We now turn to the estimation of the dynamic discrete choice model in Section 2.5. However, before proceeding to the estimation of (2.5.2) we analyze how the CCP differs in the two conditions, as this can further elucidate the mechanisms at play. 2.6.1 Estimation of the Conditional Choice Probabilities The conditional probability of selling the asset (or continuing) at period t is computed directly from the data. We exclude periods 15 and 50 since no one sold the asset in the former (first choice period) and the choice is forced in the latter (last period). Participants sell their asset in different periods, resulting in a highly unbalanced dataset. The CCPs are constructed using a logit estimator of the choices of the active participants in each period t2f16, ..., 49g as a function of the realized state variables. It is important to stress that there are two policy functions to be estimated for each period. This is because the experiment has two conditions. The CCP for the No Info condition depends only on the price and the running past maximum of the process: Prfd= 0jNo Info, x t g=L(b 1t y t +b 2t , s p,t )8t (2.6.1) 58 while in the Info condition it also depends on the expected future maximum: Prfd= 0jInfo, x t g=L(b 1t y t +b 2t s p,t +b 3t s f ,t )8t. (2.6.2) To maintain symmetry, the two logistic regressions are very similar. In principle, several other valid specifications can be used. However, since the sample size shrinks as partici- pants sell their assets over time, adding additional covariates undermines the identifica- tion of the parameters. 13 Figure 2.5: The effect of the past peak on the probability of selling the asset in the No Info condition Price past peak €3 past peak €7 past peak €5 past peak €8 1 2 3 4 5 6 7 8 9 1.00 0.75 0.50 0.25 0.00 Average probability of selling Notes: The conditional choice probability is computed by taking the average of the fitted values from (2.6.1) for all periods t2f16, ..., 49g. This figure is for illustrative purpose only and is based on a state space discretized over 200 bins. Figure 2.5 shows the projections of the time-averaged fitted CCP in the No Info con- dition. Specifically, each line represents the estimate of the probability of selling which results from averaging the fitted values of 34 logit regressions (one for each time period). 14 For the prices belowe 5 the probability of selling is the highest when the past peak ise 3, 13 Adding square and interaction terms creates a large multicollinearity problem, eventually impairing the identification of theb nt coefficients. In fact, the singular value decomposition of the matrices of covari- ates in (2.6.1) and (2.6.2) show that including these terms makes it ill-conditioned in most periods. Also clustering at subject level does not affect the results. 14 Thus, the CCPs in Figures 2.5 and 2.6 are shown just for illustration. They are out of sample estimates which do not take into account the influence of the current price on the past peak (i.e., the current price cannot be larger than the highest observed price). 59 is lower when the past peak ise 5 and is close to zero for past peakse 7 ande 8. This means that, when prices are low, the participants are strongly influenced by the size of the past peak and wait for the price to become closer to it. For the past peakse 7 ande 8, which are very common in our data, the probability of selling increases rapidly when the price approachese 7. This demonstrates that the past peak indeed serves as a reference point. Figure 2.6: The effect of the past peak and the expected future peak in the Info condition 0.00 0.25 0.50 0.75 1.00 1 2 3 4 5 6 7 8 9 Price Average probability of selling past peak €5 past peak €7 future peak €8 future peak €8 Notes: The conditional choice probability is computed by taking the average of the fitted values from (2.6.2) for all periods t2f16, ..., 49g. This figure is for illustrative purpose only and is based on a state space discretized over 200 bins. Figure 2.6 illustrates similar projections of the CCP in the Info condition. For fixed value of future regret the relationship between the curves with past regret equal toe 5 ande 7 is the same as in Figure 2.5. However, the effect of past regret is much smaller in this case. We conjecture that this is due to the presence of the future regret term which dominates the past regret. In what follows we show that there is a substitution effect be- tween the past and future regret that can explain this pattern. 2.6.2 Estimation of the Parameters In order to causally connect regret avoidance and decisions to sell in our experiment, we estimate (2.5.3) by non-linear least squares procedure (Pesendorfer and Schmidt-Dengler, 2008). Nonparametric identification is shown in detail in Appendix B.9. We only provide an intuition of the proof here, which is standard (Hotz and Miller, 1993). The most impor- tant step is to realize that the value function of the continuation choice (alternative 1) is a 60 contraction mapping. Therefore there is a unique solution to v 1 (x t ). In addition, the dif- ference of the two value functions is obtained using the formula for the CCP . Given that selling is a terminating action (v 0 (x t ) = u 0 (x t )), the per period utility, u 0 (x t ), is found by summing the CCP with v 1 (x t ). We proceed with the estimation of a parametric version of (2.5.3). We propose different specifications of the utility function (Section 2.4) to study howw,a, andl affect decisions. First, we focus on a utility that includes only past and future regret in the two conditions as in (2.4.1) and (2.4.2), and then we extend the analysis to uncover a possible interaction between the two variables as in (2.4.3). Suppose that the per period utility from selling is defined as u 0 (y t , s p,t , s f ,t )= py t R(s p,t , s f ,t ) (2.6.3) where R(,) is the regret function which is defined as R(s p,t , s f ,t )=1 fNo Infog w NI s p,t +1 fInfog w I s p,t +a I s f ,t . (2.6.4) The arguments of the regret function are the past and expected future peaks and the market conditions are denoted by the subscripts “NI” for No Info and “I” for Info. The indicator function distinguishes the utility derived in one condition from the other. The parameters of R(;r) are free to vary and indicate how strongly participants’ decisions are affected by regret. Note, in fact, that, ifw NI ,w I , anda I are not significantly different from zero, the participants are categorized as regret neutral. The estimation of (2.5.3) with the regret term as in (2.6.4) exposes the importance of past and future regret in dynamic decision making. The results are shown in the first three columns of Table 2.2 and are obtained by nonlinear least squares on the dataset including periods t2f16, ..., 48g. 15 The identification assumes that the discount factor is known (Magnac and Thesmar, 2002), so the table shows utility function coefficients forb approaching 1 (i.e.,b2f99.65%, 99.60%, 99.55%g). The results are robust across different designs and discount factors. 16 The estimation of (2.6.4) in Table 2.2 shows that participants are both past and future regret averse. In particular, in the specification (2.6.4) past regret is significant in the No Info condition, while future regret is significant in the Info condition which means that our participants are also influenced by future regret avoidance. Notice that past regret is not significant in the estimation of (2.6.4). The absence of the effect of the past peak is surprising given the discussion in Section 2.3 and the regression analysis in Tables 2.1, B.2, and B.3, which shows the centrality of the s p,t term for both conditions. The reason for this might be that the model is missing an important interaction between the past and the future regret: they might reinforce or inhibit each other. Such an interaction was previously exposed in the discussion of Figure 2.4B and regression B.2 in Section 2.3 when we compared the decisions to sell early and late in the two conditions. Its presence was 15 For consistency period 49 is dropped because choices taken in this period are directly affected by the fact that participants are forced to sell in period 50. This marginally shrinks the dataset from 112,137 to 111,613 observations. Including period 49 does not change the results. Note that the CCP must still be computed for period 49. 16 Estimations for different regret functions R() and risk preferences are provided in Appendix B.10.1. The analysis in Appendix B.10.2 includes a loss aversion parameter. 61 Table 2.2: The estimation of past and future regret (I) (II) (III) (IV) (V) (VI) Estimation of (2.6.4) Estimation of (2.6.5) b= 99.65% b= 99.60% b= 99.55% b= 99.65% b= 99.60% b= 99.55% ˆ p 1.892 1.890 1.888 1.884 1.882 1.880 (0.011) (0.011) (0.011) (0.011) (0.011) (0.011) ˆ w NI 0.313 0.379 0.464 0.364 0.427 0.508 (0.188) (0.185) (0.180) (0.188) (0.185) (0.181) ˆ w I 0.073 0.033 0.145 1.539 1.636 1.712 (0.195) (0.192) (0.188) (0.400) (0.359) (0.326) ˆ a I 0.174 0.221 0.262 1.488 1.552 1.595 (0.076) (0.074) (0.074) (0.295) (0.262) (0.238) ˆ l I 0.206 0.215 0.221 (0.045) (0.041) (0.038) N 111,613 111,613 111,613 111,613 111,613 111,613 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: The estimation of (2.5.3) with the regret terms as in (2.6.4) and (2.6.5) in periods 16 to 48 for different values of the discount factorb. The utility is assumed linear. Standard errors are in parenthesis. also used to explain changes in the probability of selling the asset with different values of the past and future peak in Figure 2.6 in Section 2.6.1. To our knowledge, no one in the literature pointed out the importance of this interaction. To account for it we reformulate the regret function to include an interaction term in the Info condition as in (2.4.3): R(s p,t , s f ,t )=1 fNo Infog w NI s p,t +1 fInfog w I s p,t +a I s f ,t +l I s p,t s f ,t . (2.6.5) The interaction term captures the cross-partial derivative of the regret function, which allows us to understand the degree of complementarity or substitutability of the two peaks. The last three columns of Table 2.2 display the results of the estimation of (2.5.3) with the regret term (2.6.5). The results confirm that participants are averse to past regret in both conditions and to future regret in theInfo condition. In addition, it indicates a pattern of substitution between the two reference points, as ˆ l I < 0. Notice also that the estimate of the coefficient on the consumption utility is higher than either the coefficient on past or future regret in the Info condition. As we will see below this implies that participants care more about consumption than regret. 17 The utility parameters estimates in Table 2.2 provide strong support for our hypothe- ses that past and future regret avoidance plays a significant role in the decisions to sell the asset. However, the utility as expressed in (2.6.3) and (2.6.5) cannot tell us if future 17 At this point we should mention that the results of the estimations are very similar in all mod- els if we assume CRRA utility function instead of the linear one. In this case the regret term becomes R(s p,t , s f ,t ;r) = 1 fNo Infog w NI U(s p,t ;r)+1 fInfog w I U(s p,t ;r)+a I U(s f ,t ;r)+l I U(s p,t ;r)U(s f ,t ;r) , where r is a risk preference parameter in U(y;r) = (y 1r 1)/(1r). The same estimation as in Table 2.2, only with an additional parameter r, is presented in Table B.5 in Appendix B.10.1, which also contains several other model specifications. Overall, the estimated risk preferences are close to risk neutrality in all alterna- tive models and the coefficients on the rest of the parameters stay similar. 62 regret is only operational in the Info condition since this specification excludes any fu- ture influences in the No Info condition. Indeed, some evidence that the future is taken into account in the No Info condition comes from the regression analysis in Section 2.3 where the variables future expected price and future expected peak significantly affects the probability to sell the asset (Table 2.1). In order to show that future regret is not play- ing a role in the No Info condition we estimate an extended structural model with past and future regret terms in both conditions. Table 2.3 shows the estimated parameters of the utility function with the regret term R(s p,t , s f ,t ;r)=1 fNo Infog w NI s p,t +a NI s f ,t +l NI s p,t s f ,t +1 fInfog w I s p,t +a I s f ,t +l I s p,t s f ,t . (2.6.6) Overall, the parameter estimates of past and future regret in the Info condition are the same as in Table 2.2. The estimates for past regret in both conditions ( ˆ w NI and ˆ w I ) increase because of the introduction of the interaction term between past and future regret in the No Info condition. 18 Importantly, the coefficients ˆ a NI and ˆ l NI are not significant in all models. Thus, we conclude that the future expected peak plays no role in the decisions to sell when the participants know that they will not observe the future prices after selling. Next, we turn to the interpretation of the coefficient ˆ l I on the interaction of past and future regret in the Info condition. Notice that it is negative as in Table 2.2. This confirms the presence of a substitution effect between the two types of regret. The size of ˆ l I allows us to conclude that participants are only affected by one type of regret at a time. In particular, they pay attention only to the largest among the two: when either past or future regret is large and the other is small, the interaction term offsets the effect of the small term (see Figure 2.7 in Section 2.7). Moreover, the presence of the interaction term implies that participants switch their focus between the past and future regret dynamically within each market depending on which peak is larger. This suggests that people can be surprisingly flexible at being past or future oriented when it comes to selling decisions in dynamic settings. Finally, we verify that our results cannot be explained by loss aversion. A loss occurs if the asset is sold at a price below the purchase price in period 15. Before, in Section 2.3, we have provided arguments that loss aversion cannot explain our data. Here we go further and explicitly estimate a structural model with utility that has a loss aversion term in it. The estimation is reported in Appendix B.10.2. The loss aversion term is not significant. This also supports our results in Table 2.3: the estimates of the past and future regret stay unchanged. We conclude that loss aversion plays no role in the decision to sell the asset. 18 The negative interaction term ( ˆ l NI ) implies a larger point estimate for ˆ w NI , similarly to what the introduction of the interaction terml I did in the Info condition in Columns 4, 5 and 6 in Table 2.2. Because consumption utility (p) does not vary in the two conditions, the regret parameters in the Info conditions increase as well. Notice that the difference between ˆ w I and ˆ w NI is almost constant in the last three columns of Table 2.2 and in Table 2.3. 63 Table 2.3: The estimation of past and future regret in both conditions (I) (II) (III) b= 99.65% b= 99.60% b= 99.55% ˆ p 1.789 1.788 1.787 (0.014) (0.014) (0.014) ˆ w NI 1.432 1.555 1.643 (0.462) (0.414) (0.376) ˆ w I 2.609 2.585 2.562 (0.474) (0.424) (0.385) ˆ a NI 0.134 0.229 0.296 (0.341) (0.303) (0.274) ˆ a I 1.762 1.719 1.679 (0.348) (0.309) (0.281) ˆ l NI 0.046 0.059 0.068 (0.051) (0.046) (0.043) ˆ l I 0.265 0.260 0.256 (0.053) (0.048) (0.043) N 111,613 111,613 111,613 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: The estimation of (2.5.3) with the regret term (2.6.6) in periods 16 to 48 for different values of the dis- count factor b. Standard errors are in parenthesis. The CCP is computed using the formula in (2.6.2) for both conditions. 2.7 Discussion We find a strong imprint of past regret on the decisions of our participants in an opti- mal stopping experiment. Our main findings, however, lie in the domain of future regret and its dynamic interaction with past regret and can be summarized as follows. First, the participants are able to contemplate the counterfactual situation in which they sell the asset today and later regret it when the price goes up. Moreover, they take this possibility into account by trying to sell the asset at a price closer to the future expected maximum. Second, the participants are not always influenced by future regret. They take it into ac- count only when they know that the information about future prices will be available after they sell the asset. Third, past and future regret do not work independently. They interact by offsetting each other which leads to only the strongest being reflected in the decisions. This means that the participants try to minimize the distance of the selling price to the highest peak be it in the past or in the future. When comparing the selling behavior in the No Info and Info conditions, it is im- portant to note that the conditions differ only in the information provided after the choice was made. Before the choice, the exactly identical information is conveyed to the decision maker. Therefore, in principle, it is possible to choose in the same way in both conditions. Namely, nothing stops the participants from calculating the expected future maximum 64 value and act upon it even if the future prices are not revealed. However, as the estima- tion of the structural model demonstrates, this is not the case and the same participant, who avoids future regret in the Info condition, chooses to ignore it in the No Info con- dition. This is particularly surprising given that making optimal selling decisions in our dynamic environment involves calculating future expected prices even without deliberation on future regret. This exposes the complexity of intertemporal choice by the regret-averse participants and, particularly, its sensitivity to the context and information available in the future. The ability to contemplate hypothetical counterfactual scenarios is also ex- perimentally investigated by Esponda and Vespa (2014) in a different environment with multiple agents with strategic interactions and sequential decisions. Figure 2.7: Substitution between Past and Future regret 1 3 5 7 9 11 13 15 1 5 9 13 17 21 25 29 33 37 41 45 49 Period Regret 1 3 5 7 9 11 13 15 1 5 9 13 17 21 25 29 33 37 41 45 49 Period Regret Interaction term Past regret Future regret Interaction term Past regret Future regret Notes: Examples of the dynamics of past and future regret in two selected markets in the Info condition for the periods t2f16, ..., 48g. The curves show the terms of the estimated regret function (i.e., past regret = ˆ w I s p,t , future regret = ˆ a I s f ,t and interaction term =j ˆ l I js f ,t s p,t ) in column 4 of Tabel 2.2. The solid vertical line shows the moment at which the participants switch the focus from future regret to past regret. The estimation of the structural model shows a significant interaction effect between past and future regret in the Info condition. Specifically, this interaction is negative and, thus, works to counteract the effect of the smaller regret term (past or future). This mech- anism, though static in nature, creates a compelling dynamic effect: the impact of the past and the future on the probability of selling changes in time as the past and future regret terms change in relative size. Figure 2.7 provides a graphical intuition. In the left graph before period 18 the past regret term, which is dominated by the future regret term, is off- set by the interaction. After this period the roles of the past and future regret terms switch and the future regret is now offset by the interaction term. Overall, the interaction term in both graphs is close to the minimum of the past and future regret terms which makes the higher regret term exert most of the influence on the decision to sell. The participants try to minimize the distance from a global highest peak or maxfs p,t , s f ,t g, thus treating the past and the (expected) future in the same way. It should be emphasized that this result has emerged endogenously without introducing the maximum of the two peaks as the 65 definition of the regret function. This also explains the different rates at which partici- pants in the No Info and Info conditions sell when the current price is in the vicinity of the past peak, as documented in Panel B of Figure 2.4. In the early periods future regret is a reference point for the participants in the Info condition but not for the participants in the No Info condition. As time goes by, the saliency of past regret increases eventually dominating the future regret term (see Figure 2.7). In our experiment this effect is detected within subjects, which means that orienta- tion towards the past or the future can change rapidly depending on the circumstances. More importantly, this implies that the behavior on financial markets can potentially be influenced by seemingly unrelated events that, nevertheless, refocus the attention of the investors on the past or expected future developments (e.g., Klibanoff et al., 1998; Bor- dalo et al., 2017). For example, in our setting the value of the expected future maximum depends on the number of periods left before the market closure: for any fixed current price the closer is the end, the lower is the expected future maximum. Therefore, sudden news that the closure will happen earlier should decrease future regret and, thus, make investors more wary of the past. This can potentially lead to two outcomes: if the past peak was high and was dominating the expected future peak then nothing should change, however, if the past peak was low and was dominated by the expected future peak, then early closure can lead to a selling spree since the dominating regret term, in this case fu- ture regret, has decreased. A similar pattern to the dynamic substitution we elicited in our study was also found across New York taxi drivers in their labor supply decisions (Crawford and Meng, 2011). While drivers have flexible schedules and can stop driving after any trip, their choices seem to target either income or hours worked. In particular, it is the furthest (from the current state) among the two objectives that is the dominant reference point. The findings of our study add to the existing literature on multiplicity of reference points (e.g., Kahneman, 1992; Baucells et al., 2011) and on their endogenous formation (e.g., K˝ oszegi and Rabin, 2006, 2007; Gill and Prowse, 2012) by fully spelling out their mechanism and estimating their relationship in a dynamic setting. We conclude that ex post information shapes agents’ actions in our dynamic setting and that agents make no attempt to integrate competing/different reference points, but rather dynamically select the most relevant one. Our results imply another interesting behavioral effect which is concerned with the potential choice between observing and not observing the future price after selling the asset. In particular, the estimates of the utility parameters suggest that having no infor- mation should be preferable to having it ( ˆ w NI < ˆ a I < ˆ w I ). So, it is not inconceivable that the investors would be willing to pay for not being able to observe the future prices of the asset (e.g., Bell, 1983; Caplin and Leahy, 2001). This can have consequences for policies di- rected at regulation of stock market trading such as short selling (selling to subsequently repurchase an asset), which could be welfare improving over bans (Beber and Pagano, 2013). Nevertheless, we would like to stress that the relative size of past and future re- gret and their interaction is an empirical question which requires case by case analysis. Moreover, we believe that our approach could be used to investigate the role of regret avoidance in real-life dynamic situations. 66 2.8 Conclusion In an experimental task which resembles a stock market we study how past and future regret avoidance influences selling decisions. We use a dynamic discrete choice model to evaluate the parameters of a utility function that incorporates regret avoidance prefer- ences and find that both past and future regret play an important role in the choices to sell. When participants in the experiment know that after they sell the asset they will no longer see the evolution of the price, their decisions to sell are strongly influenced by past regret avoidance. Namely, participants keep the asset longer in order to sell at a price close to the highest past price observed. When participants are aware that after they sell the asset they will continue to observe the price on the market, their choices to sell change: now future regret avoidance also becomes important. Participants take into account the anticipated future regret which they would experience if the price of the asset increased after they sold it and try to minimize this effect. Moreover, we find that past and future regret avoidance do not just influence the de- cisions in a simple additive way. They interact with each other. In particular, participants pay more attention to the type of regret which is more prominent: if the past highest peak looms higher than the expected future peak, then past regret avoidance enters the decision to sell. If the anticipated regret in the future is larger than the potential past regret, then future regret avoidance becomes important. This substitution effect was not previously mentioned in the literature and may be of particular interest to policy makers. 67 Chapter 3 Quality, Quality Payments, and Risk Selection in Private Medicare 1 3.1 Introduction Medicare is the primary source of health insurance for the elderly population in the United States, enrolling more than 45 million beneficiaries in 2015. Spending on Medicare reached $500 billion in 2010, or 20% of total health spending, and continues to grow at a rate of 5% each year (CMS, 2016). To combat cost and promote quality, the 2010 Affordable Care Act (ACA) introduced payment models that reward the value of care in addition to volume. 2 . Evaluating and improving the effectiveness of quality-linked payment is of central policy interest to the Medicare program. At the same time, Medicare enrollees increasingly receive service from private insurers on the Medicare Advantage (MA) program. 3 Effective cost control in the private Medicare is complicated by potential supply-side capture: every dollar increase in enrollee benefit costs the government more than a dollar in insurer payment. Moreover, insurer selection on market or enrollee characteristics carries unintended social consequences that further complicate the contract design. Because a similar contracting structure is adopted in the ACA Exchange and increasingly among state Medicaid programs, understanding the in- centive and incidence of value-based payment in the MA context has implications for a wide range of insurance markets. In this paper, we provide the first evidence on the effectiveness of value-based pay- ment in private Medicare exploiting the 2010 legislative changes introduced in the ACA and the Quality Bonus Payment (QBP) demonstration. Prior to ACA, MA payment fol- lows a competitive bidding process established in the 2003 Medicare Modernization Act (MMA): plans submit cost estimates, or bids, and rebate a fraction of the cost saving be- 1 The work in this chapter is joint with Hongming Wang (University of Southern California). 2 The goal was to link all payments to private insurers with service quality by 2012, as well as linking 85% of the payments to traditional Medicare (TM) providers by 2016, a figure that was set to increase to 90% by 2018 (Burwell, 2015) 3 MA market share increased rapidly from 23% of Medicare beneficiaries in 2009 to 31% in 2015. Pay- ment to insurers doubled from 15% of Medicare spending in 2006 to 30% in 2016 (Congressional Budget Office, 2017; Kaiser Family Foundation, 2017). 69 low a benchmark to enrollees as premium reduction or extra benefits. ACA lowered the benchmark to roughly equal the fee-for-service spending. 4 Moreover, moving from vol- ume to value, ACA awarded bonus benchmark and rebate percentage to high-quality insurers according to a star rating system introduced in 2009. The ACA payment for- mula is set to be effective in 2015; for a three-year period between 2012 and 2014, the Quality Bonus Payment (QBP) demonstration experimented with more generous quality payments than ones stipulated in the ACA. We examine the effect of differential payment to quality over the QBP period, relative to a pre-QBP baseline where payment is indiscriminate of quality. Our difference-in- difference strategy tracks baseline high and low quality contracts. Both quality exhibits similar trend before the reform in terms of pricing, enrollment and cost. After QBP , we find that high quality contracts increase bids by nearly the full size of the bonus payments, and as a result, do not pass on more rebates to enrollees relative to low quality contracts. Correspondingly, the average enrollee premium did not decrease more for high quality contracts, suggesting bonus payments are by and large retained by high-achieving insur- ers as revenues. The absence of an effect on average pricing, however, masks substantial pricing vari- ation facing enrollees across service areas. Looking within the contract market set, we uncover significant pricing differentials — higher incidence of zero-premium pricing and enrollment in counties with lower fee-for-service (FFS) risk score — for baseline high quality contracts, but not for baseline low quality contracts. The within-contract premium variation explains the risk improvement of high quality contracts despite a null effect on average premium. Consistent with the risk selection mechanism, we find baseline high quality contracts with lower FFS risk score across service areas experience even greater reduction in enrollee risk after QBP , and so do contracts with higher baseline market share in the low risk counties. We do not find strong evidence for other mechanism that may lead to improved risk profile of high quality contracts. For example, we do not find significant changes in mar- ket coverage: high quality contracts did not differentially exit counties with higher FFS risk score, or enter counties with higher baseline or ACA-revised benchmark; nor did they vary the number of plans offered, or the number of counties served. Within contract, we also do not find significant differential in prescription drug deductible across service ar- eas, although we cannot rule out differentials in other aspects of benefit design which we do not observe. Overall, evidence points to the importance of premium variation across markets in the advantageous selection of high quality MA contracts. To understand why quality-linked payments incentivize risk selection, and ultimately how the selection can be undone, in the final part of the paper, we investigate the rela- tionship between enrollee risk and contract quality. Conceptually, if lower enrollee risk contributes to higher quality, then the bonus payment can lead insurers to favor enroll- ments from low-risk regions, with stronger incentive on high quality contracts eligible for larger bonus. This is consistent with the finding that only baseline high quality con- 4 Before the legislation, the Medicare Payment Advisory Commission (MedPAC) concluded MA pay- ment is 14% higher than FFS cost. Aligning MA benchmark with FFS cost is expected to reduce program spending. 70 tracts engage in risk selection after QBP , and almost none of the bonus payment is passed through to enrollees. We exploit the same difference-in-difference variation to characterize the correlation between risk score and quality, and the associated selection incentive. We show that con- tracts with higher risk score in the baseline are less likely to perform well in patient outcome measures in the quality rating. Furthermore, high quality contracts with high baseline risk scores experience smaller improvement in outcome ratings relative to low quality contracts with a more favorable risk pool, consistent with the selection incentive for continued quality payments. We further document a negative correlation between contemporaneous risk score and outcome rating as well as the final rating, particularly for baseline high quality contracts. For these contracts, performance in outcome-related domains are the most predictive of the final rating. The selection suggests an outcome-based quality rating is biased due to baseline differ- ences in health conditions: contracts enrolling patients with more complicated diagnoses perform less well in outcome measures, and are disadvantaged in the quality rating. A better measurement of quality would compare outcomes only across patients with a sim- ilar case-mix of diagnoses, or adjust outcome by baseline risk. The adjustment is lacking in the current rating for outcome measures in the “managing chronic conditions” domain. Removing the risk bias in quality rating should lessen the selection incentive associated with quality payments. The paper contributes to a growing literature on the economic incidence of govern- ment payments to health insurers and providers (see for example Dafny, 2005; Clemens and Gottlieb, 2014 and Carey, 2018). In the Medicare Advantage context, a near zero pass-through to enrollees is striking, but not unprecedented. Cabral et al. (2018) exploits the payment floor variation in the 2000 Benefits Improvement and Protection Act (BIPA), and finds a pass-through rate of around 50%, with more than 80% of the pass-through in the form of lower premium. Since then, the MA market underwent sweeping changes in terms of risk adjustment, managed competition and the prescription drug program. Looking at year 2007-2011, Duggan et al. (2016) finds a near zero pass-through across neighboring urban and rural counties. We continue this line of research by showing the recent quality-linked payments similarly have minimal pass-through to enrollees: bid in- creased by almost the full amount of bonus payment, leaving rebate to consumers largely unchanged. The within-contract premium variation we uncover is related to the literature on se- lection in Medicare Advantage (Brown et al., 2014; Newhouse et al., 2012). A common strategy adopted by researchers is comparing the cost of enrollees who switched from traditional Medicare to MA. Based on the similar intuition, we find high quality contracts differentially lowered premium in counties where potential enrollees likely have lower cost as indicated by the FFS risk score. The within-contract variation complements exist- ing evidence on cross-contract variation in pricing and benefit design as potential mecha- nism of advantageous selection in high quality MA plans (Decarolis et al., 2017; Decarolis and Guglielmo, 2017). 5 5 Risk selection incentive changed for a handful of 5-star contracts in 2012 due to a special enrollment provision that allows enrollees to switch to a 5-star plan at any time in a year. Despite concerns of adverse 71 The selection result also adds to a nascent literature that recognizes the limitation of standard risk adjustment on all aspects of “cream-skimming” contract design (Einav et al., 2016). For example, drugs receiving low payment relative to cost are more likely placed on higher cost-sharing tier (Geruso et al., 2016), and so are drugs treating diagnosis ren- dered unprofitable by technology change (Carey, 2017). In this paper, we highlight an- other aspect of insurance contract, i.e., quality rating, as a potential source of risk se- lection.In this case, correcting for the risk confound in quality rating can suppress the selection incentive without recourse to ex post risk adjustment. Taken as a whole, our evidence from private Medicare emphasizes the role of insurer selection on the distributional incidence of quality payments, with mixed implications for welfare. Since high quality service is made less (more) costly to enrollees in low (high) risk counties, the benefit of bonus payment is not evenly felt across beneficiaries 6 . Still, total enrollee surplus may increase if quality improves in both high and low risk regions. The overall welfare effect, however, depends on the economic incidence between enrollee benefits and cost to the government, intermediated by insurer selection and pass-through. Curto et al. (2014) estimates that during 2006-2011 two thirds of the payment surplus is in the form of insurer profit and one third goes to enrollees who suffer some disutility from managed care. The benchmark and rebate variation in QBP further complicates the split between insurers and enrollees, and among enrollees, those with high and low potential gain from quality. Hence we view evidence in this paper as constructive inputs to a nor- mative characterization of value-based payment in health insurance markets, which we leave for future work. 3.2 Medicare Advantage 3.2.1 Plan Bidding Payment from government represents the largest source of revenue for MA insurers (Newhouse and McGuire, 2014). The competitive bidding model is introduced in the Medicare Modernization Act (MMA) of 2003. Under this model, the government sets statutory benchmarks capitation rates for each county from historic FFS costs, and MA insurers submit bids b to the government. CMS assigns a benchmark B to each plan as a weighted average of the county benchmarks in its service area. The bid reflects the pro- jected cost of MA enrollees plus an administrative load. If the bid is below the benchmark, then the government pays off the bid, and in addition returns a fraction of cost saving be- low the benchmark – in MMA it is 75% of B b – to insurers as rebate. The rebate is then passed on to enrollees in the form of premium reduction or extra benefits. The vast major- selection, Decarolis et al. (2017) and Decarolis and Guglielmo (2017) find 5-star contracts advantageously selected low risk enrollees with lower premium and generosity, and risk pool did not worsen relative to 4 and 4.5-star contracts. 6 Echoing the disparity concern, there is evidence that plans serving enrollees with disability (MedPAC, 2015), in low socio-economic status (SES) (NQF, 2014) and certain geography (Soria-Saucedo et al., 2016) are disfavored in the quality rating. In response, a categorical adjustment index (CAI) is applied to selected measures to adjust for SES factors in 2017. 72 ity of plans submit a bid below their benchmark, providing enrollees with more generous coverage than traditional Medicare at little extra cost above Part B premium. 7 When the bid exceeds the benchmark, the insurer is paid the benchmark from the government but receives no rebate. The excess cost b B is passed on to enrollees as extra premium. Hence government spending per enrollee is capped at the benchmark, and plans with more cost saving offer more generous coverage. In practice, bid, benchmark, and rebate are multiplied by the enrollee risk score to calculate the final payment. The risk adjustment is intended to make different risk types equally profitable for plan payment (Brown et al., 2014; Newhouse et al., 2012). For MA enrollees with an average FFS risk score, the rebate formula is as follows rebate MMA i = ( 0 if b i B i , 0.75(B i b i ) if b i < B i . 3.2.2 Quality Rating To better inform plan choice, quality rating is reported to consumers on a scale of 1 to 5 stars in the “star rating program.” While more disaggregated quality information was previously available to potential enrollees in the “Medicare and You” handbook (CMS, 2008), 2009 is the first year when performances on multiple domains are aggregated in a single star rating reported to consumers. 8 Previous research has found modest effect of quality rating on enrollment in 2009, but not significant effect in 2010 (Darden and McCarthy, 2015). The weaker demand effect in later years is partly due to supply side pricing response (McCarthy and Darden, 2017) – a mechanism we show has intensified when payment is later linked to quality – or due to consumer inattention to quality infor- mation after the policy phase-in. 9 The star rating summarizes overall plan performance across eight domains, five con- cerning Part C coverage and three concerning prescription drug coverage. To calculate the domain rating and the final star rating, plans receive scores on specific quality mea- sures within domains. Measure scores are based on performance data from a number of Centers for Medicare and Medicaid Services (CMS) administrative datasets. 10 Depend- ing on the percentile rank, each measure is assigned a star rating. The measure ratings 7 In our data 41% of the plans charge zero premium (above standard Part B premium), and 84% require no deductible for prescription drug (see Table 3.2). 8 This initiative was supported by theoretical analysis showing that a functioning quality reporting sys- tem is as important as risk adjustment in correcting market inefficiencies (Glazer and McGuire, 2006). 9 For example, a 2011 poll by Kaiser Permanente shows that almost 60% of Medicare eligible seniors are unaware of the 5 Star Ratings (Harris Interactive, 2011). 10 Sources of performance data include the Healthcare Effectiveness Data and Information Set (HEDIS), the Consumer Assessment of Healthcare Providers and Systems (CAHPS), the Health Outcomes Survey (HOS), the Complaints Tracking Module (CTM), the Independent Review Entity (IRE), the Medicare Bene- ficiary Database Suite of Systems (MBDSS), the Call Center, the Medicare Advantage and Prescription Drug System (MARx), the Prescription Drug Event (PDE), among others. Most measures reflect previous year plan quality, with most of the health outcome measures further lagged by two years. For a detailed list of measures in the 2013 rating, the source of each measure and the time frame of measurement, see Appendix Table C.1 and C.2. 73 are then averaged to generate the final rating, or within domain to generate the domain rating. The composition of measures in the final rating changed from year to year. Some measures become obsolete when new measures are introduced. Continuing measures are subject to higher quality standards. 11 Broadly speaking, in 2011-2014, quality measures are divided into the following eight domains (the data source is in parenthesis): 1. staying healthy: screening, vaccine, BMI (HEDIS), and self-reported physical and mental health (HOS) 2. managing chronic conditions: percent of enrollees diagnosed with diabetes, high blood sugar and cholesterol, etc., who have the condition controlled (HEDIS) 3. plan responsiveness: ease of getting needed care, setting up appointment (CAHPS) 4. consumer complaint: rate of complaint received, number of enrollees leaving the plan and reported difficulty in care access (CTM) 5. timely service: call center availability and timely response and satisfactory resolution on consumer appeal (IRE) 6. Part D timely service: call center availability, timely response and satisfactory resolu- tion on consumer appeal (IRE) and timely enrollment in drug plan (MARx) 7. Part D experience: ease of getting information on drug coverage and the needed drug from plan and member rating on plan (CAHPS) 8. Part D safety and adherence: percent choosing high-risk drug instead of a safer option and percent taking drugs as directed (PDE) Measure stars are aggregated to the final rating through a weighting procedure that as- signs higher weights to outcome measures and penalizes high variance across measures. 12 Possible weights are 1.0, 1.5 and 3.0. Measures of patient satisfaction and access typically receive the 1.5 weight, and measures of medical process such as screening, testing and vaccination, receive the 1.0 weight. Patient outcome measures, on the other hand, receive the highest weight (3.0), and are important predictors of the final rating. 13 11 For example, final rating in 2011 is based on 51 measure stars, 50 measure stars in 2012, and 49 measure stars in 2013. The measure “access to primary care doctor”, in particular, is dropped in 2013 because nearly all MA plans meet high quality status (above 85% for 4.0 star and 95% for 5.0 star), and the measure “plan all-cause (30-day) re-admission” revised the threshold for 5.0 rating from below 5% in 2012 to below 3% in 2013; only a handful of local coordinated care plans (CCP) with very small enrollments ever obtained 5.0 rating on this measure, and average readmission is 15% for MA enrollees (or 20% in FFS). 12 The weighting procedure started in 2012, although nearly all measures are already present in 2011. 13 For instance, in 2013 only outcome measures received the 3.0 weight. These measures are “improving physical health” and “improving mental health” in the“staying healthy” domain, management of blood sugar, blood pressure, and cholesterol, and all-cause re-admission measure in the “managing chronic con- dition” domain, and all the drug safety and adherence measures in the “Part D safety and adherence” domain. 74 Due to the data collection effort, the quality rating for enrollment period t, released in the fall of t 1, is based on performance measured over t 2, especially for outcome measures in “staying healthy” and “managing chronic conditions”. These measures cap- ture the improvement in health conditions relative to a baseline. 14 Intended as a measure of quality, patient outcome is biased due to differences in baseline risk. While low-risk enrollees with milder, more manageable conditions tend to speak to high quality of care, high-risk enrollees with more complicated conditions may see smaller improvement in outcomes despite the high quality care applied in the treatment. For an alternative measure, consider the case-mix index (CMI) intensely applied in the payment adjustment to hospital discharges. Patients are categorized by their “severity- adjusted diagnosis-related group (DRG)”, which considers up to eight additional co- morbidities in additional to the principal diagnosis, up to six procedures performed in hospital, and adjusts for socio-demographic factors such as age and sex. The case-mix adjustment for baseline severity is nearly non-existent in clinical outcome measures in the MA quality rating. 15 3.2.3 Quality Bonus Payment The 2010 ACA modified the payment formula in the Medicare Advantage in multiple ways. First, it gradually reduced the benchmark faced by MA contracts to a level closer to FFS spending. The new benchmark ranges from 95% of FFS cost in counties in the top quartile of FFS cost, to 115% in those in the lowest quartile. In addition, rebate percentage varied by quality rating, whereas it was held constant at 75% before ACA. 16 In this paper, we refer to bonus payments as the sum of extra payments from either the bonus benchmark or the bonus rebate to higher quality plans. The Quality Bonus Payment (QBP) demonstration, signed into law in November 2010, revised the ACA bonus payments in the demonstration period from 2012 to 2014. Bench- mark and rebate bonus is extended to contracts with 3.0 and 3.5 star ratings. Total bonus payment is more generous under the demonstration, and is scheduled to phase into ACA levels in 2015. Moreover, QBP revised ACA benchmark bonus by designating a set of dou- ble bonus counties — contracts eligible for a 5% benchmark bonus receive a 10% bonus in these counties. 17 While our main focus is on the bonus payment differential at the 14 For example, measures of “maintaining and improving physical (mental) health” in the “staying healthy” domain come from respondent self-reports in the Health Outcomes Survey (HOS), adjusted by socio-demographic factors. Outcome improvement measures in the “managing chronic conditions” domain come from clinical records in the Healthcare Effectiveness Data and Information Set (HEDIS), unadjusted by baseline case-mix or socio-demographic factors. 15 Girotti et al. (2013) presents a case study of how adjusting for complication severity can meaningfully alter the quality ranking in the context of vascular surgeries. 16 In ACA, bonus benchmark and rebate percentage are awarded to high-performing contracts with at least a 4.0 star rating. The highest performing, 5.0-star plans receive a 5% bonus above the ACA benchmark, and a 70% rebate to enrollees if bid is below the bonus-inclusive benchmark. Bonus benchmark and rebate are more generous in 2012-2014, when the Quality Bonus Payment demonstration is effective. 17 Extra bonus is awarded to counties based on a number of criteria, including population size, MA penetration rate, and FFS costs relative to the national average. Most counties receive some extra bonus, if not a 100% top-off. Layton and Ryan (2015) defines a double bonus county as having at least a 80% top-off: 75 contract level, we examine if high quality contracts differentially entered double bonus counties after QBP , and control for both the ACA and the QBP benchmark in cross-county analysis. Hence the QBP rebate to an insurer of quality q i serving enrollees comparable to the FFS risk pool is given by rebate QBP i = ( 0 if b i a(q i ) B i t(q i )(a(q i ) B i b i ) if b i < a(q i ) B i where B i is the average ACA benchmark rate across service area, and a(q i ) B i is the quality-adjusted benchmark relevant for plan bidding. a(q i ) adjusts for the benchmark bonus from plan quality and the top-off bonus from double bonus counties. Abstracting from the top-off, Table 3.1 shows the variation of bonus benchmarka(q i ) and rebatet(q i ) over quality rating. Although both benchmarks and rebates are lower than the 2009-2011 period, the reduction is smaller for higher quality contracts due to more generous quality bonus payments. Table 3.1: Bonus and rebates by quality scores for the period 2009-2014 Star Rating Year 1 - 2.5 3 3.5 4 4.5 5 Benchmark Bonusa(q j )= 1+ % 2009/11 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 2012 0.0% 3.0% 3.5% 4.0% 4.0% 5.0% 2013 0.0% 3.0% 3.5% 4.0% 4.0% 5.0% 2014 0.0% 3.0% 3.5% 5.0% 5.0% 5.0% Rebate Percentaget(q j ) 2009/11 75.0% 75.0% 75.0% 75.0% 75.0% 75.0% 2012 66.7% 66.7% 71.7% 71.7% 73.3% 73.3% 2013 58.3% 58.3% 68.3% 68.3% 71.7% 71.7% 2014 50.0% 50.0% 65.0% 65.0% 70.0% 70.0% 3.3 Data Summary Our data come from administrative CMS registry of all MA-PD plans offered over 2009-2014 (the Landscape File). The data contains detailed insurer (or contract) infor- mation, such as quality ratings, and within-insurer plan availability across service areas (counties). Moreover, within each county, plan characteristics, such as premium and drug a plan eligible for 5% benchmark bonus receives more than 9% bonus in this county. They find double bonus counties are not associated with higher quality, but with a greater number of plans offered. 76 deductible are observed. A separate enrollment file contains plan-county-month enroll- ment counts, which have been aggregated into plan-county-yearly counts. Because the quality rating varies at the level of contracts, to understand how quality- linked payment affects pricing and product design, we aggregate plan-county charac- teristics to the contract level, weighted by enrollment share. Plans in counties with fewer than 10 enrollees are dropped, since CMS masks the exact enrollment count in these cases. We further restrict contracts to those with at least a 3.0 rating in the baseline (2009-2010). Because contracts failing to obtain a 3.0 or above rating for three consecutive years are subject to suspension, low performing contracts face additional incentive of risk selection not generalizable to higher performing contracts. Table 3.2 summarizes key contract-year statistics in Panel A for contracts with non- missing quality rating in the previous year. 18 The treated group is defined as high quality contracts with at least a 4.0 rating in both 2009 and 2010, and the control group as low quality contracts with at most a 3.5 (but no less than 3.0) rating in 2009-2010. Column (1)-(2) pool over both treated and control contracts: an average MA-PD contract has 3 plans serving over 25 counties. Baseline high quality contracts are more likely to remain high quality (star 4.0) in the sample period, bid closer to the benchmark, and receive smaller rebates. 19 They are also more likely to charge higher premium, and less likely to offer zero-premium plans. Differences in drug deductible, on the other hand, are small and not significant. Panel B shows more disaggregated variation at the level of contract, year, and location (county). Because contracts can design plan characteristics differentially across service areas, the within-contract cross-location variation is one margin of selection overlooked in cross-contract comparisons. We cluster standard errors two-way at the level of contract and county in Panel B. We therefore allow a given contract to be arbitrarily correlated over time within county, and a given county arbitrarily correlated over time within contracts. As in Panel A, high quality contracts charge higher premium and somewhat lower drug deductible, and the difference in deductible is not statistically significant. 3.4 Contract-Level Evidence We start the empirical analysis with a contract-level difference-in-difference model. Baseline high quality contracts are more likely to experience higher bonus payments after the reform, and they form the treated group. Because the ACA was signed into law in April 2010, and MA contracts do not submit bid and benefit design for 2011 enrollment until June 2010, insurer response to quality payment incentives may already be detectable in 2011 contract design and enrollment outcomes. We hence define the variable post = 1 for year 2011 and after, and inspect the timing of the effect in detail in event studies below. 18 For the main analysis we restrict attention to continuing contracts, since bonus payment for enrollment year t is determined by year t 1 quality rating. New contracts, or contracts with missing previous rating, are eligible for bonus payments according to a different rule. In robustness analysis we examine how the entry of new contracts may respond to region characteristics (FFS risk and benchmark rate, for example) after QBP . We do not find differential entry response at the contract level. 19 Standard errors are clustered at the level of contract linked over time. 77 Table 3.2: Summary statistics (I) (II) (III) (IV) (V) (VI) (VII) Full Sample Low Quality High quality (V)-(III) Mean S.E. Mean S.E. Mean S.E. p-value Panel A: contract-year observations Risk Score 0.97 0.0075 0.97 0.0093 0.96 0.012 0.55 Star 4.0 (%) 0.35 0.025 0.17 0.018 0.75 0.032 0.00 Star Score 3.55 0.031 3.35 0.027 3.99 0.041 0.00 # County 25.09 5.40 28.19 7.74 18.18 2.21 0.22 # Plan 3.40 0.23 3.53 0.31 3.12 0.28 0.33 Enrollment (k) 334.75 34.95 328.35 39.19 349.06 71.56 0.80 Benchmark 874.10 5.72 883.08 6.52 854.06 10.87 0.023 Bid 763.38 6.28 763.65 7.58 762.80 11.25 0.95 Benchmark-Bid 110.72 5.55 119.43 6.90 91.27 8.68 0.012 Rebate 78.37 3.73 83.55 4.68 66.80 5.74 0.025 Premium 49.07 3.38 35.25 3.59 79.93 5.70 0.00 Zero Premium (%) 0.41 0.029 0.51 0.035 0.19 0.035 0.00 Drug Deduc 32.62 4.42 32.85 5.72 32.11 6.40 0.93 Zero Drug Deduc (%) 0.84 0.019 0.85 0.024 0.83 0.031 0.68 N 1,122 775 347 Panel B: contract-year-location observations Enrollment (k) 18.25 2.35 17.00 2.48 21.57 4.64 0.35 # Plan 1.76 0.073 1.59 0.088 2.22 0.093 0.00 Premium 52.69 3.78 42.93 4.21 78.55 6.71 0.00 Zero Premium (%) 0.33 0.036 0.39 0.047 0.16 0.039 0.00 Drug Deduc 28.65 5.88 30.05 7.69 24.92 6.23 0.60 Zero Drug Deduc (%) 0.85 0.030 0.84 0.040 0.87 0.031 0.44 N 20,472 14,861 5,611 Notes: Table shows summary statistics for the full sample (column 1-2) and the treated (baseline high qual- ity, column 5-6) contracts and control (baseline low quality, column 3-4) contracts. Plan characteristics are aggregated to the contract-year level in Panel A, and to contract-year-county level in Panel B, both weighted by enrollment. Standard errors are clustered at the level of contracts in Panel A, and two-way clustered at the level of contract and county in Panel B. Details are in the text. 78 The difference-in-difference model is given by y ct = b high c post t +a c +t t +e ct where we compare contracts (c) with differential baseline quality ratings over time (t). We assume that the trending of high and low contracts is parallel absent the policy. To sharpen the identification of trends, we include dummies of longitudinal contract id’s (a c ), and use within-contract variation over time to isolate the effect of bonus payments. The contract fixed effects importantly sweep out baseline heterogeneity across contracts, such as differences in service area, enrollee characteristics and provider networks, among others. However, to the extent that confounding factors may vary around the same time as the reform, the difference-in-difference estimateb will be biased. The absence of time- varying confounds is not directly testable. As with most difference-in-difference analyses, we rely on visual inspection of parallel trends before the reform to assess the validity of the model. We then apply the model to study the effect of bonus payment on risk score, market characteristics and pricing. 3.4.1 Risk Score Table 3.3 shows the effect on risk score following the reform in 2011. We show the ro- bustness of the result to different controls and level of analysis. Columns (1)-(2) measure risk score aggregated at the contract level using plan enrollment weights. Columns (3)-(4) measure risk score as unweighted average of plan risk scores. Columns (5)-(6) measure risk score at the raw plan level. For each measure, we study the robustness of results with and without contract or plan level fixed effects. Table 3.3: Effect of QBP on the risk score (I) (II) (III) (IV) (V) (VI) High Post -0.026*** -0.041*** -0.035*** -0.042*** -0.020*** -0.045*** (0.0082) (0.014) (0.012) (0.015) (0.0074) (0.015) Weights plan enrollment equal weights unweighted y mean 0.97 0.97 0.97 0.97 0.96 0.96 Fixed Effects contract contract plan R-squared 0.86 0.0068 0.76 0.012 0.79 0.0089 N 1,122 1,127 1,122 1,122 4,549 4,549 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: Table shows difference-in-difference estimates on risk score, aggregated at contract level using enrollment weights in column (1)-(2), using equal weights in column (3)-(4), and measured at the raw plan level in column (5)-(6). For each measure we show results with and without fixed effects. Stan- dard errors clustered at the contract level (column 1-4) or plan level (column 5-6) in the parenthesis. We find significant improvement in the risk pool of higher quality contracts, relative 79 to the control. The preferred specification in column (1) shows a 2.6 percentage point reduction in risk score by high quality contracts, and the effect is similar if not larger under alternative measures. Figure 3.1 examines the validity of the difference-in-difference design and the timing of the effect. Before the proposal of quality bonus payments became law in 2010, risk scores for both treatment and control groups stay parallel. The trend departs visibly in 2011: for the first time high quality contracts have lower risk score than low quality con- tracts, and the gap widens in later years. Similarly, in the event study, although the effect in 2011 is not statistically significant, the effect becomes stronger and more significant over time. Figure 3.1: Effect on risk score, event study (a) raw trend .92 .94 .96 .98 1 2009 2010 2011 2012 2013 2014 ACA QBP low quality high quality (b) event study −.08 −.06 −.04 −.02 0 .02 2009 2010 2011 2012 2013 2014 ACA QBP Notes: The left panel shows the raw trend of risk score for baseline high and low quality contracts. The right panel shows the event study estimates of the difference-in-difference model, controlling for contract and year fixed effects, with 95% confidence intervals based on robust standard errors clustered at the level of contract. Risk score is aggregated at the contract level weighted by plan enrollment. We then turn to the potential mechanism of risk selection by high quality contracts. Although risk pool on average improves, contracts facing different market structure and enrollee base may differ in their ability to risk-select. If the improvement in risk pool is concentrated among the set of contracts with certain characteristics, then the heteroge- neous effect is indicative of the mechanism of risk selection. We consider two dimensions of heterogeneity based on baseline characteristics: risk composition across service areas, and market competition measured by the Herfindahl-Hirschman index (HHI). To proceed, we first define the market set for each contract as the union of counties served in baseline 2009-2010. For each county in the market set, we attach the average FFS risk score over the baseline as a measure of potential gain from risk selection in this county: lower FFS risk score implies new enrollments into private Medicare likely have lower risk, making the county more advantageous for risk selection. We then average over counties to derive a risk selection measure at the contract level. The median across contracts is 0.99, and the 15th (85th) percentile is 0.90 (1.07). Columns (1)-(2) in Table 3.4 show significant reduction in the risk score of high quality 80 Table 3.4: Effect of QBP on risk score, by service area risk and competition (I) (II) (III) (IV) Treat Post –0.036*** –0.045** –0.018 0.0094 (0.011) (0.019) (0.012) (0.018) Treat low risk, high quality high hhi, high quality Control high risk, low quality low hhi, low quality Sample +/-median 15% tails +/-median 15% tails y mean 1.00 1.02 0.98 0.99 R-squared 0.88 0.90 0.85 0.89 N 534 211 506 191 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: Table shows difference-in-difference estimates on risk score, aggregated at contract level using enrollment weights. In column (1), treated group is baseline high quality contracts with service area risk below the median, and the control group is baseline low quality contracts with service area risk above the median. In column (3), treated group is baseline high quality contracts with HHI below the median, and the control group is baseline low quality contracts with HHI above the median. Column (2) and (4) further limits the sample to 15% tails. Construction of baseline characteristics measures is described in the main text. All regressions include contract level fixed effects. Standard errors clustered at the contract level in the parenthesis. contracts more advantageous for risk selection: those in the lower 15% of service area risk distribution decreased risk score by 4.5 percentage points, relative to low quality contracts in the upper 15% of the distribution. Figure C.1 shows that the effect is visible starting in year 2011, and becomes stronger and more significant in later years. Alternatively, one might believe contracts with greater market power are better able to risk select. To derive a measure of market power at the contract level, we first compute the HHI for each county over the baseline, and then average over the market set for contracts. The median HHI in the baseline is 0.44, and the 15th (85th) percentile is 0.31 (0.61). Columns (3)-(4) in Table 3.4 show the same effect by market competition. In the full sample, baseline high quality contracts with high market power reduced their risk score by 1.8 percentage points relative to low quality contracts with low market power, al- though the effect is not significant. The result is more tenuous when comparing the 15% tails. Figure C.2 shows the corresponding raw trends and event study estimates. 20 Over- all, unlike service area risk score, there is no clear evidence that market competition has strong bearing on risk selection in this context. Therefore, in the within-contract triple- difference analysis below, we utilize the risk score variation across service areas to detect any differential pricing response that may have contributed to changes in the risk pool. 20 Comparing high quality contracts with HHI below the 15th percentile with low quality contracts with HHI above the 85th percentile also renders insignificant estimate. 81 3.4.2 Market Characteristics Another possible explanation to the increasing risk selection that emerged in the pre- vious section concerns contracts altering the characteristics of the service areas following the reform. For example, high quality contracts may have expanded their service ar- eas to include more counties with low risk scores, or may have increased the number of plans offered in these counties. The exact mechanism of risk selection has implications for the empirical strategy suitable for the analysis. In particular, if characteristics of service area responded endogenously to bonus payment incentives, then within-contract cross- location variation should not be interpreted as exogenous. To detect changes in market characteristics attributable to changes in the market set, we replace yearly county characteristics with values in 2012, and then average over the market set for contract-year observations. The resulting variable captures the effect of market composition on contract characteristics, rather than the temporal variation in these characteristics. For example, if the service area FFS risk score improved, then there is reason to believe contracts may have entered low risk counties or exited high risk coun- ties, depending on the change in market size. Table 3.5 shows little change in market set characteristics. There is some evidence of high quality contracts expanding their market set over time, but the effect is not signifi- cant. The number of plans offered also did not change (column 5). Importantly, service area risk (column 2) barely changed for high quality contracts after the reform, suggest- ing contracts did not differentially enter or exit counties based on the baseline risk. While counties with low FFS risk score are more advantageous for selecting low cost enrollees, there is no evidence of extensive margin selection whereby high quality contracts expand their market set to include more of these low risk counties. In addition, since the QBP also varied the county benchmark rate by quality rating, we check if contracts differentially select into counties with higher ACA benchmark (col- umn 3) unadjusted by quality, or double-bonus counties (column 4) under the QBP where benchmark bonus to 5-star contracts is over 8%, or more than a 60% top-off. We see no evidence of differential selection by high quality contracts along these margins. 3.4.3 Bid, Rebate, and Pricing Since market characteristics did not change significantly to explain the risk selection result, we now turn to assess how pricing responded to quality bonus payments. Un- der the law, higher quality contracts face higher benchmark. In principle, contracts can increase the bid to receive higher payments without reducing the rebate to enrollees. Fur- thermore, the rebate bonus to quality allows the bid to increase more than the benchmark for a fixed amount of rebate. Of course, rebates need not stay constant, if part of the bonus payment is passed on to enrollees in the form of lower premium or cost-sharing. Table 3.6 studies the effect of QBP on bids and rebates. As a result of the bonuses introduced by QBP , benchmarks for high quality contracts increased by $27.84 (cf Table 3.1). In response, high quality contracts raised their bids by $37.01, resulting in a net narrowing of the benchmark-bid gap by $9.17. However, adjusting for the rebate bonus in the QBP , the final rebate accruing to enrollees did not change significantly. At the 82 Table 3.5: Effect of QBP on market characteristics (I) (II) (III) (IV) (V) # Counties Risk Benchmark High-Bonus # Plans County High Post 8.70 0.0024 1.80 –0.020 –0.17 (8.39) (0.0024) (2.94) (0.021) (0.23) y mean 25.09 0.99 799.15 0.72 3.40 R-squared 0.73 0.98 0.96 0.90 0.87 N 1,122 1,122 1,122 1,122 1,122 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: Table shows difference-in-difference estimates on market size and characteristics. Outcome is at the contract-year level. Numbers of counties and plans are counted within contract-year. risk and benchmark are contract-year averages of 2012 characteristics over the market set, and hence reflect differential county entry or exit by these characteristics. If a county later on receives an above 8% bonus benchmark for 5-star contracts, it is assigned the high-bonus status. Column (4) looks at if contracts cover more of these counties after the reform. All regressions include contract level fixed effects. Standard errors clustered at the contract level in the parenthesis. contract level, enrollees in high quality contracts received $0.40 more in rebate, but this effect is not significant. 21 Absent large changes in the rebate, changes in premium and cost-sharing are also small. Table 3.7 shows noisy effects on average premiums and the offering of zero- premium contracts. For cost-sharing, we focus on drug deductible. Although the vast majority of contracts have zero deductible, the mass at zero did not change after the re- form. Average drug deductible decreased by half. On the raw trend, however, the dif- ference appears to be driven by an early increase in deductible by low quality contracts in 2011: starting in 2012 both high and low quality contracts increased deductible at a similar rate (Figure C.3). The effect, moreover, is only marginally significant. Therefore aggregated at the level of contracts, there is no clear mapping from pricing variation to risk selection through quality. In particular, high quality contracts did not increase premi- ums or drug deductibles, measures commonly used to select low risk enrollees, nor did they decrease them, which is consistent with a null effect on rebate. The contract-level comparison, however, does not capture the within-contract cross- location pricing and benefit design. The within-contract selection can potentially alter the risk pool composition without revealing any marked changes in contract-level pricing, if, for example, price increases in higher risk areas are offset by decreases in lower risk areas. To further probe this possibility, in the analysis below, we investigate how pricing varies within contract across counties above and below the median risk county in the market set. 21 Since the QBP reform is essentially a supply-side shock directly affecting revenues rather than marginal costs, the estimates in Table 3.6 suggest that bids do not only depend on marginal costs (Song et al., 2012, 2013) – a finding highlighted in Curto et al. (2014) as well. 83 Table 3.6: Effect of QBP on bidding and rebate (I) (II) (III) (IV) Benchmark Bid Benchmark-Bid Rebate High Post 27.84*** 37.01*** –9.17 0.39 (7.10) (7.50) (6.07) (3.68) y mean 874.10 763.38 110.72 78.37 R-squared 0.83 0.84 0.83 0.87 N 1,122 1,122 1,122 1,122 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: Table shows difference-in-difference estimates on benchmark, bid and re- bate. Outcome is at the contract-year level. We aggregate plan level benchmark (an enrollment-weighted average of county benchmarks, higher for higher quality con- tracts after QBP), bid, and rebate (inclusive of rebate bonus after QBP) to the contract level using enrollment weights. All regressions include contract level fixed effects. Standard errors clustered at the contract level in the parenthesis. Table 3.7: Effect of QBP on premium and drug deductible (I) (II) (III) (IV) Premium Zero Premium Drug Deduc Zero Deduc High Post 3.14 0.032 –16.98* 0.051 (3.56) (0.025) (8.98) (0.045) y mean 49.07 0.41 32.62 0.84 R-squared 0.91 0.88 0.69 0.63 N 1,122 1,122 1,122 1,122 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: Table shows difference-in-difference estimates on premium and drug deductible. Out- come is at the contract-year level. We aggregate plan level data to the contract level using enrollment weights. All regressions include contract level fixed effects. Standard errors clus- tered at the contract level in the parenthesis. 84 3.5 Within-Contract Cross-County Evidence This section looks inside the market set, and examines if contracts are more likely to deploy high-premium, high-deductible plans in service areas less advantageous for risk selection. For identification, we assume that absent the policy, the distribution of insurance pricing across risk regions is parallel for both high and low quality contracts. As with most difference-in-difference analysis, we assess the plausibly of the identifying assumption by inspecting the pre-trend commonality for high and low risk regions within and between high and low quality contracts. To measure average prices at the contract-year-location level, we weight plan premi- ums and deductibles by enrollment. To measure a county’s relative standing in the overall risk composition across service areas, we measure the distance of county risk to the me- dian risk in the market set, and use the distance to median as the driving variation in the within-contract analysis. In particular, we use baseline market set characteristics in 2009-2010 to derive the dis- tance measure. We rank all counties served by a contract in the baseline by their baseline FFS risk score. Comparing counties with the median county gives the distance-to-median measure. Note that this measure is fixed for a given contract-location pair, and does not vary over time. We estimate the following triple-difference design y clt = b 0 risk cl high c post t +b 1 risk cl post t +b 2 high c post t +b X lt +a cl +t t +e clt , where the unit of observation is at the level of contract c, location (county) l, and year t. risk cl is the distance-to-median measure. We include year indicators t t to control for common temporal shocks, and contract-county indicators a cl to absorb unobserved het- erogeneity across contracts and service areas, and the baseline selection between the two. The fixed effects would not be adequate to address time-varying selection response if con- tracts are shown to enter or exit service areas based on local risk factors after the reform. This is not the case, however, as we showed in Section 3.4.2. In addition, we control for time-varying location-specific factors in X lt . Most notably, since the raw county benchmark is time-varying, and since QBP increased the bonus benchmark for some counties (commonly known as “double-bonus counties”), the set of which is also time varying, we include the raw benchmark, the bonus payment rate, and their interaction. 22 We hence allow for separate pricing response to benchmark variation in local markets. We cluster standard errors two-way at the level of county and contract: contracts ob- served in different counties are correlated, and so are counties entering different contracts’ service areas; within contracts (counties), counties (contracts) are assumed to be indepen- dent. Clustering at the intersection of county and contract gives similar standard errors. Table 3.8 displays the premium response to QBP across risk regions for baseline low quality (column 1) and high quality (column 2) contracts, and the differential response by high quality contracts (column 3). Low quality contracts increased premium in lower risk 22 The interaction measures the maximum benchmark faced by 5-star contracts serving the county in a given year. 85 Table 3.8: Effect of QBP on premium, within-contract cross-county variation (I) (II) (III) (IV) (V) (VI) Risk High Post 30.51** 35.61** (12.54) (14.26) Risk Post –14.99* 20.99* –14.75* –13.49 21.64 –14.66* (8.73) (11.20) (8.66) (8.87) (13.37) (8.60) High Post –1.25 –1.16 (4.86) (4.83) Counties all 15% tails Sample low high full low high full y mean 42.93 78.55 52.69 42.44 75.47 51.42 R-squared 0.85 0.85 0.87 0.85 0.86 0.87 N 14,861 5,611 20,472 4,393 1,641 6,034 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: Table shows the within-contract premium variation across risk regions. Column 1-2 show the difference-in-difference estimates on premium across risk regions for baseline low quality (column 1) and high quality (column 2) contracts. Column 3 shows the triple-difference estimate, which gives the differential pricing response by high quality contracts in higher risk counties. Column 4-6 repeat the analysis, but only include counties in the lower and upper 15% of the risk distribution within a contract’s market set. All regressions include contract- county fixed effects. Standard errors clustered two-way at the contract and county level in the parenthesis. 86 counties, whereas high quality contracts increased premium in higher risk counties. Both effects are visually perceptible on the raw trend (Figure C.4, Panel a), where the market set of each contract is divided into high (above median) and low (below median) risk regions. Hence the results are not driven by the parametric assumption that effects are linear in the deviation from median. The triple-difference estimate suggests high quality contracts increased premium by $0.31 per one percentage point increase in risk above the median. Event study shows parallel pre-trend: high and low quality contracts charged premium similarly across risk regions. After the passage of QBP , high quality contracts significantly increased premium in higher risk counties, whereas response by low quality contracts is small and not signif- icant in most years (Figure C.4, Panel b). The same pattern holds when we only include counties in the lower or upper 15% of the risk distribution given contract (columns 4-6). We then investigate any differential pricing in drug deductible. The contract-level analysis suggests that both low and high quality contracts increased deductibles after QBP (see Table 3.7 and Figure C.3, Panel c). Looking within contract across risk regions, Table 3.9 shows that both contracts raised deductibles more in regions less advantageous for risk selection, and that this expansion is not significantly larger for high quality con- tracts (see also the raw trend in Figure C.5). We similarly do not detect any significant pricing differential by quality when looking at the 15% tails of the market set. Put together, we find evidence for within-contract pricing adjustments across risk re- gions, which might explain the risk pool improvement for high quality contracts absent any significant change in average prices (including rebate) at the contract level. The ad- justment mostly affects premiums, not drug deductibles, although it may also affect other contract characteristics outside our sample. The premium adjustment, in particular, illus- trates one potential mechanism of favorable selection into Medicare Advantage: premium is higher in markets where new enrollees have higher risk, and lower in markets with lower risk. Because premium did not vary at the contract level but varied across service regions, the selection response raises questions on the distributional incidence of quality payments, and its implication for welfare. 3.6 Why Does QBP Induce Risk Selection? So far we have shown high quality contracts significantly improved risk pool after QBP , and linked the improvement to differential premium pricing across risk regions. That is, we have suggested mechanisms of how risk selection is accomplished, but have been silent on why risk selection is incentivized in the first place: what are the design fea- tures in QBP that made it profitable for high quality contracts to select low risk enrollees? This section suggests the incentive may lie with the design of the quality rating system, and is activated by the financial reward to high quality introduced in QBP . When high quality contracts are able to keep most of the quality bonus payment as profit rather than rebate to consumers, risk selection becomes profitable if lower enrollee risk contributes to higher quality and hence continued bonus payment. We highlight the linkage between risk, quality and insurer profit in a stylized model below. We then empirically characterize the correlation between risk and quality. We ex- 87 Table 3.9: Effect of QBP on drug deductible, within-contract cross-county variation (I) (II) (III) (IV) (V) (VI) Risk High Post –7.06 –22.48 (46.09) (52.21) Risk Post 36.54* 48.45 39.25** 33.62** 29.33 35.50** (18.78) (46.03) (19.46) (16.87) (51.01) (17.26) High Post –12.10 –13.42 (10.02) (9.52) Counties all 15% tails Sample low high full low high full y mean 30.05 24.92 28.65 28.62 24.91 27.61 R-squared 0.70 0.61 0.67 0.68 0.67 0.68 N 14,861 5,611 20,472 4,393 1,641 6,034 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: Table shows the within-contract variation in drug deductible across risk regions. Col- umn 1-2 show the difference-in-difference estimates on zero-premium pricing across risk re- gions for baseline low quality (column 1) and high quality (column 2) contracts. Column 3 shows the triple-difference estimate, which gives the differential pricing response by high qual- ity contracts in higher risk counties. Column 4-6 repeat the analysis, but only include counties in the lower and upper 15% of the risk distribution within a contract’s market set. All regres- sions include contract-county fixed effects. Standard errors clustered two-way at the contract and county level in the parenthesis. ploit the same difference-in-difference variation as in Section 3.4 to show that contracts with higher risk score in the baseline are less likely to perform well in patient outcome measures in the quality rating. Furthermore, high quality contracts with high baseline risk scores experience smaller improvement in outcome ratings relative to low quality contracts with a more favorable risk pool. We further document a negative correlation between risk score and the Star score, particularly for baseline high quality contracts. For these contracts, performance in outcome-related domains are the most predictive of the final rating. 3.6.1 A Model of Risk, Quality, and Insurer Profit To illustrate how the risk-quality linkage can affect insurer pricing, we build a simple 2-period model where the risk pool in the first period affects quality rating and payment in the second period. We focus on the decision of baseline high quality contracts. Revenues in each period 88 is the sum of a benchmark and a premium charged to the enrollees. 23 The benchmark B is fixed in the first period. In the second period, high quality contracts receive higher benchmark B h > B l . Contract quality is not constant: with probability l(h; r), baseline high quality con- tracts remain high quality in the second period. We model the risk-quality linkage by allowing the transition probability to depend on the risk score r from period one. If low risk score contributes to future high quality, then there is incentive to attract low risk enrollees in the current period. We assume risk adjustment is perfect, so that risk selec- tion would have no bearing on insurer profit, absent the dynamic linkage on quality and quality payments. A high quality contract chooses premium (p, p 0 ) in both periods to maximize profits P(p, p 0 )= (p c+ B h ) s h (p)+ å j2fl,hg l(j; r) p 0 c+ B j s j (p 0 ), where the insurer faces constant marginal cost c, and demand is allowed to differ by quality in s j (p), j2fl, hg. The optimal premium set in the first period is p =(c B) h 1 1 je h j 1 + Dp 0? s h (p) policy z}|{ dl d r d r d p |{z} selection i 1 , (3.6.1) whereDp 0? > 0 is the optimized profit difference between high and low quality in the second period, 24 and e h < 0 is the premium elasticity of demand for high quality con- tracts. Absent the risk-quality linkage, we have the standard result that optimal premium equals marginal cost plus a mark-up inverse to demand elasticity. When dl d r 6= 0, how- ever, optimal premium responds to the selection term d r d p . Specifically, a market is more advantageous to risk selection, if lower premium attracts enrollees below the average risk of the contract, or d r d p > 0. In these markets, when enrollee risk lowers contract quality, the term Dp 0? s h (p) dl d r d r d p is signed negative, pushing premium below the standard level where dl d r = 0. 25 Hence observed premium variation is consistent with insurer risk selection, if lower enrollee risk contributes to higher quality rating. Under this configuration, we should expect lower (higher) premium in lower (higher) risk regions, relative to the baseline period where dl d r = 0. We then examine the risk-quality linkage in detail, signing dl d r 23 Alternatively, one can think of firms submitting a bid, which then translates into consumer premium according to a known regulatory formula. 24 That is,Dp 0? = (p 0 h c+ B h )s h (p 0 h )(p 0 l c+ B l )s l (p 0 l ) > 0, wherefp 0 h , p 0 l g is the vector of optimal premiums to be charged in the second period. In addition, we assume that high quality firms have higher profits than low quality ones. 25 Alternatively, in markets less advantageous to risk selection with d r d p < 0, premium is set higher than the benchmark level. 89 empirically. 3.6.2 Difference-In-Difference Evidence on the Risk-Quality Mecha- nism Before empirically characterizing the risk-quality correlation, we present difference- in-difference evidence on the nature of the correlation using similar variation as in previ- ous sections. One challenge is that, because the rating algorithm underwent substantial revision in 2011, the same year quality bonus payment was introduced, differential trend- ing in the quality rating after the reform may reflect mechanical differences in the rating computation, rather than insurer risk selection response to payments. On the other hand, the selection response implies that low risk enrollees with fewer diagnoses are associated with higher quality, possibly through improvements in outcome measures in the quality rating. We hence focus on outcome measures, and document the relationship between ratings in these measures and insurer risk profiles in the base- line. One particular advantage of this strategy is that outcome measures are relatively stable over the sample period, allowing for a difference-in-difference characterization of the risk-outcome channel unaffected by changes in rating measurement or computation. Specifically, we focus on outcome measures that are consistently measured from 2009 to 2014. They are improving physical health, improving mental health, diabetes controlled– blood sugar, diabetes controlled–cholesterol, and blood pressure controlled from Part C. 26 We average over these measures to derive a summary star rating of patient outcome. When we regress the final rating on the constructed outcome rating, the coefficient be- fore the outcome rating mechanically increases after 2012 (Table 3.10). Although the es- timate may also reflect changes in the rating computation other than the weighting, the importance of outcome in the final rating generally increased over the 2012-2014 period (Figure 3.2). We then examine the correlation between risk and outcome measures using the difference- in-difference variation, comparing the outcome rating of contracts serving low versus high-risk enrollees in the baseline. Table 3.11 shows a ten percentage point increase in baseline risk score in 2009-2010 reduces outcome rating by 12.2 percentage points. When we group outcomes by health improvement measures in the Health Outcome Survey (col- umn 2) and chronic condition measures in the Healthcare Effectiveness Data and Informa- tion Set (column 3), the risk-outcome correlation appears entirely driven by the chronic condition measures, with significant advantage to contracts serving low-risk enrollees in the baseline (Figure C.6). We further inspect the risk-outcome correlation by baseline quality status. Specifically, the treated group is the set of baseline high quality contracts where enrollee risk score over 2009-2010 is above the median of all contracts, and the control is baseline low quality contracts with risk scores below the median. 27 If high risk enrollees are associated with 26 Part D outcome measures in the “drug safety and adherence” domain are not consistently present over the sample period. In particular, three new outcome measures (medication adherence for diabetes, hypertension and high cholesterol, respectively) are added in 2012. 27 Baseline risk score ranges from 0.74 to 1.46 in 2009-2010 for treated and control contracts, and the 90 Table 3.10: Weight increase of outcome measures in quality rating (I) (II) (III) (IV) (V) (VI) Star rating 4.0 star 4.5 star Outcome Post 0.18*** 0.24*** 0.14*** 0.19*** 0.18*** 0.20*** (0.030) (0.031) (0.036) (0.033) (0.024) (0.030) y mean 3.59 3.59 0.35 0.35 0.16 0.16 Post 2011 2012 2011 2012 2011 2012 R-squared 0.77 0.78 0.57 0.58 0.57 0.57 N 1,080 1,080 1,080 1,080 1,080 1,080 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: Table shows the difference-in-difference estimate of average outcome measure rating (outcome) in the final star rating before and after the reform year in 2011 (odd columns) or in 2012 (even columns). All outcome measures averaged in outcome are present in the rating and measured consistently throughout 2009-2014. Start- ing 2012, these measures receive a 3.0 weight in the computation of the final rating. Column 1-2 estimates the effect of weight increase on the final star rating, which ranges from 1.5 star to 5.0 star at 0.5 star increments. Column 3-4 estimates the effect on the binary outcome of having at least 4.0 stars. Column 5-6 estimates the effect on having at least 4.5 stars. Unlike other difference-in-difference analysis in the paper, outcome is mea- sured at the same period as outcome, and is not fixed at baseline (2009-2010) value. The purpose is to confirm the mechanic weight increase in the rating computation. All regressions include contract and year fixed effects. Standard errors clustered at the contract level in the parenthesis. worse outcomes measured in the quality rating, then a more favorable risk pool may help baseline low quality contracts obtain high quality standing. High quality contracts serving high risk enrollees, on the other hand, risk losing bonus payments if outscored in outcome measures by control contracts with low risk enrollees. Table 3.12 suggests that the risk-outcome correlation disadvantages high quality con- tracts with high risk enrollees, where loss of high quality standing to low-risk low-quality contracts is more likely. In odd columns, we compare high and low quality without in- teracting with baseline risk. Overall, high quality contracts are less likely to retain high outcome rating as low quality contracts are likely to obtain it, in particular due to the difficulty in consistently managing chronic conditions related to blood pressure and dia- betes. The difference is more striking, once we compare baseline high-risk high-quality contracts with low-risk low-quality contracts in even columns: falling in the upper half of the risk score distribution exposed high quality contracts to an additional 20 percentage point slippage in outcome rating, relative to low-quality competitors in the more favor- able half of the risk distribution (Figure C.7). median is 0.97. 91 Figure 3.2: Weight increase of outcome measures in quality rating (a) star rating 0 .1 .2 .3 .4 2009 2010 2011 2012 2013 2014 (b) 4 stars −.1 0 .1 .2 .3 .4 2009 2010 2011 2012 2013 2014 Notes: The figures show the event study trends of outcome measure weights in the quality star rating. The left panel shows that outcome ratings receive higher weights after 2012. The right panel shows a similar weight increase in outcome ratings for achieving at least a 4.0 star final rating. 95% confidence intervals are plotted based on robust standard errors clustered at the contract level. Table 3.11: Risk score and outcome rating (I) (II) (III) Outcome mean Health Diabetes and improved blood pressure Risk Post –1.22** –0.11 –1.37** (0.48) (0.27) (0.58) y mean 3.45 3.28 3.60 R-squared 0.63 0.22 0.69 N 997 888 991 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: Table shows the difference-in-difference estimates on outcome rat- ing, across contracts with different enrollee risk scores in the baseline (2009- 2010). Column 1 looks at the effect of baseline risk on the average rating of outcome measures. Column 2 and 3 divide the outcome measures by data source. Self-reported improvement in physical and mental health, collected from HOS, is the focus of column 2. HEDIS measures of hav- ing diabetic conditions and high blood pressure controlled are the focus of column 3. All regressions include contract and year fixed effects. Standard errors clustered at the contract level in the parenthesis. 92 Table 3.12: Quality, risk and outcome rating (I) (II) (III) (IV) (V) (VI) Outcome mean Health improved Diabetes and blood pressure High Post –0.26*** –0.44*** 0.026 0.043 –0.42*** –0.62*** (0.074) (0.10) (0.044) (0.070) (0.098) (0.13) y mean 3.45 3.38 3.28 3.30 3.59 3.49 Treated high quality (+ high risk) high quality (+ high risk) high quality (+ high risk) Control low quality (+ low risk) low quality (+ low risk) low quality (+ low risk) R-squared 0.63 0.65 0.23 0.20 0.70 0.71 N 1,089 525 952 456 1,083 522 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: Table shows the difference-in-difference estimates on outcome rating, across contracts with different baseline quality in odd columns, and further across baseline enrollee risk scores in even columns. Specifically, in even columns, treated contracts are baseline high quality with enrollee risk score higher than median (0.97), and control contracts are baseline low quality with risk score below the median. Column 1-2 look at the quality and risk differential on average outcome ratings. Column 3-4 look at the effect on self-reported improvement in physical and mental health collected from HOS. Column 5-6 look at the effect on diabetes and high blood pressure control measures from HEDIS. All regressions include contract and year fixed effects. Standard errors clustered at the contract level in the parenthesis. 93 3.6.3 Characterizing the Risk-Outcome Correlation The difference-in-difference evidence suggests a strong negative correlation between enrollee risk score and outcome rating, in particular, rating in managing chronic condi- tions such as diabetes and blood pressure measured in HEDIS. Instead of using baseline enrollee risk, in this section, we directly characterize the empirical correlation between contemporaneous risk score and outcome rating. To do this, we note that outcome mea- sures relevant for year t quality rating, announced in the fall of year t 1, are collected from patients enrolled in the contract two years prior in t 2. Due to the timing, we ex- pect a strong negative correlation only between year t rating and year t 2 risk score, but not across other lag or lead periods. Table 3.13 shows the correlation between year t outcome rating in diabetes and blood pressure control and risk scores from multiple periods. That is, in addition to contempora- neous correlation, we also examine correlation with risk score one year in lag (riskscore t3 ) up to two years in lead (riskscore t ). We further stratify the exercise by baseline contract quality. The risk-outcome correlation is weak among low quality contracts (baseline 3.0- 3.5 stars), but becomes more negative and significant as we restrict the sample to higher quality contracts. For the set of contracts achieving at least a 4.5 star rating in the base- line, a ten percentage point increase in enrollee risk score is associated with 33 percentage point decrease in chronic outcome rating. There is, however, no clear and consistent pat- tern between risk score and outcome for different lag and lead periods. Similar results hold for the correlation between risk score and final star rating (Table 3.14). 3.7 Discussion Central to our finding is the premium variation within contract across risk regions. Specifically, high quality contracts differentially attract low-risk enrollees with lower pre- mium in low-risk counties, and improve risk score relative to low quality contracts. Ab- sent changes in average prices, selection implies that within contract, rebates are trans- ferred from high risk to low risk enrollees. The insurer selection thus calls into question the distributional incidence of quality payment, with immediate policy and welfare im- plications. First, the benefit of quality improvement may be weighed down by the social cost of unequal access to quality, as high-performing contracts disproportionately serve low-risk enrollees in low-risk counties. To the extent that enrollees in worse health conditions benefit more from quality care, return to care is higher if enrollment increased more in areas with higher baseline risk. In this context, disparity is worsened by a negative cor- relation between risk and quality, which tends to penalize contracts serving high-risk enrollees. Alternatively, a positive risk-quality correlation may improve equity by en- couraging more high-quality entry in high risk counties, although it is not clear why a quality measure should respond to the risk composition. More fundamentally, one may question the role of baseline health in measures of plan quality – if quality reflects the “value-added” of health care on health, with higher quality improving health more, then baseline health should be swept out of quality ratings as a 94 fixed effect. In that sense, the empirical correlation with pre-enrollment risk measures should be tenuous. However, using health improvement as indicator of quality may still fall short, if baseline health affects treatment efficacy interactively. This would be the case if, for example, patients with milder conditions recover sooner than those with more severe conditions, and the difference narrows but does not disappear at higher quality. Therefore to effectively take out the risk confound in quality measures, the current outcome measures need to be adjusted by the severity of baseline health conditions. The idea is that, conditional on a similar case-mix of diagnoses and potential interactions, dif- ferential improvements in patient outcome are more plausibly attributable to health care quality rather than baseline health. A ready way to control for the risk score in the Star computation, as it predicts health care costs based on past diagnoses. Other adjustments may include socio-demographic factors used in HOS, and the intensively coded case-mix index for hospital payments. In our analysis, we find the risk-quality correlation operates through the outcome measures in the “managing chronic conditions” domain. Most of these measures treat health improvement, i.e., having chronic conditions controlled, as indicator of quality. For example, a measure of blood pressure control is given by the fraction of baseline hy- pertension patients (denominator) with blood pressure below 140/90 (numerator) in the measurement period. However, these measures do not adjust for the severity of baseline conditions. This allows baseline risk score, a crude measure of severity, to correlate sig- nificantly and negatively with performance in chronic outcome measures. By contrast, self-reported health improvement in HOS is adjusted by respondent socio-demographic characteristics, and we find little residual correlation between risk score and health im- provement measures in the “staying healthy” domain of the quality rating. Hence our results suggest the risk-quality correlation, as well as its perverse incentive on risk selection, is largely suppressed if chronic outcome measures in HEDIS are appro- priately adjusted for baseline severity of conditions. Currently, any such adjustment is lacking for these outcomes. An alternative approach is to adjust for enrollee risk score ex-post at the stage of quality payment. In practice, it would require policy makers form the right belief as to the bias in quality rating ( dl dr in Equation 3.6.1) and the magnitude of the selection response ( dr dp ) to effectively offset the selection incentive. We thereby ar- gue that adjusting for ex-ante risk in the quality rating is simple to implement, recovers a less biased measure of quality, and can go a long way in reducing the selection incentives associated with quality payments. 95 Table 3.13: Risk-outcome correlation across periods (I) (II) (III) (IV) (V) (VI) (VII) (VIII) (IX) (X) (XI) (XII) Risk score t3 0.90 1.56* 0.97 (1.14) (0.90) (1.20) Risk score t2 0.39 –1.07 –3.34** (0.75) (1.09) (1.44) Risk score t1 1.30* –0.67 0.68 (0.69) (0.73) (1.08) Risk score t 1.53*** –0.47 –1.54 (0.53) (0.71) (1.32) Baseline star 3.0-3.5 4.0 4.5 3.0-3.5 4.0 4.5 3.0-3.5 4.0 4.5 3.0-3.5 4.0 4.5 R-squared 0.67 0.85 0.66 0.65 0.84 0.84 0.63 0.78 0.80 0.63 0.75 0.74 N 336 146 46 472 210 70 611 269 91 760 340 126 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: Table shows OLS-estimated correlation between outcome rating in diabetes and blood pressure management and enrollee risk score across multiple periods. Contemporaneous correlation occurs between year t outcome rating and year t 2 risk score. Correlation with lag risk score in t 3 and lead risk score up to year t is also examined. For each time pair, table shows separate correlation for baseline low quality (3.0-3.5 stars), high quality (4.0 stars and above) and very high quality (4.5 stars and above) contracts. All regressions include contract and year fixed effects. Standard errors clustered at the contract level in the parenthesis. 96 Table 3.14: Risk-quality correlation across periods (I) (II) (III) (IV) (V) (VI) (VII) (VIII) (IX) (X) (XI) (XII) Risk score t3 0.94* 1.15 1.72 (0.55) (0.81) (1.61) Risk score t2 –0.18 0.28 –2.76*** (0.49) (1.00) (0.80) Risk score t1 0.49 1.54** –1.23* (0.37) (0.59) (0.60) Risk score t 0.44 0.88 –1.06 (0.29) (0.54) (0.77) Baseline star 3.0-3.5 4.0 4.5 3.0-3.5 4.0 4.5 3.0-3.5 4.0 4.5 3.0-3.5 4.0 4.5 R-squared 0.73 0.66 0.14 0.67 0.64 0.71 0.65 0.62 0.73 0.66 0.57 0.66 N 337 136 38 479 202 64 618 259 82 792 338 118 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: Table shows OLS-estimated correlation between final star rating and enrollee risk score across multiple periods. Contemporaneous corre- lation occurs between year t star rating and year t 2 risk score. Correlation with lag risk score in t 3 and lead risk score up to year t is also examined. For each time pair, table shows separate correlation for baseline low quality (3.0-3.5 stars), high quality (4.0 stars and above) and very high quality (4.5 stars and above) contracts. All regressions include contract and year fixed effects. Standard errors clustered at the contract level in the parenthesis. 97 3.8 Conclusion We examine the insurer selection response to quality bonus payments in the Medicare Advantage (MA) market. The 2012 onset of the Quality Bonus Payment (QBP) demon- stration varied payment generosity by quality rating, which we exploit in the difference- in-difference analysis. We find that pass-through of the bonus payments to enrollees is minimal: high quality contracts eligible for higher bonus payments increased bids by nearly the full amount of the bonus, leaving rebate to enrollee unchanged. Correspond- ingly, premium did not differentially decrease, or generosity increase, for enrollees in high quality contracts. Within contract, however, we uncover significant premium variation across high and low cost counties for high quality contracts, but not for low quality contracts. Coupled with a higher baseline concentration in low risk counties, risk pool improved significantly for high quality contracts after the payment reform. We provide suggestive evidence that a negative correlation between enrollee risk score and patient health outcome can explain the selection response. In this case, low risk enrollees contribute to continued high quality rating and bonus payments. These results have important normative implications for quality bonus payments in the MA market and similar value-based models elsewhere. One fundamental issue is the measurement of quality. To take out the risk confound, the current outcome measures need to be adjusted for the case-mix and severity of baseline conditions, and ideally be made conditional on risk scores. Failure to do so raises complicated distributional is- sues. For example, high quality care is made less accessible to the low-income, high-risk population, who potentially benefit more from quality. The equity concern among in- framarginal enrollees, and a near zero pass-through on average, illustrate the subtle but critical role of insurer selection in the welfare incidence of value-based payments. 98 Appendix A Appendix to Chapter 1 A.1 Auction Webpage Figure A.1: A screenshot of the webpage for a listing at the time of data collection Title Charity Pictures % donated Countdown Current price Info reserve price Auction leader Description Notes: Screenshot of a webpage of a running auction on Charitystars.com for an AC Milan jersey worn and signed by the player Giacomo Bonaventura. The standing price is GBP 110: this bid was placed by an Italian bidder with username “Supermanfra”. A total of five bids are placed at this point. Although at the current highest bid the reserve price is not met, this can change by the end of the auction. The auction will be active for other 3 days and 18 hours and will expire on June 7th at 7AM. 85% of the proceeds will be donated to “Play for Change”. 99 A.2 Data Description The data was collected using a Python script that searched a list of keywords across the pages dedicated to soccer items on the company website, available at http://www.charitystars.com. The script would gather all the available information regarding the auction, the charity, the listing and the bid history. This information was augmented with data from other sources. For example, a similar python script was used to recover footballers’ quality scores from a renowned videogame (FIFA). Information on each charity’s mission was obtained from both Charitystars as well as each charity’s website. The analysis considers only a subset of the available auctions (see Section 3.3), according to the following conditions: (i) transaction prices higher than the reserve price, (ii) reserve prices greater than zero, (iii) two or more bidders, (iv) minimum increment is withine 25 and (v) maximum donation of 85% of the final price. A.2.1 Description of the Variables The regressions in Section 3.3 and in the Appendix display only some of the actual variables used in the analyses due to space limitations. These variables were distinguished in four groups based on their relevance. 1. Main Variables: these are the variables used in all regression tables and in the structural model. They are listed in Table A.1 and their meaning is described by their label. Some variables whose meaning is not immediately clear are described in the following list: The variable Length counts the number of days between the first bid and the closing date (the listing date of the auction is unknown). The dummy Extended time is 1 if two or more bidders placed a bid in the last minutes of the auction. In this case the time is extended until all but 1 bidders drop out Auctions within 3 weeks (same team) counts the number of auctions listing jerseys of the same team as the one of the auctioned item. It only includes auctions within a 3 week window from the end of the auction. It considers all auctions not only those with final price larger thane 100 and smaller thane 1000. Auctions up to 2 weeks ago (same player/team) counts the number of auctions for a jersey worn by the same player playing with the same team in the same year as the match of the jersey that is auctioned. It considers all the listings up to 2 weeks from the end of the auction (Charitystars’ auctions last between 1 and 2 weeks). It considers all auctions not only those with final price larger thane 100 and smaller thane 1000. Count auctions same charity is a progressive count of the number of listings for each charity. The dummy Player belongs to FIFA 100 list is 1 if the player is in the FIFA 100 list (the list of the best soccer players ever). The variable Number of goals scored is equal to the number of goals scored by the player with the auctioned jersey in a particular match if this number is mentioned in the content of the listing. It is zero otherwise. The dummy Player belongs to an important team is 1 if the player plays for one of the fol- lowing teams (alphabetic order): AC Milan, Argentina, Arsenal FC, AS Roma, Atletico 100 de Madrid, Barcelona FC, Bayern Munich, Belgium, Borussia Dortmund, Brazil, Chelsea FC, Colombia, England, FC Internazionale, France, Germany, Italia, Juventus FC, Liv- erpool FC, Manchester City, Manchester United, Netherlands, PSG, Real Madrid, Sevilla FC, Spain, SS Lazio, SSC Napoli, Uruguay. 1 2. Add. Charity Dummies: this group includes dummies for heterogeneity across charities based on the mission of each charity. These dummies are not exclusive bins as most charities do more than only one activity. There are 101 different charities in total. The dummy variables used Helping disables individuals for charities involved in assistance to disable subjects. Infrustructures in developing countries for charities building infrastructures in develop- ing countries. Healthcare for charities dealing with healthcare and health research. Humanitarian scopes in developing countries for charities helping people in situation of poverty and undernourishment. Children’s wellbeing for charities providing activities (e.g., education and sport) to the youth. Neurodegenerative disorders for charities helping those suffering from neurodegenera- tive disorders. Charity belongs to the soccer team are charities linked to a football team. Improving access to sport charities give opportunity of integration through sport activi- ties. Italian charity. English charity. 3. League/Match Dummies: these are dummies for soccer league and match heterogeneity. They include: Dummies for each major competition (Champions League, Europa League, Serie A, Italian Cup, Premier League, La Liga, Copa del Rey, European Supercup, Italian Supercup, Spanish Supercup, UEFA European Championship, Qualifications to UEFA European Championship, World Cup, Qualification to the World Cup 2 ). Dummies weather the listings mentions that the match was won (Won) and for unoffi- cial/replica jerseys which are not worn but only signed (Unofficial). There are only 79 jerseys in the dataset that are replica, and they are all signed by the player. 4. Time Dummies: this group include Month dummies (12 variables) and Year dummies (2 vari- ables). 1 In unreported analysis player quality was accounted also using the players’ evaluation from the videogame FIFA. These variables do not affect prices significantly and are dropped. 2 All remaining competitions are treated as friendly matches. 101 Table A.1: Summary statistics Variable Mean St.Dev. Q(25%) Q(50%) Q(75%) Auction characteristics Percentage donated (q) 0.70 0.27 0.78 0.85 0.85 Transaction price ine 364.25 187.50 222.00 315.00 452.50 Reserve price ine 179.03 132.02 100.00 145.00 210.00 Minimum increment ine 1.71 3.15 1.00 1.00 1.00 Number of bidders 7.83 3.27 5.00 7.00 10.00 Sold at reserve price (d) 0.04 0.20 0.00 0.00 0.00 Length (in # days) 8.08 3.07 7.00 7.00 7.00 Extended time (d) 0.43 0.50 0.00 0.00 1.00 Web-listing details Length of description (in # words) 141.89 42.11 123.00 140.00 161.25 Content in English (d) 0.30 0.47 0.00 0.00 1.00 Content in Spanish (d) 0.00 0.07 0.00 0.00 0.00 Length of charity description (in # words) 123.47 56.62 107.00 107.00 120.00 Number of pictures 5.67 1.98 5.00 6.00 7.00 Auctions within 3 weeks (same team) 1.46 4.08 0.00 0.00 1.00 Auctions up to 2 weeks ago (same player/team) 5.06 7.92 0.00 1.00 7.00 Count auctions same charity 128.35 151.94 14.00 54.00 216.50 Player and match characteristics Player belongs to FIFA 100 list (d) 0.11 0.31 0.00 0.00 0.00 Unwashed jersey (d) 0.09 0.29 0.00 0.00 0.00 Jersey is signed (d) 0.52 0.50 0.00 1.00 1.00 Jersey is signed by team players/coach (d) 0.06 0.24 0.00 0.00 0.00 Jersey worn during a final (d) 0.03 0.17 0.00 0.00 0.00 Number of goals scored 0.03 0.20 0.00 0.00 0.00 Player belongs to an important team (d) 0.88 0.32 1.00 1.00 1.00 Charity provenience Charity is Italian (d) 0.90 0.29 1.00 1.00 1.00 Charity is English (d) 0.08 0.28 0.00 0.00 0.00 Charity’s activity Helping disables individuals (d) 0.35 0.48 0.00 0.00 1.00 Infrustructures in dev. countries (d) 0.09 0.29 0.00 0.00 0.00 Healthcare (d) 0.23 0.42 0.00 0.00 0.00 Humanit. scopes in dev. countries (d) 0.14 0.34 0.00 0.00 0.00 Children’s wellbeing (d) 0.84 0.36 1.00 1.00 1.00 Neurodegenerative disorders (d) 0.06 0.23 0.00 0.00 0.00 Charity belongs to a soccer team (d) 0.10 0.29 0.00 0.00 0.00 Improving access to sport (d) 0.63 0.48 0.00 1.00 1.00 Notes: Overview of the main covariates used in all specifications in the reduced form analysis and in the structural model. (d) stands for dummies. Only auctions with price betweene 100 ande 1000. Prices are in Euro. If the listing was in GBP the final price was converted in euro using the exchange rate of the last auction day. 102 A.2.2 Prices and Revenues This section reports the density plots for transaction prices and reserve prices for the most common auction types. Figure A.2: Density of key variables by percentage donated (a) Transaction Price p2(100, 1000) 0.000 0.002 0.004 0.006 0 250 500 750 1000 Price pdf q = 10% q = 78% q = 85% (b) Reserve Price p2(100, 1000) 0.000 0.002 0.004 0.006 0 250 500 750 1000 Reserve Price pdf q = 10% q = 85% Notes: Panel (a) and Panel (b) show the density of the transaction price and reserve price respectively for selected auctions. The plotted densities are computed using a Gaussian kernel and Silverman’s rule-of- thumb bandwidths (Silverman, 1986). 103 A.3 Omitted Proofs This section outlines the proofs that are omitted in the text. Lemmas 1, 2 and 3 report ancillary results that are useful for the other proofs. A.3.1 Lemma 1 Lemma 1. lim x!0 x log x = 0. Proof: lim x!0 x log x = lim x!0 log x 1/x . Applying L’Hospital’s Rule lim x!0 1/x 1/x 2 = lim x!0 x = 0. A.3.2 Proof of Lemma 1 The equilibrium bid for a bidder with private valuation v and charitable parametersa and b in a sym- metric second-price charity auction where the auctioneer donates q is: b (v;a,b, q)= 8 > > < > > : 1 1+q(ab) ( v+ R v v 1F(x) 1F(v) 1qb qa +1 dx ) , ifa> 0^ q> 0 v 1qb , ifa= 0_ q= 0. Proof: A similar proof can also be found in Engers and McManus (2007). This proof is only reported for completeness. All the following results hold for 0< q 1. Let F (k) (n) (v) be distribution of the kth highest element out of n; the problem in (1.3.2) can be rewritten as E[u(v;a,b, q)]= Z s v v(1 qb i )b(u) dF(u) n1 | {z } i wins and pays b II + qa i b(s)(n 1)F(s) n2 [1 F(s)] | {z } i loses and bids b i = b II + qa i Z v s b(u)dF (2) (n1) (u) | {z } i loses and price p= b II > b i . Here F (2) (n1) (u) = F(u) n1 +(n 1)F(u) n2 (1 F(u)) is the distribution of the second highest value, given that the number of agents is n 1 because bidder i is counted out as his bid is below b II . The equilibrium bidding function is found where dE[U(v,s)] ds j s=v = 0. 104 dE[u(v;a,b, q)] ds s=v =0 =v ¶F(s) n1 ¶s + b(qb 1) ¶F(s) n1 ¶s + qab(n 2) ¶F(s) n1 ¶s 1 F(s) F(s) + qab 0 (n 1)[1 F(s)]F(s) n2 qab ¶F(s) n1 ¶s qab(n 2) ¶F(s) n1 ¶s 1 F(s) F(s) = 0. After deleting and moving terms, v f(v)= (1+ qa qb)b(v) f(v) qab 0 (v)[1 F(v)]. (A.3.1) This differential equation can be finally solved by multiplying both sides of (A.3.1) by [1F(s)] 1qb qa qa and integrating. v f(v) [1 F(v)] 1qb qa qa = 1+ qa qb qa b f(v)[1 F(v)] 1qb qa + b 0 [1 F(v)] 1+qaqb qa , 1 qa Z v v t[1 F(t)] 1qb qa dF(t)= Z v v ¶b[1 F(t)] 1+qaqb qa ¶t dt. This leads to the symmetric bidding function: b (v;a,b, q)= 8 > < > : 1 qa R v v t[1F(t)] 1qb qa dF(t) [1F(v)] 1+qaqb qa , if qa> 0^ q> 0 v 1qb , ifa= 0_ q= 0. (A.3.2) Note that the constant of integration that arises after integrating the RHS of the FOC is 0 (to see this, check the bidding function when v = v). Further integrating the integral in the top row by parts yields (1.3.3): b (v;a,b, q)= 1 1+ q(ab) ( v+ Z v v 1 F(x) 1 F(v) 1qb qa +1 dx ) which collapses to v 1qb whena or q are zero. Finally, this is a legitimate bidding function because it is increasing in v: ¶b (v;a,b, q) ¶v = 8 < : 1 qa R v v 1F(x) 1F(v) 1qb qa +1 dx f(v) 1F(v) > 0, ifa> 0^ q> 0 1 1qb > 0, ifa= 0_ q= 0. (A.3.3) 105 A.3.3 Reserve Price Engers and McManus (2007) discuss the optimal reserve price and participation fee across the most common sealed-bid charity auctions. This section studies the optimal reserve price, r , (with no participation fee) in second-price charity auctions, and shows that it is increasing in q. Following Engers and McManus (2007), there exists a unique threshold type ˆ v2 (v, v), so that bidders do not bid for v < ˆ v and bidders bid b (v;a,b, q) r in v ˆ v. This ˆ v is defined by (see Engers and McManus, 2007, page 968): [(1 qb)r ˆ v]F( ˆ v) n1 = qa(n 1)F( ˆ v) n2 [1 F( ˆ v)][b ( ˆ v;a,b, q) r]. An increase in r or a decrease in q are associated with an increase in ˆ v to keep the equation bal- anced. Thus ¶ ˆ v/¶r > 0 and ¶ ˆ v/¶q < 0. To simplify the analysis, I assume that the threshold bidder ˆ v bids exactly r so that b( ˆ v;a,b, q) = r. This is a fair assumption in an English auction, especially if the parallel with the button auction is maintained. This assumption implies that ¶ 2 ˆ v/¶r¶q < 0, which means that in case of a simultaneous increase in q and r, the sign of this derivative is dominated by the effect of q. If the auctioneer maximizes gross revenues, it will set r such that (conditional on q): r = arg max r n Z v ˆ v F( ˆ v) n1 r+ Z v ˆ v b (x)dF n1 (x) f(v)dv = arg max r n [1 F( ˆ v)]F( ˆ v) n1 r+ Z v ˆ v b (v)[1 F(v)](n 1)F n2 (v) f(v)dv . The first order conditions can be rearranged to yield r = 1 F( ˆ v) f( ˆ v) ¶ ˆ v ¶r 1 . In conclusion, r is increasing in q because of the increasing hazard rate assumption and because ¶ ˆ v/¶q < 0. The analysis would not have changed if the auctioneer were to set the reserve price to maximize net revenues (i.e., the net revenue factor(1 q) cancels out in the FOC as it does not depend on r). 3 A.3.4 Lemma 2 and Lemma 3 The following lemmas show conditions for b(v)= v whena b and b(v)= v/(1 qb) when a< b. These results are necessary to prove both Lemma 2 and Lemma 3. Lemma 2. Assume that a b. The bid function b(v) crosses the 45 line only once if b(v) v, and either never or two times if b(v)< v. Proof: First, I focus on the case b(v) v. The bid function evaluated at the upper bound, b(v) = 3 This result holds also if the auctioneer’s objective is to maximize profits. In this case, the cost of procur- ing an item, c, is sunk; the auctioneer sustain c independently of the outcome of the auction. Therefore, c cannot affect an optimally set reserve price. 106 v 1+qaqb implies that b(v)< v. 4 Thus, given the requirement that b(v)< v, one need to show that there exists only one ˆ v such that b( ˆ v) ˆ v8v2[v, ˆ v] and b( ˆ v)< ˆ v, then b(v)< v8v2( ˆ v, v] . The following condition holds at b(v)= v (ab)q= 1 v Z v v 1 F(x) 1 F(v) 1qb qa +1 dx, which is obtained substituting b(v) = v in the LHS of (1.3.3). Multiplying both sides of the equa- tion by(1/qa) f(v)/[1 F(v)] gives 1 qa f(v) 1 F(v) (ab)q= 1 v ¶b(v) ¶v , (A.3.4) where the RHS includes (A.3.3). Assume that there are three values v 1 < v 2 < v 3 such that the bid computed at each value is equal to the value itself. Given that b(v) is differentiable and b(v)6= v for v62fv 1 , v 2 , v 3 g, it must be that b(v) < v for v2 (v 1 , v 2 ) and v2 (v 3 , v] and b(v) > v for v2 (v, v 1 ) and v2 (v 2 , v 3 ). The increasing hazard rate property gives 1 qa f(v 2 ) 1 F(v 2 ) (ab)q> 1 qa f(v 1 ) 1 F(v 1 ) (ab)q 1 qa f(v 3 ) 1 F(v 3 ) (ab)q> 1 qa f(v 2 ) 1 F(v 2 ) (ab)q. Because (A.3.4) must hold at v 1 , v 2 and v 3 , ¶b(v 2 ) ¶v 2 ¶b(v 1 ) ¶v 1 > v 2 v 1 > 1, ¶b(v 3 ) ¶v 3 ¶b(v 2 ) ¶v 2 > v 3 v 2 > 1, a contradiction. In fact, while the ratio of the derivative at v 2 and v 1 must be larger than 1, as the curve intersects the 45 line from below the line, this cannot happen at v 3 and v 2 , because the intersection happens from above the line. The bid function crosses the 45 line at v 2 from below, while it crosses the same line from above at v 3 , implying ¶b(v 3 ) ¶v 3 < ¶b(v 2 ) ¶v 2 . Figure A.3b provides a graphical representation. Because v 1 , v 2 and v 3 are arbitrary values, the proof holds for all v. Given that b(v) v, b(v) < v and because b(v) cannot cross the 45 line more than twice without violating the increasing hazard rate property, it must be that b(v) = v at most once. The second case (b(v)< v) follows immediately from the previous derivation, given that b(v) cannot cross the 45 line more than twice without violating the increasing hazard rate assumption. This implies that b(v)= v for either two values v 1 and v 2 or no value at all. In this case, in order to respect the increasing hazard rate property, the bid function meets the diagonal line from below 4 This result is obtained by applying L’Hospital’s rule to R v v 1F(x) 1F(v ) 1qb qa +1 dx and the increasing haz- ard rate assumption. 107 at the first cutoff and from above at the second cutoff, making a cutoff like v 3 infeasible. Lemma 3. Assume thata < b. The bid function b(v) crosses the line v/(1 qb) only once if b(v)(1 qb) v, and either never or two times if b(v)(1 qb)< v. Proof: This proof is similar to that in Lemma 2, the bid evaluated at the upper bound is b(v) = v 1+qaqb implying that b(v)< v 1qb . The remaining derivations follow immediately from the Proof of Lemma 2 by replacing the points v 1 < v 2 < v 3 with the points ˙ v 1 < ˙ v 2 < ˙ v 3 such that b(v) = v 1qb for v2f ˙ v 1 , ˙ v 2 , ˙ v 3 g and b(v)6= v 1qb otherwise. A.3.5 Proof of Lemma 2 If a > 0, there exists a value v such that all bidders with private values in(v , v] decrease their bids after a marginal change ina. Proof: Assume q> 0 and let ˜ a= qa and ˜ b= qb. Take derivative of (1.3.3) w.r.t. q fora> 0 ¶b (v;a> 0,b, q) ¶q =q R v v 1F(x) 1F(v) 1+˜ a ˜ b ˜ a 1+ (1 ˜ b)(1+˜ a ˜ b) ˜ a 2 log 1F(x) 1F(v) dx+ v (1+ ˜ a ˜ b) 2 . (A.3.5) The integral is continuous and finite everywhere with respect to x by Lemma 1. The derivative will cross the x-axis at v= v where the numerator is zero, 1 ˜ b ˜ a 2 Z v v 1 F(x) 1 F(v ) 1+˜ a ˜ b ˜ a log 1 F(x) 1 F(v ) dx = v + R v v 1F(x) 1F(v ) 1+˜ a ˜ b ˜ a dx 1+ ˜ a ˜ b = b(v ). (A.3.6) At v6= v , (A.3.5) is positive (negative) if the LHS in the first line of (A.3.6) is greater (smaller) than the RHS. To show uniqueness of v I focus on the derivative of (A.3.5) at v . To limit some cumbersome notation, denote R v v 1F(x) 1F(v ) 1+˜ a ˜ b ˜ a dx byf. The derivative of (A.3.5) w.r.t. v at v is negative if 1 ˜ b ˜ a 2 f 1 ˜ b ˜ a 2 1+ ˜ a ˜ b ˜ a Z v v 1 F(x) 1 F(v ) 1+˜ a ˜ b ˜ a log 1 F(x) 1 F(v ) dx 1 ˜ a f. (A.3.7) At v , the second term on the LHS can be replaced by the RHS of (A.3.6). Solving this inequality gives the following condition 1 ˜ b ˜ a 2 f+ v +f ˜ a 1 ˜ a f ) (1+ ˜ a ˜ b)f ˜ a(v +f) ) b(v )(1+ ˜ a ˜ b) v ˜ ab(v ) ) b(v )(1 ˜ b) v , (A.3.8) 108 where in the third row both sides of the inequality are divided by (1+ ˜ a ˜ b) and expressed f in terms of bids and values using the optimal bid function (1.3.3). Therefore, if the condition in (A.3.8) is respected, (A.3.5) is decreasing at v . The following result will be used below. The limit of (A.3.5) is negative for v! v. In fact, repeatedly applying L’Hospital’s rule to the the limit of the first term yields lim v!v q R v v (1 F(x)) 1+˜ a ˜ b ˜ a 1+ (1 ˜ b)(1+˜ a ˜ b) ˜ a 2 log 1F(x) 1F(v) dx (1+ ˜ a ˜ b) 2 (1 F(v)) 1+˜ a ˜ b ˜ a = 0. while the limit of the last term (at the numerator) is lim v!v qv=qv< 0. There are two cases: in Case 1 v is unique and in Case 2 either v does not exist or there are two cutoffs. CASE 1. The first case assumes that, depending on the parametersa and b, either b(v) v if a b or b(v)(1 ˜ b) v ifa b. To complete the proof of uniqueness I rely on two results: (i) the limit of (A.3.5) is negative at the upper bound of the support of v, and (ii) there is no region on the support of v such that b(v)(1 ˜ b) < v and b(v)(1 ˜ b) > v to its left and right. Therefore, once (A.3.5) becomes negative, it cannot switch sign from negative to positive and back to negative again, implying that if v exists, it is unique. For a b Lemma 2 states that there exists at most only one v2 [v, v] such that b(v) = v. Because of monotonicity, there exists at most one value of v such that b(v)(1 ˜ b) = v. Lemma 3 states a similar result for the complementary case (a < b). Denote by v the value such that b(v )(1 ˜ b) = v . For v < v , b(v)(1 ˜ b) > v and for v > v , b(v)(1 ˜ b) < v. Given the two Lemmas and that (A.3.5) is continuous and negative when evaluated at the upperbound, then v v . To the contrary, assume that v > v , then (A.3.5) must be increasing at v . This implies that (A.3.5) is positive at v, a contradiction. This also implies that if (A.3.5) is negative at v it will be negative for all v. Therefore, if v exists, it is unique and separates those who increase their bid (low value bidders) from those who decrease it (high-value bidders). CASE 2. The second case analyzes the complement to Case 1 (i.e., that depending ona and b either b(v) < v or b(v)(1 ˜ b) < v). Due to Lemma 2 and Lemma 3 there exist either no cutoff or exactly two cutoffs v 2 fv 1 , v 2 g such that (A.3.6) is increasing at v 1 and decreasing at v 2 , with v 1 < v 2 because the limit of (A.3.5) is negative at the upper bound. In fact, it must be that b(v 1 )(1 ˜ b)< v 1 and b(v 2 )(1 ˜ b)> v 2 . Hence, there exists a value v such that (at least some) bidders with values below v increase their bids, while all bidders with values above v decrease it after a marginal increase ina. A.3.6 Proof of Lemma 3 If b a, bids are increasing in q for all bidders. If a > b, there exists a private value ˜ v such that bidders with private values in( ˜ v, v] decrease their bids after a marginal increase in q. Proof: Assume q> 0 and let ˜ a= qa and ˜ b= qb. First we analyze the derivative of b(v) w.r.t. q whena= 0, which is: ¶b (v;a= 0,b, q) ¶q = bv (1 ˜ b) 2 > 0. The derivative in this case is always positive asb< 1 and q< 1, meaning that bids increase in q. Turn now to the derivative with respect to q whena is positive. This proof has multiple steps. (i) I establish that for b a > 0 the bid is increasing in q8v. (ii) I focus on the remaining case 109 (b< a) and show that the derivative of the bid w.r.t. q can have both positive and negative values. (iii) I show that, at the value such that the derivative is zero (called ˜ v), if the bid is larger than the value, then b(v) is always decreasing. (iv) In the final step, I show conditions for the uniqueness of ˜ v. Steps (ii) - (iv) are similar to the proof of Lemma 2. Step 1. Take derivative of (1.3.3) w.r.t. q fora> 0 is ¶b (v;a> 0,b, q) ¶q = R v v 1F(x) 1F(v) 1+˜ a ˜ b ˜ a a(1+˜ a ˜ b) ˜ a 2 log 1F(x) 1F(v) (ab) dx(ab)v (1+ ˜ a ˜ b) 2 . (A.3.9) The integral is continuous and finite everywhere with respect to x by Lemma 1. Inspection of this equation reveals that is positive if b a (these refers to warm glow or pure altruism models). Therefore, bids are increasing in q ifb> a for all v. Step 2. Turn to the remaining case (0 < a < b or shill bidders model). (A.3.9) crosses the x-axis at ˜ v. By rewriting (A.3.9), at ˜ v Z v v 1 F(x) 1 F(v) 1+˜ a ˜ b ˜ a a(1+ ˜ a ˜ b) ˜ a 2 log 1 F(x) 1 F(v) dx =(ab) 0 @ v+ Z v v 1 F(x) 1 F(v) 1 ˜ b ˜ a +1 1 A dx v= ˜ v =(ab)(1+ ˜ a ˜ b)b( ˜ v). (A.3.10) where the second line replaces the expression to the RHS with the optimal bid function in (1.3.3). Thus, (A.3.9) can be positive or negative. Step 3. This step shows that the derivative is decreasing at ˜ v if b( ˜ v) ˜ v. Given that the RHS of (A.3.10) is increasing in v everywhere, it will also be increasing in v at ˜ v. To show that there is at most one ˜ v, it suffices to show that the LHS is a decreasing function of v, at ˜ v. The derivative of the LHS w.r.t. v is Z v ˜ v 1 F(x) 1 F( ˜ v) 1 ˜ b ˜ a +1 a 1+ ˜ a ˜ b ˜ a 2 1+ 1+ ˜ a ˜ b ˜ a log 1 F(x) 1 F( ˜ v) dx f( ˜ v) 1 F( ˜ v) , (A.3.11) while the derivative of the RHS can be rewritten as (ab)(1+ ˜ a ˜ b) ˜ a b( ˜ v)(1+ ˜ a ˜ b) ˜ v f( ˜ v) 1 F( ˜ v) . (A.3.12) Putting together (A.3.11) and (A.3.12) and using (A.3.10) to rewrite (A.3.11) in terms of bids and values, (A.3.9) is decreasing at ˜ v if b( ˜ v)(1+ ˜ a ˜ b) ˜ v a 1+ ˜ a ˜ b ˜ a 2 +(ab) (1+ ˜ a ˜ b) 2 ˜ a b( ˜ v) (ab)(1+ ˜ a ˜ b) ˜ a b( ˜ v)(1+ ˜ a ˜ b) ˜ v ) a 1+ ˜ a ˜ b ˜ a 2 b( ˜ v) a ˜ a 2 ˜ v+ ab ˜ a ˜ v= a 1+ ˜ a ˜ b ˜ a 2 ˜ v ) b( ˜ v) ˜ v. where R v ˜ v 1F(x) 1F( ˜ v) 1+˜ a ˜ b ˜ a dx is rewritten in terms of bid minus values. This means that (A.3.9) is 110 positive at the left of ˜ v and negative to the right of ˜ v. Therefore, as long as the equilibrium bid at the cut-off value ˜ v is greater than the cut-off itself, bids will be decreasing in q for all v > ˜ v, if a> b. Step 4 Whena> b, the limit of (A.3.9) for v! v is negative. In fact, under the increasing hazard rate condition (Assumption 1.3) applying L’Hospital’s rule to the first term (in the numerator) of (A.3.9) yields lim v!v R v v (1 F(x)) 1+˜ a ˜ b ˜ a a(1+˜ a ˜ b) ˜ a 2 log 1F(x) 1F(v) (ab) dx (1+ ˜ a ˜ b) 2 (1 F(v)) 1+˜ a ˜ b ˜ a = 0, while the limit of the remaining part is lim v!v (ab)v=(ab)v< 0. There are two cases: in Case 1 ˜ v is unique and in Case 2 either ˜ v does not exist or there are two ˜ v. CASE 1. The first case assumes b(v) v. To show that ˜ v is unique I merge two results: (i) the limit of (A.3.9) is negative at the upper bound of the support of v, and (ii) there is no region on the support of v such that b(v)< v inside and b(v)> v to its left and right. Therefore, it cannot switch sign from negative to positive and back to negative again, implying that if ˜ v exists, it is unique. Recall from Lemma 2 that when b(v) v, b(v) intersects the 45 line only once, at ˜ ˜ v, such that b(v) > v for v < ˜ ˜ v and b(v) < v for v > ˜ ˜ v. The result in step 3 coupled with the requirements (i) that (A.3.9) is negative when evaluated at the upper bound, (ii) that (A.3.9) is continuous on the support of v, and (iii) Lemma 2, necessarily means that (A.3.9) cannot switch sign more than once, imply that ˜ v < ˜ ˜ v as otherwise¶b(v)/¶qj v=v > 0. In fact, for ˜ v ˜ ˜ v (A.3.9) is increasing at ˜ v, which implies that (A.3.9) is positive for v > ˜ v. Then, (A.3.9) must switch sign again to negative in order to satisfy the¶b(v)/¶qj v=v < 0 condition, but this is not possible in this region because of ˜ ˜ v is unique and b(v)< v for v> ˜ v ˜ ˜ v. (see Figure A.3a). In addition, the uniqueness of ˜ ˜ v implies that ˜ v does not exists if (A.3.9) is negative at v. In this case, the derivative of the bid w.r.t q will always be negative. Therefore, if ˜ v exists, it is unique and separates those who increase their bid (low value bidders) from those who decrease it (high-value bidders). CASE 2. The second case assumes b(v)< v. Lemma 2 proves that there are either no ˜ ˜ v or that there are exactly two ˜ ˜ v so that the bid function cuts the 45 line twice. It follows that there exist either no cutoff or exactly two ˜ v =f ˜ v 1 , ˜ v 2 g such that (A.3.10) is increasing at ˜ v 1 and decreasing at ˜ v 2 , with ˜ v 1 < ˜ v 2 because the limit of (A.3.9) is negative at the upper bound. In fact, it must be that b( ˜ v 1 )< ˜ v 1 and b( ˜ v 2 )> ˜ v 2 . Hence, whena > b there exists a value ˜ v such that (at least some) bidders with values below ˜ v increase their bids, while all bidders with values above ˜ v decrease it after a marginal increase in q. When insteada b all bidders increase their bids after a marginal increase in q. A.3.7 Proof of Proposition 1 Whena = 0, the expected consumer surplus in a charity auction is equal to the consumer surplus in a non-charity auction. It is greater whena> 0. Proof: In a second-price non-charity auction a bidder’s dominant strategy is to bid her private 111 Figure A.3: Illustration of the proofs of Lemma 3 and Lemma 2 (a) Lemma 3 ∗∗ () 45° > < () ∗ (b) Lemma 2 " # $ () 45° Notes: Panel (a) shows the effect of a marginal increase in q when a > b assuming that b(v) > v. The complementary case would show two ˜ v, such that the derivative (dotted line) is negative for the lowest value bidders, positive for the bidders with values between ˜ v 1 and ˜ v 2 and negative for the highest value bidders. The plot for the proof of Lemma 2 would be similar to Panel (a) with the exception that the 45 line is replaced by the v/(1 qb) line. Panel (b) shows that the bid is steeper at v 2 than at v 3 . Lemma 2 states that if b(v) oscillates around the 45 line it violates the increasing hazard rate assumption. value (i.e. b NC (x)= x). The ex-ante consumer surplus is therefore: CS NC = Z v v Z v v v b NC (x)dF(x) n1 dF(v) = Z v v v(1 F(v) n1 )+ Z v v F(x) n1 dx dF(v), (A.3.13) where the second equality is derived integrating by parts. Showing that CS NC is identical to the consumer surplus in an analogous charity auction where bidders do not gain from externalities (i.e.,a= 0) is trivial because the expected payment in the former is equal to the expected payment minus warm glow of donating in the latter. 5 For the consumer surplus of a charitable second-price auction whena> 0, CS C = Z v v Z v v v(1bq) b C (x)dF(x) n1 dF(v) + qa b C (v)F(v) n2 1 F(v) + qa Z v v b C (x)dF (2) (n1) (x), (A.3.14) where b C (x) is defined as in (1.3.3) and F (2) (n1) (x)= F(x) n1 +(n 1)F(x) n2 (1 F(x)). Plugging- 5 That is, if the expected payment is x, then x = x 1bq (1bq). 112 in the bidding function in (A.3.14), and after some algebra, one obtains: CS C = Z v v ( v(1 F(v) n1 )+ Z v v F(x) n1 dx Z v v 1 F(x) 1 F(v) 1qb+qa qa dxF(v) n1 1 qb 1 qb+ qa Z v v 1 F(x) 1 F(v) 1qb+qa qa F(x) n1 dx + qa 1 qb+ qa " v+ Z v v (1 F (2) (n1) (x))dx+ Z v v 1 F(x) 1 F(v) 1qb+qa qa F (2) (n1) (x)dx Z v v F(x) n1 dx #) dF(v). (A.3.15) Importantly, the first line in this equation is CS NC in (A.3.13). Therefore, in order to prove the theorem I only need to show that the remaining two lines are positive. In order to simplify the computations, approximate CS C with d CS C where the expression in the second line R v v 1F(x) 1F(v) 1qb+qa qa dxF(v) n1 is substituted with R v v 1F(x) 1F(v) 1qb+qa qa F(x) n1 dx as follows d CS C = CS NC + Z v v ( Z v v 1 F(x) 1 F(v) 1qb+qa qa F(x) n1 dx 1 qb 1 qb+ qa Z v v 1 F(x) 1 F(v) 1qb+qa qa F(x) n1 dx + qa 1 qb+ qa " v+ Z v v (1 F (2) (n1) (x))dx+ Z v v 1 F(x) 1 F(v) 1qb+qa qa F (2) (n1) (x)dx Z v v F(x) n1 dx #) dF(v). (A.3.16) Because F(x) n1 > F(v) n1 for x > v, the last expression is smaller than the former. Hence d CS C can be viewed as a lower bound for CS C . Therefore if d CS C > CS NC then also CS C > CS NC . The remainder of this proof heavily relies on L’Hospital’s rule and integration by parts to show that this ordering holds. In particular I will show that the third line (which involves sums of positive terms) is greater than the second line. To save on notation, denote 1F(x) 1F(v) byF and 1qb+qa qa byy. Integrating by part the first term in the second line of (A.3.16) (i.e., R v v R v v F y F(x) n1 dxdF(v)) gives " Z v v F y F(x) n1 dxF(v) v v Z v v F(v) n + Z v v F y y f(v) 1 F(v) F(x) n1 dxF(v)dv # . (A.3.17) The first term in brackets is 0, while the second term (negative) and the third term (positive) will be cancelled out using a combination of the second expression in the second line and the term+ 1 y R v v F y [F(x) n1 +(n 1)F(x) n2 (1 F(x))]dx in the middle of the third line of (A.3.16). 113 Starting from the former, and integrating it by parts: Z v v 1 qb 1 qb+ qa Z v v F y F(x) n1 dx dF(v)= " 1 qb 1 qb+ qa Z v v F y F(x) n1 dxF(v) v v Z v v 1 qb 1 qb+ qa F(v) n + Z v v 1 qb 1 qb+ qa F y y f(v) 1 F(v) F(x) n1 F(v)dx dv # . (A.3.18) The first term in the square brackets is zero because of the L’Hospital’s rule. 6 In addition, the sec- ond two terms in (A.3.17) and (A.3.18) are similar, with the only difference being the multiplicative constant and the integration regions. However, because: Z v v A(x)dx = Z v v A(x)dx Z v v A(x)dx, where A(x) is a continuous function. The last term in (A.3.18) can be rewritten as Z v v Z v v 1 qb 1 qb+ qa F y y f(v) 1 F(v) F(x) n1 dx F(v) dv= = Z v v Z v v 1 qb 1 qb+ qa F y y f(v) 1 F(v) F(x) n1 dx F(v) dv Z v v Z v v 1 qb 1 qb+ qa F y y f(v) 1 F(v) F(x) n1 dx F(v) dv, (A.3.19) where the term in the second line is positive while the remaining term is negative. Given this algebra, I can cancel out the last term in (A.3.17) by summing the last term in (A.3.19) with a similar one but with 1/y as a multiplicative factor (i.e. 1/y+(1 qb)/(1 qb+ qa) = 1). This term is found by integrating by parts the term in the second line of (A.3.16) that was previously mentioned: Z v v 1 y Z v v F y [F(x) n1 +(n 1)F(x) n2 (1 F(x))] dx dF(v) = 1 y " Z v v F y [F(v) n1 +(n 1)F(v) n2 (1 F(v))]dxF(v) v v Z v v [F(x) n +(n 1)F(x) n1 (1 F(x))]dv Z v v Z v v F y y f(v) 1 F(v) [F(x) n1 +(n 1)F(x) n2 (1 F(x))] dx F(v) dv # . (A.3.20) Once again the first term in brackets goes to zero. Moreover, a portion of the last term (i.e., R v v F y y f(v) 1F(v) F(x) n1 dxF(v)dv ) can be summed with the last term in (A.3.19) to cancel out the last term in (A.3.17). Similarly, the second term in (A.3.17) cancels out with the sum of the second term in (A.3.18) and a portion of the second term in (A.3.20) (i.e., R v v F(x) n dv). 6 In fact the lim v!v 1qb 1qb+qa R v v F y F(x) n1 dx = 0, while the expression is also zero for v! v because F(v)= 0. 114 To conclude the proof, the sum of the remaining terms in (A.3.20) and (A.3.16) must be positive. To show that the remaining part of (A.3.20) is positive, rewrite it as: Z v v (n 1) F(v) n2 (1 F(v)) Z v v (1 F(x)) y (n 1)F(x) n2 (1 F(x))dx y(1 F(v)) y1 f(v) F(v)dv. (A.3.21) Integration by parts of the second line of (A.3.21) yields " Z v v (1 F(x)) y (n 1)F(x) n2 (1 F(x))F(v)dx(1 F(v)) y v v + Z v v (n 1) F(v) n2 (1 F(v))F(v) dv Z v v Z v v (1 F(x)) y (n 1)F(x) n2 (1 F(x)) f(v) dx (1 F(v)) y dv # . (A.3.22) The first term evaluated at the limits of the support of v is zero. 7 In addition, the term in the second line of (A.3.22) is equal to the first term in (A.3.21) but with opposite signs so they cancel out, while the last term is positive. Finally, the sum of the first and last term in the third line of (A.3.16) is positive. Therefore, d CS C > CS NC implying also that CS C > CS NC . A.3.8 Proof of Proposition 2 Define h(p e ) = ¶p e ¶q q p e as the elasticity of the expected price, p e , to the donation, q. When a = 0, the auctioneer should not donate. Whena> 0, the revenue optimal donation solvesh(p e )= q 1q . Proof: Assume that the marginal cost is zero for simplicity. Then, the producer surplus is equal to the net revenue to the auctioneer for each object sold: PS(a,b, q)= 8 > < > : R v v (1 q) 1 1+q(ab) n v+ R v v 1F(x) 1F(v) 1qb qa +1 dx o dF (2) (n) (v), ifa> 0^ q> 0 R v v (1 q) v 1qb dF (2) (n) (v), ifa= 0_ q= 0. (A.3.23) Whena = 0 the derivative of the producer surplus w.r.t. q is negative asb2 (0, 1). Therefore, the auctioneer is always better off by setting q= 0. Consider the other case (a > 0). First suppose that q = 1: this cannot be optimal because it would leave the auctioneer with zero profits. In this case, setting q = 0 would be a profitable 7 This result follows from L’Hospital’s rule. In fact lim v!v (1 F(v)) y+1 (n 1)F(v) n1 y(1 F(v)) y1 f(v) + R v v (1 F(x)) y+1 (n 1)F(v) n2 dx f(v) y(1 F(v)) y1 f(v) = 0. The first term goes to zero, while to prove that the second term goes to zero as well I divide numerator and denominator by f(v) and apply L’Hospital’s rule again. 115 deviation, proving that q = 1 cannot be a solution for a profit maximizer auctioneer. To simplify the notation, given a and b, denote the bid of a bidder with valuation v in an auction where ˜ q is donated by b(v, ˜ q). The expected net revenue in a second-price charity auction is Z v v (1 q)b(v, q)dF (2) (n) (v). Let h be the elasticity of the expected price p e = R v v b(v, q)dF (2) (n) (v) with respect to a marginal change in q: h = ¶ ln p e ¶ ln q = ¶p e ¶q q p e . By the Dominated Convergence Theorem, I can interchange differentiation and integration, so that the derivative of the expected price with respect to q can be rewritten as ¶p e ¶q = R v v ¶b(v,q) ¶q dF (2) (n) (v). Using the elasticity formula, R v v ¶b(v,q) ¶q dF (2) (n) (v)= h p e q . The optimal amount donated is the q that solves the FOCs of the auctioneer’s problem (the second-order conditions are satisfied): Z v v b(v, q)+(1 q) ¶b(v, q) ¶q dF (2) (n) (v)= 0. Substitutinghp e for the derivative of the bid, the optimal q is given by: h = q 1 q . To illustrate the result in this proof, Figure A.4 shows that the auctioneer should not donate when a= 0. A.3.9 Proof of Lemma 4 a,b and F(v) are not identified without additional restrictions. Proof: The model is not identified without (i) auxiliary data, or (ii) additional distributional as- sumptions. Denote a second-price charity auction with primitives F(v),a,b and q byG 2 (F,a,b, q). For simplicity, assume that q = 1. It is easy to see that the model is not identified whena = 0. In fact, it is not possible to tell apart the following two expected utility models: 8 u(v;a,b, q)= ( v b II +bb II , if i wins 0, otherwise , e u(v;a,b, q)= ( v 1b b II , if i wins 0, otherwise , implying that the modelG 2 (F,a= 0,b, q= 1) is observationally equivalent to the model e G 2 ( e F,a= 0, e b, q= 1), with ˜ b= 0 and e F = F((1b)v i ). In both models bidder i bids b(v)= v 1b = ˜ v= ˜ b( ˜ v). Setting a > 0 does not improve identification. In this case the model G 2 (F,a,b, q = 1) is observationally equivalent toG 2 (F,a,b, q = 1), where b = 0,a = a 1b and F(v) = F((1b)v). Therefore, it is impossible to determine the tuple(a,b, F). 8 I would like to thank Jorge Balat for these examples. 116 Figure A.4: Illustration of the results in Propositions 1 and 2 (a)a= 0 PS charity PS non-charity CS charity CS non-charity , −ℎ ℎ 0 1 1−() ℎℎ 1− (b)a> 0 , 1− 1−() 0 1 PS charity PS non-charity ℎℎ −ℎ ℎ Notes: The plots display a bidder’s willingness to pay (y axis) in relation to her probability of losing the auction (x axis). Let v denote the private value of the winner in the non-charity auction. In the charity auction, the willingness to pay, w, is the sum of a bidder’s private value plus the expected benefit from winning the auction (bp e ) and the expected externality from losing the auction (ap e ). The two panels show how producer surplus and consumer surplus change when the auctioneer passes from q = 0 to q > 0. In Panel (a) a = 0, and the produced surplus in the charity auction is necessarily smaller than in the non- charity auction. The consumer surplus stays unchanged. In Panel (b) the positive externality increases bidder’s willingness to pay (b > a). This is displayed by a shift and a rotation of the dashed demand line compared to Panel (a). This implies a greater consumer surplus in charity auctions (not drawn). The size of the new producer suprlus (shaded rectangle) will depend on q. In conclusion, in Panel (a) the auctioneer should not donate while in Panel (b) the auctioneer may find optimal to donate if the shaded area is greater than the checked area. Both plots maintainb a. A.3.10 Proof of Proposition 3 If all bids are observed, under Assumptions 1 and 2, the parameters a and b and the distribution of values F(v) are identified by variation in q across auctions. Proof: To simplify the notation I denote a bid only by b(v) and the bid distribution, density and hazard by G(b), g(b) and l G (b), respectively. The researcher observes two types of auction, A and B, and that the only difference among them is the fraction of the transaction price that will be donated, i.e. q A 6= q B . Because the distribution of values F() is the same across auctions A and B, then for each value corresponding to thet-quantile of the value distribution, v x , the distribution of bids computed at that t-quantile must be equal, i.e. G(b x jq A ) = G(b x jq B ). Therefore, after rewriting the first order condition for each set of auctions (A.3.1) as in (1.4.1) I can match the FOCs from the two auctions (A.3.1) based on the quantiles of the bid distribution. This gives the following equation for each quantile of v x : v A x v B x = b A x b B x +(ab)(q A b A x q B b B x )a(q A l G (b A x ) q B l G (b B x )), (A.3.24) where G(b x ) = G(b A x ) = G(b B x ). Since v A x v B x = 0, eq. A.3.24 can be rewritten in matrix notation as D(b x )= B x ab a , (A.3.25) 117 whereD(b x )=(b A x b B x ) and B x is the matrix[q A b A x q B b B x ; q A l G (b A x ) q B l G (b B x )]. It can be shown that the matrix B x has full rank (the two columns are linearly independent). To prove this assume that B x is not invertible and therefore that its columns are linearly dependent (i.e. b x = kl G (b x ) for both auctions A and B). Dependence leads to G(b x ) = 1 b x g(b x )/k for a constant k > 0. Note that k must be positive because otherwise (i) G(b x ) > 1 as g(b x ) 0,8b x and (ii) the FOC equation x(b x ,a,b, q), which was defined in (1.4.1), may not be monotonically increasing in b x . The previous differential equation admits a solution g(b x )= c(b x ) (k+1) , where c is an integration constant. Thus, G(b x ) = 1 c(b x ) k /k. Evaluating the CDF at b x = 0 yields G(0)=¥,8k> 0. Moreover, the inverse hazard rate l G (b x )= 1 1+ c(b x ) k /k c(b x ) (k+1) = b x k for k> 0, is increasing in b x . This implies that 1 F(v x ) f(v x ) = 1 G(b(v x )) g(b(v x )) b 0 (v x ) = 1 k b(v x ) b 0 (v x ) , which is an increasing function because (i) the optimal bidding function b(v) is increasing in the private value v x and (ii) the bidding function b(v x ) maximizes a bidder’s utility (b 00 (v x ) 0). This means that the inverse hazard rate is not decreasing and that therefore b(v x ) is not a best response for v x . This is a contradiction that violates Proposition 1 proving that the columns in B x are not linearly dependent and that B x is invertible. 9 Given that B x has full rank,a,b and F(v) are nonparametrically identified. A.3.11 Proof of Proposition 4 If only the winning bid is observed,a,b and F(v) are nonparametrically identified by first deriving the distribution of bids that would have been observed in parallel second-price auctions, and then by applying Proposition 3. Proof: To simplify the notation I denote a bid only by b(v) and the bid distribution, density and hazard by G(b), g(b) and l G (b), respectively. Assume that the researcher observes two kind of auctions A and B, characterized by q A and q B respectively (with q A 6= q B ). The starting point is to note that G(b) = F(v), and that also in charity auctions the distribution of the winning bid is equal to the distribution of the second-highest bid: G w (b) = G 2 (n) (b). Therefore, the distribution of bids that would have been realized in an equivalent second-price auction is found using the classic inversion of the latter relation. In particular, G(b) is found as the root (in[0, 1]) of G w (b) nG(b) n1 +(n 1)G(b) n . Now, the FOCs (1.4.1) can be written for eacha andb. Therefore, one can apply the same logic in Proposition 3, and identifya,b and F(v). 9 If k = 1, then g(b x ) = 0 for b x < 0 and g(b x ) > 0 for b x 0. Therefore g() is the Dirac delta function, which is not differentiable and does not admit a decreasing inverse hazard rate. In turn, given that F(v) = G(b(v)), the non-differentiability of G() implies that also the distribution of values F() is not differentiable, a contradiction. 118 A.3.12 Proof of Corollary 1 a,b and F(v) are also nonparametrically identified when the dataset includes more than 2 types of auctions. Proof: To simplify the notation I denote a bid only by b(v) and the bid distribution, density and hazard by G(b), g(b) andl G (b), respectively. Assume that q has dimension K C and that K x quan- tiles of the distribution of values are observed. The FOC (1.4.1) in matrix notation becomes V K x K C =(ab) B K x K C Q C K C K C + B K x K C a L K x K C Q C K C K C , (A.3.26) where V is a matrix of dimension K x K C displaying the value v x for the xquantile (row) in auction of type C (column), and 0 otherwise. Similarly, Q C is a diagonal matrix with entries equal to the percentage donated q C and 0. The other matrices are defined as: B= 2 6 4 b 1 0 b 2 0 . . . b K C 0 . . . . . . . . . . . . b 1 1 b 2 1 . . . b K C 1 3 7 5 , L= 2 6 4 l 1 G (b 1 0 ) l 2 G (b 2 0 ) . . . l K C G (b K C 0 ) . . . . . . . . . . . . l 1 G (b 1 1 ) l C 2 G (b 2 1 ) . . . l K C G (b K C 1 ), 3 7 5 where superscripts indicate that the amount donated is equal to q j for j2 [1, K C ] and subscripts indicate the x quantiles of the distribution of values or bids. There exists a projection M (with rank K C 1) such that V M = 0. Postmultiplying (A.3.26) by M and moving terms, the following equation represents the FOC where the dependent variable is a known object B M =(ab) B Q C MaL Q C M. After stacking the matrices in vectors, the last equation can be represented by the system of equa- tions y= b l ab a , where y = vec(B M), b = vec(B Q C M), l = vec(L Q C M), and vec() indicates the vectorization of the matrices in parentheses. Nonparametric identification requires showing that b and l are not proportional to each other (i.e., that B andL are linearly independent). Nonproportionality follows directly from the argu- ment in the proof of Proposition 3 in Appendix A.3.10. Hence, b and l are not linearly dependent, establishing identification ofa,b and F(v). 119 A.4 Bargaining with Celebrities This section provides a micro foundation to the condition for the optimal q in (1.7.2). The surplus to the firm is the difference of the net revenues (1 q)p and the fixed cost k, which is a unit cost accounting, for example, for procuring and storing the item, publishing the listing online as well as managerial cost related to an auction. k does not vary with q. Celebrities cares for the amount that is ultimately donated. For simplicity they incur no cost in giving the item. The bargaining weights arew for the firm and 1w for the celebrity. In this bargaining framework, q maximizes (1 q)p e k w (qp e ) 1w , (A.4.1) where p e denotes the expected highest price, and is a function of the distribution of values, the charity parameters (i.e., a and b), the number of bidders and q. The first-order condition with respect to q can be rearranged to obtain p e q 1 (1 q)p e w (1 q)p e (1w)k ! = 1 q q hp e p e . (A.4.2) h is the elasticity of the expected price to a change in q. The RHS is the same as in (1.7.2), while the LHS is a function of the primitives. The LHS can be interpreted as a marginal cost (c 0 (q)). Whenw = 1, all bargaining power is in the hand of Charitystars. The LHS becomes 0, and Charitystars acts as a monopolist by choosing the q that solvesh = q 1q , as in the revenue maximization case (see Proposition 2). Because there is no bargaining, setting a greater q does not yield any cost savings (i.e., c 0 (q)= 0). Whenw = 0, the celebrity holds all the bargaining power. The firm will donate as much as possible as the condition for the optimal q is not feasible (i.e.,h =1) if the elasticity of supply is positive (as in the warm glow model). Charitystars reaps the largest cost saving when the LHS is the smallest possible (p e /q), which happens as w! 0. For w2 (0, 1), the LHS is increasing in w, implying that the stronger is the celebrity (smallw), the greater is the marginal cost savings. Since the term in parentheses is always in the unit interval, the LHS will always be negative if the net expected price is greater than the unit cost (i.e., (1 q)p e > k). This condition must hold for the firm to operate, and it is ensured by the way the reserve price is set in practice (to break-even). Thus, c 0 (q)< 0. Finally, the LHS in (A.4.2) can be rearranged by adding and subtractingw in the term in paren- theses p e q (1 q)p e k+w 2 k (1 q)p e k+wk w ! p e q (1w), which gives a clean interpretation of the marginal cost in terms of the bargaining weight and prim- itives of the model. Therefore, the monopolistic approach taken in the main text can be extended to account for a simple bargaining problem between Charitystars and the celebrity. Optimal fraction donated with more covariates. Figure A.5 shows the optimal percentage do- nated by intersecting marginal revenues and marginal costs as in Section 1.7. Marginal costs and revenues are derived as in the main body with the addition of covariates belonging to the groups: “Additional Charity Dummies”, “League/Match Dummies” and “Time Dummies” (the same re- gressors used in the fourth column of Table 1.2). Control variables are defined in Appendix A.2. 120 Figure A.5: Optimal fraction donated (q) - accounting for more covariates −600 −500 −400 −300 −200 −100 0 0.00 0.25 0.50 0.75 1.00 Percentage donated (q) MR, MC (EUR) M Net Revenue MC − Quadratic Notes: The plot shows the optimal percentage donated as the intersection of marginal costs and marginal benefits. The number of bidders is assumed to be 8. The density f(v) and the distribution F(v) are ap- proximated using a cubic spline. Only auctions with price betweene 100 ande 1000. Marginal revenues in euro are computed as in Figure 1.10. The covariates used in (1.5.1) include the total number of bids as in Appendix A.5.5. 121 A.5 Additional Tables and Figures Figure A.6: Number of bidders and number of auctions over time (a) Monthly median number of bidders over time 0 2 4 6 8 10 Median Number of Bidders (by Month) 2014 2015 2016 2017 2018 2019 Months (b) Monthly number of auctions over time 0 20 40 60 80 100 Number of Auctions (by Month) 2014 2015 2016 2017 2018 2019 Months Notes: Plot (a) shows the median number of bidders by month and Plot (b) shows the number of auctions by month. Only auctions of actually worn soccer jerseys are considered. Last month in the sample is November 2018 Table A.2: Relation between log(Price) and percentage donated (small dataset) (I) (II) (III) (IV) log(Bidders) 0.158 0.182 0.182 0.180 (0.031) (0.028) (0.028) (0.028) Fraction Donated (q) 0.050 0.127 0.146 0.157 (0.051) (0.046) (0.052) (0.052) log(Reserve Price) 0.261 0.254 0.252 (0.027) (0.029) (0.030) Main Variables Y Y Y Y Add. Charity Dummies Y Y League/Match Dummies Y Y Time Dummies Y Adjusted R-squared 0.186 0.293 0.314 0.352 BIC 510 415 507 559 N 713 713 713 713 * – p< 0.1; ** – p< 0.05; *** – p< 0.01. Notes: OLS regression of log of the transaction price on covariates. Only auctions with price betweene 100 ande 400. Control variables are defined in Appendix A.2. Robust standard errors in parenthesis. 122 Figure A.7: Plot of the coefficient for q from a quantile regression 0.2 0.4 0.6 0.8 0.1 0.2 0.3 0.4 Quantile of log(Price) Coefficient of Percentage Donated (q) Quantile Regression OLS Notes: Coefficients from a series of quantile regressions of the log of the transaction price on q and covari- ates as in the first column of Table 1.3 in the main text. The shaded regions is the confidence interval. The dashed (dotted) line reports the coefficient of the OLS regression (5% confidence interval). Only auctions with price betweene 100 ande 1000. Boostrappedq (fraction donated) standard errors with 400 repetitions. 123 Figure A.8: Plot of the coefficient for q from a quantile regression (small dataset) 0.2 0.4 0.6 0.8 0.0 0.1 0.2 0.3 Quantile of log(Price) Coefficient of Percentage Donated (q) Quantile Regression OLS Notes: Coefficients from a series of quantile regressions of the log of the transaction price on q and covari- ates as in the first column of Table A.3 in the main text. The shaded regions is the confidence interval. The dashed (dotted) line reports the coefficient of the OLS regression (5% confidence interval). Only auctions with price betweene 100 ande 400. Boostrapped standard errors with 400 repetitions. 124 Table A.3: Linearity of the relation between log(Price) and percentage donated (small dataset) (I) (II) (III) (IV) OLS Q(0.25) Q(0.50) Q(0.75) log(Reserve Price) 0.261 0.372 0.288 0.182 (0.027) (0.049) (0.044) (0.033) log(Bidders) 0.182 0.188 0.171 0.124 (0.028) (0.034) (0.045) (0.040) Fraction Donated (q) 0.127 0.164 0.171 0.146 (0.046) (0.056) (0.071) (0.070) Main Variables Y Y Y Y Adjusted/Pseudo R-squared 0.293 0.265 0.181 0.147 N 713 713 713 713 * – p< 0.1; ** – p< 0.05; *** – p< 0.01 Note: OLS Regression and quantile regressions of log of the transaction price on covariates. Only auctions with price betweene 100 ande 400. Boostrapped standard errors with 400 repetitions. The null hypothesis that q is the same in column (II), (III) and (IV) is not rejected at common levels. Control variables are defined in Appendix A.2. Robust standard errors in parenthesis. Table A.4: Relation between the rate of daily bidders and percentage donated (I) (II) (III) Fraction Donated (q) 0.067 0.082 0.052 (0.069) (0.071) (0.073) Main Variables Y Y Y Charity Dummies Y Y League/Match Dummies Y Pseudo R-squared 0.131 0.133 0.144 N 713 713 713 * – p< 0.1; ** – p< 0.05; *** – p< 0.01 Note: Poisson regression of the number of bidders on co- variates. The length of the auction is used as exposure variable and is not included among the covariates. The database is restricted to auctions with prices in[100, 400]. Control variables are defined in Appendix A.2. Robust standard errors in parenthesis. 125 Table A.5: OLS and IV regressions for the transaction price. (I) (II) (III) (IV) OLS IV IV IV Reserve Price 0.770 0.807 0.834 0.803 (0.042) (0.181) (0.184) (0.193) Bidders 12.793 13.319 13.341 12.256 (1.480) (1.540) (1.597) (1.617) Fraction Donated (q) 90.687 141.796 146.408 182.071 (17.068) (84.163) (88.907) (96.339) Main Variables Y Y Y Y Charity Dummies Y Y Y League/Match Dummies Y Y Adjusted R-squared 0.537 0.516 0.516 0.456 N 1,109 1,107 1,106 1,106 * – p< 0.1; ** – p< 0.05; *** – p< 0.01 Note: OLS and IV regression of the transaction price on the percentage donated and covariates. The reserve price and the percentage donated are instrumented using the average reserve price and average percentage donated across all concurrent auctions (for each auction I take all the auctions ending in the previous and successive five days to the end of the auction). Both the null hypothesis of underidentification (the Kleibergen-Paap rk LM statistic) and weak identification (Kleibergen-Paap rk Wald F statistic) are rejected at common values. The Hausman test does not reject the null hypothesis of exogeneity of the reserve price and q at common values. League/Match Dummies are partialled out in Column (IV). Control variables are defined in Appendix A.2. Robust standard errors in parentheses. 126 Table A.6: OLS and IV regressions for the number of daily bidders. (I) (II) (III) (IV) OLS IV IV IV Fraction Donated (q) 0.077 0.145 0.192 0.186 (0.054) (0.237) (0.250) (0.264) Main Variables Y Y Y Y Charity Dummies Y Y Y League/Match Dummies Y Y Adjusted R-squared 0.296 0.356 0.355 0.249 N 1,109 1,107 1,106 1,106 * – p< 0.1; ** – p< 0.05; *** – p< 0.01 Note: OLS and IV regression of the number of daily bidders (i.e., Number of Bidders / Length) and covariates. The reserve price and the percentage donated are instrumented using the average reserve price and average percentage donated across all concur- rent auctions (for each auction I take all the auctions ending in the previous and successive five days to the end of the auction). Both the null hypothesis of underidentification (the Kleibergen-Paap rk LM statistic) and weak identification (Kleibergen-Paap rk Wald F statistic) are rejected at common values. The Hausman test does not reject the null hypothesis of exogeneity of the reserve price and q at common values. League/Match Dummies are partialled out in Column (IV). Control variables are defined in Appendix A.2. Ro- bust standard errors in parentheses. 127 Table A.7: Evidence of bargaining: IV regressions (I) (II) (III) (IV) OLS IV OLS IV August 0.074 0.107 (0.030) (0.039) July & August 0.068 0.112 (0.024) (0.034) Main Variables Y Y Y Y Add. Charity Dummies Y Y Y Y League/Match Dummies Y Y Y Y Adjusted R-squared 0.354 0.270 0.357 0.187 N 1,109 1,107 1,109 1,107 * – p< 0.1; ** – p< 0.05; *** – p< 0.01 Note: The table presents the OLS estimate for the dummy variables August (1 if the month is August, 0 otherwise) and July and August (1 if the month is either July or August, 0 otherwise) as in equation (1.7.1). The reserve price and the number of bidders are instrumented using the average reserve price and the number of bidders across all concurrent auctions (for each auction I take all the auctions ending in the previous and successive five days to the end of the auction). Both the null hypothesis of underidentification (the Kleibergen-Paap rk LM statistic) and weak identification (Kleibergen-Paap rk Wald F statistic) are rejected at common values. The Hausman test does not reject the null hypothesis of exogeneity of the reserve price and q at common values. League/Match Dummies are partialled out in Column (IV). Only auctions with price betweene 100 ande 1000. Robust standard errors in parentheses. 128 A.5.1 The Nationality of the Bidders Table A.8: Nationalities of the bidders Italian UK France Other EU North Am China Asia East Asia Rest World Tot Winner 560 74 41 119 62 130 35 28 59 1,108 50.54% 6.68% 3.70% 10.74% 5.60% 11.73% 3.16% 2.53% 5.32% – Second 603 79 28 113 51 117 33 26 58 1,108 54.42% 7.13% 2.53% 10.20% 4.60% 10.56% 2.98% 2.35% 5.23% – Total 1,163 153 69 232 113 247 68 54 117 – Notes: Nationalities of the bidders by geographic area. “Rest of the World” includes Eastern Europe, Middle East, Africa, Oceania, Latina America and Unknown nationalities (which comprises 12 winners and highest losers). 129 Table A.9: Regression of log(Price) on bidder nationality (I) (II) (III) Fraction Donated (q) 0.230 0.230 0.235 (0.048) (0.048) (0.048) Win: Italy –0.043 –0.038 –0.058 (0.024) (0.024) (0.064) Italian Team –0.068 (0.031) Win: North America 0.058 (0.077) Win: France –0.095 (0.086) Win: European Union –0.008 (0.071) Win: China 0.016 (0.070) Win: UK –0.020 (0.076) Win: Unknown –0.154 (0.134) Win: Asia –0.079 (0.089) Win: South-East Asia –0.121 (0.089) Main Variables Y Y Y Adjusted R-squared 0.460 0.462 0.461 N 1,108 1,108 1,108 * – p< 0.1; ** – p< 0.05; *** – p< 0.01 Notes: OLS regressions of log of the transaction price on covari- ates to test the symmetry assumption over different nationalities of the winner. The first column tests Italian vs Non-Italian winners. The coefficient shows that Italian winners bid less than others, however Column (II) reveals that this correlation vanishes when a dummy variable for whether the football jersey is from an Italian team is also present. No geographic dummy variable is signifi- cant in Column (III). Only auctions with price betweene 100 and e 1000. Control variables are defined in Appendix A.2. Robust standard errors in parenthesis. 130 A.5.2 Asymmetric Behavior Table A.10: Regression of log(Price) on recurrent winners (I) (II) (III) (IV) 100< p< 1000 100< p< 400 log(Reserve Price) 0.351 0.372 0.262 0.271 (0.023) (0.022) (0.027) (0.026) log(Bidders) 0.295 0.063 0.181 0.028 (0.029) (0.037) (0.028) (0.034) Fraction Donated (q) 0.227 0.207 0.120 0.110 (0.048) (0.046) (0.046) (0.044) Recurrent Winner 0.047 0.030 0.035 0.021 (0.023) (0.022) (0.022) (0.022) Total Number of Bids Placed 0.218 0.143 (0.023) (0.022) Main Variables Y Y Y Y Adjusted R-squared 0.461 0.503 0.295 0.334 N 1108 1108 713 713 * – p< 0.1; ** – p< 0.05; *** – p< 0.01 Notes: OLS regressions of the log of the transaction price on covariates to test the symmetry assumption. The dummy variable Recurrent Winner is 1 if the winner of the auction won more than 3 auctions (the median in the data). Control variables are defined in Appendix A.2. Robust standard errors in parenthesis. 131 A.5.3 Additional Tables from the Structural Model Table A.11: First step of the structural estimation (I) (II) (III) (IV) 100< p< 1000 100< p< 400 d UH 0.341 0.267 Minimum Increment –0.010 0.003 –0.036 –0.018 Minimum Increment 2 0.0001 0.0004 0.002 0.001 log(Bidders) –0.014 0.312 –0.136 0.150 Sold at Reserve Price 0.555 0.042 0.490 0.056 Length 0.045 0.071 0.005 0.055 Length 2 –0.003 0.003 0.001 0.002 Extended Time 0.010 0.072 0.091 0.073 Length of Description 0.002 0.002 0.001 0.001 Content in English 0.116 –0.0003 –0.004 –0.054 Content in Spanish –0.185 –0.244 0.310 0.174 Length of Charity Description –0.0002 –0.0003 –0.0004 –0.001 Number of Pictures –0.074 –0.060 0.010 –0.002 Number of Pictures 2 0.009 0.006 0.002 0.001 Auctions within 3 weeks 0.013 0.016 –0.016 0.007 Auctions up to 2 weeks ago 0.004 0.011 –0.005 0.008 Count Auctions Same Charity 0.0004 –0.001 0.0001 –0.001 Player belongs to FIFA 100 list 0.216 0.201 0.168 0.098 Unwashed Jersey 0.143 0.282 –0.029 0.140 Jersey is Signed –0.405 –0.054 –0.320 –0.042 Jersey is signed by the team players/coach –0.592 –0.172 –0.493 –0.041 Jersey Worn During a Final 0.348 0.411 –0.280 0.204 Number of Goals Scored 0.192 0.247 0.012 0.336 Player Belongs to an Important Team 0.230 0.291 0.144 0.169 Charity is Italian –0.086 0.143 –0.168 0.113 Charity is English 0.304 0.233 0.034 0.230 Helping Disables –0.142 0.019 –0.214 –0.006 Infrastructures in Developing Countries –0.069 0.152 –0.482 –0.138 Healthcare –0.152 –0.232 –0.116 –0.057 Humanitarian Scopes in Developing Countries 0.159 0.165 0.037 –0.027 Children’s Wellbeing 0.117 0.121 –0.056 0.038 Neurodgenerative Disorders 0.489 0.273 –0.020 0.094 Charity Belongs to the Soccer Team 0.037 –0.239 0.375 0.016 Improving Access to Sport –0.041 –0.026 –0.124 0.043 Adjusted R-squared 0.280 0.468 0.313 0.364 N 730 730 470 470 * – p< 0.1; ** – p< 0.05; *** – p< 0.01 Notes: The table reports the two regressions in the first step of the structural model. Columns (I) and (III) regress log(Reserve Price) on covariates, while Columns (II) and (IV) regress log(Price) on the unobserved heterogeneity ( d UH) and covariates. Control variables are defined in Appendix A.2. P-value computed using robust standard errors (S.E. not reported). 132 Table A.12: Logit regression of q on covariates. (I) (II) Coefficient S.E. Coefficient S.E. log(Reserve Price) 0.846 (0.254) 0.795 (0.486) log(Bidders) –0.973 (0.353) –1.384 (0.464) Length –0.577 (0.215) –0.542 (0.307) Length 2 0.016 (0.007) 0.013 (0.012) Minimum Increment –0.669 (0.203) –0.820 (0.339) Minimum Increment 2 0.026 (0.007) 0.031 (0.012) PriceEqualRes 0.905 (0.583) 1.174 (0.869) Lenght of description 0.026 (0.007) 0.031 (0.009) Content in English –0.446 (0.453) –0.556 (0.666) Content in Spanish 0.000 (.) 0.000 (.) Length of Charity Desc. 0.006 (0.003) 0.011 (0.004) Number of Pictures 0.319 (0.356) 0.887 (0.578) Number of Pictures 2 –0.043 (0.033) –0.103 (0.053) Within 3 Weeks –0.933 (0.222) –0.765 (0.190) Count 2 weeks –0.011 (0.021) –0.006 (0.032) Count Auctions Same Charity 0.025 (0.003) 0.026 (0.003) Extended Time –0.339 (0.310) –0.019 (0.421) FIFA 100 0.408 (0.390) 0.958 (0.534) Jersey not Washed –1.096 (0.834) 0.000 (.) Signed –0.854 (0.396) –0.579 (0.532) Signed Team –0.876 (0.746) –1.215 (0.855) Goals scored 0.447 (0.579) 0.446 (1.005) Italian Charity –1.539 (1.391) –2.540 (1.242) English Charity 5.195 (1.458) 5.503 (1.759) Disability 1.840 (0.425) 1.507 (0.633) Development –0.901 (0.914) –0.899 (0.860) Health –1.624 (0.621) –1.257 (0.812) Humanitarian –0.387 (1.057) 0.613 (1.647) Children and Youth –2.270 (0.470) –2.959 (0.679) Neurodegenerative dis. –1.681 (0.747) –1.960 (0.907) Team Related –0.602 (1.071) –1.509 (1.228) Sport –1.883 (0.504) –1.138 (0.744) Pseudo R-squared 0.527 0.546% N 729 442 * – p< 0.1; ** – p< 0.05; *** – p< 0.01 Notes: Logit regression of q on covariates. The dependent variable is 1 if q = 0.1. Only auctions with q2f10%, 85%g. Column (I) refers to auctions whose transaction price is in the interval e(100, 1000), while the interval ise(100, 400) in Column (II). Control variables are defined in Appendix A.2. Robust standard errors are in the odd columns. 133 A.5.4 Robustness Checks for the Structural Estimations This section reports structural estimates for different versions of the models. In particular, the following tables replicate the results in the main text (i) by using only data in thee 100 -e 400 interval, (ii) by comparing auctions with q at 10% and 78% (instead of 85%), 10 and (iii) by using a larger set of covariates. Overall, the results highlights the robustness of the estimates in the main text (Table 1.6). Table A.13: Structural estimation when q2f10%, 85%g and pricee 100 ande 400 Number of bidders a b Quantile n [95% CI] [95% CI] 99% 16 17.2% 37.6% [5.3%, 32.1%] [8.0% 61.8%] 95% 14 17.0% 37.5% [4.6%, 29.7%] [8.5% 60.2%] 90% 12 16.7% 37.5% [4.1%, 28.9%] [12.8% 60.9%] 75% 10 16.2% 37.4% [3.6%, 27.5%] [5.3% 61.4%] 50% 7 15.2% 37.1% [3.8%, 27.3%] [8.9% 61.2%] Notes: a and b are defined in equation (1.3.1). Results from the structural estimation of a and b for selected quantiles of the distribution of the number of bidders. The 95% confidence intervals are reported in square brackets. The CI are found by bootstrap with replace- ment (401 times). The dataset is restricted to all auc- tions such that q2f10%, 85%g and the price between e 100 ande 400. 470 observations in total. 10 Employing the auctions with q =f78%, 85%g do not yield consistent estimates because the full rank condition assumption breaks down as the two q are almost identical. See the simulations in Appendix A.8 for a numerical example. 134 Table A.14: Structural estimation when q2f10%, 78%g and pricee 100 ande 1000 Number of bidders a b Quantile n [95% CI] [95% CI] 99% 16 22.6% 51.8% [11.1%, 30.6%] [32.4% 68.8%] 95% 14 24.0% 52.1% [11.0%, 33.6%] [34.3% 69.2%] 90% 12 24.5% 52.2% [13.3%, 33.7%] [33.3% 71.7%] 75% 10 24.8% 52.3% [10.7%, 32.8%] [34.2% 68.2%] 50% 7 25.1% 52.4% [12.7%, 33.7%] [35.1% 69.4%] Notes: a and b are defined in equation (1.3.1). Results from the structural estimation of a and b for selected quantiles of the distribution of the number of bidders. The 95% confidence intervals are reported in square brackets. The CI are found by bootstrap with replace- ment (401 times). The dataset is restricted to all auctions such that q2f10%, 78%g and the price betweene 100 ande 1000. 366 observations in total. Table A.15: Structural estimation when q2f10%, 78%g and pricee 100 ande 400 Number of bidders a b Quantile n [95% CI] [95% CI] 99% 16 24.5% 52.0% [9.9%, 39.4%] [36.7% 82.2%] 95% 14 24.2% 51.9% [9.3%, 34.4%] [34.7% 81.4%] 90% 12 23.8% 51.8% [9.5%, 34.3%] [35.3% 81.2%] 75% 10 23.3% 51.7% [9.0%, 35.8%] [30.4% 79.2%] 50% 7 21.8% 51.3% [6.5%, 32.6%] [28.6% 83.7%] Notes: a and b are defined in equation (1.3.1). Results from the structural estimation of a and b for selected quantiles of the distribution of the number of bidders. The 95% confidence intervals are reported in square brackets. The CI are found by bootstrap with replace- ment (401 times). The dataset is restricted to all auc- tions such that q2f10%, 78%g and the price between e 100 ande 400. 258 observations in total. 135 A.5.5 Different Set of Covariates In this section the log(Total Number of Bids Placed) is added to the covariates. This variable helped explaining differences in competition in Table A.10. In fact, the more bids are submitted by a given number of bidders (a control for the number of unique bidders is also included), the more intense is the competition in the auction. The estimates of the parameters a and b do not change substantially from those reported in the main text (Table 1.6). In addition, Figure A.9a reports the same out-of-sample validation exercise proposed in the main text (see Section 1.5.3). It is based on the comparison between the pdf of the density obtained from estimating the model using auctions with q2f10%, 85%g (the a and b parameters are shown in Table A.16) with that derived by projecting the full three-step estimation procedure onto the auctions with q= 78%. Table A.16: Structural estimation when q2f10%, 85%g and pricee 100 ande 1000 Number of bidders a b Quantile n [95% CI] [95% CI] 99% 16 17.4% 42.7% [7.6%, 26.8%] [23.2% 57.7%] 95% 14 17.2% 42.7% [7.5%, 25.2%] [18.7% 56.1%] 90% 12 16.9% 42.7% [7.3%, 25.5%] [20.7% 57.6%] 75% 10 16.5% 42.6% [6.8%, 25.7%] [21.4% 60.3%] 50% 7 15.5% 42.4% [6.0%, 23.5%] [19.8% 57.5%] Notes: a and b are defined in equation (1.3.1). Results from the structural estimation of a and b for selected quantiles of the distribution of the number of bidders. The 95% confidence intervals are reported in square brackets. The CI are found by bootstrap with replace- ment (401 times). The dataset is restricted to all auc- tions such that q2f10%, 78%g and the price between e 100 ande 1000. 731 observations in total. 136 Table A.17: Structural estimation when q2f10%, 85%g and pricee 100 ande 400 Number of bidders a b Quantile n [95% CI] [95% CI] 99% 16 14.5% 33.8% [3.0%, 29.4%] [3.6% 57.0%] 95% 14 14.3% 33.7% [2.7%, 27.7%] [8.0% 57.1%] 90% 12 14.1% 33.7% [3.9%, 26.8%] [3.6% 56.2%] 75% 10 13.7% 33.6% [2.2%, 26.0%] [2.4% 56.6%] 50% 7 12.8% 33.4% [2.1%, 22.5%] [6.4% 53.0%] Notes: a and b are defined in equation (1.3.1). Re- sults from the structural estimation ofa and b for se- lected quantiles of the distribution of the number of bidders. The 95% confidence intervals are reported in square brackets. The CI are found by bootstrap with replacement (401 times). The dataset is restricted to all auctions such that q2f10%, 78%g and the price betweene 100 ande 400. 470 observations in total. 137 A.5.6 Out-of-Sample and Overidentification Test Figure A.9: Robustness checks (a) Out-of-sample fit with additional covariates 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 −1.0 −0.5 0.0 0.5 1.0 Private Value pdf q = 10% q = 78% (b) Overidentification test 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 −1.0 −0.5 0.0 0.5 1.0 Private Value pdf Main Above Median Below Median Notes: Panel (a) Replication of the out-of-sample validation in Section 1.5.3 adding the variable log(Total Number of Bids) to the covariates in the first step. The plot shows the comparison of the density of the private values estimated from the structural model employing data from auctions with q=f10%, 85%g and the density of the private values estimated by projecting the three-step estimation on the q= 78% auc- tions (as in Figure 1.5a). The null hypothesis (equality) cannot be rejected at 0.1874 level. The computation assumes n = 16, but the same result can be replicated with different n. The plotted densities are computed using a Gaussian kernel and Silverman’s rule-of-thumb bandwidth (Silverman, 1986). Panel (b) compares the estimated densities in the main text (Main, solid line) with the density computed on two subsets of the moment conditions. The subset “Above Median” (“Below Median”) includes only the moment related to observations computed above (below or equal to) the median. The different sets of moments seem to produce the same densities. A.5.7 Estimation of q by Type of Provider of the Object In the main paper, I estimate the average marginal cost across all fractions donated. A piece of information that might be useful to further demonstrate that the firm donates beyond what is profita optimal is to find the optimal percentage donated across different (types of) providers of the item. This information is only available for about 70% of the listings. When available, I observe whether the object is provided by a private party (called “Best Memorabilia”, 80 auctions) or by either a footballer, a coach or a charity (675 auctions). Because footballers and coaches are closely tied to certain charities, I separate the auctions in the sample in two based on whether the provider of the auctioned item is a private individual or not, and estimate marginal costs on each subsample in the same way as in Section 1.7. The estimation shows that the costs for the first group (private providers) are not significantly correlated with q (p 1 = 162.457, SE : 58.333;p 2 = 371.865; SE : 575.514;p 3 = 641.163, SE : 605.981). 11 Thus, Charitystars should never donate when a private provides the object, as there are 11 The null hypothesis that p 2 p 3 = 0 cannot be rejected (F-test 0.7376, p-value = 0.3931). The same regression without quadratic term yields p 1 = 221.455(SE : 17.144),p 2 =233.035(SE : 66.140). From 138 no cost benefit associated with it. Yet, Charitystars donates a positive amount in all these auctions (17% on average). The marginal cost for the second group (including footballers and charities) are negative and upward sloping (p 1 = 245.135, SE : 7.940;p 2 =543.429; SE : 55.247;p 3 = 337.464, SE : 57.260). Figure A.10 plots the optimal q obtained for this group. I find that q = 0.37, which is very close to that estimated in the full sample (see Figure 1.10a). The qualitative result does not change if I replicate the analysis to account only for the auctions provided by a charity (472 auctions,p 1 = 254.827, SE : 12.248;p 2 =652.462; SE : 110.489;p 3 = 454.759, SE : 116.100). Figure A.10: Optimal fraction donated for jerseys provided by footballers and charities −600 −500 −400 −300 −200 −100 0 0.00 0.25 0.50 0.75 1.00 Percentage donated (q) MR, MC (EUR) M Net Revenue MC − Players, Charities MC − Charities only Notes: The figure shows the optimal percentage donated as the intersection of marginal net benefit (solid line) and marginal costs for the case where the provider is either a charity or a footballer (dotted line) and for the case where the provider is a charity (dashed line). The density f(v) and the distribution F(v) are approximated using a cubic spline. Only auctions with price betweene 100 ande 1000. Marginal revenues in euro are computed in multiple steps. (i) Subtract the median number of bidders times its estimated coefficient in the OLS regression (1.5.1) from the fitted values of the same regression. (ii) Compute the expected revenues obtained as the expectation of the second-highest bid using the primitives estimated in Section 1.5.1 (F(),a,b). (iii) Sum the fitted values in (i) with the homogenized expected price in (ii) and apply the log-level transformation. The covariates used in (1.5.1) and (1.7.3) include the total number of bids as in Appendix A.5.5. A.5.8 Estimation of q with Different Heterogeneity In the main paper, I homogeneize all bids and reserve prices, and sum back the value of the heterogeneity from the median auction to determine both marginal revenues and marginal costs. In this section, I replicate the same analysis but considering the heterogeneity at the 1 st (Figure A.11a) and 3 rd (Figure A.11c) quartiles. The optimal donation for the 1 st quartile case is 26% (SE: 0.004) while for the 3 rd (SE: 0.004). The results confirm the analysis in Section 1.7. Figure A.10, the optimal q at this marginal cost is 0. 139 Figure A.11: Optimal donation and profits for different levels of heterogeneity (a) Optimal fraction donated (25-percentile) −600 −500 −400 −300 −200 −100 0 0.00 0.25 0.50 0.75 1.00 Percentage donated (q) MR, MC (EUR) M Net Revenue MC − Quadratic MC − Cubic (b) Optimal profits (25-percentile) median donation −25 0 25 50 75 100 125 0.00 0.25 0.50 0.75 1.00 Percentage donated (q) Profits (c) Optimal fraction donated (75-percentile) −600 −500 −400 −300 −200 −100 0 0.00 0.25 0.50 0.75 1.00 Percentage donated (q) MR, MC (EUR) M Net Revenue MC − Quadratic MC − Cubic (d) Optimal profits (75-percentile) median donation −25 0 25 50 75 100 125 0.00 0.25 0.50 0.75 1.00 Percentage donated (q) Profits Notes: Panel (a) shows the optimal percentage donated as the intersection of marginal costs (dotted and dashed lines) and marginal net benefit (solid line). Panel (b) displays how profits change with q. The vertical line at 85% indicate the median donation by Charitystars. The number of bidders is assumed to be 7. The density f(v) and the distribution F(v) are approximated using a cubic spline. Only auctions with price betweene 100 ande 1000. Marginal revenues in euro are computed in multiple steps. (i) Subtract the median number of bidders times its estimated coefficient in the OLS regression (1.5.1) from the fitted values of the same regression. (ii) Compute the expected revenues obtained as the expectation of the second- highest bid using the primitives estimated in Section 1.5.1 (F(),a,b). (iii) Sum the fitted values in (i) with the homogenized expected price in (ii) and apply the log-level transformation. The covariates used in (1.5.1) and (1.7.3) include the total number of bids as in Appendix A.5.5. 140 A.5.9 Estimation of q on a Subset of Auctions In this section, I estimate costs using only auctions for q2f0.10, 0.20, 0.72, 0.78, 0.80, 0.85g. In this way I remove the auction formats with less than 15 observations. The cost parameters I estimates are (robust standard errors in parentheses)p 0 = 229.34(SE : 7.404),p 1 =369.93(SE : 59.49), p 2 = 151.65(SE : 62.91). The dashed line in Figure A.12a reports the new cost estimates, while the dotted line replicates the results from the main text (Table 1.9). The profit-maximizing donation is 0.26. The profits with the new estimates are in Figure A.12b. The 95% CI interval is [0.03, 0.425] (bootstrapping with 400 repetitions). The figure supports the results in Section 1.7. Figure A.12: Optimal fraction donated (a) Marginal costs and marginal net benefit −600 −500 −400 −300 −200 −100 0 0.00 0.25 0.50 0.75 1.00 Percentage donated (q) MR, MC (EUR) M Net Revenue MC − All Auctions MC − Subset (b) Optimal profits median donation −25 0 25 50 75 100 0.00 0.25 0.50 0.75 1.00 Percentage donated (q) Profits Notes: Panel (a) shows the optimal percentage donated as the intersection of marginal costs (dotted and dashed lines) and marginal net benefit (solid line). Panel (b) displays how profits change with q. The vertical line at 85% indicate the median donation by Charitystars. The number of bidders is assumed to be 7. The density f(v) and the distribution F(v) are approximated using a cubic spline. Only auctions with price betweene 100 ande 1000. Marginal revenues in euro are computed in multiple steps. (i) Subtract the median number of bidders times its estimated coefficient in the OLS regression (1.5.1) from the fitted values of the same regression. (ii) Compute the expected revenues obtained as the expectation of the second- highest bid using the primitives estimated in Section 1.5.1 (F(),a,b). (iii) Sum the fitted values in (i) with the homogenized expected price in (ii) and apply the log-level transformation. The covariates used in (1.5.1) and (1.7.3) include the total number of bids as in Appendix A.5.5. A.5.10 Estimation of q Using IVs for the Reserve Price and q This section replicates the analysis in Figure A.13 by using instrumental variable to account for possible endogeneity in q and the reserve price. On the demand side, I perform a two-stage least square regression in 1.5.1 where the reserve price is instrumented with the average reserve price in concurrent auctions (within 5 days). The instrument is valid in absence of common shocks to the simultaneous auctions Notice that the covariates include the number of listings of jerseys from the same team in the previous 3 weeks and for the same player in the previous 2 weeks. The Hausman test does not reject the null that the reserve price is exogenous. On the cost side, I follow the 141 same steps in 1.7 but I instrument the percentage donated in the regression to compute marginal costs (Table 1.9) with the average percentage donated in concurrent auctions and its square value (p 0 = 255.2, p value : 0.002;p 1 =486.3, p value : 0.346;p 2 = 252.7, p value : 0.595). The Hausman test does not reject the null that q is exogenous. The resulting optimal q is 0.31. Figure A.13: Optimal donation with instruments for reserve price and q (a) Optimal fraction donated −600 −500 −400 −300 −200 −100 0 0.00 0.25 0.50 0.75 1.00 Percentage donated (q) MR, MC (EUR) M Net Revenue MC − With Instrument (b) Optimal profits median donation −25 0 25 50 75 100 125 150 0.00 0.25 0.50 0.75 1.00 Percentage donated (q) Profits Notes: Panel (a) shows the optimal percentage donated as the intersection of marginal costs (dotted and dashed lines) and marginal net benefit (solid line). Panel (b) displays how profits change with q. The vertical line at 85% indicate the median donation by Charitystars. The number of bidders is assumed to be 7. The density f(v) and the distribution F(v) are approximated using a cubic spline. Only auctions with price betweene 100 ande 1000. Marginal revenues in euro are computed in multiple steps. (i) Subtract the median number of bidders times its estimated coefficient in the OLS regression (1.5.1) from the fitted values of the same regression. (ii) Compute the expected revenues obtained as the expectation of the second- highest bid using the primitives estimated in Section 1.5.1 (F(),a,b). (iii) Sum the fitted values in (i) with the homogenized expected price in (ii) and apply the log-level transformation. The covariates used in (1.5.1) and (1.7.3) include the total number of bids as in Appendix A.5.5. 142 A.5.11 Additional Figures Returning winners Figure A.14 compares the densities of the homogeneized pseudo-winning bids from the first stage of the estimation procedure across bidders who won multiple objects (more than the median, 3) and the other bidders. The null hypothesis that these densities are equal cannot be rejected. The two plots differ based on whether the focus is on the large sample (Panel a) or the small sample (Panel b). Controlling for additional covariates further reduces the distance between the two densities. Figure A.14: Density of the homogenized transaction prices by returning winners (a) Returning vs Non-Returning winners p2(100, 1000) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 −1.2 −0.9 −0.6 −0.3 0 0.3 0.6 0.9 1.2 1.5 Pseudo−winning bids pdf Collectors Others (b) Returning vs Non-Returning winners p2(100, 400) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 −1.2 −0.9 −0.6 −0.3 0 0.3 0.6 0.9 1.2 1.5 Pseudo−winning bids pdf Collectors Others Notes: Density of the pseudo-winning bids in the structural model by returning winners. Returning win- ners (Collectors) are auction winners who won at least 4 bids (the median is 3). The Kolmogorov-Smirnov test does not reject the null hypothesis (equality) at 0.1554 level in Panel (a) and at 0.1423 in Panel (b). Adding the “Total Number of Bids Placed” among the covariates in the first step of the estimation proce- dure yields a p-value greater than 40%. The plot is obtained using only auctions with q2f10%, 85%g. The plotted densities are computed using a Gaussian kernel and Silverman’s rule-of-thumb bandwidths (Silverman, 1986). 143 A.6 Counterfactual Scenario with Different Altruistic Pa- rameters Given the estimated distribution of values, ˆ F(v), one can experiment with different a and b parameters to assess the elasticity of bids to changes in the charitable parameters. For exam- ple, Figure 1.3b showed that a harsh version of the volunteer-shill model of giving (a = 0.5 and b= 0.1) may result in lower gross revenues to the auctioneer in charity auctions than non-charity auctions. Figure A.15b performs the same analysis with the estimated distribution of values. The CDF shows that all bidders below the 0.8 quantile of the value distribution increase their bids sub- stantially, while the remaining bidders shade their bids below valuation. Additional computations show that even though 20% of the highest value bidders submit smaller bids, expected revenues are still above non-charity auctions. Similarly, whenb> a, revenues in charity auctions dominate those in non-charity auctions (Figure A.15a). This analysis shows graphically that the outcome to the auctioneer does not only depend ona andb, but also on how these two parameters relate with the distribution of values. In fact, it is the latter to establish the likelihood of a bidder to win or lose the auction, which in turns triggers the willingness of the bidder to raise her bids based on the charitable motives and the percentage donated. Figure A.15: Counterfactual scenario with different charity parameters (a) Estimated F(v); q= 1 Warm glow (b> a> 0) 0.0 0.2 0.4 0.6 0.8 1.0 117 175 261 389 580 865 Private Value / Bid CDF Private Value Bid α = 0.1 , β = 0.5 (b) Estimated F(v); q= 1 Volunteer shill (a> b> 0) 0.0 0.2 0.4 0.6 0.8 1.0 117 175 261 389 580 865 Private Value / Bid CDF Private Value Bid α = 0.5 , β = 0.1 Notes: a and b are defined in equation (1.3.1). Bids are computed drawing 200 values from the estimated distribution of private values F(v) and the selecteda andb; q= 1. Prices are converted in euro by summing the median of the fitted prices in the first step of the estimation (1.5.1). The first step of the estimation also includes log(Total Number of Bids Placed) as a covariate. Panel (a) assumes warm glow bidding while Panel (b) assumes volunteer shill bidding. Only auctions with price betweene 100 ande 1000. 144 A.7 Revenue Comparison Across Auction Formats This section investigates revenues under different scenarios. Figure A.16 compares the ex- pected revenues under different auction formats: the second-price auction (dashed lines), the all-pay auction (dotted lines) and a non-charity second-price auction (solid line). 12 Engers and McManus (2007) theoretically show that first-price charity auctions perform worst than the other two charitable formats studied in this section and are not reported in the figure to simplify the exposition. 13 Figure A.16: Expected gross revenues per auction (a) Expected gross revenues; q= 85% 200 250 300 350 400 450 3 5 7 9 11 13 15 17 n Revenues 2nd−price All pay 2nd−price, q = 0 (b) Expected gross revenues; q= 10% 200 250 300 350 400 450 3 5 7 9 11 13 15 17 n Revenues 2nd−price All pay 2nd−price, q = 0 Notes: Revenue comparison across mechanisms for different number of bidders. The percentage donated is set to 85% and 10% in Panel (a) and Panel (b) respectively. The density f(v) and the distribution F(v) are approximated using a cubic spline. Only auctions with price between e 100 and e 1000. Revenues in euro are computed in multiple steps. (i) Subtract the median number of bidders times its estimated coefficient in the OLS regression (1.5.1) from the fitted values of the same regression. (ii) Compute the expected revenues obtained as the expectation of the second-highest bid using the primitives estimated in Section 1.5.1 (F(),a,b). (iii) Sum the fitted values in (i) with the homogenized expected price in (ii) and apply the log-level transformation. Realized revenues are determined at the median number of bidders for each auction type. The covariates used in (1.5.1) include the total number of bids as in Appendix A.5.5. In both figures, the second price format outperforms the all-pay auction for all number of bid- ders in the graph. Charitystars cannot raise more funds by switching to all-pay auctions, a method that was highlighted in the theoretical literature as the best mechanism from a revenue standpoint, especially when the pool of bidders is large (e.g., Goeree et al., 2005; Engers and McManus, 2007). 14 12 Revenues are computed as described in the note to Table 1.7. The optimal bid in an all-pay auction is b A (v)=(vF(v) n1 R v v F(x) n1 dx)/(1 qb), similar to the equilibrium studied in Engers and McManus (2007) for the q= 1 case. 13 This is also true for Charitystars’ data. The intuition for this outcome is that in a first-price auction losing bidders do not have an incentive to increase their bids. This happens because these bidders cannot affect the transaction price as they do in second-price auctions. 14 In the charity all-pay format each bidder gains from the sum of the contributions of the others and can accept to bid a value equal to her own private profit. This cannot happen in winner-pay formats because 145 An additional reason to prefer second-price auctions over all-pay auctions is the variance of the expected revenues. Figure A.18 in Appendix A.5.11 shows that the variance of the all-pay auc- tions sharply increases with the number of bidders, while it decreases with n for sealed bid for- mats. Therefore, English auctions do not only maximize Charitystars’ expected revenues, but also reduce the volatility of its cash flows: a key objective for any start-up. This fact could explain the preference for English auctions among most online charity marketplaces (e.g., Charitystars.com, eBay for Charity, CharityBuzz.com, BiddingForGood.com and many others). The comparison across charity and non-charity formats is also in Figure A.16a. The revenue difference between the two type of auctions appear to be rather small, reaching little above $50 for high n. Still, this implies a 12% premium over the non-charity auctions, that is twice as much as that estimated for eBay’s Giving Works (Elfenbein and McManus, 2010). These across auction comparisons have some limitations. For example, differential bidder- entry across mechanisms is one of them. This may be problematic if Charitystars users had a stronger taste for certain auctions than others. For instance, according to Figure A.16b when 17 bidders are expected in an all-pay auction but only 6 in a second-price auction, switching to the all-pay auction would grant Charitystars revenues in excess ofe 50 over the second-price model. Figure A.17: Expected revenues across different auction formats 40 50 60 70 80 90 5 10 15 Number of Bidders Revenues All pay First price Non−charity Second price Notes: Revenue comparison across different auction mechanisms. The plot shows that the distribution of bids and private value as in Figure 1.3b, which result in lower gross revenues in second-price charity auction than in non-charity auctions. The primitives are q = 85%,a = 50%, b = 10%, F()N(50, 25) on [0, 100]. such a bid would be suboptimal to surely loosing the auction and earning the value of the externality. This reasoning does not apply when the number of bidders is low. In this case the total contribution in the all-pay format is not high enough and bidders shades their bids as a result, making the second-price auction the optimal choice for the auctioneer. It can be shown numerically that the difference in Figure A.16 between all-pay and second-price auctions goes asymptotically to 0 with the number of bidders. 146 Figure A.18: Variance of the revenues across different auction formats (a) Variance gross revenues; q= 85% 0 0.05 0.1 0.15 0.2 3 5 7 9 11 13 15 17 n Variance First price Second price All pay (b) Variance gross revenues; q= 10% 0 0.05 0.1 0.15 0.2 3 5 7 9 11 13 15 17 n Variance First price Second price All pay Notes: The figure compares the variance of the revenues across mechanisms for different number of bid- ders. The percentage donated is set to 85% and 10% in Panel (a) and Panel (b) respectively. The density f(v) is approximated using a cubic spline. Only auctions with price betweene 100 ande 1000. The variances are computed without accounting for covariates. 147 A.8 Monte Carlo Simulations Objectives. The Monte Carlo simulations in this section fulfil two goals: (i) to show that the estimation routine described in Section 1.5 return consistent estimates of the parameters, and (ii) to support with some empirical evidence the claim that the estimates are not consistent when the amount donated in the two auction types is very close. Design of the experiments. There are two auction types (A and B) such that q A = .10 and q B = .85. Private values are generated for all bidders drawing from a uniform distribution in[0, 1] in Tables A.18 and A.19 and in [1, 1] in Tables A.20. There are 10 bidders in each auctions. They bid according to the bid function in (1.3.3). The true charitable parameters area 0 = .25 andb 0 = .75. The steps of the estimation procedure are outlined below: 1. Draw values from the distribution F(v) for each bidder in the two auctions. In total 20 values. 2. Compute the bids for each bidder in the two auctions. Save the winning bid in each auction. 3. Nonparametrically estimate the density of the winning bids (either by Triweight, or Gaus- sian Kernel). The bandwidth is chosen using the rule-of-thumb. Trimming follows Guerre et al. (2000) who suggested trimming observations close to 0.5 bandwidth to the bound- ary. 15 4. Given the number of bidders (n = 10) invert the distribution of the winning bids to deter- mine the distribution and density of the bids as in (1.5.2) and (1.5.3). 5. Compute the distribution and density of auctions of type A for each losing bids in the inter- val between the smallest winning bid and the largest winning bid of type A. 6. Compute the distribution and density of type B (q= .85) over 100,000 points. 7. Match the quantile of the distribution of type B with those of the distribution of type A through (1.4.1). 8. Find the couple (a,b) that minimizes the objective function (1.5.4) starting from a random seed. The search algorithm constraints the parameters in the unit interval. 9. Save the estimates and restart from 1. These steps are repeated 401 times. The tables below report the mean, median, quantiles and root mean squared errors fora andb for each combination of parameters. Results. First, let’s asses the consistency of the estimates. Different experiments are reported in Tables A.19 and A.20, showing that the estimates are close to the true parameters. In particular, even with a small number of observations (the first line in each panel), the mean and medians are always within 3% of the true parameters. 15 For the Gaussian case the h pd f = 1.06sn 1/5 and h CDF = 1.06sn 1/3 where s = minfs.d.(b k w ), IQR/1.349g, where b k w is the vector of winning bid for auction of type k, and h CDF = 1.587sn 1/3 . For the triweight case h pd f = h CDF = 2.978sn 1/5 (?Li et al., 2002; ?; Lu and Perrigne, 2008). 148 These tables are composed by different panels: each panel refers to a different kernel used to estimate the distributions (and densities) of the winning bids. The Gaussian and Triweigth kernels give similar results. Within each panel, the rows differ on the number of auctions used to estimate the primitives. The number of bidders in each auction is always constant and equal to 10. Since for each auction only the winning bid is used, I empirically consider the asymptotic properties of the estimator by looking at the rate at which the root mean squared error (RMSE) decreases as the number of auctions grows (i.e., comparing RMSE across columns). 16 Comfortingly, this rate is close to p n for all experiments. To study the consistency of the estimates when there is only limited variation over q across auctions I run similar experiments varying q instead of the nonparametric kernel. From Table A.18 it is clear thata andb cannot be estimated consistently when q A ' q B as the mean and median of the estimated parameters are about 0 and .50 instead of .25 and .75 fora andb respectively. Table A.18: Distance between q A and q B – Monte Carlo simulations T A T B m a m b Med a Med b 25% a 75% a 25% b 25% b q A = 80%, q B = 85% 500 0.0069 0.5333 0.0000 0.5328 0.0000 0.0000 0.5053 0.5589 1000 0.0094 0.5355 0.0000 0.5302 0.0000 0.0078 0.5114 0.5560 q A = 78%, q B = 85% 500 0.0158 0.5414 0.0000 0.5350 0.0000 0.0151 0.5137 0.5606 1000 0.0227 0.5477 0.0028 0.5376 0.0000 0.0348 0.5181 0.5667 q A = 50%, q B = 85% 500 0.2027 0.7086 0.1914 0.6991 0.1360 0.2520 0.6455 0.7579 1000 0.2154 0.7196 0.2071 0.7132 0.1696 0.2636 0.6763 0.7620 q A = 20%, q B = 85% 500 0.2468 0.7467 0.2383 0.7398 0.1984 0.2891 0.7033 0.7852 1000 0.2462 0.7463 0.2445 0.7444 0.2166 0.2764 0.7186 0.7730 Notes: Monte Carlo simulations of the second and third step of the estimation process. Auction types are denoted by A and B. Each panel shows the estimated parameters for different percentage donated. The bandwidths in step 2 are computed with a Gaussian Kernel. The data is generated according toa= 25%,b= 75% and F(v) is assumed uniform in[0, 1]. Each auction has 10 bidders. 401 repetitions. 16 I am analyzing the asymptotic properties of this class of estimators theoretically in another project, which is still a work in progress. 149 Table A.19: Monte Carlo simulation 1 T A T B m a m b Med a Med b 25% a 75% a 25% b 25% b 10% a 90% a 10% b 90% b RMSE a RMSE b Gaussian kernel 34 112 0.2760 0.7723 0.2681 0.7706 0.1513 0.4202 0.6577 0.8963 0.0631 0.4954 0.5846 0.9900 0.1587 0.1469 172 560 0.2682 0.7658 0.2647 0.7627 0.2160 0.3195 0.7176 0.8136 0.1725 0.3699 0.6781 0.8583 0.0789 0.0726 100 0.2637 0.7615 0.2449 0.7442 0.1759 0.3506 0.6802 0.8368 0.1148 0.4459 0.6234 0.9345 0.1225 0.1135 500 0.2507 0.7500 0.2428 0.7452 0.2089 0.2914 0.7122 0.7855 0.1813 0.3258 0.6881 0.8190 0.0586 0.0534 1000 0.2498 0.7494 0.2475 0.7470 0.2227 0.2764 0.7253 0.7726 0.1965 0.3056 0.7010 0.8020 0.0412 0.0377 Triweigth kernel 34 112 0.2318 0.7391 0.2051 0.7136 0.1172 0.3500 0.6281 0.8479 0.0460 0.4725 0.5644 0.9848 0.1522 0.1453 172 560 0.2310 0.7346 0.2267 0.7309 0.1797 0.2802 0.6875 0.7820 0.1347 0.3323 0.6421 0.8277 0.0767 0.0718 100 0.2855 0.7837 0.2820 0.7797 0.1953 0.3742 0.6990 0.8601 0.1172 0.4853 0.6293 0.9806 0.1314 0.1238 500 0.2547 0.7543 0.2535 0.7522 0.2115 0.2910 0.7145 0.7895 0.1855 0.3304 0.6866 0.8254 0.0579 0.0536 1000 0.2503 0.7507 0.2507 0.7503 0.2209 0.2765 0.7233 0.7763 0.1998 0.3031 0.7054 0.7996 0.0412 0.0378 Notes: Monte Carlo simulations of the second and third step of the estimation process. Auction types are denoted by A and B. The bandwidths in step 2 are computed either with a Gaussian Kernel (top panel) or with a Triweigth kernel (bottom panel). The data is generated according to a= 25%,b= 75%, q A = 10%, q B = 85% and F(v) is assumed uniform in[0, 1]. Each auction has 10 bidders. 401 repetitions. 150 Table A.20: Monte Carlo simulation 2 T A T B m a m b Med a Med b 25% a 75% a 25% b 25% b 10% a 90% a 10% b 90% b RMSE a RMSE b Gaussian kernel 34 112 0.2785 0.7687 0.2716 0.7639 0.1557 0.4026 0.6717 0.8779 0.0812 0.4961 0.6013 0.9790 0.1580 0.1350 172 560 0.2661 0.7611 0.2636 0.7592 0.2169 0.3128 0.7194 0.8048 0.1763 0.3588 0.6851 0.8410 0.0735 0.0627 500 0.2513 0.7492 0.2472 0.7477 0.2131 0.2871 0.7191 0.7777 0.1887 0.3203 0.6949 0.8064 0.0537 0.0449 1000 0.2506 0.7491 0.2480 0.7469 0.2255 0.2755 0.7282 0.7705 0.2023 0.3035 0.7080 0.7919 0.0380 0.0319 Triweigth kernel 34 112 0.2342 0.7586 0.2166 0.7450 0.1206 0.3501 0.6429 0.8787 0.0543 0.4388 0.5805 0.9900 0.1416 0.1473 172 0.2341 0.2341 0.7499 0.2323 0.7481 0.1777 0.2820 0.6968 0.7998 0.1422 0.3304 0.6588 0.8457 0.0753 0.0722 500 0.2673 0.7659 0.2632 0.7636 0.2262 0.3055 0.7289 0.8038 0.1952 0.3457 0.6976 0.8355 0.0591 0.0549 1000 0.2583 0.7587 0.2578 0.7589 0.2305 0.2838 0.7349 0.7827 0.2103 0.3110 0.7127 0.8025 0.0403 0.0364 Notes: Monte Carlo simulations of the second and third step of the estimation process. Auction types are denoted by A and B. The bandwidths in step 2 are computed either with a Gaussian Kernel (top panel) or with a Triweigth kernel (bottom panel). The data is generated according toa = 25%, b= 75%, q A = 10%, q B = 85% and F(v) is assumed uniform in[1, 1]. Each auction has 10 bidders. 401 repetitions. 151 Appendix B Appendix to Chapter 2 B.1 Experimental Design In the experiment participants made choices in 48 “stock markets,” presented to each of them in individually generated random order. In each market a participant was shown the price dynam- ics unfolding in real time either until the asset was sold or until market closure after 50 periods. The price updated each 0.8 seconds. First, participants observed the market price evolve for 15 periods. Then they “entered” the market. In the instructions this was presented as if they bought an asset in period 15. After this, participants kept observing the evolution of the market price and had to decide when to “sell the asset.” The payoff, or profit, that each participant received in each market was equal to the selling price minus the entry price. Participants were paid for only one randomly chosen market. No one could lose money if the profit of the chosen market was nega- tive, since participants were given an initial endowment ofe 10 that covered the highest possible loss. Each participant was making choices in two types of markets, which differed only in the amount of information that participants received after they have sold the asset. In the No Info condition, after selling the asset, no information about the future evolution of the price was pro- vided. In the Info condition, after selling the asset, participants observed how the price changed until the end of that market. In both cases the participants could not change their decision after they have sold the asset. The market condition (No Info or Info) was shown from period 1 on in the upper-left corner of the market graph (see figures below). Overall, 154 participants took part in the experiment. All sessions were run in March 2017 at the CEEL laboratory, Department of Economics, University of Trento. Another set of 135 partici- pants took part in the experiment in June 2016 in the same laboratory. These data are not reported in this paper. In the June 2016 experiment participants were not informed about the process that generated the price and were not given initial training (see below). Otherwise the two experiments were identical. One session in the June 2016 experiment was aborted due to the network overload and the data was discarded. The data for one participant in the June 2016 experiment was dis- carded, as she had to leave the experiment in the middle of the market task. No other sessions or pilots were conducted. The experiments were programmed in z-Tree (Fischbacher, 2007). 153 B.1.1 Market Details The price dynamics for each market was generated randomly using the process y t+1 = ay t + (1a)#, where y t+1 is the price in period t+ 1, a = 0.6 is a fixed constant for all markets and # U[0, 10] is an iid random variable (uniform on [0, 10]). In period 1 each market started from pricee 2.5,e 5, ore 7.5. Thus, the price changed in the range frome 0 toe 10. All participants saw the same price dynamics for a given market. Each market lasted for 50 periods, which was known to the participants. In period 15 of each market the participants were forced to enter the market. This was explained to them in the instructions in terms of their buying an object on the market in period 15 for the current market price (see instructions in Appendix B.11). Then the participants were instructed that they can sell the asset at any time before period 50 and that their earnings in that market would be equal to the difference between the selling price and the entry price (if they did not sell their earnings were equal to the price in period 50 minus the price in period 15). The prices on the market were presented in actual Euros, so no tokens were used and there was no need for having an exchange rate. All the information about the current market condition, the entry price, the selling price and the current price was presented on the screen at appropriate times. Descriptions under Figures B.1 and B.2 explain. Figure B.1: The screen presented to the participants Notes: The left picture shows the market price evolution before period 15, which is marked by a vertical red line. At period 15 the market “stopped,” so that participants could inspect the entry price. An ENTER (ENTRATA) button should have been pressed to start the market again. After period 15 the participants could check the entry price by looking at the top left of the screen where it was indicated in red (right picture). To sell the asset participants needed to press EXIT (USCITA) button. The timing of each market was as following. The new price was shown each 0.8 seconds. 1 This was long enough for participants to be able to react and sell the asset at the current price if they chose to do so. In the Info condition participants had to observe the evolution of the price until period 50: they could not skip to the next market. In the No Info treatment, after selling the asset, they had to wait until the market reached period 50 (without observing the price). This was done in order to 1) remove the incentive to go quicker through the task and 2) make No Info and Info conditions as similar as possible. 1 The experiment was implemented in z-Tree (Fischbacher, 2007), which does not allow for precise time control. Thus, the actual time between periods could have been slightly larger. 154 Figure B.2: The screen in the two conditions Notes: The right picture shows the market in Info condition after a participant sold the asset (the period of selling is indicated by a blue vertical line). After selling the asset, the participant could see the selling price in blue and the profit in green or red, depending on whether the profit was positive or negative (on top of the screen). In addition, the participant observed the future evolution of the price until period 50 (the price changed each 0.8 seconds). In the No Info condition (left picture) everything was the same except that the participant did not observe the future price, but still had to wait until the market closure. The sentence at the bottom of the left picture says: “Please wait until the market is closed.” B.1.2 Price Dynamics and Training Participants were explicitly informed about the process that generates the price (see instruc- tions in Appendix B.11). The formula y t+1 = ay t +(1a)# was explained to them and four examples of the price range in the next period depending on the current price were given. Participants went through a series of six training markets which could not be chosen for the payment. The training markets were in all respects identical to the real markets except the phrase ROUND DI PROVA (“training round”) written across the background in a very large font. Out of six training markets two started ate 2.5, two ate 5, and two ate 7.5. One market in each pair was presented in the No Info and one in the Info condition. The sequence of markets and conditions were independently randomized individually for each participant. B.1.3 Overall Design Details Participants chose in 48 markets. The price dynamics for each market was pre-generated using the rule described above (see Figure B.3 below). Thus, each participant chose in exactly the same markets. For the three subsets of 16 markets the starting price was equal toe 2.5,e 5, ore 7.5. The order of the markets was randomized in real time for each participant. Thus, there is only an infinitesimal probability that any two participants saw the same sequence of markets. The market condition, No Info or Info, was determined in the following way. Half of the 16 markets of each kind (starting ate 2.5,e 5,e 7.5) were randomly assigned to the condition No Info and another half to the condition Info. Thus, equal number of markets of each of the three kinds were shown in the two conditions. The participants assigned to the computers with odd numbers saw markets in these predetermined conditions. The participants assigned to the computers with even numbers saw the same markets in the opposite conditions. Thus, for each given market, there is an (approximately) equal number of participants who saw that market in the No Info and Info 155 conditions. When participants sold the asset they could see their profit (see Figure B.2). However, the par- ticipants were informed that they will be paid for only one randomly chosen market. In order to avoid losses, the participants were givene 10 at the beginning of the experiment, so their earnings after the market task weree 10 plus the profit in one randomly chosen market (which could have been negative). B.1.4 Additional Tasks After choosing in the sequence of 48 markets the participants were presented with the Halt and Laury task (Holt and Laury, 2002). We did not use the original payoffs from Holt and Laury (2002) as our participants could have seen those before. Instead we took the equivalent payoffs from Eijkelenboom et al. (2016). The instructions and the screenshots are presented in Appendix B.12.2. The participants, in addition to their earnings in the market task, received the payoff from one of the lotteries that they chose in the Holt and Laury task. In the end of the experiment the participants were given a sequence of standard demographic questions. 156 B.1.5 Market Prices Figure B.3: Prices in 48 markets. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 157 B.2 Behavior of Regret-Free Agent The regret-free rational agent obtains utility U(y t ) when she sells the asset at time t at the price y t . In each period she estimates the expected future utility that takes into account her optimal choices and sells the asset if U(y t ) maxfE y t+1 [U(y t+1 )jy t ],E y t+1 [v t+2 jy t ]g where v t+2 = maxfE y t+2 [U(y t+2 )jy t+1 ],E y t+2 [v t+3 jy t+1 ]g and the value function in the last period T is v T =E y T [U(y T )jy T1 ]. 2 In the experiment the price evolution is described by a Markov chain, thus, all expectations are conditional on the past price. We show analytically that a risk-averse agent should optimally sell the asset at a lower price than a risk-neutral agent and risk-loving agent should sell at a higher price. Intuitively, an ex- tremely risk-averse agent sells immediately at any price level as a sure outcome today outweighs an uncertain outcome tomorrow, whereas the certainty equivalent required by a risk-loving agent to sell at the same price is higher. Thus, we formulate a prediction concerning risk attitudes: Proposition. Optimal policy is to sell the asset above some threshold different for each period. Other things equal, the probability of selling the asset increases in the degree of risk aversion. Proof. An agent without regret sells if u(y t ) maxfE y t+1 [u(y t+1 )jy t ],E y t+1 [v t+2 jy t ]g (B.2.1) where v t+2 = maxfE y t+2 [u(y t+2 )jy t+1 ],E y t+2 [v t+3 jy t+1 ]g and v T = E y T [u(y T )jy T1 ]. Assuming that agent has CRRA utility function, this implies that the selling rule is y 1r t maxfE y t+1 [y 1r t+1 jy t ],E y t+1 [ ˙ v t+2 jy t ]g where ˙ v t+2 = maxfE y t+2 [y 1r t+2 jy t+1 ],E y t+2 [ ˙ v t+3 jy t+1 ]g and ˙ v T =E y T [y 1r T jy T1 ]. Let ˜ v t denote the value function in inequality (B.2.1) with u(y t ) = y t and let ˜ y t be the price at which a risk-neutral agent is indifferent whether to sell the asset or not: ˜ y t = maxfE y t+1 [y t+1 j ˜ y t ],E y t+1 [ ˜ v t+2 j ˜ y t ]g (B.2.2) Would a risk-seeking (averse) agent sell at the same value or continue? The answer depends onr. Agent sells at ˜ y t if and only if ˜ y 1r t maxfE y t+1 [y 1r t+1 j ˜ y t ],E y t+1 [ ˙ v t+2 j ˜ y t ]g. (B.2.3) Plugging (B.2.2) into (B.2.3) we get maxfE y t+1 [y t+1 j ˜ y t ] 1r ,E y t+1 [ ˜ v t+2 j ˜ y t ] 1r g maxfE y t+1 [y 1r t+1 j ˜ y t ],E y t+1 [ ˙ v t+2 j ˜ y t ]g. This inequality holds (strictly) only for a risk-averse agent with r2 (0, 1). To show this we start 2 By design the participants in the last period are forced to sell at the current price. 158 from period T 1. Notice that E y T1 [ ˜ v T jy T2 ] 1r = å i Prfy T1,i jy T2 gE y T [y T jy T1,i ] ! 1r and E y T1 [ ˙ v T jy T2 ]= å i Prfy T1,i jy T2 gE y T [y 1r T jy T1,i ] (B.2.4) where, given y T2 ,i enumerates all possible values of y T1 denoted by y T1,i . Next notice that the RHS’s of (B.2.4) can be rewritten as å i Prfy T1,i jy T2 g å x i Prfy T,x i jy T1,i gy T,x i ! 1r = å z p z y T,z ! 1r and å i Prfy T1,i jy T2 g å x i Prfy T,x i jy T1,i gy 1r T,x i = å z p z y 1r T,z (B.2.5) respectively. Herex i enumerates y T for eachi andz enumerates all combinations ofi andx i . Now, the RHS of the first equation in (B.2.5) is bigger than the RHS of the second by strict concavity of () 1r . Thus we can conclude thatE y T1 [ ˜ v T jy T2 ] 1r >E y T1 [ ˙ v T jy T2 ] for allr2(0, 1). Now we consider period T 2. For some fixed y T2 we want to show that maxfE y T1 [y T1 jy T2 ] 1r ,E y T1 [ ˜ v T jy T2 ] 1r g> maxfE y T1 [y 1r T1 jy T2 ],E y T1 [ ˙ v T jy T2 ]g. (B.2.6) This is straightforward since we have just shown thatE y T1 [ ˜ v T jy T2 ] 1r >E y T1 [ ˙ v T jy T2 ], which are the second terms of the max operators. According to the same strict concavity argument as above,E y T1 [y T1 jy T2 ] 1r > E y T1 [y 1r T1 jy T2 ], the first terms of the max operators. Thus, LHS max operator has all terms bigger than corresponding terms of the RHS max operator, which proves that the inequality (B.2.6) holds. Since (B.2.6) holds for all y T2 , it is true that E y T2 [ ˜ v T1 jy T3 ] 1r =E y T2 [maxfE y T1 [y T1 jy T2 ] 1r ,E y T1 [ ˜ v T jy T2 ] 1r gjy T3 ]> E y T2 [maxfE y T1 [y 1r T1 jy T2 ],E y T1 [ ˙ v T jy T2 ]gjy T3 ]=E y T2 [ ˙ v T1 jy T3 ]. This is a precursor to the one more step of the same derivation for period T 3 as E y T1 [ ˜ v T j y T2 ] 1r > E y T1 [ ˙ v T jy T2 ] was for the period T 2 step. Therefore, iterating this process, we show that (B.2.3) holds with strict inequality for all t as long asr2 (0, 1). When the agent is risk- seeking, orr< 0, (B.2.3) holds strictly with the opposite sign. The proof is the same only with all > replaced by<. Next we show that for any admissibler and each period there is a unique threshold such that an agent with CRRA utility, who follows optimal policy, always sells above this threshold and always keep the asset below it. Notice thatE y t+1 [y 1r t+1 jy t ]=E # [(ay t +(1a)#) 1r ] is a strictly in- creasing continuous function of y t . 3 Consider m(y t ) = maxfE y t+1 [y 1r t+1 jy t ],E y t+1 [ ˙ v t+2 jy t ]g. This is a function of y t that for some y t is equal toE # [(ay t +(1a)#) 1r ] and for some y t toE y t+1 [ ˙ v t+2 jy t ]. 3 Here and below#, possibly with sub-indexes, is a uniformly distributed random variable on[0, 10]. 159 Now, we can use the expressions ˙ v t = maxfE y t [y 1r t jy t1 ],E y t [ ˙ v t+1 jy t1 ]g for all t t+ 2 to expandE y t+1 [ ˙ v t+2 jy t ] into a sequence of expectations and max operators. Thus, eventually, m(y t ) is a piecewise function that is equal toE # [(ay t +(1a)#) 1r ] or pieces of weighted averages of functions of the form E y t+1 [...E y t [y 1r t jy t1 ]...jy t ]=E # t+1 ...E # t [(a tt y t +(1a tt )E t ) 1r ] (B.2.7) where E t is a weighted average of random variables # t+1 ,# t+2 , ...,# t . All functions in (B.2.7) are continuous and strictly increasing in y t . Therefore, m(y t ) is a continuous and strictly increasing since it is a series of max operators applied to weighted averages of continuous increasing func- tions. It is also true that m is strictly concave (convex) for r2 (0, 1) (r < 0), which also follows from the fact that it is a series of max operators of weighted averages of strictly concave (convex) functions. Now, we would like to know the relationship between m(y t ) and y 1r t . This will tell us what the optimal policy is. Notice that m(0) > 0 1r and m(10) < 10 1r since m(y t ) consists of mean reverting expectations. So for low y t the optimal policy is to keep the asset and for high y t to sell. It is left to show that m(y t ) crosses y 1r t at a single point. Consider any point y where y 1r = m(y). We want to show that at this point the derivatives of y 1r and m(y) are different. As was mentioned above, m(y) is a weighted average of functions in (B.2.7). Thus, y 1r = å i p i E # t+1 ...E # ti [(a t i t y+(1a t i t )E t i ) 1r ]= å i p i E t i [(a t i t y+(1a t i t )E t i ) 1r ] (B.2.8) for some enumerationfp i ,t i g i and withE t i being short forE # t+1 ...E # ti . Notice that the derivatives of functions (B.2.7) with respect to y t are of the form a tt (1r)E t (a tt y t +(1a tt )E t ) r , sinceE t transforms into a summation of the terms(a tt y+(1a tt )E t ) 1r weighted with some probabilities and the derivative transcends the summation. Keeping this in mind let us rewrite (B.2.8) as (1r)y r = å i p i a t i t (1r)E t i [() r ]+ 1r y å i p i E t i [(1a t i t )E t i () r ] where() r stands for(a t i t y+(1a t i t )E t i ) 1r . This, in turn, can be seen in terms of derivatives (1r)y r = dm(y) dy + 1r y å i p i E t i [(1a t i t )E t i () r ]. Here LHS is the derivative of LHS of (B.2.8) at y and RHS is the derivative of m at y plus a positive number. Thus, at y the derivative of y 1r t is higher than the derivative of m(y t ). This implies that these two functions cross at a unique point: they cannot coincide on an interval, since then their derivatives would have been equal and they cannot cross on a disjoint set since this would have contradicted the strict concavity or convexity of m. Thus, we have established that the optimal policy for any CRRA utility function is to sell above some unique threshold y t and to keep the asset below it. Combining this observation with the result that risk the averse agent sells at a price where risk-neutral agent is indifferent and that the risk-seeking agent keeps the asset at that price, we can conclude that risk-averse agent must have the selling threshold at a price below the risk-neutral agent and the risk-seeking agent must have the threshold above it. Therefore, a risk-averse agent, given the same prices, sells before a risk-neutral agent and a risk-seeking agent sells after. 160 B.3 Supplementary Graphs Figure B.4: The effect of a new price peak on the sale probability Price is below the past peak Price is the new peak Price range (5, 7] (7, 8] > 8 0.8 0.6 0.4 0.2 0.0 Selling rate Notes: The percentage of sales when the price reaches a new peak (dark grey) and when the price is below the current past peak (light grey). Only observations above the optimal selling price threshold of the risk- neutral no regret agent are considered. The error bars are1SE. Figure B.5: The propensity to sell the asset in the two conditions over time Sales within €0.5 of past peak Sales within €1.0 of past peak Ratio of selling in No Info to Info Period Notes: The ratio of the number of sales up to period t in the No Info to Info condition starting from period 33. 161 B.4 Description of the Variables Table B.1: Overview of variables Variable Mean Median St. Dev. Range Definition Choice 0.94 1.00 0.24 f0, 1g 1 if the participant keeps the asset and 0 if she sells it Info f0, 1g 1 if the market condition is Info and 0 if it is No Info Time 26.61 25.00 8.44 [16, 49] Time period Price 4.79 4.86 1.43 [1.20, 8.36] Current price Price 2 24.96 23.59 13.83 [1.43, 69.95] Current price squared Future Expected Price 5.00 5.00 0.08 [3.48, 7.02] Expected future price (over all remaining periods) conditional on the current price Past Peak 7.58 7.52 0.59 [5.53, 8.56] Highest price in the past Future Expected Peak 7.64 7.78 0.45 [3.48, 8.24] Highest expected future peak conditional on the current price and time (see Appendix B.6 for details) HL 0.60 0.60 0.17 [0, 0.9] Risk aversion parame- ter from Holt and Laury task (normalized from [0, 10] to[0, 1]). 1 is very risk-averse, 0 is very risk-seeking Early f0, 1g 1 for first 25, 28, 30, or 32 markets depend- ing on specification, 0 otherwise Notes: Variables used in the regression Tables 2.1, B.2, and B.3 (Appendix B.5). The statistics refers to all periods when a choice is made (periods 16 to 49). 162 B.5 Additional Regressions Table B.2: Random effects logit regression of the choice to keep the asset with risk preferences Pr[choice= keep] (I) (II) (III) (IV) (V) (VI) Price –0.497 –0.416 –0.237 –0.243 –0.243 –0.243 (0.146) (0.161) (0.145) (0.145) (0.145) (0.145) Price 2 –0.102 –0.113 –0.136 –0.136 –0.136 –0.136 (0.013) (0.014) (0.013) (0.013) (0.013) (0.013) Time –0.088 –0.090 –0.082 –0.083 –0.083 –0.083 (0.004) (0.004) (0.005) (0.005) (0.005) (0.005) Future expected price 1.423 1.223 1.226 1.218 1.218 1.217 (0.230) (0.251) (0.205) (0.203) (0.203) (0.203) Past Peak 0.522 0.617 0.617 0.643 (0.041) (0.053) (0.053) (0.140) Future Expected Peak 0.343 0.272 0.271 0.247 (0.080) (0.093) (0.093) (0.244) Future Expected Peak Info 0.132 0.133 0.133 (0.074) (0.074) (0.074) Past PeakInfo –0.208 –0.208 –0.209 (0.072) (0.072) (0.072) Info 0.511 0.552 0.553 (0.754) (0.757) (0.756) HL –0.721 –0.718 –0.723 –0.689 –0.691 (0.335) (0.338) (0.339) (0.341) (3.225) Info HL –0.069 –0.067 (0.229) (0.229) HL Past Peak –0.042 (0.224) HL Future Expected Peak 0.042 (0.392) Constant 4.525 5.939 –1.044 –1.116 –1.135 –1.139 (1.161) (1.274) (1.090) (1.214) (1.222) (2.259) N 112,137 89,951 89,951 89,951 89,951 89,951 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: choice is zero at the time the participant sells the asset and one otherwise. Observations are all periods in all markets for all participants in which they made a choice (periods 16 to 49). Participants whose choices in Holt-Laury task were inconsistent with expected utility maximization were dropped. Errors are clustered by participant. 163 Table B.3: Early sales in the two conditions (I) (II) (III) (IV) Pr[choice= keep] early: 25 early: 28 early: 30 early: 32 Price –0.331 –0.323 –0.280 –0.292 (0.134) (0.135) (0.133) (0.134) Price 2 –0.124 –0.124 –0.128 –0.128 (0.012) (0.012) (0.012) (0.012) Time –0.092 –0.120 –0.130 –0.112 (0.005) (0.006) (0.006) (0.006) Future Expected Price 1.470 1.646 1.621 1.484 (0.191) (0.191) (0.190) (0.186) Past Peak 0.602 0.588 0.604 0.586 (0.045) (0.045) (0.045) (0.045) Future Expected Peak 0.190 0.057 0.022 0.179 (0.084) (0.088) (0.096) (0.088) Future Expected Peak Info 0.089 0.095 0.227 0.168 (0.078) (0.079) (0.088) (0.085) Past Peakinfo –0.204 –0.196 –0.212 –0.205 (0.065) (0.065) (0.065) (0.065) Info 0.728 0.624 –0.136 0.199 (0.726) (0.714) (0.765) (0.755) Info Early 0.176 0.159 –0.065 0.022 (0.072) (0.081) (0.087) (0.089) Early –0.239 –0.718 –0.854 –0.657 (0.070) (0.072) (0.078) (0.074) Constant –1.670 –0.385 0.185 –0.704 (1.086) (1.095) (1.121) (1.090) N 112,137 112,137 112,137 112,137 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: The logit regressions support the intuition in Figure 2.4B. The dummy variable early is 1 if the cur- rent period is smaller or equal than the value specified in each column title and 0 otherwise. Participants in the Info condition sell less often early on because of the possibility of future regret: the coefficient on the interaction of info and early is significant and positive until Column III. Observations are all periods in all markets for all participants in which they made a choice (periods 16 to 49). Errors are clustered by participant. The descriptions of all the variables can be found in Appendix B.4. 164 Table B.4: The correlation between sale price and future regret for sales happening at different times (I) (II) (III) (IV) t2[15, 20] t2(20, 25] t2(25, 30] t2(30, 40] Past Peak –0.220 –0.106 0.036 0.307 (0.043) (0.024) (0.024) (0.028) Future Expected Peak 10.312 8.534 7.716 3.394 (0.324) (0.181) (0.232) (0.081) Info –6.108 –3.126 1.188 –0.769 (2.670) (1.745) (2.350) (0.851) Future Expected Peak Info 0.755 0.385 –0.149 0.106 (0.330) (0.217) (0.299) (0.111) Constant –74.391 –60.211 –54.062 –21.437 (2.440) (1.419) (1.781) (0.697) Adjusted R-squared 78.44% 83.94% 79.11% 58.70% N 1,604 1,474 1,278 1,594 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: Each regression is performed on a subset of the data based on when the sale happened, as indi- cated in each column header. The dependent variable is the observed price at the time of sale. The table shows that sale prices positively correlates with the future expected peak in the Info condition only in the early periods. Errors are clustered by participant. The descriptions of all the variables can be found in Appendix B.4. 165 B.6 The Computation of Future Regret At period t future regret is defined as the expectation of the highest order statistic of the future T t prices. At every period t2f2, ..., Tg, y t+1 = ay t +(1a)u t is observed, where u t is an i.i.d. random draw from the uniform distribution on[a, b]. We use the notation y k t to indicate the price expected in period t given the current price in period k. T, a and y k (price at time k) are known. Assume a given period k2f1, ..., T 2g, noting that the expected future peak in the period before the last is just the expectation of the price in the next period. Then we can recover the expected price for any future period beyond the current period (8t> k) with the following formula: y k t = a tk y k +(1a) tk å j=1 u tj a j1 (B.6.1) The distribution of y k t is Pfy k t vg= Pfa tk y k +(1a) t1 å j=k u tj a j1 vg = F (tk) (v)= Z v 0 f (tk) (s)ds where f (tk) (s) is the pdf of the sum of(t k) uniform distributions with different supports. The support of this distribution is(a tk y k ,a tk y k + 10(1a)å tk j=1 a j1 ). This is again when all u’s are 0 or all u’s are 10. Note that when t k = 1 f (1) (s)= 1 ay k +(1a)10ay k = 1 (1a)10 and F (1) (s)= say k (1a)10 . The expected future peak is computed as: Future peak period k = Z 10 0 vd Tk Õ j=1 F (j) (v) = Z 10 0 v Tk å j=1 f (j) (v) Tk Õ h6=j F (h) (v)dv = Z 10 0 v Tk å j=1 f (j) (v) Tk Õ h6=j Z v 0 f (h) (s)ds dv To derive f (tk) (v) analytically we use recent results in the statistical literature (Potuschak and Muller, 2009). For simplicity assume that k = 1. In fact, the random variable in (B.6.1) is the sum of independent uniformly distributed [0,10] random variables times (1a)a j1 , plusa t1 y 1 t1 , which is equal to the summation of t 1 uniformly distributed random variables in [a t1 y 1 t1 ,a t1 y 1 t1 + 10(1a)a j1 ],8j2f1, ..., t 1g. According to Potuschak and Muller (2009, section 2.2.2, page 180), the density is f (n) (s)= 1 2 n (n 1)!Õ k a k 2 n å j=1 s j maxfa.# j js å k c k j, 0g n1 (B.6.2) where . indicates the dot product, lower bar means vector, a = f5(1a), 5a(1a), 5a 2 (1 a), ...5a t1 (1a)g, c=fa t1 y 1 t1 + 5(1a),a t1 y 1 t1 + 5a(1a),a t1 y 1 t1 + 5a 2 (1a), ...a t1 y 1 t1 + 5a t1 (1a)g,8 1 j t 1. s j and# j are matrices which deal with positive and negative signs (see Potuschak and Muller (2009)). We can rewrite the distribution as follows: 166 Pfy 1 t vg= F (t) (v)= Z v 0 f (t1) (s)ds The support of this distribution is[a t1 y 1 ,a t1 y 1 + 10(1a)å t1 j=1 a j1 ]. Note that f (1) (s)= 1 ay 1 +(1a)10ay 1 = 1 (1a)10 and F (1) (s)= say 1 (1a)10 . B.6.1 Normal Approximation (B.6.2) is problematic, because, as the number of uniform RVs to be summed increases, the denominator goes to zero since a k ! 0. This makes estimation intractable. Another unappealing feature of this equation is that computation is extremely slow. Therefore, we follow Potuschak and Muller (2009) who proposed to approximate f (n) (v) = f (tk) (v) with the following normal distribution: y k t N å k c k , å k (2 a k ) 2 12 The approximation is based on the fact that the sum of uniform distributions is centered around å k c k with variance 1 12 (b a) 2 , where b and a are the upper and lower bounds of the support of the sum of uniform distributions. It can be shown that the sum of such i.n.d. uniformly distributed random variables converges to a normal distribution by the Liapounov Central Limit Theorem. The condition for convergence is: lim N!¥ å N i=1 E[jy i m i j 2+b ] (å N i=1 s 2 i ) 2+b 2 = 0, for some choice ofb> 0, where E[y i ]= m i and V[X i ]= s 2 i . To see this assumeb= 1 for simplicity and denote X i = y i m i . Becausem i = c i and the support of y i is[c i a i , c i + a i ], X i is uniformly distributed in the interval [a i , a i ] = [5(1a)a i1 , 5(1a)a i1 ]. The numerator of the CLT condition involves E[jX i j 3 ]= R a i a i jsj 3 f i (s)ds= R a i a i jsj 3 1 2a i ds. Solving the integral we get: E[jX i j 3 ]= 1 2a i 1 4a i s 4 sgn(s) a i a i = 125 4 (1a) 3 a 3(i1) Therefore, the numerator is 125 4 å N i (1a) 3 a 3(i1) . Similarly, the denominator can be rewritten using the formula for the variance of the normal distribution as 25 3 3 2 å N i (1a) 2 a 2(i1) 3 2 (use the fact that s 2 i = 1 12 (c i + a i (c i a i )) 2 = 1 12 (2 a i )) 2 ). Taking the ratio of these two quantites, 167 the result is W å N i (1a) 3 a 3(i1) å N i (1a) 2 a 2(i1) 3 2 , where 0< W < 1 is a constant. Finally, we can establish that: lim N!¥ = å N i=1 E[jX i j 3 ] (å N i=1 s 2 i ) 3 2 = W å N i=1 (1a) 3 a 3(i1) å N i=1 (1a) 2 a 2(i1) 3 2 = 0 because the denominator contains positive interaction terms. Therefore,å y i N å k c k ,å k (2a k ) 2 12 . Figure B.6: pdf, sum of 3 uniform RVs Figure B.7: pdf, sum of 13 uniform RVs Figure B.8: CDF, sum of 3 uniform RVs Figure B.9: CDF, sum of 13 uniform RVs 168 B.7 Discretization of the State Space and Transition Matrix After discretization of the state space, the process describing the evolution of the price at each period of time can be represented by a discrete Markov chain. In fact, the only determinant of price in the next period is the price in the previous period. The discretization is done following Tauchen (1986). See also (Aguirregabiria and Magesan, 2016, page 23). The stochastic shock follows the following AR(1) process: y i,t+1 = m+ry i,t +# (B.7.1) where y i,t+1 , y i,t are the prices for participant i =f1, ..., Ng at time t+ 1 and t respectively, and # N(0,s 2 i ). This panel structure is composed of 48 sequences (the individual dimension) and 50 periods (the time dimension). ˆ m and ˆ r are found using the covariance estimator. The estimates are ˆ m = 1.97, ˆ r = 0.60 and ˆ s = 1.16. The estimate ofr is very close to the parametera which updates the price from period y t to y t+1 (a= 0.6). Letfy 1 , ..., y K g denote the support of the discretized variable ˜ Y i,t , where y 1 > y 2 > ...> y K1 > y K with K = 400 are the points in the support. Tauchen (1986) suggests using y K = m 1r + m s 2 1r 2 1 2 y 1 = m 1r m s 2 1r 2 1 2 and y k are K 2 equidistant points within y K and y 1 , such that the distance between any two points is w. m is the density of the K points (m is set to 3). This choice of the parameters results in a support with lower bound (y 1 ) equal toe0.59 ca., upper bound (y 200 ) equal toe9.32 ca., and interval between adjacent points (w) equal toe0.02 ca. The probability of transitioning from state y to y 0 is defined as p i,j = Pr(y 0 = y j jy= y i ), which describes the element in the transition matrix in row i and column j. Because of the normality assumption, 4 the transition probability to a state k, 1< k< K, from i is: p i,k =F y k + w 2 ˆ m ˆ ry i ˆ s F y k w 2 ˆ m ˆ ry i ˆ s which can be thought as the probability thatry i +#2 [ry j w 2 ,ry j + w 2 ]. Analogously, the transi- tion probability to the first and last state are: p i,1 =F y 1 + w 2 ˆ m ˆ ry i ˆ s p i,K = 1F y K w 2 ˆ m ˆ ry i ˆ s Tauchen (1986) shows that this conditional distribution converges in probability to the true con- ditional distribution for the stochastic process in (B.7.1). In fact, it can be shown that such a dis- cretization implies a stationary distribution with AR(1) parameters ofr= 0.60 (equal to thea used 4 The standardization implies that the distribution is a standard normal. 169 in the experiment). B.8 Full Derivation of the Dynamic Discrete Choice Model In this section we present the dynamic discrete choice model that will be used for the structural estimation of the risk and regret parameters of the utility function. The following derivations are also sketched in Section 2.5. Analogously to the logit panel regressions in Table 2.1, participants’ choice between selling the asset or continuing still follows a threshold rule. However, they now take into account the Markovian nature of the problem. In particular, a participant’s intertemporal utility is E å t=1 b t1 u d (x t )+# d t where b2 (0, 1) is a discount factor and # d t is an error term. As is customary in the dynamic discrete choice literature (Abbring, 2010; Aguirregabiria and Mira, 2010) it is assumed to be known and equal for all participants. 5 d is the participant’s binary choice at time t T: d= ( 1, keep the asset 0, sell the asset. u d (x t ) is the payoff after choosing alternative d; the observables are described by the realization of x t , which is a tuple consisting of the current price y t , the past maximum s p,t , and the expected future maximum price s f ,t . We use a utility function which incorporates past and future regret as well as risk preferences. That is, we are interested in a utility function of the type u(x t ) = U(x t ) R(x t ), where U(x t ) is a consumption utility function and R(x t ) measures regret. The flow (per period) payoff from choice d at period t is u d +# d t where the error term # d t is independent of x. As in Murphy (2015), the error term is assumed to be # d = ˜ # d s # g where ˜ # d is distributed Type I extreme value with location parameter equal to zero and scale parameter s # = 1 6 . By the properties of the Type I extreme value distribution, the mean of ˜ # d is g (the Euler’s constant). # d is therefore mean zero. Given these preliminaries, denote by V(x t ,# t ) = max d2f0,1g fv d (x t )+# d g the value function at the beginning of period t with # t = f# 0 t ,# 1 t g and define the alternative specific value function (ASVF) for option d2f0, 1g at time t as: v d (x t )= ( 0+bEfv(x t+1 )jx t , d= 1g if d= 1 (keep) u 0 (x t ) if d= 0 (sell) (B.8.1) where the payoff of continuing is normalized to 0. Note that choosing to sell the asset implies null future payoffs (terminating action). The ex-ante value function in (B.8.1), can be rewritten as the expectation over the error term,# t , of the value function at time t v(x t ) Z V(x t ,# t )dL(# t ) 5 Identification of the discount factor is possible only under an exclusion restriction (Magnac and Thes- mar, 2002), and its estimation is generally hard. In order to circumvent this issue, we show that the estima- tions are robust to different values ofb. 6 The standard deviation of the error term is not identifiable in general, and therefore assumed to be equal to 1. 170 whereL() is the logit distribution and V(x t ,# t ) = max d2f0,1g fv d (x t )+# d t g. Define the alternative specific value function (ASVF) as: v d (x t )= u d (x t )+bEfv t+1 (x t+1 )jx t ,g, d2f0, 1g. (B.8.2) Because of the property of the Bellman equation, the optimal decision rule can be summarized as follows: d= ( 1 if v 1 (x t ) v 0 (x t ) # 0 t # 1 t at t 0 otherwise where v d () is defined as in (B.8.2). Denote the Conditional Choice Probability (CCP) of selling (action 0) as Prfd= 0jx t g p 0 (x t ): p 0 (x t )= exp(v 0 (x t )) exp(v 0 (x t ))+ exp(v 1 (x t )) = 1 1+ exp(v 1 (x t ) v 0 (x t )) . (B.8.3) Therefore p 0 (x t )=Lfv 1 (x t ) v 0 (x t )g. Due to the properties of the logit distributionLfg: f p 0 (x t ) ln 1 p 0 (x t ) ln p 0 (x t ) v 1 (x t ) v 0 (x t ). (B.8.4) f() is estimable from choice data using (B.8.3) and (B.8.4). Hence the difference in the alternative specific value functions, v 1 (x t ) v 0 (x t ), is known for every t. We can write the two ASVFs as follows: v 0 (x t )= u 0 (x t ) v 1 (x t )= 0+b Z X t+1 Z # maxfv 0 (x t+1 )+# 0 t+1 , v 1 (x t+1 )+# 1 t+1 )gdL(#)dF(x t+1 jx t ), (B.8.5) where the expectation in the second equation is only over the continuation alternative (1), because the transition matrix in case the absorbing choice (0) is chosen is zero for all x t (i.e. F(x t+1 jx t , d = 0)= 0). The estimation is based on the difference of the two ASVFs in (B.8.5): v 1 (x t ) v 0 (x t )=u(x t )+b Z X t+1 Z # maxfv 0 (x t+1 )+# 0 t+1 , v 1 (x t+1 )+# 1 t+1 )gdL(#)dF(x t+1 jx t ) (B.8.6) Notice that the LHS of (B.8.6) can be computed directly from the data using (B.8.4). The properties of the logit distribution are helpful to rewrite equation B.8.6 in a form that allows for estimation by non-linear least squares. In fact, the ASVF for continuing (second equation in B.8.5) can be rewritten as follows v 1 (x t )= b Z X t+1 Z # maxfv 0 (x t+1 )+# 0 t+1 , v 1 (x t+1 )+# 1 t+1 gdL(#)dF(x t+1 jx t ) = b Z X t+1 g+ log exp(v 0 (x t+1 )g)+ exp(v 1 (x t+1 )g) dF(x t+1 jx t ) = b Z X t+1 g+ log 1+ exp(v 1 (x t+1 ) v 0 (x t+1 )) exp(v 0 (x t+1 )g) dF(x t+1 jx t ) = b Z X t+1 u 0 (x t+1 ) log(Prfd t+1 = 0jx t+1 g) dF(x t+1 jx t ) 171 where d t+1 is the decision in the next period andg is the Euler’s constant. The last row uses (B.8.3). Therefore the difference of the two ASVFs in (B.8.6) becomes v 1 (x t ) v 0 (x t )=u 0 (x t )+b Z X t+1 v 0 (x t+1 ) log(Prfd t+1 = 0jx t+1 g) dF(x t+1 jx t ). By replacing the dependent variable in the last equation with f(p 0 (x t )) and by discretizing the state spaceX t the objective function can be rewritten in an estimable form: f(p 0 (x t ))=u 0 (x t )+b å X t+1 v 0 (x t+1 ) log(Prfd t+1 = 0jx t+1 g) f(x t+1 jx t ) =u 0 (x t )+b å X t+1 u 0 (x t+1 ) log(p 0 (x t+1 )) f(x t+1 jx t ) which concludes the derivation. Note that the regret components are functions of price (y t is the only random variable) and time. In fact, s p,t = max tt y t and s f ,t = g(y t , t), where g is a known function that is increasing in the first argument and decreasing in the second. 7 Therefore, Prfy t+1 , s p,t+1 , s f ,t+1 jx t , d= 1g= f(y t+1 , s p,t+1 , s f ,t+1 jy t , s p,t , s f ,t )= f(y t+1 , s p,t+1 , s f ,t+1 jy t , s p,t ). The transition of the past peak is fully defined by the future price: if y t+1 s p,t then s p,t+1 = y t+1 and s p,t+1 = s p,t otherwise. For clarity, consider the following example: given the information available at period t< T, the expected utility from keeping the asset one period longer, in the Info condition, is given by E[u(x t+1 )jx t ]= å y t+1 [1 fy t+1 s p,t g u(y t+1 , y t+1 , g())+1 fy t+1 <s p,t g u(y t+1 , max tt y t , g())] f(y t+1 jy t ). Finally, the transition of the expected future peak is completely determined by the price and time according to the function g(y t , t). 7 g() is not strictly monotonic in the two arguments because of the discretization imposed to the data. 172 B.9 Nonparametric Identification Identification of the objects of interest is standard and the proof is exposed here for complete- ness. The first step of the identification procedure requires the identification of the transition matrix of the Markovian process and of the conditional choice probabilities (CCP) (see equations 2.6.1 and 2.6.2), which are obtained directly from the data. The second step involves the nonparametric identification of the utility function, and is stan- dard. Consider the following assumptions: Assumption 1: Additive separability. The flow utility is separable in the observables and unobserv- able arguments, U(d, x t ,#)= u d (x t )+# d . Assumption 2: The unobservables are iid. The unobservable state variables, # t = (# 0 t ,# 1 t ), are iid across time. Moreover# d is distributed Type I extreme value. Assumption 3: Transition matrix. Next period state variables, x t+1 , are independent on the realiza- tion of this period unobservable state variables, # t . The support of the observable state variables is finite and discrete. The transition across periods follows a first order Markov process. Assumption 4: Flow utility. The flow utility of action 1 (continue to next period) is zero. Action 0 is a terminating action. Assumption 5: Discount factor. The discount factor is known (b2(0, 1)). Nonparametric identification of the utility function is obtained employing a contraction map- ping argument, given that the transition matrix and the CCP are known. Therefore, Dv(x t ) = v 1 (x t ) v 0 (x t ) is known (obtained by inverting the CCP as shown in the main text - Section 2.5). Also, as a reminder, the alternative specific value functions are defined by v d (x t )= ( 0+bE d fv t+1 (x t+1 )jx t g if d= 1 (keep) u 0 (x t ) if d= 0 (sell) Step 1: Define the function ˆ H(r 0 , r 1 jx t ) = E[max d2f0,1g fr d +# d gjx t ]. Under the distributional assumption on the error term 8 , ˆ H(jx t ) exists and has the additive property: ˆ H(r 0 +k, r 1 +kjx t )= ˆ H(r 0 , r 1 jx t )+k (see Rust (1994) and Magnac and Thesmar (2002)). This property is useful as it allows us to rewrite the emax function as the sum of a known object and an unknown function: ˆ H(v 0 (x t ), v 1 (x t ); x t )= ˆ H(v 0 (x t ) v 1 (x t ), 0jx t )+ v 1 (x t ) ˆ H(Dv(x t ), 0jx t )+ v 1 (x t ) where ˆ H(Dv(x t ), 0jx t ) is identified because the difference in value function, Dv(x t ) = v 0 (x t ) v 1 (x t ), and the distribution of the error term, L(), are known. To simplify the notation set ˆ H(x t+1 )= ˆ H(Dv(x t ), 0jx t ). Step 2: The alternative specific value function when the participant chooses to keep the asset, v 1 (x t ), is the unique solution of a functional equation. The following Lemma proves that v 1 (x t ) is a contraction. Lemma: Denote byX the space of the observables and byC(X) the Banach space of all continu- 8 The error term,# t =(# 0 t ,# 1 t ), has support onR 2 and finite expectationE[# d ]<¥ for d2f0, 1g. 173 ous, bounded functionsw :X!R. And define the operatorG :C(X)!C(X) by: Gw(x)= bE 1 fw(x t+1 )jx t g Then, under the supremum norm,jjwjj = sup x2X jw(x)j,G is a contraction mapping with modu- lusb. Proof: For any two functions w, ˆ w 2C(X), we need to establish thatjjGwG ˆ wjj mjjw ˆ wjj, for m2 (0, 1). First, rewriteE 1 fw(x t+1 )jx t g = E[max d2f0,1g fw d (x t+1 )+# d gjd t = 1, x t ] = EfH(x t+1 )+w 1 (x t+1 )jd= 1, x t g by using the derivation in the first step. Then proceed as follows: jjGwG ˆ wjj = sup x t 2X bEfH(x t+1 )+w 1 (x t+1 )jd t = 1, x t gbEfH(x t+1 )+ ˆ w 1 (x t+1 )jd t = 1, x t g = sup x t 2X b EfH(x t+1 )+w 1 (x t+1 ) H(x t+1 ) ˆ w 1 (x t+1 )jd t = 1, x t g b sup x t+1 2X w 1 (x t+1 ) ˆ w 1 (x t+1 ) = bjjw ˆ wjj Therefore G is a contraction mapping with modulus b. The second line moves the arguments from the second expectation to the first. The third line removes the equal terms (H(x t+1 )) and the conditional expectation ( follows from this). The fourth line is from the definition of the supremum norm. Therefore, v 1 (x t ) exists and is unique. Step 3: In the previous steps we identified nonparametricallyDv(x t ) = v 0 (x t ) v 1 (x t ) (directly from the data), and v 1 (x t ) (by the Contraction Mapping Theorem). Therefore, v 0 (x t ) = Dv(x t )+ v 1 (x t ) and because v 0 (x t ) consists only of the flow utility (it corresponds to the terminating action), then u 0 (x t )=Dv(x t )+ v 1 (x t ). 174 B.10 Additional Estimations of the Structural Model B.10.1 Different Regret Functions This section reports estimates for several models displaying different parameterization of the regret-averse utility function and risk-aversion. All estimations are consistents with the findings displayed in Section 2.6. The tables below show NLS estimates assuming the following discount rates: b2f99.65%, 99.60%, 99.55%g. The objective function is (2.5.3) in Section 2.5. The util- ity function is u(y t , s p,t , s f ,t ) = pU(y t ;r) R(s p,t , s f ,t ;r), where U(y t ;r) represents either a risk- neutral agent (r = 0) or CRRA with risk aversion parameter r (e.g., x 1r 1 1r ), and R(,;r) is the regret function. The dataset is discretized over 400 points according to the procedure laid out in Section B.7. The following utility function (Model 1) is estimated in Table B.5 u(y t , s p,t , s f ,t ;r)= pU(y t ;r)wU(s p,t ;r)aU(s f ,t ;r). The first three columns refer to the linear utility case while the remaining part of the table reports estimates for the CRRA case. Table B.6 includes different coefficients for the two conditions and an interaction term as shown in (2.6.5). Two models are reported with different interaction terms. In Model 2 the re- gret term is specified as R=1 fNo Infog w NI U(s p,t ;r)+1 fInfog w I U(s p,t ;r)+a I U(s f ,t ;r)+l I U(s p,t s f ,t ;r) while in Model 3 the regret term is: R=1 fNo Infog w NI U(s p,t ;r)+1 fInfog w I U(s p,t ;r)+a I s f ,t +l I s p,t . The last two equations assume CRRA utility because in the linear case they would produce the same estimate as those in the rightmost columns of Table 2.2. Finally, Table B.8 estimatespU(y t ;r) R(s p,t , s f ,t ,r) where the regret term is defined as R(s p,t , s f ,t ;r)=1 fNo Infog w NI U(s p,t ;r)+a NI U(s f ,t ;r)+l NI U(s p,t ;r)U(s f ,t ;r) +1 fInfog w I U(s p,t ;r)+a I U(s f ,t ;r)+l I U(s p,t s f ,t ;r) in Model 4 and R(s p,t , s f ,t ;r)=1 fNo Infog w NI U(s p,t ;r)+a NI U(s f ,t ;r)+l NI U(s p,t s f ,t ;r) +1 fInfog w I U(s p,t ;r)+a I U(s f ,t ;r)+l I U(s p,t s f ,t ;r) in Model 5, where U(;r) is a CRRA utility function (the estimates report very mild risk-seeking preferences, while the regret parameters do not change substantially). Overall, the results are very similar across all tables, and corroborate our conclusions outlined in Section 2.7. Section B.10.2 estimates a similar model allowing for loss aversion. 175 Table B.5: Estimation of Model 1 (I) (II) (III) (IV) (V) (VI) Model 1: Linear Utility Model 1: CRRA Utility b= 99.65% b= 99.60% b= 99.55% b= 99.65% b= 99.60% b= 99.55% ˆ r 0.061 0.061 0.062 (0.017) (0.017) (0.017) ˆ p 2.068 1.890 1.888 2.068 2.068 2.069 (0.011) (0.011) (0.011) (0.052) (0.052) (0.052) ˆ w 0.168 0.213 0.313 0.236 0.308 0.400 (0.144) (0.142) (0.139) (0.170) (0.170) (0.169) ˆ a 0.198 0.219 0.255 0.122 0.161 0.196 (0.075) (0.074) (0.073) (0.086) (0.085) (0.083) N 111,613 111,613 111,613 111,613 111,613 111,613 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: The estimation of (2.5.3) with the regret terms as in Model 1, specified in Appendix B.10.1 in periods 16 to 48 for different values of the discount factorb. The CCP are defined as in (2.6.1) and (2.6.2). Standard errors are in parenthesis. Table B.6: Estimation of Model 2 and Model 3 (I) (II) (III) (IV) (V) (VI) Model 2 Model 3 b= 99.65% b= 99.60% b= 99.55% b= 99.65% b= 99.60% b= 99.55% CRRA Utility ˆ r 0.070 0.071 0.072 0.074 0.075 0.076 (0.017) (0.017) (0.017) (0.017) (0.017) (0.017) ˆ p 2.089 2.090 2.092 2.100 2.101 2.103 (0.053) (0.053) (0.053) (0.054) (0.052) (0.054) ˆ w NI 0.548 0.596 0.663 0.567 0.616 0.683 (0.225) (0.224) (0.221) (0.227) (0.226) (0.223) ˆ w I 2.234 2.351 2.442 2.272 2.368 2.442 (0.588) (0.530) (0.484) (0.570) (0.511) (0.465) ˆ a I 1.965 2.044 2.099 1.948 2.007 2.046 (0.450) (0.401) (0.365) (0.424) (0.376) (0.340) ˆ l I 0.318 0.331 0.341 0.241 0.248 0.253 (0.080) (0.074) (0.068) (0.054) (0.049) (0.045) N 111,613 111,613 111,613 111,613 111,613 111,613 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: The estimation of (2.5.3) with the regret terms as in Models 2 and 3, specified in Appendix B.10.1 in periods 16 to 48 for different values of the discount factor b. The CCP are defined as in (2.6.1) and (2.6.2). Standard errors are in parenthesis. 176 Table B.7: Estimation of (2.5.3) with the regret terms as in (2.6.4) (I) (II) (III) (IV) (V) (VI) Estimation of (2.6.4) Estimation of (2.6.5) b= 99.65% b= 99.60% b= 99.55% b= 99.65% b= 99.60% b= 99.55% CRRA Utility ˆ r 0.060 0.060 0.062 0.070 0.071 0.073 (0.017) (0.017) (0.017) (0.053) (0.017) (0.017) ˆ p 2.066 2.066 2.068 2.089 2.090 2.092 (0.052) (0.052) (0.052) (0.053) (0.053) (0.053) ˆ w NI 0.454 0.499 0.567 0.548 0.596 0.662 (0.219) (0.218) (0.215) (0.225) (0.224) (0.221) ˆ w I 0.007 0.092 0.202 1.917 2.020 2.100 (0.224) (0.223) (0.221) (0.515) (0.464) (0.424) ˆ a I 0.120 0.169 0.212 1.647 1.714 1.757 (0.086) (0.085) (0.084) (0.374) (0.332) (0.300) ˆ l I 0.295 0.307 0.317 (0.072) (0.066) (0.061) N 111,613 111,613 111,613 111,613 111,613 111,613 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: The estimation of (2.5.3) with the regret terms as in (2.6.4) and (2.6.5) in periods 16 to 48 for different values of the discount factorb. Standard errors are in parenthesis. Table B.8: Estimation of (2.5.3) with the regret terms as as in Model 4 and 5 (I) (II) (III) (IV) (V) (VI) Model 4 Model 5 b= 99.65% b= 99.60% b= 99.55% b= 99.65% b= 99.60% b= 99.55% CRRA Utility ˆ r 0.134 0.131 0.133 0.134 0.133 0.131 (0.022) (0.022) (0.026) (0.021) (0.022) (0.021) ˆ p 1.474 1.476 1.478 1.474 1.476 1.478 (0.048) (0.048) (0.048) (0.048) (0.048) (0.048) ˆ w NI 0.431 0.633 0.784 0.415 0.635 0.799 (0.435) (0.393) (0.360) (0.470) (0.425) (0.388) ˆ w I 1.526 1.600 1.650 1.670 1.751 1.804 (0.459) (0.415) (0.380) (0.499) (0.451) (0.413) ˆ a NI 0.235 0.075 0.042 0.252 0.074 0.057 (0.314) (0.278) (0.250) (0.351) (0.311) (0.280) ˆ a I 1.189 1.230 1.252 1.332 1.380 1.406 (0.329) (0.291) (0.262) (0.371) (0.329) (0.297) ˆ l NI 0.018 0.002 0.017 0.016 0.002 0.015 (0.043) (0.039) (0.036) (0.038) (0.035) (0.032) ˆ l I 0.163 0.170 0.174 0.144 0.150 0.154 (0.048) (0.044) (0.040) (0.040) (0.049) (0.037) N 111,613 111,613 111,613 111,613 111,613 111,613 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: The estimation of (2.5.3) with the regret terms as as in Model 4 and 5, specified in Appendix B.10.1 in periods 16 to 48 for different values of the discount factor b. The CCP are defined as in (2.6.2) for both conditions. Standard errors are in parenthesis. 177 B.10.2 Loss Aversion Table B.9 reports estimates for the model in (2.6.6) allowing for loss aversion. Loss aversion is defined as the utility loss due to selling at a price below the entry price. The regret function including loss aversion, ˜ R(s p,t , s f ,t ) is defined as: 1 fNo Infog w NI s p,t +a NI s f ,t +l NI s p,t s f ,t +1 fInfog w I s p,t +a I s f ,t +l I s p,t s f ,t +y1 fy t <entry priceg (y t entry price) Table B.10 shows the same analysis allowing for CRRA risk preferences. In both models the coefficient y multiplies the negative loss. Define ˜ R(s p,t , s f ,t ;r,y) to include both regret and loss aversion as: 1. 1 fNo Infog w NI U(s p,t ;r)+a NI U(s f ,t ;r)+l NI U(s p,t ;r) U(s p,t ;r) +1 fInfog w I U(s p,t ;r)+a I U(s f ,t ;r)+l I U(s p,t ;r) U(s f ,t ;r) +y1 fy t <entry priceg (y t entry price) 2. 1 fNo Infog w NI U(s p,t ;r)+a NI U(s f ,t ;r)+l NI U(s p,t s f ,t ;r) +1 fInfog w I U(s p,t ;r)+a I U(s f ,t ;r)+l I U(s p,t s f ,t ;r) +y1 fy t <entry priceg (y t entry price) In these tables y is constrained to be non-negative, as participants would enjoy a loss other- wise. Table B.9: Estimation of regret and loss-aversion parameter in the risk-neutral case (I) (II) (III) b= 99.65% b= 99.60% b= 99.55% Linear Utility ˆ p 1.789 1.830 1.829 (0.022) (0.022) (0.022) ˆ w NI 1.432 1.255 1.386 (0.464) (0.416) (0.378) ˆ w I 2.609 2.240 2.267 (0.477) (0.427) (0.388) ˆ a NI 0.134 0.214 0.316 (0.341) (0.303) (0.274) ˆ a I 1.761 1.680 1.682 (0.348) (0.309) (0.281) ˆ l NI 0.265 0.247 0.064 (0.053) (0.048) (0.043) ˆ l I 0.046 0.050 0.249 (0.005) (0.046) (0.044) ˆ y 0.000 0.000 0.000 (0.024) (0.024) (0.024) N 111,613 111,613 111,613 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: Periods: 16 to 48. Standard errors are in paren- thesis. ˆ y is the estimated coefficient of loss aversion. 178 Table B.10: Estimation of models 1 and 2 with loss aversion parameter (I) (II) (III) b= 99.65% b= 99.60% b= 99.55% Model 1 ˆ r 0.134 0.050 0.048 (0.025) (0.024) (0.024) ˆ p 1.474 1.695 1.699 (0.063) (0.069) (0.070) ˆ w NI 0.431 0.805 1.062 (0.435) (0.444) (0.407) ˆ w I 1.526 1.974 1.983 (0.459) (0.469) (0.429) ˆ a NI 0.235 0.030 0.119 (0.314) (0.314) (0.283) ˆ a I 1.189 1.530 1.514 (0.329) (0.330) (0.298) ˆ l NI 0.018 0.013 0.035 (0.043) (0.050) (0.046) ˆ l I 0.163 0.238 0.237 (0.048) (0.056) (0.052) ˆ y 0.000 0.000 0.000 (0.026) (0.027) (0.027) Model 2 ˆ r 0.054 0.045 0.051 (0.025) (0.024) (0.024) ˆ p 1.691 1.709 1.693 (0.069) (0.070) (0.070) ˆ w NI 0.484 0.663 0.949 (0.537) (0.489) (0.443) ˆ w I 1.846 2.443 2.040 (0.569) (0.526) (0.470) ˆ a NI 0.255 0.138 0.109 (0.404) (0.363) (0.324) ˆ a I 1.516 1.983 1.622 (0.427) (0.389) (0.344) ˆ l NI 0.017 0.004 0.027 (0.052) (0.049) (0.044) ˆ l I 0.192 0.260 0.208 (0.059) (0.058) (0.051) ˆ y 0.000 0.000 0.000 (0.027) (0.027) (0.027) N 111,613 111,613 111,613 *** p< 0.01 ** p< 0.05 * p< 0.10 Notes: Periods: 16 to 48. Standard errors are in paren- thesis. ˆ y is the estimated coefficient of loss aversion. 179 B.11 Instructions (English) B.11.1 Market Task General Instructions Dear Participants, You are participating in a decision making experiment which consists of a main part and a ques- tionnaire. If you follow the instructions carefully, you can earn a considerable amount of money depending on your decisions and random events. Your earnings will be paid to you at the end of the experiment. During the experiment you are not allowed to communicate with anybody. In case of ques- tions, please raise your hand. Then we will come to your seat and answer your questions. Any violation of this rule excludes you immediately from the experiment and all payments. In the end of the experiment the payment will be made in CASH. The Task In this experiment you will make decisions in 48 different tasks. Each task is separate and does not depend on the previous tasks in any way. At the beginning of each task you receive 10 Euro. You can earn or lose money depending on your choices. This money will be added or subtracted from 10 Euro. 180 Structure of the Task Imagine that you are participating in a financial market and that you should decide at each market (trial) when to sell an object. At the beginning of each market (trial) you observe the price of an object for 15 periods (each period lasts 0.8 seconds). During these periods you can see how the price of the object evolves before you enter the market which means that you cannot make any decisions during these 15 periods. The picture on the right shows the example of the price of the object varying during this starting phase. When you see a vertical red line drawn across the graph, this means that the starting phase of price observation is over. The current price of the object at this point corresponds to the price at which you enter the market. On the top of the screen you can see the current price displayed in each period (betweene 0 ande 10). 181 The Process Guiding the Value In every market the value changes according to the following process. If the value in the current period is V, then the value in the next period depends on 1) the current value V and 2) the randomly generated number S. In particular, the value in the next period is equal to 0.6V+ S, where S is a number between 0 and 4. This means that in each period any number between 0 and 4 (for example, 2.1789 or 3.51) has equal probability of being chosen and will contribute to the future value. Therefore, any number in the interval between 0.6V and 0.6V+ 4 has equal probability to be the value of the object in the next period. The table below shows some examples. Notice also that in each period the current value cannot be higher thane 10 and lower thane 0. CURRENT INTERVAL FOR THE VALUE IN THE NEXT PERIOD VALUE MINIMAL VALUE MAXIMAL VALUE e 2 e 1.2 e 5.2 e 4 e 2.4 e 6.4 e 6 e 3.6 e 7.6 e 8 e 4.8 e 8.8 182 Entering the Market After you have observed the evolution of the value for 15 periods the market stops at the red vertical line and the button ENTRATA (ENTER) appears at the bottom of the screen (see top figure). When you press the button you enter the market. This means that you “buy” the object at the current value and spende 2.59 as indicated at the top of the screen. You do not have a choice at which price to buy the object. Once you press the button three things happen: 1) the Valore di entrata (Entry price) appears on top of the screen in red (see bottom figure); 2) the value starts to change again and 3) the button changes to USCITA (EXIT). Exiting the Market The choice you make in the market is when to exit. This is the point at which you “sell” the object and obtain the amount of money equal to the current value. Your profit in the market is the amount you received at the exit minus the amount you paid when you entered. For example, if you entered at the value ofe 2.59 and exited at the value ofe 2.68 your profit is 2.68 – 2.59 = 0.09, or 9 cents. If you entered at the value ofe 2.59 and exited at the value ofe 2.45 your profit is 2.45 – 2.59 = -0.14, or minus 14 cents. Thus, YOUR PROFIT CAN BE NEGATIVE. If you do not choose to exit before the closure of the market at period 50, your profit will be calculated using the last period value of the object. 183 Observed and Unobserved Future There are two possible scenarios, which can happen after you press the USCITA (EXIT) but- ton, or sell the object. In one scenario you will observe the evolution of the value of the object until the market closure (after period 50). In the other case you will not observe the evolution of the value. You will be informed about which scenario you are in BEFORE the opening of each market. Before each market you will observe a screen with two possible phrases: “INFO DOPO l’uscita” (Information after exit) or “NO INFO al’uscita” (No information after exit) (see figures). The former indicates that the market which you will choose in next is the one with observable future value and the latter – the market with non-observable future value. To make sure that you remember which scenario you are in, the “INFO DOPO” and “NO INFO” signs will appear in the top left corner of the screen while the market is evolving. 184 After Exiting the Market After you exit the market, or press USCITA (EXIT) button, you will be provided with the information on your profit. Top figure illustrates the scenario with observable future and the bottom figure – with non-observable future. In both cases, you will see the “Valore di uscita” (exit value) in blue and profit in green (if positive) or red (if negative). In case of non-observable future you will be also asked to wait until the market closure which is the same time it would have taken the market to reach closure if you could have observed the future value. When the market closes you can press PROSEGUI (CONTINUE) button to proceed to the next market. Payment You payment in the experiment is determined as follows. Before the experiment you are given an endowment ofe 10. After you finish choosing in all 50 markets, one of them will be chosen at random and the profit that you made in that market will be added to your endowment. So, if you earnede 3 in the chosen market, your total payment will bee 10 +e 3 =e 13. If your profit was -e 3, your total payment will bee 10 -e 3 =e 7. Notice that your profit can change between -e 10 ande 10. Thus you can earn minimum ofe 0 and maximum ofe 20. Trial Markets Before the beginning of the task you will have an opportunity to familiarize yourself with the interface in 6 trial markets which will look exactly the same as the actual markets but with TRIAL DI PROVA (TRIAL MARKET) written on the screen. You will not be paid for your decisions in trial markets. 185 B.12 Instructions (Italian) B.12.1 Market Task Informazioni Generali Gentile partecipante, Prenderai parte ad un esperimento comprendente due compiti decisionali e un questionario. Se segui le istruzioni attentamente potrai guadagnare una considerevole somma di denaro, che dipenderà dalle decisioni che prenderai durante l’esperimento. La somma da te guadagnata ti verrà pagata al termine dell’esperimento. Ti chiediamo per favore di non comunicare con gli altri partecipanti durante l’esperimento. Nel caso tu abbia delle domande, chiedi allo sperimentatore alzando la mano. A quel punto lo sperimentatore verrà alla tua postazione e risponderà alle tue domande. Al termine dell’esperimento il pagamento verrà effettuato in CONTANTI. Compito di Scelta In questo compito ti verrà chiesto di prendere una decisione in 48 diversi problemi. Ogni problema è a se stante e non dipende dall’esito ottenuto nei problemi precedenti. All’inizio del compito riceverai una somma di partenza pari a 10 euro. In ogni problema potrai guadagnare o perdere un certo ammontare di denaro, il quale verrà sommato o sottratto a questi 10 euro. 186 Struttura di Campito di Scelta Immagina di essere all’interno di un mercato finanziario e di dover decidere, ad ogni trial, quando incassare l’ammontare investito. Ogni mercato (trial) inizia osservando il valore dell’oggetto del tuo investimento per 15 periodi (ogni period dura 0.8 secondi). Durante questa prima fase, vedrai come il valore dell’oggetto si è evoluto nei precedenti 15 periodi del mercato. Durante questi 15 periodi non potrai prendere nessuna decisione. La figura a destra ti mostra un esempio di come il valore dell’oggetto può variare durante questa prima fase. Quando la linea verticale rossa verrà raggiunta, significa che i 15 periodi della fase di osservazione saranno terminati. A quel punto il valore corrente dell’oggetto corrisponderà al tuo valore d’entrata nel mercato. La dicitura “Valore corrente” in alto ti mostra il valore dell’oggetto in ogni periodo (tra e 0 ee 10). 187 Il Processo Che Stabilisce il Valore In ogni mercato il prezzo cambia seguendo un particolare processo. Dato il valore corrente in un periodo del mercato, V, il valore nel periodo successivo (all’interno dello stesso mercato) dipende da 1) il valore corrente, V, e 2) un numero generato in maniera random, S. In particolare, il valore nel periodo seguente è uguale a 0.6V+ S, dove S è un numero tra 0 e 4. Ciò significa che in ogni periodo qualunque numero tra 0 e 4 (per es. 2.1789 o 3.51) ha la stessa probabilità di essere scelto e di contribuire al valore futuro. Perciò ogni numero nell’intervallo tra 0.6V e 0.6V+ 4 ha la stessa probabilità di essere il valore dell’oggetto nel prossimo periodo. La tabella qui di seguito riporta alcuni esempi. Nota che in ogni periodo il valore corrente non può essere maggiore die 10 né minore die 0. VALORE INTERVALLO DEL VALORE NEL PERIODO SUCCESSIVO CORRENTE VALORE MINIMO VALORE MASSIMO e 2 e 1.2 e 5.2 e 4 e 2.4 e 6.4 e 6 e 3.6 e 7.6 e 8 e 4.8 e 8.8 188 Entrare nel Mercato Dopo aver osservato 15 periodi il mercato si fermerà alla linea verticale rossa e il pulsante “EN- TRATA” apparirà in basso (vedi la figura in alto a destra). A questo punto per entrare nel mercato dovrai premere il tasto “ENTRATA.” Questo significa che effettivamente tu compri l’oggetto al valore corrente. Nell’esempio indicato nella figura in alto spenderestie 2.59. Non ti sarà possibile evitare di entrare nel mercato e non potrai scegliere tu stesso a quale prezzo comprare l’oggetto. Una volta premuto il pulsante “ENTRATA” il valore dell’oggetto comincerà a variare nuovamente e ti compariranno tre nuove informazioni a schermo (figura in basso a destra): 1) il “Valore di en- trata” in rosso in alto a sinistra; 2) il valore attuale dell’oggetto; 3) il pulsante “USCITA.” Uscire dal Mercato (Uscita) L’unica scelta a tua disposizione in ogni mercato sarà quando uscire. Questa scelta corrisponde al momento in cui decidi di vendere l’oggetto e intascare la somma di denaro pari al “Valore corrente.” Il tuo guadagno nel mercato sarà la differenza tra il “Valore corrente” al momento di vendita dell’oggetto e il “Valore di entrata.” Ad esempio, se tu entri quando l’oggetto valee 2.59 ed esci al valore die 2.68 il tuo guadagno sarà pari ae 2.68 -e 2.59 =e 0.09, o 9 centesimi. Se invece entri al “Valore di entrata” pari a e 2.59 ed esci quando il “Valore corrente” è e 2.45, il tuo guadagno sarà die 2.45 -e 2.59 =e -0.14, o un guadagno negativo di 14 centesimi. Perciò, IL TUO GUADAGNO NEL MERCATO PUO’ ESSERE NEGATIVO. Se non esci prima della fine del mercato, che dura 50 periodi, il tuo guadagno sarà calcolato usando il valore corrente nell’ultimo periodo. 189 Futuro Osservato o non Osservato Ci sono due possibili scenari alternativi che si possono realizzare dopo che hai cliccato sul pulsante “USCITA,” ovvero venduto l’oggetto. In uno scenario ti verrà mostrata l’evoluzione del valore dell’oggetto fino alla chiusura del mercato (50esimo periodo). Nell’altro caso, dopo la vendita dell’oggetto non osserverai nulla, e un nuovo mercato inizierà. Sarai informato riguardo allo scenario in cui cui ti trovi PRIMA dell’inizio di ogni mercato. Prima di ogni mercato, os- serverai una schermata con due possibili frasi: “INFO DOPO l’uscita” o “NO INFO all’uscita” (vedi le figure a destra). La prima dicitura indica che ti trovi in un mercato in cui l’evoluzione del valore dopo la vendita è osservabile, mentre la seconda dicitura ti informa che il futuro valore dell’oggetto non è osservabile. Per ricordarti in quale scenario ti trovi, le diciture “INFO DOPO” e “NO INFO” sono mostrate in alto a sinistra della schermata in cui vedi l’evoluzione del mercato. 190 Dopo Essere Usciti dal Mercato Dopo la tua uscita dal mercato, o dopo aver premuto il pulsante “USCITA,” riceverai infor- mazioni sul tuo guadagno. La figura in alto a destra ti mostra lo scenario “INFO DOPO,” dove il futuro è osservabile, mentre la figura in basso ti mostra lo scenario “NO INFO,” dove il futuro non è osservabile. In entrambi i casi, in alto a destra visualizzerai il “Valore di uscita” in blu, ed il tuo “Guadagno” in verde se positivo e in rosso se negativo. Inoltre, nello scenario Info Dopo dovrai attendere il termine del mercato, che corrisponde al tempo che il mercato avrebbe impie- gato per raggiungere la sua naturale conclusione (50 periodi) se tu non avessi venduto l’oggetto prima. Raggiunto l’ultimo periodo potrai esaminare la tua prova; per accedere al prossimo mer- cato dovrai cliccare sul pulsante “Prosegui.” Pagamento Il tuo guadagno nell’esperimento viene calcolato come segue. Prima dell’esperimento ti ven- gono datie 10 a disposizione. Quando hai finito di scegliere in tutti i 48 mercati, uno di questi verrà scelta in modo casuale e il guadagno che tu fai in quel mercato sarà sommato aie 10 di partenza. Perciò, se tu guadagnie 3 nel mercato scelto, il tuo pagamento totale saràe 10 +e 3 = e 13. Nel caso di un guadagno negativo, ad esempio -e 3, il tuo pagamento totale saràe 10 -e 3 =e 7. Nota che il tuo guadagno può variare tra -e 10 e +e 10, perciò il tuo pagamento totale varia tra un minimo die 0 e un massimo die 20. Mercati di Prova Prima dell’inizio del compito ti viene data l’opportunità di familiarizzare con l’interfaccia in 6 mercati di prova che assomigliano in tutto e per tutto ai mercati reali a cui parteciperai successi- vamente, con l’unica differenza che in questi mercati la dicitura TRIAL DI PROVA compare sullo schermo. Non verrai pagato per le tue decisioni nei mercati di prova. 191 B.12.2 Holt and Laury Task (Italian) DESCRIZIONE DELLA SECONDA PARTE DELL’ESPERIMENTO In questa parte dell’esperimento ti verranno presentate 10 coppie di lotterie. Ogni lotteria ti garantisce di ottenere, con una certa probabilità, una tra due possibili vincite. Per ogni coppia di lotterie, il tuo compito sarà quello di scegliere la lotteria che preferisci giocare. Di seguito ti verrà presenata una descrizione dettagliata del compito. Premere il pulsante OK per continuare. DESCRIZIONE DEL COMPITO Nella parte destra dello schermo sono riportate le 10 coppie di lotterie. Ci sono 10 righe che corrispondono alle 10 scelte che dovrai effettuare. Ogni riga rappresenta una scelta tra due lotterie. Per effettuare le tue scelte sarà sufficiente cliccare in corrispondenza della lotteria che preferisci. Una volta che avrai scelto una lotteria, essa diventerà di colore rosso. Dopo che avrai effettuato le tue 10 scelte, il computer selezionerà in modo casuale una delle 10 righe. Infine, la lotteria da te scelta verrà giocata dal computer e tu riceverai la vincita corrispon- dente all’esito della lotteria. La tua vincita ti verrà mostrata a schermo dopo che avrai completato e validato tutte le tue scelte. Ricorda, l’ammontare di denaro rappresentato nelle diverse lotterie è reale, perciò sarai pa- gato/a in base alle scelte che effettuerai e secondo le regole appena descritte. Se hai qualche dubbio sulla procedura ed il metodo di pagamento sentiti libero/a di chiedere chiarimenti allo sperimentatore. 192 193 Appendix C Appendix to Chapter 3 C.1 Additional Figures and Tables This Appendix contains figures and tables that are omitted in Chapter 3. 195 Figure C.1: Effect on risk score, by service area risk, event study (a) raw trend .9 .95 1 1.05 2009 2010 2011 2012 2013 2014 ACA QBP high−risk low−quality low−risk high−quality (b) event study −.08 −.06 −.04 −.02 0 .02 2009 2010 2011 2012 2013 2014 ACA QBP (c) raw trend, 15% tails .9 .95 1 1.05 1.1 2009 2010 2011 2012 2013 2014 ACA QBP high−risk (>85 pct.) low−quality low−risk (<15 pct.) high−quality (d) event study, 15% tails −.15 −.1 −.05 0 .05 2009 2010 2011 2012 2013 2014 ACA QBP Notes: Panel (a) shows raw trend of contract-level risk score, for high quality contracts with below median service area risk and low quality contracts with above median service area risks. Panel (b) shows the event study estimates in 95% confidence intervals based on robust standard error clustered at the level of contracts. Corresponding raw trend and event study estimates for the 15% tails are in Panel (c) and (d), respectively. 196 Figure C.2: Effect on risk score, by market competition, event study (a) raw trend .92 .94 .96 .98 1 2009 2010 2011 2012 2013 2014 ACA QBP low−hhi low−quality high−hhi high−quality (b) event study −.06 −.04 −.02 0 .02 2009 2010 2011 2012 2013 2014 ACA QBP (c) raw trend, 15% tails .9 .95 1 1.05 2009 2010 2011 2012 2013 2014 ACA QBP low−hhi (<15 pct.) low−quality high−hhi (>85 pct.) high−quality (d) event study, 15% tails −.05 0 .05 2009 2010 2011 2012 2013 2014 ACA QBP Notes: Panel (a) shows raw trend of contract-level risk score, for high quality contracts with below median HHI and low quality contracts with above median HHI. Panel (b) shows the event study estimates in 95% confidence intervals based on robust standard error clustered at the level of contracts. Corresponding raw trend and event study estimates for the 15% tails are in Panel (c) and (d), respectively. 197 Figure C.3: Effect on premium and drug deductible, event study (a) raw trend, premium 20 40 60 80 100 2009 2010 2011 2012 2013 2014 ACA QBP low quality high quality (b) event study, premium −10 −5 0 5 10 2009 2010 2011 2012 2013 2014 ACA QBP (c) raw trend, drug deductible 25 30 35 40 45 2009 2010 2011 2012 2013 2014 ACA QBP low quality high quality (d) event study, drug deductible −40 −20 0 20 2009 2010 2011 2012 2013 2014 ACA QBP Notes: Panel (a) shows the raw trend of average premium at the contract level. Panel (b) shows the event study estimates for premium with 95% confidence intervals based on robust standard error clustered at the level of contracts. Panel (c) and (d) show the raw trend and event study estimates for average drug deductible at the contract level. 198 Figure C.4: Effect on premium, within-contract cross county variation, event study (a) raw trend 40 50 60 70 80 90 2009 2010 2011 2012 2013 2014 ACA QBP low−risk low−quality high−risk low−quality low−risk high−quality high−risk high−quality (b) event study −50 0 50 2009 2010 2011 2012 2013 2014 ACA QBP low quality high vs. low high quality (c) raw trend, 15% tails 40 50 60 70 80 90 2009 2010 2011 2012 2013 2014 ACA QBP low−risk low−quality high−risk low−quality low−risk high−quality high−risk high−quality (d) event study, 15% tails −40 −20 0 20 40 60 2009 2010 2011 2012 2013 2014 ACA QBP low quality high vs. low high quality Notes: Panel (a) shows the raw trend of premium for high and low quality contracts, and their respective high and low risk regions. A high risk region given contract has baseline FFS risk score above the median in the market set. Panel (b) shows the event study estimates for low quality contracts (left line), high quality contracts (right line), and the differential effect on high quality contracts (middle line). Plotted 95% confidence intervals are based on robust standard errors clustered two-way at the level of county and contract. Panel (c) and (d) show the corresponding raw trend and event study estimates, limiting counties to those in the lower or upper 15% of the risk distribution given contract. 199 Figure C.5: Effect on drug deductible, within-contract cross county variation, event study (a) raw trend 10 20 30 40 50 2009 2010 2011 2012 2013 2014 ACA QBP low−risk low−quality high−risk low−quality low−risk high−quality high−risk high−quality (b) event study −100 0 100 200 300 2009 2010 2011 2012 2013 2014 ACA QBP low quality triple difference high quality (c) raw trend, 15% tails 10 20 30 40 2009 2010 2011 2012 2013 2014 ACA QBP low−risk low−quality high−risk low−quality low−risk high−quality high−risk high−quality (d) event study, 15% tails −100 0 100 200 2009 2010 2011 2012 2013 2014 ACA QBP low quality triple difference high quality Notes: Panel (a) shows the raw trend of drug deductible for high and low quality contracts, and their respective high and low risk regions. A high risk region given contract has baseline FFS risk score above the median in the market set. Panel (b) shows the event study estimates for low quality contracts (left line), high quality contracts (right line), and the differential effect on high quality contracts (middle line). Plotted 95% confidence intervals are based on robust standard errors clustered two-way at the level of county and contract. Panel (c) and (d) show the corresponding raw trend and event study estimates, limiting counties to those in the lower or upper 15% of the risk distribution given contract. 200 Figure C.6: Risk score and outcome rating, event study (a) average outcome rating, raw trend 2.8 3 3.2 3.4 3.6 2009 2010 2011 2012 2013 2014 ACA QBP low risk high risk (b) average outcome rating, event study −2 −1 0 1 2 2009 2010 2011 2012 2013 2014 ACA QBP (c) health improved, raw trend 3.1 3.2 3.3 3.4 3.5 2009 2010 2011 2012 2013 2014 ACA QBP low risk high risk (d) health improved, event study −1.5 −1 −.5 0 .5 2009 2010 2011 2012 2013 2014 ACA QBP (e) diabetes and blood pressure, raw trend 2.8 3 3.2 3.4 3.6 3.8 2009 2010 2011 2012 2013 2014 ACA QBP low risk high risk (f) diabetes and blood pressure, event study −3 −2 −1 0 1 2 2009 2010 2011 2012 2013 2014 ACA QBP Notes: Figure shows the variation of outcome rating by baseline enrollee risk. In the raw trends (left panels), a high risk contract has baseline (2009-2010) enrollee risk score above the sample median (0.97). Right panels show the event study estimates from difference-in-difference specifications using continuous variation in baseline enrollee risk score. Panel (a) and (b) show the trending of average outcome measure ratings by risk. Panel (c) and (d) show the trending of health improvement measures reported in HOS. Panel (e) and (f) show the trending of diabetes and blood pressure control from HEDIS clinical measures. Event study graphs show 95% confidence intervals based on standard errors clustered at the level of contract. 201 Figure C.7: Quality, risk and outcome rating, event study (a) average outcome rating, raw trend 2.5 3 3.5 4 2009 2010 2011 2012 2013 2014 ACA QBP low quality high quality low quality + low risk high quality + high risk (b) average outcome rating, event study −.6 −.4 −.2 0 .2 .4 2009 2010 2011 2012 2013 2014 ACA QBP high vs. low quality high vs. low quality and risk (c) health improved, raw trend 3.1 3.2 3.3 3.4 3.5 2009 2010 2011 2012 2013 2014 ACA QBP low quality high quality low quality + low risk high quality + high risk (d) health improved, event study −.4 −.2 0 .2 .4 2009 2010 2011 2012 2013 2014 ACA QBP high vs. low quality high vs. low quality and risk (e) diabetes and blood pressure, raw trend 2.5 3 3.5 4 4.5 2009 2010 2011 2012 2013 2014 ACA QBP low quality high quality low quality + low risk high quality + high risk (f) diabetes and blood pressure, event study −1 −.5 0 .5 2009 2010 2011 2012 2013 2014 ACA QBP high vs. low quality high vs. low quality and risk Notes: Figure shows the variation of outcome rating by baseline quality and enrollee risk. A high risk contract has baseline (2009-2010) enrollee risk score above the sample median (0.97). Left panels show the raw trend of outcome ratings and component ratings for baseline high vs.low contracts in dotted lines, and for baseline high-risk high-quality vs. low-risk low-quality contracts in solid lines. Right panels show the event study estimates from corresponding difference-in-difference specifications. Panel (a) and (b) show the trending of average outcome measure ratings by quality and risk. Panel (c) and (d) show the trending of health improvement measures reported in HOS. Panel (e) and (f) show the trending of diabetes and blood pressure control from HEDIS clinical measures. Event study graphs show 95% confidence intervals based on standard errors clustered at the level of contract. 202 Table C.1: Part C measures in the quality rating, 2013 ID name category weight source time frame Domain 1: Staying Healthy: Screenings, Tests and Vaccines C01 Breast Cancer Screening Process Measure 1 HEDIS 01/01/2011 - 12/31/2011 C02 Colorectal Cancer Screening Process Measure 1 HEDIS 01/01/2011 - 12/31/2011 C03 Cardiovascular Care – Cholesterol Screening Process Measure 1 HEDIS 01/01/2011 - 12/31/2011 C04 Diabetes Care – Cholesterol Screening Process Measure 1 HEDIS 01/01/2011 - 12/31/2011 C05 Glaucoma Testing Process Measure 1 HEDIS 01/01/2011 - 12/31/2011 C06 Annual Flu Vaccine Process Measure 1 CAHPS 02/15/2012 - 05/31/2012 C07 Improving or Maintaining Physical Health Outcome Measure 3 HOS 04/18/2011 - 07/31/2011 C08 Improving or Maintaining Mental Health Outcome Measure 3 HOS 04/18/2011 - 07/31/2011 C09 Monitoring Physical Activity Process Measure 1 HOS/HEDIS 04/18/2011 - 07/31/2011 C10 Adult BMI Assessment Process Measure 1 HEDIS 01/01/2011 - 12/31/2011 Domain 2: Managing Chronic (Long Term) Conditions C11 Care for Older Adults – Medication Review Process Measure 1 HEDIS 01/01/2011 - 12/31/2011 C12 Care for Older Adults – Functional Status Assessment Process Measure 1 HEDIS 01/01/2011 - 12/31/2012 C13 Care for Older Adults – Pain Screening Process Measure 1 HEDIS 01/01/2011 - 12/31/2013 C14 Osteoporosis Management in Women who had a Fracture Process Measure 1 HEDIS 01/01/2011 - 12/31/2014 C15 Diabetes Care – Eye Exam Process Measure 1 HEDIS 01/01/2011 - 12/31/2015 C16 Diabetes Care – Kidney Disease Monitoring Process Measure 1 HEDIS 01/01/2011 - 12/31/2016 C17 Diabetes Care – Blood Sugar Controlled Intermediate Outcome Measures 3 HEDIS 01/01/2011 - 12/31/2017 C18 Diabetes Care – Cholesterol Controlled Intermediate Outcome Measures 3 HEDIS 01/01/2011 - 12/31/2018 C19 Controlling Blood Pressure Intermediate Outcome Measures 3 HEDIS 01/01/2011 - 12/31/2019 C20 Rheumatoid Arthritis Management Process Measure 1 HEDIS 01/01/2011 - 12/31/2020 C21 Improving Bladder Control Process Measure 1 HOS/HEDIS 04/18/2011 - 07/31/2011 C22 Reducing the Risk of Falling Process Measure 1 HOS/HEDIS 04/18/2011 - 07/31/2011 C23 Plan All-Cause Readmissions Outcome Measure 3 HEDIS 01/01/2011 - 12/31/2020 Domain 3: Member Experience with Health Plan C24 Getting Needed Care Patients’ Experience and Complaints Measure 1.5 CAHPS 02/15/2012 - 05/31/2012 C25 Getting Appointments and Care Quickly Patients’ Experience and Complaints Measure 1.5 CAHPS 02/15/2012 - 05/31/2012 C26 Customer Service Patients’ Experience and Complaints Measure 1.5 CAHPS 02/15/2012 - 05/31/2012 C27 Overall Rating of Health Care Quality Patients’ Experience and Complaints Measure 1.5 CAHPS 02/15/2012 - 05/31/2012 C28 Overall Rating of Plan Patients’ Experience and Complaints Measure 1.5 CAHPS 02/15/2012 - 05/31/2012 C29 Care Coordination Patients’ Experience and Complaints Measure 1 CAHPS 02/15/2012 - 05/31/2012 Domain 4: Member Complaints, Problems Getting Services, and Improvement in the Health Plan’s Performance C30 Complaints about the Health Plan Patients’ Experience and Complaints Measure 1.5 CTM 01/01/2012 - 06/30/2012 C31 Beneficiary Access and Performance Problems Measures Capturing Access 1.5 CMS 01/01/2011 - 12/31/2011 C32 Members Choosing to Leave the Plan Patients’ Experience and Complaints Measure 1.5 MBDSS 01/01/2011 - 12/31/2011 C33 Health Plan Quality Improvement Outcome Measure 1 CMS 2012 rating Domain 5: Health Plan Customer Service C34 Plan Makes Timely Decisions about Appeals Measures Capturing Access 1.5 IRE 01/01/2011 - 12/31/2011 C35 Reviewing Appeals Decisions Measures Capturing Access 1.5 IRE 01/01/2011 - 12/31/2011 C36 Call Center – Foreign Language Interpreter and TTY/TDD Availability Measures Capturing Access 1.5 Call Center 01/30/2012 - 05/18/2012 C37 Enrollment Timeliness Process Measure 1 MARx 01/01/2012 - 06/30/2012 Notes: Table lists the name of Part C measures in the 2013 quality rating, with detailed information on the data source of the measure, and the relevant measurement period in the source. Weight attached to each measure in the final rating is also listed. 203 Table C.2: Part D measures in the quality rating, 2013 ID name category weight source time frame Domain 1: Drug Plan Customer Service D01 Call Center – Pharmacy Hold Time Measures Capturing Access 1.5 Call Center 02/06/2012 - 05/18/2012 D02 Call Center – Foreign Language Interpreter and TTY/TDD Availability Measures Capturing Access 1.5 Call Center 01/30/2012 - 05/18/2012 D03 Appeals Auto–Forward Measures Capturing Access 1.5 IRE 01/01/2011 - 12/31/2011 D04 Appeals Upheld Measures Capturing Access 1.5 IRE 01/01/2012 - 6/30/2012 D05 Enrollment Timeliness Process Measure 1 MARx 01/01/2012 - 06/30/2012 Domain 2: Member Complaints, Problems Getting Services, and Improvement in the Drug Plan’s Performance (identical to part C domain 4; redundant and not used in the final rating) D06 Complaints about the Drug Plan Patients’ Experience and Complaints Measure 1.5 CTM 01/01/2012 - 06/30/2012 D07 Beneficiary Access and Performance Problems Measures Capturing Access 1.5 CMS 01/01/2011 - 12/31/2011 D08 Members Choosing to Leave the Plan Patients’ Experience and Complaints Measure 1.5 MBDSS 01/01/2011 - 12/31/2011 D09 Drug Plan Quality Improvement Outcome Measure 1 CMS 2012 rating Domain 3: Member Experience with the Drug Plan D10 Getting Information From Drug Plan Patients’ Experience and Complaints Measure 1.5 CAHPS 02/15/2012 - 05/31/2012 D11 Rating of Drug Plan Patients’ Experience and Complaints Measure 1.5 CAHPS 02/15/2012 - 05/31/2012 D12 Getting Needed Prescription Drugs Patients’ Experience and Complaints Measure 1.5 CAHPS 02/15/2012 - 05/31/2012 Domain 4: Member Experience with the Drug Plan D13 MPF Price Accuracy Process Measure 1 PDE 01/01/2011 - 09/30/2011 D14 High Risk Medication Intermediate Outcome Measures 3 PDE 01/01/2011 - 12/31/2011 D15 Diabetes Treatment Intermediate Outcome Measures 3 PDE 01/01/2011 - 12/31/2011 D16 Part D Medication Adherence for Oral Diabetes Medications Intermediate Outcome Measures 3 PDE 01/01/2011 - 12/31/2011 D17 Part D Medication Adherence for Hypertension (RAS antagonists) Intermediate Outcome Measures 3 PDE 01/01/2011 - 12/31/2011 D18 Part D Medication Adherence for Cholesterol (Statins) Intermediate Outcome Measures 3 PDE 01/01/2011 - 12/31/2011 Notes: Table lists the name of Part D measures in the 2013 quality rating, with detailed information on the data source of the measure, and the relevant measurement period in the source. 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Abstract (if available)

Abstract This dissertation explores different topics in Industrial Organization under the lenses of Behavioral Economics. The first chapter examines the rationale for investing in Corporate Social Responsibility (CSR). CSR includes all those programs that allow firms to better engage with their stakeholders. It has a vast array of applications, ranging from charitable donations to fair trade. To address this question, the chapter focuses on the optimal donation of an existing internet company which purchases celebrity belongings to subsequently auction them. In each auction, a fraction of the transaction price is donated to a charity. The data have been collected from the website of the company. After structurally estimating consumer preferences for charity and goods, as well as the cost of purchasing the items for the firm, the analysis shows that most of the gains from donating come from cost savings rather than an increase in consumers' willingness to pay. This result suggests that consumers may not provide enough incentives for firms to behave prosocially. Further, the model indicates that the firm's donations largely exceeds the donation level that maximizes profits. This result suggests that firms may engage in CSR not just to maximize profits, but also to give back to society, a finding that is in line with the recent growth of benefit corporations and social entrepreneurship. ❧ The second chapter studies a dynamic environment where subjects are endowed with an asset and profit from selling it. An experiment is conducted to understand how subjects form reference points and how these reference points affect sale decisions. Participants know beforehand whether they will observe future prices after they sell the asset or not. Without future prices participants are affected only by regret about previously observed high prices (past regret), but, when future prices are available, they also avoid regret about expected after‐sale high prices (future regret). Moreover, as the relative sizes of past and future regret change, participants dynamically switch between them. This demonstrates how multiple reference points dynamically influence sales. ❧ The third chapter investigates a value‐added policy reform in the US Medicare Advantage, which tied subsidies to Medicare insurers with quality of service. The chapter focuses on the supply‐side reaction of the insurers and finds that the introduction of the policy is associated with a greater (lower) premium in high (low) risk counties for higher quality plans. At the same time, the risk pool improved significantly for high‐quality insurance plans. The chapter shows evidence that enrollee's baseline health status enters in the computation of the quality measure, which created incentives for high‐quality plans to select away from riskier counties. The selection response calls into question the distributional implication of quality payments and, more broadly, highlights the difficulty of implementing value‐added policies.

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Asset Metadata

Creator Fioretti, Michele (author)

Core Title Behavioral approaches to industrial organization

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Economics

Publication Date 04/12/2019

Defense Date 03/04/2019

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag behavioral economics,industrial organization,Medicare,OAI-PMH Harvest,objectives of the firm,regret avoidance,social responsibility,structural estimation,value‐added policy

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Ridder, Geert (committee chair), Coricelli, Giorgio (committee member), Moon, Hyungsik Roger (committee member), Yang, Sha (committee member)

Creator Email fioretti.mi@gmail.com,fioretti@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-138397

Unique identifier UC11675445

Identifier etd-FiorettiMi-7189.pdf (filename),usctheses-c89-138397 (legacy record id)

Legacy Identifier etd-FiorettiMi-7189.pdf

Dmrecord 138397

Document Type Dissertation

Format application/pdf (imt)

Rights Fioretti, Michele

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA