HOW VALUABLE IS A GOOD REPUTATION?

HOW VALUABLE IS A GOOD REPUTATION? A SAMPLE SELECTION MODEL OF INTERNET AUCTIONS* Jeffrey Livingston** University of Maryland September 2002

Abstract: On the online auction site eBay, by convention, sellers do not ship goods to winning bidders until after they have received payment, so there is an opportunity for sellers to take advantage of bidders’ trust. Realizing this, the designers of eBay created a system that relies on selfenforcement using reputation. It is almost as if eBay’s structure was designed by people who are familiar with folk theorems on self-enforcement. A simple model of bidder behavior guides an empirical analysis of how bidders respond to sellers with better reputations. Sellers do receive significant returns to honest behavior. JEL classification codes: L14, L15, D83, D12

* I thank Peter Murrell and Bill Evans for guidance and many helpful comments and suggestions. Omar Azfar, Peter Cramton, Mohamed El-Hodiri, John List, Deborah Minehart, and especially the participants of the Maryland graduate student Microeconomics seminar have also offered helpful comments on this paper and previous versions of it. John Deke offered useful advice in data collection methods. Finally, thanks to Matthew Langley, who wrote the Perl script that parsed the web pages into useable data. Any remaining errors are my own. ** [email protected]

I. Introduction When the creators of the Internet auction site eBay were designing their system, what were they thinking? It is almost as if eBay’s structure was designed by people who are familiar with folk theorems on self-enforcement. The theorems show that agents who find it in their short-run interest to behave dishonestly might instead fulfill agreements in order to gain a reputation for honesty. Now, due to either the genius or the luck of the eBay designers, an ideal market has been created for testing the theory. The purpose of this paper is to evaluate whether eBay sellers receive rewards for having good reputations. To do so, I analyze data from eBay auctions that reveal how bidders respond to reports about a seller’s past behavior. I first construct a simple theoretical model of bidder behavior. This model is used to guide empirical work, which is the core of the paper. The analysis shows that bidders do in fact reward sellers who have stronger reputations by placing higher bids in their auctions, and by bidding in their auctions more often. EBay provides a valuable opportunity to study reputation because by convention, sellers do not send goods to winning bidders until after they have received payment. The seller can simply pocket the money, or send an item of poor quality. A consumer who is defrauded by a seller has little recourse, because the identity of a seller is known only through an email address, which can be anonymously obtained.1 Whether a seller will behave honestly depends almost exclusively on mechanisms of self-enforcement.2 On eBay, self-enforcement might occur through reputation effects. EBay allows winning bidders to post ratings of sellers' actions that can be positive, neutral, or negative, as well as comment on the transaction. This information is also presented as a feedback rating that is equal to the number of positive reports, minus the number of negative reports. Potential bidders can use this information to form expectations about how the seller will behave in the future. Sellers may find it in their interest to fulfill agreements, since future bidders may not trust a seller with a history of treating buyers poorly. For self-enforcement to work, the response of bidders to a better reputation must be

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strong enough to make the seller's long-term benefits from being honest outweigh the short-term gains from cheating. There are reasons to doubt that this reputation mechanism works. First, rational bidders might not reward sellers who establish good reputations, because reports about how the seller has behaved may not be credible. Sellers could build a reputation by selling relatively inexpensive items, and then cheat in auctions of more expensive goods. For example, a seller with a history of over six thousand properly conducted transactions sold hundreds of porcelain collectibles on January 4th 2002, but did not send the winners anything after receiving payments of about $300,000.3 Also, a clever seller can fake positive reports by assuming a different identity, bidding enough to win his own auction, and leaving a good rating. Second, bidders have no incentive to leave reports, because doing so takes time, but adds nothing to their payoffs. However, Resnick and Zeckhauser (2001) find in a sample of 36,233 eBay auctions that bidders left reports 52 percent of the time. Third, punishments might not be severe enough to encourage honest behavior. All a seller loses by cheating is the benefit of a previously established reputation. Sellers who breach contracts can easily start over with a new identity. Thus, whether bidders react to reports about a seller's history is an empirical question. To analyze whether bidders' reactions are in fact significant, I construct a theoretical model of bidder behavior that is used to guide the subsequent empirical analysis. As noted, sellers who ruin their reputations can start over as a new seller who has yet to establish a transaction history. Not surprisingly, in the data sellers have very few negative reports. In order to examine what a seller gives up by cheating, therefore, both the model and the empirical analysis focus on the improved outcomes experienced by sellers who have established a reputation for acting honestly, relative to sellers who have no reports about their behavior. The model demonstrates how bidders might increase a seller’s expected return to behaving honestly. Bidders make two decisions that influence the seller’s expected payoffs. If bidders are more willing to participate in the auctions of sellers who have received positive reports, then the

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auction is more likely to result in a sale. If they bid more when they do participate, then revenues given that a sale is made will be higher. The model predicts that bidders are more likely to bid, and that these bids will be higher, if a seller has even a few positive reports. However, these effects are not linear. There are either increasing or decreasing returns to additional positive reports, depending on prior beliefs about the probability that the seller is honest. The theory serves three purposes. First, it pinpoints the two critical bidder decisions that should be empirically examined, whether to bid and how much to bid. Second, it predicts how those decisions are affected by the seller’s reputation. Third, it aids the formulation of estimating procedures by showing that the determinants of the size of the winning bid are intimately related to factors that affect whether any bids are received. The researcher should thus be weary of sample selection problems. The paper then turns to the empirical analysis, using a cross-section of auctions of Taylor Made Firesole irons, a variety of golf clubs. The analysis first establishes how a bidder’s participation decision is affected by a seller’s reputation. Two probit models are used. The first evaluates whether at least one bid is more likely to be placed if the seller has more positive reports. The second looks at whether an auction is more likely to result in a sale if the seller has more positive reports. Sellers will also be encouraged to act honestly if bidders bid more when sellers have better reputations. Using Ordinary Least Squares to analyze this question is inappropriate because the sample of observations is endogenously determined. As the theory shows, bidders might choose not to place a bid, so some auctions do not generate an observation on the dependent variable, the winning bid. The procedure proposed by Heckman (1974) is used to counter the potential bias due to sample selection. This procedure uses full-information maximum likelihood (FIML) to estimate both the equation that determines selection (the participation decision) and the equation of interest (the relationship between the amount the bidder bids and the seller’s reputation). It permits variables to be included in the selection equation that are not in the equation of interest. This is an important feature

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of the procedure, because theory predicts that some factors will affect the participation decision, but not the decision of how much to bid. These factors, which are used as exclusion restrictions, include the minimum-allowable bid and whether a secret reserve price is used. The empirical analysis shows that a seller’s reputation has a substantial impact on the decisions that bidders make. Sellers who have even a few positive reports are more likely than sellers who have no history to receive bids and to have their auctions result in a sale. They also receive higher bids. However, there are severely decreasing marginal returns to positive reports, as the theoretical model suggests can happen. Experienced bidders drive these gains. Bidders with little experience on eBay tend to trust sellers regardless of their history. Experienced bidders are less naïve. They do not bid as much if there are no reports about how a seller has behaved in the past, but once a seller establishes a reputation for honest behavior, they bid as much as inexperienced bidders do. Previous work that estimates the returns to reputation in Internet auctions has found that bid amounts barely increase as sellers improve their reputations, if they increase at all. This work includes papers by Eaton (2002), Houser and Wooders (2001), Lucking-Reiley et. al. (2000), McDonald and Slawson (2002), Melnik and Alm (2002) and Resnick and Zeckhauser (2001). These studies underestimate the returns to reputation, for several reasons. First, in most cases they assume that the relationship between the highest bid received and the number of positive reports received by the seller is linear or log-linear. If marginal returns to reputation are severely decreasing, as the analysis presented here suggests, these functional forms may only pick up the small returns that occur after an initial reputation is established. Second, the estimates either do not account for sample selection bias, or account for it incorrectly. The paper is organized as follows. Section II presents the model of bidder behavior. The model is used to construct several testable hypotheses about the effect of a seller’s reputation, which are derived in sections III and IV. The data is described in section V. The hypotheses are tested in

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Sections VI and VII. Section VIII considers whether bidders of different experience levels behave differently. Section IX concludes. II. A Model of Bidder Behavior The model is based on the design of eBay. At the beginning of the first period of a seller’s life, he is matched with a set of n symmetric, risk neutral bidders. The seller transacts with those bidders, and the winning bidder reports how the seller behaved. In the next period, the seller is matched with a new set of bidders. These bidders update their beliefs about the seller’s type using the report left by the winning bidder from the previous period, and the above process is repeated until the seller dies.4 In each period, the seller offers for sale a single item in a sealed-bid, second price auction.5 Each bidder i values the object being sold at vi, which is a realization of random variable Vi that is independently drawn from a continuous distribution F on support [v, v] . The seller values the item at vs < v, guaranteeing that gains from trade are possible. Valuations are private information. When the auction begins, the seller can set a minimum allowable bid level M.6 This choice is not explicitly modeled. Assume M is some function of vs, so M = g(vs).7 Bidders then decide whether to place a bid, and if they do, how much to bid. The bidders’ actions depend on their beliefs about the probability that the seller will behave honestly.8 After bidders move and the auction is completed, the winning bidder sends payment to the seller, who then chooses whether to cooperate with or betray the winning bidder. Let the seller’s move in period t be denoted by Ct for cooperate, or Bt for betray. If the seller plays Ct, then the winning bidder receives the good from the seller. If the seller plays Bt, then the winning bidder receives nothing of worth from the seller. The winning bidder earns a positive payoff if Ct is played, but a negative payoff if Bt is played, because the money sent to the seller is lost.9 Sellers have only two possible types, honest (H) or dishonest (D). Their behavior is predetermined: H-type sellers always play Ct and D-type sellers always play Bt.10 Let p1 be the

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subjective assessment of the probability that the seller is an H-type that each bidder identically holds at the beginning of a seller’s life.11 Similarly, let the bidders’ updated assessments at the beginning of period t be pt. After the seller plays either Ct or Bt, the winner can report whether the seller was honest. I assume that the winner always submits a report, and that these reports are not distorted for any strategic reasons.12 However, since there is concern that reports may not be accurate, they are assumed to be noisy. If the seller plays Ct, the probability that the winner reports that Ct was played is α , and if Bt is played, the probability that the winner reports that Ct was played is β , where

0 ≤ β < α ≤ 1 . I call a report that the seller played Ct a “good” report, and a report that Bt was played a “bad” report.13 Assume that if a seller plays Ct, a good report is more likely than a bad one, and if a seller plays Bt, a bad report is more likely than a good one, so β