THE Internet auction site ebay provides a valuable

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1 HOW VALUABLE IS A GOOD REPUTATION? A SAMPLE SELECTION MODEL OF INTERNET AUCTIONS Jeffrey A. Livingston* 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 self-enforcement using reputation. Several recent studies have found that bidders give little or no reward to sellers who have better reputations. I show that in fact, sellers are strongly rewarded for the first few reports that they have behaved honestly, but marginal returns to additional reports are severely decreasing. I. Introduction THE Internet auction site ebay provides a valuable opportunity to study how reputation can be used to encourage self-enforcement of contracts. On ebay, 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 address, which can be anonymously obtained. 1 Rather than formally enforcing contracts between buyers and sellers, ebay relies on mechanisms of selfenforcement. 2 It 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, because future bidders may not trust a seller with a history of treating buyers poorly. For self-enforcement to work, bidders must respond strongly enough to better reputations to make the seller s long-term benefits from being honest outweigh the short-term gains from cheating. Received for publication September 25, Revision accepted for publication December 20, * Bentley College. I thank Peter Murrell and Bill Evans for guidance and many helpful comments and suggestions. Two anonymous referees, Omar Azfar, Peter Cramton, Mohamed El-Hodiri, John List, Deborah Minehart, Patrick Scholten, and especially the participants of the Maryland graduate student microeconomics seminar have also offered helpful comments on this paper and previous versions of it. Participants in seminars at Bentley College, Indiana University, Loyola Marymount University, and the University of Pittsburgh also offered useful input. Sean Corcoran offered many fruitful suggestions during the revision process. John Deke offered useful advice on data collection methods. Finally, thanks to Matthew Langley and Bidisha Ghosh, who provided excellent research assistance. Of course, any remaining errors are my own. 1 Sellers are also required to provide a credit card number to confirm their identity, but it is possible for a malicious seller to obtain a fraudulent credit card. 2 ebay does offer insurance for the first $200 of the worth of an item, and buyers can use a third party such as escrow service, to enforce the transaction. Escrow services are usually used only for transactions where the stakes are high, such as for automobiles. There are reasons to doubt that ebay s reputation mechanism should work. 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 4, 2002, but did not send the winners anything after receiving payments of approximately $300, 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, in a sample of 36,233 ebay auctions, Resnick and Zeckhauser (2002) find that bidders left reports 52% 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 are not banned from ebay, for they can easily create a new identity. Thus, the goal of this study is to examine whether bidders do reward sellers who establish better reputations, and to quantify those rewards if they do exist. The analysis is guided by a theoretical model of bidder behavior. A seller who ruins his reputation can start over as a new seller who has yet to establish a transaction history. Both the model and the empirical analysis therefore measure how much sellers would lose if their reputation were ruined, by examining how bidders react to sellers who have established a reputation for acting honestly, relative to sellers who have no reports about their behavior. 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 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. Once bidders are largely convinced that the seller tends to act honestly, they bid as much and as often as they would if the sellers did not have an incentive problem. There is no room for improvement, so additional reports have little or no impact on seller welfare. 3 Rumors are that the seller had large gambling debts to pay off. See the discussion at &cid ; for the full discussion of this incident, see slashdot.org/article.pl?sid 02/02/22/ &mode thread&tid 98. The Review of Economics and Statistics, August 2005, 87(3): by the President and Fellows of Harvard College and the Massachusetts Institute of Technology

2 454 THE REVIEW OF ECONOMICS AND STATISTICS The insights gleaned from this model guide the empirical analysis, which examines a cross-section of auctions of Taylor Made Firesole irons, a variety of golf clubs. This 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. The analysis then examines whether bid amounts are affected when a seller s reputation improves. Because ebay auctions are equivalent to second price auctions, the price paid by the winning bidder is the second highest bid. Because no bidders chose to participate in some auctions, data on the amount of the second highest bid are sometimes unavailable. A sample selection model is accordingly used to estimate the relationship between a seller s reputation and the amount of the second highest bid. 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, reports beyond the first few have a much smaller impact on the returns to reputation, suggesting that early reports are enough to convince bidders of a seller s honest intentions. Previous work that estimates the returns to reputation in Internet auctions typically finds 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), Mc- Donald and Slawson (2002), Melnik and Alm (2002), Resnick and Zeckhauser (2002), and Resnick et al. (2002). 4 These studies may underestimate the returns to reputation, because they typically assume that the relationship between the winning bid amount 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. The paper is organized as follows. Section II presents the model of bidder behavior. The model is used to predict how a seller s reputation will affect bidder behavior. These predictions are derived in section III. The data are described in section IV. The effect of a seller s reputation on bidder behavior is estimated in sections V and VI. Section VII concludes. 4 A nice survey and summary of findings of the various papers that have explored the link between an ebay seller s reputation and the returns to reputation can be found in Bajari and Hortascu (2004). 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 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. 5 In each period, the seller offers for sale a single item in a sealed-bid, second-price auction. 6 Each bidder i values the object being sold at v i, which is a realization of a random variable V i that is independently drawn from a continuous distribution F on support [v, v ]. Valuations are private information. When the auction begins, the seller can set a minimum allowable bid level M, 7 though this choice is not explicitly modeled and M assumed to be exogenous. 8 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. 9 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 C t for cooperate, or B t for betray. If the seller plays C t, then the 5 Though it has no effect on the model, for completeness assume that a seller survives until the next period with probability. 6 ebay auctions are English auctions where the seller can choose an end date after which no further bids are accepted. ebay uses a feature called proxy bidding that, in theory, makes behavior in the auctions strategically equivalent to that in second-price auctions. Using this feature, bidders can submit a bid equal to the most they would be willing to pay. The computer then raises that person s bid one increment above any bids that come later, unless the next bid is higher than the bidder s maximum. Lucking-Reiley et al. (2000) suggest that many bidders do use this feature, though others wait until the closing seconds of an auction to place a bid. Likewise, Roth and Ockenfels (2000) model ebay s auction process. They show that bidding your true value at the beginning of the auction is one equilibrium strategy, as in a second-price auction, but it is not a dominant strategy. Another equilibrium exists where bidders wait until the last second of an auction to submit a bid equal to their true valuation, though the computer might not process the bid. They find that bidders do often wait until the closing seconds to bid. Regardless of the timing of the bids, both models predict that bidders will eventually try to bid their true value. 7 On ebay, sellers can set both a minimum bid M, and a reserve price. M is a publicly observable reserve price, but ebay s reserve price is secret. The bidders do not know what this price is, but they do know whether a secret reserve price is being used. Roth and Ockenfels (2000) do not allow for the choice of a secret reserve price, because they do not want to be distracted by the additional strategic prospects that it entails. I follow their lead in the model that follows. 8 Sellers would choose M to maximize expected profits. This choice is left in the background, because the focus is not on how sellers strategically react to bidder behavior, but rather on how bidder behavior changes if M is different. See Milgrom and Weber (1982) for discussion of how the ability to set a reserve price affects seller behavior. 9 Honest behavior can mean a variety of things: Will the seller actually send the good once payment has been received? Will the item be of the advertised quality? Will the item be shipped in a timely fashion? Regardless of the bidders concern, each potential dilemma results in a decrease in the value a bidder expects to receive if she wins the auction.

3 HOW VALUABLE IS A GOOD REPUTATION? 455 winning bidder receives the good from the seller. If the seller plays B t, then the winning bidder receives nothing of worth from the seller. The winning bidder earns a positive payoff if C t is played, but a negative payoff if B t is played, because the money sent to the seller is lost. 10 Sellers have only two possible types, honest (H) or dishonest (D). Nature chooses the seller s type. For simplicity, assume that the seller s move is determined by his type. 11 H-type sellers play C t with probability and B t with probability 1, and D-type sellers play C t with probability and B t with probability 1. H-type sellers are assumed to be more likely to cooperate than D-type sellers, so 0 1. After the seller plays either C t or B t, the winner can report whether the seller was honest. On ebay, bidders can leave either positive, neutral, or negative reports. To simplify the model, assume that only positive or negative reports are possible. I assume that the winner always submits a report, that the reports are always accurate, and that the reports are not distorted for any strategic reasons. 12 The winning bidder leaves a positive report if the seller plays C t, and a negative report if the seller plays B t. Let g t be the number of positive reports that a seller has received at the beginning of period t, and let n t be the number of negative reports that the seller has received at the beginning of period t. These reports are used to formulate beliefs about the seller s type, and accordingly beliefs about the chance that the seller will play C t. Let p 1 be the 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. 13 Similarly, let the bidders updated assessments at the beginning of period t be p t. The equilibrium is completely specified by calculating the optimal decisions that each pool of bidders makes in each period. We can think of the model as a game between a set of bidders and nature, which randomly chooses the type of the seller. The model is solved via backward induction. 10 More generally, one could assume that the value that the bidder receives if the seller plays B t is a proportion of what she receives if he plays C t : Let V i H be the random variable from which bidder i s value is drawn if the seller plays C t, and V i L be the random variable from which bidder i s value is drawn if the seller plays B t. Then V i L V i H, where This simple model is used in order to examine how bidder behavior will be effected by a seller s reputation, rather than the complex dynamics that govern how a rational seller will choose to behave given the bidders strategies, and vice versa. 12 In fact, there is no strategic reason to submit a report at all. Reports are not always submitted in practice. The model can take into account this possibility. If no report is left, then the bidders in the next period have no new information, so they simply do not update their beliefs. 13 I do not model how bidders form the initial subjective beliefs. The beliefs will be based on the bidders perceptions of the proportion of H-type agents in the population. Let p* be the true proportion of H-type agents, in the community, where p* [0, 1]. Bidders will take account of information they have about the overall history of past transactions in the market when they form these beliefs. For models of this process, see Bower, Garber, and Watson (1996) and Tirole (1996). Begin with the bidders choice of how much to bid. Vickrey (1961) examines bidder behavior in second-price auctions of the variety studied here, where bidders are risk-neutral and they have independent private values. He shows that it is a dominant strategy for bidders to bid their true values when there is no possibility that the seller will cheat by playing B t. Now consider what happens if sellers can play B t. It can be shown that a similar result is true: bidders optimally bid their expected value of the good. Because H-type sellers play C t with probability, D-type sellers play C t with probability, and the bidder receives 0 value if the seller plays B t, bidder i s expected payoff given that she wins the auction is [ p t (1 p t )]v i. Here [ p t (1 p t )]V i is the random variable from which bidder i s expected value is drawn. If each V i is replaced with [ p t (1 p t )]V i in the model of Vickrey (1961) and we allow for the presence of the publicly known reserve price M, the proof is identical and still holds. The bid function b t (v i, p t ) that results can be written as b t v i, p t p t 1 p t v i. (1) Predictably, if bidders feel that a seller will only send the object with probability p t (1 p t ), then the bidders will shade their bids by that probability. Now consider a bidder s decision whether to bid. She will place a bid if her optimal bid exceeds M: b t v i, p t p t 1 p t v i M. (2) Together, equations (1) and (2) determine the bidders equilibrium behavior. Note that the minimum bid, M, affects the participation decision in equation (2), but not the decision how much to bid in equation (1). Also, the way the bidders behave is affected by p t (the belief about the seller s type) in two ways: through equation (2) it affects their decision about whether they want to place a bid, and through equation (1) it affects the level of their bids, if they do decide to bid. How p t is formed is described next. In period 1, bidders base their decisions on their initial subjective belief about the probability p 1 that the seller is an H-type. Depending on the seller s type, he plays either C 1 or B 1, and the winning bidder reports on how the seller behaved. In period 2, a new pool of bidders confronts the seller. These bidders update their beliefs about the seller s type using the report from the previous period according to Bayes rule. So long as the seller remains in the market, the same process repeats in following periods, where the new prior belief is equal to the posterior belief from the previous period. Generally, in period t, a bidder s belief that the seller is an H-type is gt 1 nt p 1 p t, n t, t gt 1 nt p 1 gt 1 nt 1 p 1. (3) Combining equations (1) and (3), the bid function in period t becomes

4 456 THE REVIEW OF ECONOMICS AND STATISTICS b t v i, p t gt 1 (1 ) nt p 1 gt (1 ) nt p 1 gt (1 ) nt (1 p 1 ) gt 1 (1 ) nt (1 p 1 ) gt (1 ) nt p 1 gt (1 ) nt (1 p 1 ) v i, (4) and combining equations (2) and (3), bidder i submits a bid if gt 1 (1 ) nt p 1 gt (1 ) nt p 1 gt (1 ) nt (1 p 1 ) gt 1 (1 ) nt (1 p 1 ) (5) gt (1 ) nt p 1 gt (1 ) nt (1 p 1 ) v i M. Analysis of equations (4) and (5) generates predictions about how bidders react to reports about a seller s transaction history. III. Predictions of the Model On ebay, sellers who ruin their reputations can sell under a new identity. Therefore, the model should predict how bidder decisions will evolve if the seller receives a positive report in every period, starting from the beginning of the seller s history. The model predicts that returns to the first few positive reports can be large, but at some point marginal returns to reports will begin to decrease. Once bidders become largely convinced that the seller is an H-type, there is little room for improvement, so further positive reports will have little effect on bidder behavior. To see this, consider first how the bid changes if the number of positive reports, g t, increases. Because g t enters into b t (v i,p t ) only through p t, we have [ b t (v i, p t )]/ ( )v i p t /. Using logarithmic differentiation, we have p t p t ln p t, (6) where ln p t g t ln n t ln 1 ln p 1 ln gt 1 nt p 1 gt 1 nt 1 p 1. (7) Let D g t(1 ) n tp 1 g t(1 ) n t(1 p 1 ). Then ln p t ln gt (1 ) nt p 1 ln D gt (1 ) nt (1 p 1 ) D ln. (8) Recalling the definition of p t and 1 p t, substituting equation (8) into (6) yields so p t p t 1 p t ln ln 0, (9) b t v i, p t v i p t 1 p t ln ln 0. Therefore, bid amounts increase if g t, the number of positive reports held by the seller, increases. However, marginal returns to positive reports will not be constant. The rate at which the bid level increases with g t is found by taking its second derivative with respect to g t : 2 b t v i, p t 2 ln ln v i p t p 2 t so 2 b t i, p t 2 ln ln v i p t if pt 2, 0 if p t 1 2, 0 if p t p t, (10) The reaction of b t (v i, p t ) to changes in g t depends on the perception at the start of the period of the probability that the seller is an H-type. If more positive reports are received, b t (v i, p t ) increases at an increasing rate if p t 1, but at a 2 decreasing rate if p t 1. Once the bidders are more than 2 50% sure that the seller is an H-type, the marginal impact of positive reports on the bid amount begins to decrease. Returns will decrease more and more severely as p t approaches 1, because bidders will never bid more than their valuations. This result suggests that if the first few reports largely convince bidders that the seller is an H-type, the majority of the gains to reputation will accrue to the first few positive reports. Once bidders are convinced that a seller is an H-type, further positive reports will have little or no impact on bid amounts, because there is little room for improvement. The econometric specifications will be structured in a way that is able to capture this effect. Now consider the bidders decisions whether to place a bid in a seller s auction. Recall that equation (2) shows that bidder i will place a bid if b t v i, p t p t 1 p t v i M. A bidder will participate if her optimal bid exceeds the minimum allowable bid, so if b t (v i, p t ) increases, equation (2) is more likely to be satisfied. Therefore, changes in g t

5 HOW VALUABLE IS A GOOD REPUTATION? 457 have the same impact on the chance that an individual bidder participates as they have on the decision how much to bid. Accordingly, if a seller receives a string of positive reports and M does not change from period to period, the probability that a bidder chooses to place a bid increases in each successive period. The rate at which this probability increases may be increasing or decreasing, depending on the prior belief that the seller is honest, and most of the gains from having a good reputation may come with the first few reports. It should be noted that these are predictions about how individual bidders will react to reports about a seller s reputation. The empirical analysis looks at how these reports affect aggregate, not individual, behavior: the probability that at least one bid is received, the probability that an auction results in a sale, and the amount of the winning bid. These predictions are useful, however, in that aggregate behavior will react in the same way that individual behavior reacts, because bidders are identical in every aspect other than the draws of their valuations. If a seller receives an additional positive report, then individual bidders will be more likely to be willing to place a bid, so it will be more likely that an auction will receive at least one bid, and more likely that an auction will result in a sale. Also, each individual bidder will raise her optimal bid, so the amount of the second highest bid (which is equal to the winning bid) will increase. IV. Data To test the predictions of the theoretical model, from October 20, 2000 through August 20, 2001, data were collected from 861 ebay auctions of Taylor Made Firesole irons, a variety of golf clubs. Table 1 presents definitions and summary statistics for the variables used in this study. The unit of observation is a single auction. The dependent variables capture whether a bid was placed in an auction, whether the auction resulted in a sale, and the winning bid in each auction. YESBIDS takes a value of 1 if at least one bid was placed in an auction, and SOLD takes a value of 1 if the auction resulted in a sale. At least one bidder submitted a bid in 85% of the auctions, and 68% of the auctions resulted in a sale. TOTPRICE, the effective level of the winning bid, is equal to the winning bid, plus shipping charges. 14 Prices are high enough for bidders to be concerned about seller fraud. The mean price paid, including shipping charges, was $ The reported history of the seller is the critical explanatory variable. As sellers who receive negative reports can begin anew on ebay under a new identity, I examine the effect of reputation by looking at how bidders reward sellers 14 Sellers usually choose a fixed shipping price that the bidder must agree to before placing a bid, but occasionally they require bidders to pay actual shipping charges, which are not specified. In this case, shipping charges are taken to be the median of the fixed price charged in the rest of the sample, which is $15. who gain additional positive reports, relative to sellers who have yet to establish a trading history. Ideally, dummy variables would be used to identify the marginal impact of each additional positive report, but the data set is not rich enough to allow that specification. Instead, the sample distribution of the number of positive reports held by the seller in each auction is divided into quartiles, and dummy variables are created that indicate whether an auction falls into each quartile. The first quartile is further divided by splitting off auctions where the seller has zero positive reports into a separate group. POS0 is a dichotomous variable that takes a value of 1 if the seller has zero positive reports. POS1 takes a value of 1 if the auction is in the remainder of the first quartile of the number of positive reports received. Auctions where POS1 equals 1 will still be referred to as the first quartile, though the reader should keep in mind that this group is not the true first quartile, for it excludes auctions where the seller has no positive reports. POS2 POS4 take a value of 1 if the auction is in the second through fourth quartiles of positive reports received, respectively. Auctions for which POS0 equals 1 make up 8% of the sample. Sellers have few reports in most auctions. The auction at the 25th percentile has a seller with only 25 positive reports. The other quartiles cover much broader ranges of positive reports received. The auctions at the 50th, 75th and 100th percentiles have sellers with 175, 672, and 8035 positive reports, respectively. Negative and neutral reports are also included in the empirical analysis. NNRATIO is the fraction of reports that a seller has received that are neutral or negative. There are few such reports in the sample. The mean of NNRATIO is only 0.02, and its standard deviation is only Previous work tests for the effect of reputation by including either the logarithm of ebay s feedback score or the logarithm of the number of positive reports, plus 1 to avoid taking the logarithm of 0 (LNPOS). These specifications control for bad reports in the same way, using the logarithm of the number of negative reports. I include LNBAD, the logarithm of the sum of neutral and negative reports plus 1, in order to capture the effect of all bad reports. The theoretical model presented above shows that the minimum allowable bid (MINBID) should affect the participation decision, but not the decision of how much to bid. It shows that a bid will be placed if the optimal bid of the bidder with the highest valuation exceeds the minimum bid. Higher minimum bids may also discourage bidders from placing a bid for another reason. Vickrey s model assumes that the auction occurs in isolation, but in reality, typically many auctions of Taylor Made Firesole irons are active at 15 I do not use the same specification for negative and neutral reports as I do for positive reports, because doing so would mask the returns to positive reports. In the data, sellers who have more bad reports than average also have far more positive reports than average (the correlation between positive reports received and neutral or negative reports received is 0.8), because sellers who sell hundreds or thousands of items are bound to have occasional misunderstandings with their customers.

6 458 THE REVIEW OF ECONOMICS AND STATISTICS TABLE 1. VARIABLE DEFINITIONS AND SAMPLE CHARACTERISTICS Variable Name YESBIDS SOLD TOTPRICE Definition Dependent Variables 0-1 dummy variable that equals 1 if at least one bid is placed in an auction 0-1 dummy variable that equals 1 if auction resulted in a sale Highest bid in an auction, plus shipping charges Reported History of Seller Mean and (Standard Deviation) 0.85 (0.36) 0.68 (0.47) (84.69) POS0 0-1 dummy variable that equals 1 if seller has 0 positive reports 0.08 (0.27) POS1 0-1 dummy variable that equals 1 if seller has 1 25 positive reports (first quartile 0.17 (0.38) of positive reports received, less those with 0 reports) POS2 0-1 dummy variable that equals 1 if seller has positive reports (second 0.25 (0.43) quartile of positive reports received) POS3 0-1 dummy variable that equals 1 if seller has positive reports (third 0.25 (0.44) quartile of positive reports received) POS4 0-1 dummy variable that equals 1 if seller has more than 675 positive reports 0.25 (0.43) (fourth quartile of positive reports received) NNRATIO Fraction of reports that are negative or neutral 0.02 (0.06) LNPOS log (number of positive reports 1) 4.73 (2.29) LNBAD log (number of neutral and negative reports 1) 1.14 (1.12) Other Variables Affecting Participation Decision MINBID Minimum-allowable bid (chosen by seller) (185.44) MBMEAN Average minimum bid among other auctions that were either active at the (51.50) time the auction ended or ended on the same day MBDIFF Difference between MINBID and MBMEAN (180.10) MBDL1 0-1 dummy variable that equals 1 if 0.23 MBDL2 MBDH1 MBDH2 COMPET CC LATE PRIME MBDIFF is less than $ dummy variable that equals 1 if MBDIFF is at least $ but less than dummy variable that equals 1 if MBDIFF is at least 0 but less than $ dummy variable that equals 1 if MBDIFF is at least $ Controls for Auction, Item, or Market Heterogeneity Number of other auctions of the same good in progress at the time the auction ended 0-1 dummy variable that equals 1 if the seller allows payment by credit card 0-1 dummy variable that equals 1 if the auction ends between midnight and 4:00 A.M. Pacific time 0-1 dummy variable that equals 1 if the auction ends between 3:00 P.M. and 7:00 P.M. Pacific time (0.42) 0.23 (0.42) 0.27 (0.45) 0.27 (0.44) (9.85) 0.52 (0.50) 0.01 (0.12) 0.17 (0.38) Variable Name WEEKEND TABLE 1. (CONTINUED) Definition Mean and (Standard Deviation) 0-1 dummy variable that equals 1 if the auction ends on a weekend 0.26 (0.44) LENGTH3 0-1 dummy variable that equals 1 if the auction lasts 3 days 0.17 (0.37) LENGTH5 0-1 dummy variable that equals 1 if the auction lasts 5 days 0.18 (0.39) LENGTH7 0-1 dummy variable that equals 1 if the auction lasts 7 days 0.45 (0.50) LENGTH dummy variable that equals 1 if the auction lasts 10 days 0.06 (0.23) RETAIL Retail price of clubs (79.97) NEW 0-1 dummy variable that equals 1 if the clubs being auctioned are new 0.44 (0.50) LEFT 0-1 dummy variable that equals 1 if the clubs being auctioned are left-handed 0.02 (0.15) SENIOR 0-1 dummy variable that equals 1 if the clubs being auctioned are for seniors 0.03 (0.16) LADIES 0-1 dummy variable that equals 1 if the clubs being auctioned are for ladies 0.02 (0.12) SECRES 0-1 dummy variable that equals 1 if a secret reserve price is used 0.47 (0.50) any given time, so bidders have a choice about which auction they want to participate in. Livingston (2003) argues that higher minimum bids discourage bidders from placing bids in a particular auction, because other auctions that have lower minimum bids may offer better chances to obtain the same item for a lower price. To capture this effect, I identify the other auctions of Firesole irons that either were active at the time an auction ended or ended on the same day, find the average minimum bid used in those auctions (MBMEAN), and calculate the difference between an auction s minimum bid and this average (MBDIFF). Auctions are then categorized by this difference: those that use minimum bids that are less than the average minimum bid used by competitors, and those that use minimum bids that are at least as high as the average used by competitors. These categories are further divided at the category median minimum bid difference. MBDL1 equals 1 if the difference is less than $153.13, MBDL2 equals 1 if the difference is at least $ but less than $0, MBDH1 equals 1 if the difference is at least $0 but less than $167.50, and MBDH2 equals 1 if the difference is at least $ Previous work controls for other differences among the auctions. I include these variables to make the analysis as comparable as possible to this work. If more auctions of Firesole irons are in progress at the time the auction ends, the added competition may draw bidders away and drive the market price down. COMPET is the number of other auctions of Firesole irons that either were active at the time the auction ended, or ended on the same day. Allowing buyers to pay by credit card makes payments instantaneous, so the bidder should receive the item sooner, and buyers may be willing to bid more if their transaction is insured by their credit card company. CC equals 1 if the seller allows

7 HOW VALUABLE IS A GOOD REPUTATION? 459 payment by credit card. Auctions that end in late hours of the day may not receive as much activity. LATE equals 1 if the auction ends between midnight and four o clock A.M. Pacific Daylight Time. Similarly, auctions that end in prime shopping hours may receive more activity. PRIME equals 1 if the auction ends between three and seven o clock P.M. Pacific Daylight Time. 16 Auctions that end on the weekend may also receive more activity. WEEKEND equals 1 for auctions that end on a weekend. Finally, sellers can run auctions that last either 3, 5, 7, or 10 days. More bidders may observe and participate in auctions that run longer, so the winning bid may be higher. LENGTH3, LENGTH5, LENGTH7, and LENGTH10 equal 1 if the auction lasts 3, 5, 7, or 10 days, respectively. Finally, sellers can set a secret reserve price, as well as the minimum bid level. Bidders know whether a secret reserve price is being used, but they do not know what the price is. SECRES equals 1 if the auction uses a secret reserve price. Firesole irons vary along a few observable characteristics. Data are collected on these differences. The retail price of the clubs (RETAIL) captures several differences that affect the value of the clubs. 17 NEW takes a value of 1 if the set of clubs is new, not used. New clubs have more value than used clubs. Also, the market may be segmented in that some golfers have different characteristics, and some submarkets may be thinner than others. Dummy variables indicate whether the clubs are left-handed (LEFT), senior (SENIOR), or ladies clubs (LADIES). V. Effect of a Seller s Reputation on Bidders Participation Decisions Are bidders more willing to place a bid if a seller has a good reputation? The model predicts that an individual bidder is more likely to place a bid if the seller has more positive reports. Therefore, the probability that a seller receives any bids, as well as the probability that the seller s auction results in a sale, should increase as he gains additional positive reports. However, at some point there should be severely decreasing marginal returns to additional positive reports. To test these hypotheses, I estimate the relationships as probit models. According to the theoretical model presented above, at least one bid will be placed if the optimal bid of the bidder with the highest valuation exceeds the minimum allowable bid. Let w* i represent the unobserved expected difference between the high bidder s optimal bid and M. Assume bidder i has the highest valuation. Then according to our theoretical model, a bid should be received if 16 Previous studies, such as McDonald and Slawson (2002), also based the coding of these variables on Pacific time. 17 These differences include the type of shaft the club has (graphite, SensiCore, or steel), and the number of clubs included in the set. A large majority of the sets include a pitching wedge through a 3-iron, but a seller occasionally throws in an extra club or some other extra item, such a golf bag or a box of golf balls. I was able to identify the retail price of these extra items any time one was included. w* 1 p t v t M 0. As discussed, this decision may be more complicated than described by our simple model that auctions do not actually occur in isolation. The bidder s optimal bid and the level of the minimum bid will play a role, but other factors may come into play when a bidder decides whether to participate. To try to capture the influence of some of these factors, w* 1 is now assumed to be a linear function of observed variables z, where the vector z includes 1, POS1, POS2, POS3, POS4, NNRATIO, COM- PET, CC, LATE, PRIME, WEEKEND, LENGTH5, LENGTH7, LENGTH10, RETAIL, NEW, LEFT, SENIOR, LADIES, MBDL2, MBDH1, MBDH2, and SECRES. The model has the form w* 1j z j ε j, j 1, 2,..., n, (11) and w 1i is defined as follows: w 1j 1 if w* 1j 0, 0 if w* 1j 0, j 1, 2,..., n. (12) The probability that at least one bid is placed in auction j is prob w 1j 1 prob ε j z j 1 z j z j, (13) where ε j is N(0,1) and is the cumulative distribution function of the standard normal distribution. The results of estimating this model are presented in column 1 of table 2. Positive reports have statistically and economically significant effects on the chance that a bidder participates in a seller s auction, but the first few reports have a much larger effect on this probability than later reports do. The probability that a bid is placed is higher if the seller has from 1 to 25 positive reports than in auctions with sellers who have yet to receive a positive report. This probability is higher for auctions where the seller has from 26 to 175 positive reports, higher where the seller has from 176 to 672 positive reports, and higher where the seller has more than 672 positive reports, than to the probability for auctions where the seller has no positive reports. To put these effects in perspective, in the sample, the observed probability of receiving a bid is 0.85 across all auctions. The returns to reports are severely decreasing. Column 1 of table 3 presents likelihood ratio tests of the hypotheses that higher quartiles of positive reports have an additional effect on the probability that at least one bid is received. They show that the estimated coefficients on the first three positive-report-quartile dummy variables are not statistically significantly different from each other, suggesting that after the first 25 reports have been received, the next several hundred reports have no effect on the chance that at least one bidder places a bid. The coefficient on the fourth quartile of positive reports received is significantly different from the coefficients on the other three quartiles, however.

8 460 THE REVIEW OF ECONOMICS AND STATISTICS Independent Variable TABLE 2. MARGINAL EFFECTS OF POSITIVE REPORTS ON PARTICIPATION DECISION Pr(at Least One Bid Received) (1) Pr(Sale) (2) POS ** 0.209*** (0.014) (0.049) POS *** 0.175*** (0.015) (0.056) POS *** 0.294*** (0.016) (0.047) POS *** 0.240*** (0.020) (0.052) NNRATIO 0.148* (0.084) (0.263) COMPET (0.001) (0.002) CC 0.024* 0.159*** (0.014) (0.035) LATE (0.055) (0.137) PRIME (0.020) (0.042) WEEKEND (0.013) (0.039) LENGTH ** (0.019) (0.057) LENGTH *** (0.017) (0.042) LENGTH *** (0.039) (0.086) RETAIL ( ) (0.0002) NEW 0.029* 0.105*** (0.016) (0.040) LEFT (0.093) (0.119) SENIOR 0.255* (0.132) (0.100) LADIES (0.064) (0.128) SECRES 0.072*** 0.300*** (0.020) (0.039) MBDL (0.053) (0.049) MBDH *** 0.203*** (0.074) (0.054) MBDH *** 0.313*** (0.091) (0.056) N Pseudo R Standard errors in parentheses. * Significant at 10%; ** significant at 5%; *** significant at 1%. Still, these results suggest that there are returns of approximately 3.4 percentage points to just the first 1 to 25 reports, but several hundred more reports must be received before the chance of receiving a bid goes up by another 5.3 percentage points, so the marginal return for each individual report beyond the first 25 must be extremely small. The qualitative results of these estimates are robust to changes in the definitions of the positive report categories, 18 and to the 18 I tried specifications that categorized the positive reports in many different ways, each time using auctions where no positive reports were received as the reference group. Some of the specifications I tried include dummy variables indicating the deciles of positive reports; dummy variables indicating whether 1 to 5 reports, 6 to 10 reports, 11 to 25 reports, TABLE 3. DO HIGHER POSITIVE REPORT QUARTILES HAVE ADDITIONAL EFFECTS ON PARTICIPATION DECISIONS? Null Hypothesis Pr(at Least One Bid Received) (1) LR Statistic p- Value Pr(Sale) (2) LR Statistic p- Value Quartile 1 coeff. quartile 2 coeff Quartile 1 coeff. quartile 3 coeff Quartile 1 coeff. quartile 4 coeff Quartile 2 coeff. quartile 3 coeff Quartile 2 coeff. quartile 4 coeff Quartile 3 coeff. quartile 4 coeff Coefficients on first 3 quartiles are equal Coefficients on all quartiles are equal inclusion of time effects in the model. 19 There is little change in the results if different specifications that exclude some of the controls are used. The effect of reputation on a seller s expected returns depends on whether sellers who have better reputations are more likely to have their auctions result in a sale. Auctions may receive bids but not result in a sale if the seller sets a secret reserve price R that is not met. In the terms of our theoretical model, an auction will result in a sale if p t v i max(m, R) for at least one bidder. A probit model that is similar to the one specified above can also be estimated. These results are reported in column 2 of table 2. Sellers in the first quartile of positive reports received are 21 percentage points more likely than sellers with zero positive reports to successfully sell their goods, sellers in the second quartile are 18 percentage points more likely, sellers in the third quartile are 29 percentage points more likely, and sellers in the fourth quartile are 24 percentage points more likely. Relative to the mean of 68% of auctions that resulted in a sale, these are large effects. But again, although the first few positive reports have a large impact on the probability that an auction results in a sale, there is strong evidence that the marginal returns to additional positive reports are severely decreasing. Column 2 of table 3 presents likelihood ratio tests of the hypotheses that higher quartiles of positive reports have additional effects on the probability of sale. Though the null hypothesis that the coefficients on all quartile dummies are the same is rejected, we cannot reject the null hypotheses that the coefficient on quartile 1 is no different from the coefficient on quartile 2, quartile 3, or quartile 4, implying that reports beyond the first 25 have no 26 to 50 reports, 51 to 100 reports, or more than 100 reports were received; and dummy variables indicating the quartile of positive reports received, but with auctions where only one report was received separated out from the first quartile. Each specification yields estimates that lead to the same qualitative conclusion as reported in the main text. In the final specification mentioned, even the first positive report appears to have a large effect on the probability of sale and the winning bid amount. 19 If dummy variables indicating the week in which the auction was held are included in this regression, the estimates of the marginal effects of POS1 POS4 are 0.029, 0.042, 0.040, and 0.064, respectively.

9 HOW VALUABLE IS A GOOD REPUTATION? 461 additional impact on the probability of sale. 20 Again, these results are not sensitive to changes in how the positive reports are categorized or to the exclusion of controls from the specification, and they are robust to the inclusion of time effects. 21 Two other parameters are of interest. A larger percentage of neutral or negative reports reduces the probability that at least one bid is received (the test is significant at the 10% level), but appears to have no effect on the probability that the auction results in a sale. The difference between the minimum bid and the average minimum bid used by other active auctions of the same item, which is to be used as an exclusion restriction in the sample selection model of the amount of the winning bid that follows, has a significant effect on both the probability that a bid is received and the probability that the auction results in a sale. I argued previously that auctions that use high minimum bids relative to other auctions of the same item will receive fewer bids, because bidders may take their business to the auctions that appear to offer a better chance of obtaining the good for a lower price. This argument is supported by the data. In the sample, at least one bid was placed in 99% of the auctions where the minimum bid was less than the average minimum bid used by competitors, but in only 73% of auctions where the minimum bid was more than the average used by competitors. This effect is also seen in the regressions. Auctions that used minimum bids that were more than the average used by competitors were much less likely to receive a bid than auctions that used minimum bids that were more than $ below average. If the minimum bid is at least as high as the average among competitors but less than $ more, the auction is 21 percentage points less likely to receive a bid. If the minimum bid is at least $ more than the average, the auction is 42 percentage points less likely to receive a bid. Relative minimum bids had a similar effect on the chance that an auction results in a sale. VI. Effect of a Seller s Reputation on the Decision of How Much to Bid A seller s expected returns depend not only on the probability that his auction results in a sale, but also upon the amount of the winning bid, given that a sale occurs. The theoretical model presented earlier predicts that an individual bidder will place a larger bid if the seller has more positive reports. Therefore, the winning bid (which is equal to the second highest bid) should also increase if the seller gains additional positive reports, although there should be severely decreasing returns to these reports. 20 However, as an anonymous referee points out, we would expect these results to be more noisy than the results on whether a bid is received, because whether a sale occurs depends upon whether at least one bid exceeds the secret reserve price, which we do not observe. We only observe whether one is in use. 21 If dummy variables indicating the week in which the auction was held are included in this regression, the estimates of the marginal effects of POS1 POS4 are 0.212, 0.196, 0.279, and 0.219, respectively. The previous section shows that bids may not be placed if the seller has yet to establish a reputation or if the minimum bid level is set too high. In ebay auctions, the winner pays an amount equal to the second highest bid received, so the recorded amount of the second highest bid is equal to the minimum bid if either no bids or one bid is placed. Therefore, the amount of the second highest bid is censored when fewer than two bids are placed. Models that do not control for this fact will produce biased estimates of the effect of reputation. Some previous studies of reputation in Internet auctions, including Eaton (2002), Kaufman and Wood (2001a, 2001b), McDonald and Slawson (2002), and Resnick and Zeckhauser (2002) use models that do not address this problem. To demonstrate the bias that results from not controlling for this problem, I estimate the relationship between positive reports and the winning bid amount by OLS, using only observations where at least two bids were received. 22 OLS estimates of this relationship will be biased because observations where the seller has few positive reports will only have data on the bid level if some unobserved factor pushes at least two bidders optimal bids above the minimum bid, so that two or more bids are placed. Other observations, where the seller has a weak reputation but no such factor boosted the bids, will not have data on the bid level. Hence, within the sample of observations, the number of positive reports is inversely correlated with the error term, so OLS estimates of the effect of reputation will be downward biased. 23 For reasons that will be discussed shortly, to eliminate this bias, the problem is treated as an incidental truncation problem rather than a censoring problem, so a sample selection model is estimated. The sample selection model is specified as follows. Let b* j be the recorded amount of the second highest bid in auction j. Then b* j is assumed to be a linear function of observed variables x, where the vector x includes 1, POS1, POS2, POS3, POS4, NNRATIO, COMPET, CC, LATE, PRIME, WEEKEND, LENGTH5, LENGTH7, LENGTH10, RETAIL, NEW, LEFT, SENIOR, and LADIES. The model has the form b* j x j u j, w* 2j z j v j, (14) b j b* j if w* 2j M j, M j if w* 2j M j, j 1, 2,..., n, 22 To be clear, this regression uses all observations where at least two bids were received, regardless of whether the auction resulted in a sale. So long as at least two bids were placed, the recorded amount of the second highest bid is still theoretically equal to the second highest bidder s willingness to pay, even if the highest bid does not exceed the secret reserve price. 23 Relative to models that do take account of the censoring problem, OLS will underestimate the effect of reputation, because the observations that are not used by the OLS estimator, but are used by models that control for censoring, have lower numbers of positive reports as well as more negative error terms, so there is less opportunity to observe the larger winning bids that result from additional positive reports. I thank an anonymous referee for pointing this out.

10 462 THE REVIEW OF ECONOMICS AND STATISTICS where w* 2j represents the value of placing a bid to the bidder with the second highest valuation, z is as previously defined, 24 M j is the minimum bid used in auction j, and (u j, v j ) are i.i.d. draws from a bivariate normal distribution with zero mean, variances 2 u and 2 v, covariance uv, and correlation. As noted by Amemiya (1985), setting b j equal to M j when it is censored has no effect on the likelihood function, and merely signifies the event w* 2j M j. 25 Studies such as Lucking-Reiley et al. (2000), Melnik and Alm (2002), and Resnick et al. (2002) do address the sample selection problem using tobit models, treating the minimum bid as a censoring point below which the true winning bid would fall. 26 The tobit model is a special case of the sample selection model that constrains the selection equation to be identical to the equation of interest. When u v, 1, x z, and, the sample selection model is equivalent to the tobit model (Bockstael et al., 1990). If any of these conditions does not hold, then the sample selection model should be used instead of tobit. These conditions will hold if bidders do decide whether to participate in an auction purely according to whether their optimal bids exceed the minimum bid, as suggested by our theoretical model. However, their decisions are likely more complex than indicated by our simple model, so the true selection equation might be quite different from the true bid amount equation. First, there may be unobserved factors that affect the participation decision, but do not affect the bid amount decision, so may be less than 1. Second, the minimum bid should affect the selection equation but not the winning bid amount equation, so z and x may not be identical. As argued previously, higher minimum bids may drive bidders away to other auctions of the same item that are also accepting bids. Accordingly, the selection equation should control for this possible effect. However, the minimum bid should not appear in the bid amount equation, for bid amounts theoretically do not vary with publicly known reserve prices. The tobit model does not allow for this specification. Because there may be both unobserved and observed factors that affect the selection equation but not the bid amount equation, the constraints of the tobit model may result in biased estimates of the return to reputation. The sample selection model is estimated using fullinformation maximum likelihood (FIML). The parameters of the model can be estimated by maximizing the following likelihood function: 24 Recall that z includes MBDL2, MBDH1, and MBDH2 as exclusion restrictions, because we expect that the minimum bid level will effect the selection equation, but it theoretically has no effect on bid amounts. 25 Note carefully that an observation is not incidentally truncated if no sale occurs, so long as at least two bids are received. Even if the secret reserve price is not met when two or more bids are placed, the second highest bid is still theoretically equal to the second highest bidder s willingness to pay. 26 Houser and Wooders (2001) have a small data set of 94 observations where at least one bid was placed in each auction, so they argue that the sample selection issue is not relevant for their data. TABLE 4. MARGINAL EFFECT OF POSITIVE REPORTS ON SECOND HIGHEST BID Independent Variable OLS (1) Tobit (2) Sample Selection Model Bid Amount Equation (3) Selection Equation (4) POS * 0.27 (11.19) (11.75) (10.96) (0.24) POS ** 28.66** 31.78*** 0.50** (10.91) (11.45) (10.75) (0.24) POS *** 30.38*** 37.18*** 0.48** (10.89) (11.54) (10.74) (0.24) POS *** 39.35*** 42.82*** 0.95*** (10.89) (11.63) (10.84) (0.27) NNRATIO (42.93) (41.54) (42.61) (1.04) COMPET 0.46* * 0.01 (0.25) (0.27) (0.25) (0.01) CC (5.15) (5.55) (5.10) (0.13) LATE ** ** (22.60) (22.25) (22.11) (0.45) PRIME (6.51) (6.86) (6.43) (0.16) WEEKEND (5.77) (6.06) (5.68) (0.13) LENGTH *** *** (7.32) (7.66) (7.40) (0.18) LENGTH *** *** (6.30) (6.41) (6.39) (0.15) LENGTH *** 26.44** 0.62** (11.30) (11.78) (11.26) (0.28) RETAIL 0.41*** 0.36*** 0.40*** (0.03) (0.03) (0.03) (0.001) NEW 81.50*** 82.79*** 83.05*** 0.02 (5.50) (5.82) (5.42) (0.14) LEFT 58.33*** 49.78*** 58.04*** 0.15 (16.19) (17.77) (16.07) (0.43) SENIOR *** *** (16.85) (16.80) (16.65) (0.41) LADIES 44.86** 47.46** 42.59** 0.33 (18.27) (19.71) (18.11) (0.48) SECRES 16.41*** *** (5.33) (5.73) (5.52) (0.16) MBDL2 1.15** (0.48) MBDH1 2.22*** MBDH2 (0.40) 3.44*** (0.40) Intercept (29.38) (31.63) (29.21) (0.90) N R Standard errors in parentheses. * Significant at 10%; ** significant at 5%; *** significant at 1%. L b j M j P w* 2j M j b j b* j f b j w* 2j M j P w* 2j 0. (15) The results of the estimation are presented in table 4. Column 3 reports the results of the estimation of the bid amount equation, and column 4 reports the results of the estimation of the selection equation. 27 On average, sellers 27 The results from the selection equation are also interesting. The selection equation examines the probability that an auction receives at least two bids. The effects that positive reports have on this probability are similar to the effects they have on the probability that at least one bid is

11 HOW VALUABLE IS A GOOD REPUTATION? 463 TABLE 5. DO HIGHER POSITIVE REPORT QUARTILES HAVE ADDITIONAL EFFECTS ON THE WINNING BID AMOUNT? Amount of Winning Bid Null Hypothesis LR Statistic p-value Quartile 1 coeff. quartile 2 coeff Quartile 1 coeff. quartile 3 coeff Quartile 1 coeff. quartile 4 coeff Quartile 2 coeff. quartile 3 coeff Quartile 2 coeff. quartile 4 coeff Quartile 3 coeff. quartile 4 coeff Coeffs. of first 3 quartile dummies are equal Coeffs. of all quartile dummies are equal who have just 1 to 25 positive reports can expect to receive second highest bids that are $20.42 higher than sellers who have no positive reports (though this estimate is statistically significant at only the 10% level). The second highest bidder bids $31.78 more when the seller has 26 to 175 positive reports, $37.18 more when the seller has 176 to 672 positive reports, and $42.82 more when the seller has more than 672 positive reports, than in auctions where the seller has no positive reports. The results again show that the first several reports have a strong effect on behavior, but the marginal effect of subsequent reports is much smaller. The bidders with the second highest valuation bid $20.42 more when sellers have 1 to 25 positive reports than they bid when sellers have zero positive reports (approximately 5% of the average selling price of $409.96). However, they bid only $22.40 more when sellers have more than 672 positive reports than they do when sellers have 1 to 25 positive reports, implying that returns to each individual report shrink dramatically after the first few have been received. Likelihood ratio tests, presented in table 5, show that this additional gain is statistically significant. However, the incremental effects on the bid level of moving from quartile 1 to quartile 2, from quartile 2 to quartile 3, and from quartile 3 to quartile 4 are not statistically significant. Also, the difference between the coefficients on the first three quartile dummies is not statistically significant. These results suggest that marginal returns to positive reports are severely decreasing, and that bidders are quickly convinced of a seller s honest intentions, so that reports beyond the first few have little effect on bid amounts. Again, the qualitative results are not sensitive to changes in how the positive reports are categorized or to the exclusion of controls, and they are robust to the inclusion of time effects. 28 placed, though the estimated effect of the first 1 to 25 reports is not statistically significant. Also, note that the exclusion restrictions in the selection equation (the minimum bid controls) have statistically significant effects. 28 If dummy variables indicating the week in which the auction was held are included in the regressions, the estimates of the coefficients of POS1 POS4 are 22.20, 31.83, 41.79, and 44.45, respectively, and the effect of the first quartile of positive reports becomes statistically significant at the 5% level. Previous studies of the effect of reputation in Internet auctions have consistently found that positive reports have little or no impact on the choice of how much to bid. For example, Melnik and Alm (2002) find that doubling the seller s feedback rating (positive reports minus bad reports) from 452 to 904 will increase the winning bid by only $0.18, for a good where the mean price was $ This result is representative of the other studies, though most do not find a statistically significant effect on the level of bids. Eaton (2002) and Resnick and Zeckhauser (2002) do find that reputation has a significant effect on the probability that an auction results in a sale. Each of these studies follows a strategy similar to the one adopted here: they look at the effect of reputation in auctions of a particular kind of good, such as collectible coins or electric guitars. These papers may underestimate the effect of reputation on the winning bid level because they use restrictive functional forms to control for reputation that do not capture strong returns to the first few reports. In the specifications of each of these papers, the number of positive reports or ebay s feedback rating enters the equation linearly or log-linearly. 29 The small returns estimated by assuming a linear or log linear relationship most likely reflect the small marginal returns gained after several positive reports have already been received. In fact, if we estimate a log linear specification with the data set used here, similar results are obtained. Table 6 presents these estimates. The estimated return to positive reports is very small and statistically insignificant, regardless of the estimation procedure used. The returns to reputation are also underestimated if the incidental truncation problem is not controlled for properly, though not nearly as severely as when an overly restrictive specification of positive reports is used. Consider first what happens when the problem is not controlled for. In the OLS estimates, which are presented in column 1 of table 4, the effect of the first quartile of positive reports is statistically insignificant at any reasonable level of confidence, and the coefficient estimates for the first, second, third and fourth quartiles are 11%, 24%, 24%, and 26% lower than the 29 Eaton (2002), McDonald and Slawson (2002), and Resnick et al. (2002) try different specifications as well. Eaton splits the sample into groups where the seller has a feedback rating of less than 40, from 40 to 100, and more than 100. He still finds no impact of reputation on the level of bids. McDonald and Slawson include dummy variables that indicate whether the seller was in the 90th percentile of ebay s feedback rating, and whether the seller s feedback rating is lower than the median. They calculate that sellers in the 90th percentile earn 3.67% more than sellers with a rating of 0. Resnick et al. (2003) conducted a field experiment where matched pairs of vintage postcards are sold by a seller with over 2000 positive reports under his own well-established identity and under a new identity. The analysis looks at the difference between the log winning bids of these pairs. The new identities gain reports over the course of the experiment, so the established ID is compared with both IDs that have no reports and IDs that have some positive reports. They find that bids were 8.1% higher in the auctions run using the experienced ID than in those run by the new IDs, for an item where the average winning bid $ Each of these specifications lumps sellers who have no history in with sellers who have a somewhat established history, so they do not capture the early initial gains to reputation that I find.

12 464 THE REVIEW OF ECONOMICS AND STATISTICS Variable TABLE 6. COMPARISON WITH RESULTS OF PREVIOUS WORK OLS (1) Tobit (2) Sample Selection Model: Bid Amount Equation (3) Selection Equation (4) LNPOS (0.006) (0.008) (0.006) (0.046) LNBAD ** * (0.013) (0.016) (0.012) (0.105) ln (COMPET) (0.020) (0.025) (0.020) (0.158) CC (0.017) (0.022) (0.017) (0.138) LATE *** ** (0.074) (0.090) (0.073) (0.462) PRIME (0.021) (0.027) (0.021) (0.168) WEEKEND (0.019) (0.024) (0.019) (0.139) LENGTH *** 0.039* 0.542*** (0.024) (0.028) (0.024) (0.186) LENGTH *** *** (0.020) (0.024) (0.021) (0.150) LENGTH * 0.147*** 0.085** 0.597** (0.037) (0.046) (0.037) (0.288) ln (RETAIL) 0.784*** 0.656*** 0.771*** (0.083) (0.107) (0.082) (0.749) NEW 0.199*** 0.201*** 0.204*** (0.018) (0.023) (0.018) (0.148) LEFT 0.280*** 0.245*** 0.281*** (0.053) (0.071) (0.052) (0.481) SENIOR *** *** (0.055) (0.042) (0.055) (0.431) LADIES 0.103* 0.128* 0.102* (0.059) (0.077) (0.059) (0.496) SECRES 0.056*** ** 0.929*** (0.017) (0.021) (0.018) (0.155) MBDL ** (0.484) MBDH *** MBDH2 (0.415) 3.284*** (0.418) Intercept * (0.565) (0.725) (0.560) (5.118) Observations R Standard errors in parentheses. * Significant at 10%; ** significant at 5%; *** significant at 1%. corresponding FIML estimates, respectively. Using a tobit model instead of a sample selection model also underestimates the effect of reputation. If the decision to place a bid is affected by different concerns, either observed or unobserved, than the decision of how much to bid, then the estimates from the tobit model will be biased. In fact, there is evidence that there is some difference in the unobserved factors affecting each decision. If these factors were the same, then, the correlation between u and v (the unobserved factors affecting the winning bid amount and the participation decisions, respectively), would be equal to 1. It is estimated to be only 0.66, and the upper limit of the 95% confidence interval of this estimate is Estimation of a tobit model does in fact produce different estimates of how much more bidders bid if the seller has a better reputation, particularly for the effect of the first 25 reports. These results are presented in column 2 of table 4. The effect of the first 25 positive reports is not statistically significant at any reasonable level of confidence, and the coefficient estimates for the first, second, third, and fourth quartiles are 27%, 10%, 18%, and 8% lower than the corresponding FIML estimates, respectively. VII. Conclusion A long-standing claim in economics has been that contracts can be self-enforced using reputation as a motivation. Sellers who value future payoffs highly may choose to perform in order to establish a reputation for behaving honestly. If instead they establish bad reputations, future buyers will not be willing to transact with them. Using data from Internet auctions, the analysis examines how positive reports about a seller s past behavior affect the probability that his auction will receive at least one bid, the probability that his auction will result in a sale, and the amount of the winning bid. The results are dramatic. If the seller has even a few positive reports, then the chance that the auction receives a bid, the chance that the auction results in a sale, and the amount of the winning bid all increase substantially. These early reports are apparently enough to largely convince bidders that the seller tends to perform, because the returns to additional positive reports are not nearly as strong. These effects are strong enough that they could encourage sellers to perform out of a fear of losing future payoffs. Sellers may not experience a large loss of payoffs due to the occasional misunderstanding, but if they accumulate more bad reports they would have to abandon their identity and start trading anew as a seller with no established record. Sellers with no history do not enjoy outcomes that are as good as those enjoyed by sellers who have an established track record. Early work on Internet auctions has found that a seller s reputation has a surprisingly small impact on bidder behavior. These studies typically assume that the relationship between the winning bid and the seller s reputation is log linear. The theoretical model presented in section II shows that there can be severely decreasing returns to additional positive reports, and the empirical results show that marginal returns to positive reports are initially strong but decrease at an extremely fast rate. Specifications that posit a log linear relationship most likely find that reputation has a small effect on bid amounts because they only capture the small marginal returns gained after several positive reports have already been received. Further, the studies may not correctly control for sample selection bias in estimation of the bid amount equation. Because of these differences, the analysis presented here shows that a seller s reputation is much more valuable than has been previously estimated.

13 HOW VALUABLE IS A GOOD REPUTATION? 465 REFERENCES Amemiya, Takeshi, Advanced Econometrics (Oxford, UK: Basil Blackwell, 1985). Bajari, Patrick, and Ali Hortacsu, Economic Insights from Internet Auctions, Journal of Economic Literature 42:2 (2004), Bockstael, Nancy E., Ivar E. Strand Jr., Kenneth E. McConnell, and Firuzeh Arsanjani, Sample Selection Bias in the Estimation of Recreation Demand Functions: An Application to Sportfishing, Land Economics 66:1 (1990), Bower, Anthony G., Steven Garber, and Joel C. Watson, Learning about a Population of Agents and the Evolution of Trust and Cooperation, International Journal of Industrial Organization 15 (1996), Eaton, David H., Valuing Information: Evidence from Guitar Auctions on ebay, Murray State University working paper (2002). Houser, Daniel, and John Wooders, Reputation in Auctions: Theory, and Evidence from ebay, University of Arizona mimeograph (2000). Kaufman, Robert J., and Charles A. Wood, What Makes a Buyer Pay More for the Same Item in Internet Auctions? University of Minnesota Management Information Systems Research Center mimeograph (2001a). Running Up the Bid: Modeling Seller Opportunism in Internet Auctions, University of Minnesota Management Information Systems Research Center mimeograph (2001b). Livingston, Jeffrey A., What Attracts a Bidder to a Particular Internet Auction? (pp ), in M. Baye (Ed.), Advances in Applied Microeconomics, Vol. 12: Organizing the New Industrial Economy (Oxford, UK: Elsevier Ltd., 2003). Lucking-Reiley, David, Doug Bryan, Naghi Prasad, and Daniel Reeves, Pennies from ebay: the Determinants of Price in Online Auctions, Vanderbilt University mimeograph (2000). McDonald, Cynthia G., and V. Carlos Slawson, Jr., Reputation in an Internet Auction Market, Economic Inquiry 40:3 (2002), Melnik, Mikhail I., and James Alm, Does a Seller s ECommerce Reputation Matter? Evidence from EBay Auctions, Journal of Industrial Economics 50:3 (2002), Milgrom, Paul, and Robert Weber, A Theory of Auctions and Competitive Bidding, Econometrica 50:5 (1982), Resnick, Paul, and Richard Zeckhauser, Trust among Strangers in Internet Transactions: Empirical Analysis of ebay s Reputation System, in M. Baye (Ed.), The Economics of the Internet and E-Commerce (Amsterdam: Elsevier Science, 2002). Resnick, Paul, Richard Zeckhauser, John Swanson, and Kate Lockwood, The Value of Reputation on ebay: A Controlled Experiment, University of Michigan working paper (2002); edu/ presnick/papers/postcards/. Roth, Alvin E., and Axel Ockenfels, Last Minute Bidding and the Rules for Ending Second-Price Auctions: Theory and Evidence from a Natural Experiment on the Internet, Harvard University mimeograph (2000). Tirole, Jean, A Theory of Collective Reputations (with Applications to the Persistence of Corruption and to Firm Quality), Review of Economic Studies 63 (1996), Vickrey, William, Counterspeculation, Auctions, and Competitive Sealed Tenders, Journal of Finance 16:1 (1961), 8 37.

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