HOW VALUABLE IS A GOOD REPUTATION? A SAMPLE SELECTION
                 MODEL OF INTERNET AUCTIONS
                        ...
454                                     THE REVIEW OF ECONOMICS AND STATISTICS

   The insights gleaned from this model gu...
HOW VALUABLE IS A GOOD REPUTATION?                                                                              455

winni...
456                                                                           THE REVIEW OF ECONOMICS AND STATISTICS

    ...
HOW VALUABLE IS A GOOD REPUTATION?                                                                     457

have the same ...
458                                         THE REVIEW OF ECONOMICS AND STATISTICS

      TABLE 1.—VARIABLE DEFINITIONS   ...
HOW VALUABLE IS A GOOD REPUTATION?                                                                  459

payment by credit...
460                                                    THE REVIEW OF ECONOMICS AND STATISTICS

              TABLE 2.—MARG...
HOW VALUABLE IS A GOOD REPUTATION?                                                                     461

additional imp...
462                                       THE REVIEW OF ECONOMICS AND STATISTICS

where w * represents the value of placin...
How Reputation
How Reputation
How Reputation
How Reputation
Upcoming SlideShare
Loading in …5
×

How Reputation

529
-1

Published on

Published in: Business, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
529
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
6
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

How Reputation

  1. 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 There are reasons to doubt that eBay’s reputation mech- ship goods to winning bidders until after they have received payment, so there is an opportunity for sellers to take advantage of bidders’ trust. anism should work. First, rational bidders might not reward Realizing this, the designers of eBay created a system that relies on sellers who establish good reputations, because reports self-enforcement using reputation. Several recent studies have found that about how the seller has behaved may not be credible. 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 Sellers could build a reputation by selling relatively inex- they have behaved honestly, but marginal returns to additional reports are pensive items, and then cheat in auctions of more expensive severely decreasing. goods. For example, a seller with a history of over six I. Introduction thousand properly conducted transactions sold hundreds of porcelain collectibles on January 4, 2002, but did not send T HE Internet auction site eBay provides a valuable opportunity to study how reputation can be used to encourage self-enforcement of contracts. On eBay, by con- the winners anything after receiving payments of approxi- mately $300,000.3 Also, a clever seller can fake positive reports by assuming a different identity, bidding enough to vention, sellers do not send goods to winning bidders until win his own auction, and leaving a good rating. Second, after they have received payment. The seller can simply bidders have no incentive to leave reports, because doing so pocket the money, or send an item of poor quality. A takes time, but adds nothing to their payoffs. However, in a consumer who is defrauded by a seller has little recourse, sample of 36,233 eBay auctions, Resnick and Zeckhauser because the identity of a seller is known only through an (2002) find that bidders left reports 52% of the time. Third, email address, which can be anonymously obtained.1 punishments might not be severe enough to encourage Rather than formally enforcing contracts between buy- honest behavior. All a seller loses by cheating is the benefit ers and sellers, eBay relies on mechanisms of self- of a previously established reputation. Sellers who breach enforcement.2 It allows winning bidders to post ratings of contracts are not banned from eBay, for they can easily sellers’ actions that can be positive, neutral, or negative, as create a new identity. well as comment on the transaction. This information is also Thus, the goal of this study is to examine whether bidders presented as a feedback rating that is equal to the number of do reward sellers who establish better reputations, and to positive reports, minus the number of negative reports. quantify those rewards if they do exist. The analysis is Potential bidders can use this information to form expecta- guided by a theoretical model of bidder behavior. A seller tions about how the seller will behave in the future. Sellers who ruins his reputation can start over as a new seller who may find it in their interest to fulfill agreements, because has yet to establish a transaction history. Both the model and future bidders may not trust a seller with a history of the empirical analysis therefore measure how much sellers treating buyers poorly. For self-enforcement to work, bid- would lose if their reputation were ruined, by examining ders must respond strongly enough to better reputations to how bidders react to sellers who have established a reputa- make the seller’s long-term benefits from being honest tion for acting honestly, relative to sellers who have no outweigh the short-term gains from cheating. reports about their behavior. Bidders make two decisions that influence the seller’s expected payoffs. If bidders are Received for publication September 25, 2002. Revision accepted for more willing to participate in the auctions of sellers who publication December 20, 2004. * Bentley College. have received positive reports, then the auction is more I thank Peter Murrell and Bill Evans for guidance and many helpful likely to result in a sale. If they bid more when they do comments and suggestions. Two anonymous referees, Omar Azfar, Peter participate, then revenues given that a sale is made will be Cramton, Mohamed El-Hodiri, John List, Deborah Minehart, Patrick Scholten, and especially the participants of the Maryland graduate student higher. The model predicts that bidders are more likely to microeconomics seminar have also offered helpful comments on this bid, and that these bids will be higher, if a seller has even a paper and previous versions of it. Participants in seminars at Bentley College, Indiana University, Loyola Marymount University, and the Uni- few positive reports. However, these effects are not linear. versity of Pittsburgh also offered useful input. Sean Corcoran offered Once bidders are largely convinced that the seller tends to many fruitful suggestions during the revision process. John Deke offered act honestly, they bid as much and as often as they would if useful advice on data collection methods. Finally, thanks to Matthew Langley and Bidisha Ghosh, who provided excellent research assistance. the sellers did not have an incentive problem. There is no Of course, any remaining errors are my own. room for improvement, so additional reports have little or 1 Sellers are also required to provide a credit card number to confirm no impact on seller welfare. 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 3 Rumors are that the seller had large gambling debts to pay off. See the buyers can use a third party such as escrow service, to enforce the discussion at www.slashdot.org: http://slashdot.org/comments.pl?sid transaction. Escrow services are usually used only for transactions where 28414&cid 3054010; for the full discussion of this incident, see http:// the stakes are high, such as for automobiles. slashdot.org/article.pl?sid 02/02/22/1941255&mode thread&tid 98. The Review of Economics and Statistics, August 2005, 87(3): 453–465 © 2005 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology
  2. 2. 454 THE REVIEW OF ECONOMICS AND STATISTICS The insights gleaned from this model guide the empirical II. A Model of Bidder Behavior analysis, which examines a cross-section of auctions of The model is based on the design of eBay. At the Taylor Made Firesole irons, a variety of golf clubs. This beginning of the first period of a seller’s life, he is matched analysis first establishes how a bidder’s participation deci- with a set of N symmetric bidders. The seller transacts with sion is affected by a seller’s reputation. Two probit models those bidders, and the winning bidder reports how the seller are used. The first evaluates whether at least one bid is more behaved. In the next period, the seller is matched with a new likely to be placed if the seller has more positive reports. set of bidders. These bidders update their beliefs about the The second looks at whether an auction is more likely to seller’s type using the report left by the winning bidder from result in a sale if the seller has more positive reports. The the previous period, and the above process is repeated until analysis then examines whether bid amounts are affected the seller dies.5 when a seller’s reputation improves. Because eBay auctions In each period, the seller offers for sale a single item in a are equivalent to second price auctions, the price paid by the sealed-bid, second-price auction.6 Each bidder i values the winning bidder is the second highest bid. Because no object being sold at v i , which is a realization of a random bidders chose to participate in some auctions, data on the variable V i that is independently drawn from a continuous amount of the second highest bid are sometimes unavail- distribution F on support [v , v ]. Valuations are private able. A sample selection model is accordingly used to information. estimate the relationship between a seller’s reputation and When the auction begins, the seller can set a minimum the amount of the second highest bid. allowable bid level M, 7 though this choice is not explicitly The empirical analysis shows that a seller’s reputation modeled and M assumed to be exogenous.8 Bidders then has a substantial impact on the decisions that bidders make. decide whether to place a bid, and if they do, how much to Sellers who have even a few positive reports are more likely bid. The bidders’ actions depend on their beliefs about the than sellers who have no history to receive bids and to have probability that the seller will behave honestly.9 their auctions result in a sale. They also receive higher bids. After bidders move and the auction is completed, the However, reports beyond the first few have a much smaller winning bidder sends payment to the seller, who then impact on the returns to reputation, suggesting that early chooses whether to cooperate with or betray the winning reports are enough to convince bidders of a seller’s honest 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 intentions. Previous work that estimates the returns to reputation in 5 Though it has no effect on the model, for completeness assume that a Internet auctions typically finds that bid amounts barely seller survives until the next period with probability . increase as sellers improve their reputations, if they increase 6 eBay auctions are English auctions where the seller can choose an end at all. This work includes papers by Eaton (2002), Houser date after which no further bids are accepted. eBay uses a feature called proxy bidding that, in theory, makes behavior in the auctions strategically and Wooders (2001), Lucking-Reiley et al. (2000), Mc- equivalent to that in second-price auctions. Using this feature, bidders can Donald and Slawson (2002), Melnik and Alm (2002), 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, Resnick and Zeckhauser (2002), and Resnick et al. (2002).4 unless the next bid is higher than the bidder’s maximum. Lucking-Reiley These studies may underestimate the returns to reputation, et al. (2000) suggest that many bidders do use this feature, though others because they typically assume that the relationship between 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 the winning bid amount and the number of positive reports bidding your true value at the beginning of the auction is one equilibrium received by the seller is linear or log linear. If marginal 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 returns to reputation are severely decreasing, as the analysis auction to submit a bid equal to their true valuation, though the computer presented here suggests, these functional forms may only might not process the bid. They find that bidders do often wait until the pick up the small returns that occur after an initial reputation closing seconds to bid. Regardless of the timing of the bids, both models predict that bidders will eventually try to bid their true value. is established. 7 On eBay, sellers can set both a “minimum bid” M, and a “reserve The paper is organized as follows. Section II presents the 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 model of bidder behavior. The model is used to predict how whether a secret reserve price is being used. Roth and Ockenfels (2000) do a seller’s reputation will affect bidder behavior. These pre- not allow for the choice of a secret reserve price, because they do not want dictions are derived in section III. The data are described in to be distracted by the “additional strategic prospects” that it entails. I follow their lead in the model that follows. section IV. The effect of a seller’s reputation on bidder 8 Sellers would choose M to maximize expected profits. This choice is behavior is estimated in sections V and VI. Section VII left in the background, because the focus is not on how sellers strategically concludes. 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 4 A nice survey and summary of findings of the various papers that have advertised quality? Will the item be shipped in a timely fashion? Regard- explored the link between an eBay seller’s reputation and the returns to less of the bidders’ concern, each potential dilemma results in a decrease reputation can be found in Bajari and Hortascu (2004). in the value a bidder expects to receive if she wins the auction.
  3. 3. HOW VALUABLE IS A GOOD REPUTATION? 455 winning bidder receives the good from the seller. If the Begin with the bidders’ choice of how much to bid. seller plays B t , then the winning bidder receives nothing of Vickrey (1961) examines bidder behavior in second-price worth from the seller. The winning bidder earns a positive auctions of the variety studied here, where bidders are payoff if C t is played, but a negative payoff if B t is played, risk-neutral and they have independent private values. He because the money sent to the seller is lost.10 shows that it is a dominant strategy for bidders to bid their Sellers have only two possible types, honest (H) or true values when there is no possibility that the seller will dishonest (D). Nature chooses the seller’s type. For simplic- cheat by playing B t . Now consider what happens if sellers ity, assume that the seller’s move is determined by his can play B t . It can be shown that a similar result is true: type.11 H-type sellers play C t with probability and B t with bidders optimally bid their expected value of the good. probability 1 , and D-type sellers play C t with proba- Because H-type sellers play C t with probability , D-type bility and B t with probability 1 . H-type sellers are sellers play C t with probability , and the bidder receives 0 assumed to be more likely to cooperate than D-type sellers, value if the seller plays B t , bidder i’s expected payoff given so 0 1. that she wins the auction is [ p t (1 p t )]v i . Here After the seller plays either C t or B t , the winner can [ pt (1 p t )]V i is the random variable from which report whether the seller was honest. On eBay, bidders can bidder i’s expected value is drawn. If each V i is replaced leave either “positive,” “neutral,” or “negative” reports. To with [ p t (1 p t )]V i in the model of Vickrey (1961) simplify the model, assume that only positive or negative and we allow for the presence of the publicly known reserve reports are possible. I assume that the winner always sub- price M, the proof is identical and still holds. mits a report, that the reports are always accurate, and that The bid function b t (v i , p t ) that results can be written as the reports are not distorted for any strategic reasons.12 The b t v i, p t pt 1 p t v i. (1) 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 Predictably, if bidders feel that a seller will only send the number of positive reports that a seller has received at the object with probability p t (1 p t ), then the bidders beginning of period t, and let n t be the number of negative will shade their bids by that probability. reports that the seller has received at the beginning of period Now consider a bidder’s decision whether to bid. She will t. These reports are used to formulate beliefs about the place a bid if her optimal bid exceeds M: seller’s type, and accordingly beliefs about the chance that the seller will play C t . Let p 1 be the subjective assessment b t v i, p t pt 1 pt vi M. (2) of the probability that the seller is an H-type that each Together, equations (1) and (2) determine the bidders’ bidder identically holds at the beginning of a seller’s life.13 equilibrium behavior. Note that the minimum bid, M, af- Similarly, let the bidders’ updated assessments at the begin- fects the participation decision in equation (2), but not the ning of period t be p t . decision how much to bid in equation (1). Also, the way the The equilibrium is completely specified by calculating bidders behave is affected by p t (the belief about the seller’s the optimal decisions that each pool of bidders makes in type) in two ways: through equation (2) it affects their each period. We can think of the model as a game between decision about whether they want to place a bid, and a set of bidders and nature, which randomly chooses the through equation (1) it affects the level of their bids, if they type of the seller. The model is solved via backward induc- do decide to bid. How p t is formed is described next. tion. In period 1, bidders base their decisions on their initial subjective belief about the probability p 1 that the seller is an 10 More generally, one could assume that the value that the bidder H-type. Depending on the seller’s type, he plays either C 1 or receives if the seller plays B t is a proportion of what she receives if he plays C t : Let V iH be the random variable from which bidder i’s value is B 1 , and the winning bidder reports on how the seller drawn if the seller plays C t , and V iL be the random variable from which behaved. In period 2, a new pool of bidders confronts the bidder i’s value is drawn if the seller plays B t . Then V iL V iH, where 0 seller. These bidders update their beliefs about the seller’s 1. 11 This simple model is used in order to examine how bidder behavior type using the report from the previous period according to will be effected by a seller’s reputation, rather than the complex dynamics Bayes’ rule. So long as the seller remains in the market, the that govern how a rational seller will choose to behave given the bidders’ same process repeats in following periods, where the new strategies, and vice versa. 12 In fact, there is no strategic reason to submit a report at all. Reports are prior belief is equal to the posterior belief from the previous not always submitted in practice. The model can take into account this period. Generally, in period t, a bidder’s belief that the seller possibility. If no report is left, then the bidders in the next period have no is an H-type is new information, so they simply do not update their beliefs. 13 I do not model how bidders form the initial subjective beliefs. The gt nt beliefs will be based on the bidders’ perceptions of the proportion of 1 p1 H-type agents in the population. Let p* be the true proportion of H-type pt gt, nt, t gt nt gt nt . (3) 1 p1 1 1 p1 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 Combining equations (1) and (3), the bid function in period Bower, Garber, and Watson (1996) and Tirole (1996). t becomes
  4. 4. 456 THE REVIEW OF ECONOMICS AND STATISTICS gt 1 (1 )ntp1 pt bt vi, pt gt pt 1 p t ln ln 0, (9) (1 )ntp1 gt (1 )nt(1 p1) gt (4) gt 1 (1 ) n t(1 p 1) so gt nt gt v i, (1 ) p1 (1 ) n t(1 p 1) b t v i, p t v ip t 1 p t ln ln 0. gt and combining equations (2) and (3), bidder i submits a bid Therefore, bid amounts increase if g t , the number of posi- if tive reports held by the seller, increases. gt 1 (1 )ntp1 However, marginal returns to positive reports will not be gt constant. The rate at which the bid level increases with g t is (1 )ntp1 gt (1 )nt(1 p1) found by taking its second derivative with respect to g t : gt 1 (1 nt ) (1 p1) (5) gt (1 nt ) p1 gt (1 )nt(1 p1) vi M. 2 bt vi, pt pt pt2 ln ln vi gt2 gt gt Analysis of equations (4) and (5) generates predictions about how bidders react to reports about a seller’s transac- pt ln ln vi 1 2pt , tion history. gt 0 III. Predictions of the Model so On eBay, sellers who ruin their reputations can sell under a new identity. Therefore, the model should predict how 1 bidder decisions will evolve if the seller receives a positive 0 if pt , 2 report in every period, starting from the beginning of the 2 bt , pt 1 i seller’s history. The model predicts that returns to the first 2 0 if pt , (10) few positive reports can be large, but at some point marginal g t 2 returns to reports will begin to decrease. Once bidders 1 0 if pt . become largely convinced that the seller is an H-type, there 2 is little room for improvement, so further positive reports will have little effect on bidder behavior. The reaction of b t (v i , p t ) to changes in g t depends on the To see this, consider first how the bid changes if the perception at the start of the period of the probability that number of positive reports, g t , increases. Because g t enters the seller is an H-type. If more positive reports are received, 1 into b t (v i, pt) only through p t , we have [ b t (v i , p t )]/ g t b t (v i , p t ) increases at an increasing rate if p t 2 , but at a 1 ( )v i p t / g t . Using logarithmic differentiation, we decreasing rate if p t 2 . Once the bidders are more than have 50% sure that the seller is an H-type, the marginal impact of positive reports on the bid amount begins to decrease. Returns pt ln pt will decrease more and more severely as pt approaches 1, pt , (6) because bidders will never bid more than their valuations. gt gt This result suggests that if the first few reports largely where convince bidders that the seller is an H-type, the majority of the gains to reputation will accrue to the first few positive ln pt gt ln nt ln 1 ln p1 reports. Once bidders are convinced that a seller is an (7) gt nt gt nt H-type, further positive reports will have little or no impact ln 1 p1 1 1 p1 . on bid amounts, because there is little room for improve- ment. The econometric specifications will be structured in a Let D g t (1 ) ntp 1 g t (1 ) n t(1 p 1 ). Then way that is able to capture this effect. gt Now consider the bidders’ decisions whether to place a ln pt (1 )n tp1 bid in a seller’s auction. Recall that equation (2) shows that ln ln gt D bidder i will place a bid if gt (8) (1 ) n t(1 p 1) b t v i, p t pt 1 pt vi M. ln . D A bidder will participate if her optimal bid exceeds the Recalling the definition of p t and 1 p t , substituting minimum allowable bid, so if b t (v i , p t ) increases, equation equation (8) into (6) yields (2) is more likely to be satisfied. Therefore, changes in g t
  5. 5. HOW VALUABLE IS A GOOD REPUTATION? 457 have the same impact on the chance that an individual who gain additional positive reports, relative to sellers who bidder participates as they have on the decision how much have yet to establish a trading history. to bid. Accordingly, if a seller receives a string of positive Ideally, dummy variables would be used to identify the reports and M does not change from period to period, the marginal impact of each additional positive report, but the probability that a bidder chooses to place a bid increases in data set is not rich enough to allow that specification. each successive period. The rate at which this probability Instead, the sample distribution of the number of positive increases may be increasing or decreasing, depending on the reports held by the seller in each auction is divided into prior belief that the seller is honest, and most of the gains quartiles, and dummy variables are created that indicate from having a good reputation may come with the first few whether an auction falls into each quartile. The first quartile reports. is further divided by splitting off auctions where the seller It should be noted that these are predictions about how has zero positive reports into a separate group. POS0 is a individual bidders will react to reports about a seller’s dichotomous variable that takes a value of 1 if the seller has reputation. The empirical analysis looks at how these re- zero positive reports. POS1 takes a value of 1 if the auction ports affect aggregate, not individual, behavior: the proba- is in the remainder of the first quartile of the number of bility that at least one bid is received, the probability that an positive reports received. Auctions where POS1 equals 1 auction results in a sale, and the amount of the winning bid. will still be referred to as the first quartile, though the reader These predictions are useful, however, in that aggregate should keep in mind that this group is not the true first behavior will react in the same way that individual behavior quartile, for it excludes auctions where the seller has no reacts, because bidders are identical in every aspect other positive reports. POS2–POS4 take a value of 1 if the auction than the draws of their valuations. If a seller receives an is in the second through fourth quartiles of positive reports additional positive report, then individual bidders will be received, respectively. Auctions for which POS0 equals 1 more likely to be willing to place a bid, so it will be more make up 8% of the sample. Sellers have few reports in most likely that an auction will receive at least one bid, and more auctions. The auction at the 25th percentile has a seller with likely that an auction will result in a sale. Also, each only 25 positive reports. The other quartiles cover much individual bidder will raise her optimal bid, so the amount broader ranges of positive reports received. The auctions at of the second highest bid (which is equal to the winning bid) the 50th, 75th and 100th percentiles have sellers with 175, will increase. 672, and 8035 positive reports, respectively. Negative and neutral reports are also included in the IV. Data empirical analysis. NNRATIO is the fraction of reports that a seller has received that are neutral or negative. There are To test the predictions of the theoretical model, from few such reports in the sample. The mean of NNRATIO is October 20, 2000 through August 20, 2001, data were only 0.02, and its standard deviation is only 0.06.15 collected from 861 eBay auctions of Taylor Made Firesole Previous work tests for the effect of reputation by includ- irons, a variety of golf clubs. Table 1 presents definitions ing either the logarithm of eBay’s feedback score or the and summary statistics for the variables used in this study. logarithm of the number of positive reports, plus 1 to avoid The unit of observation is a single auction. The dependent taking the logarithm of 0 (LNPOS). These specifications variables capture whether a bid was placed in an auction, control for bad reports in the same way, using the logarithm whether the auction resulted in a sale, and the winning bid of the number of negative reports. I include LNBAD, the in each auction. YESBIDS takes a value of 1 if at least one logarithm of the sum of neutral and negative reports plus 1, bid was placed in an auction, and SOLD takes a value of 1 in order to capture the effect of all bad reports. if the auction resulted in a sale. At least one bidder submit- The theoretical model presented above shows that the ted a bid in 85% of the auctions, and 68% of the auctions minimum allowable bid (MINBID) should affect the partic- resulted in a sale. TOTPRICE, the effective level of the ipation decision, but not the decision of how much to bid. It winning bid, is equal to the winning bid, plus shipping shows that a bid will be placed if the optimal bid of the charges.14 Prices are high enough for bidders to be con- bidder with the highest valuation exceeds the minimum bid. cerned about seller fraud. The mean price paid, including Higher minimum bids may also discourage bidders from shipping charges, was $409.96. placing a bid for another reason. Vickrey’s model assumes The reported history of the seller is the critical explana- that the auction occurs in isolation, but in reality, typically tory variable. As sellers who receive negative reports can many auctions of Taylor Made Firesole irons are active at begin anew on eBay under a new identity, I examine the effect of reputation by looking at how bidders reward sellers 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 14 Sellers usually choose a fixed shipping price that the bidder must positive reports. In the data, sellers who have more bad reports than agree to before placing a bid, but occasionally they require bidders to pay average also have far more positive reports than average (the correlation “actual shipping charges,” which are not specified. In this case, shipping between positive reports received and neutral or negative reports received charges are taken to be the median of the fixed price charged in the rest of is 0.8), because sellers who sell hundreds or thousands of items are bound the sample, which is $15. to have occasional misunderstandings with their customers.
  6. 6. 458 THE REVIEW OF ECONOMICS AND STATISTICS TABLE 1.—VARIABLE DEFINITIONS AND SAMPLE CHARACTERISTICS TABLE 1.—(CONTINUED) Mean and Mean and Variable (Standard Variable (Standard Name Definition Deviation) Name Definition Deviation) Dependent Variables WEEKEND 0-1 dummy variable that equals 1 if the 0.26 auction ends on a weekend (0.44) YESBIDS 0-1 dummy variable that equals 1 if at least 0.85 LENGTH3 0-1 dummy variable that equals 1 if the 0.17 one bid is placed in an auction (0.36) auction lasts 3 days (0.37) SOLD 0-1 dummy variable that equals 1 if 0.68 LENGTH5 0-1 dummy variable that equals 1 if the 0.18 auction resulted in a sale (0.47) auction lasts 5 days (0.39) TOTPRICE Highest bid in an auction, plus shipping 409.96 LENGTH7 0-1 dummy variable that equals 1 if the 0.45 charges (84.69) auction lasts 7 days (0.50) LENGTH10 0-1 dummy variable that equals 1 if the 0.06 Reported History of Seller auction lasts 10 days (0.23) RETAIL Retail price of clubs 855.09 POS0 0-1 dummy variable that equals 1 if seller 0.08 (79.97) has 0 positive reports (0.27) NEW 0-1 dummy variable that equals 1 if the 0.44 POS1 0-1 dummy variable that equals 1 if seller 0.17 clubs being auctioned are new (0.50) has 1–25 positive reports (first quartile (0.38) LEFT 0-1 dummy variable that equals 1 if the 0.02 of positive reports received, less those clubs being auctioned are left-handed (0.15) with 0 reports) SENIOR 0-1 dummy variable that equals 1 if the 0.03 POS2 0-1 dummy variable that equals 1 if seller 0.25 clubs being auctioned are for seniors (0.16) has 26–175 positive reports (second (0.43) LADIES 0-1 dummy variable that equals 1 if the 0.02 quartile of positive reports received) clubs being auctioned are for ladies (0.12) POS3 0-1 dummy variable that equals 1 if seller 0.25 SECRES 0-1 dummy variable that equals 1 if a 0.47 has 176–675 positive reports (third (0.44) secret reserve price is used (0.50) quartile of positive reports received) POS4 0-1 dummy variable that equals 1 if seller 0.25 has more than 675 positive reports (0.43) (fourth quartile of positive reports received) any given time, so bidders have a choice about which NNRATIO Fraction of reports that are negative or 0.02 auction they want to participate in. Livingston (2003) argues neutral (0.06) that higher minimum bids discourage bidders from placing LNPOS log (number of positive reports 1) 4.73 (2.29) bids in a particular auction, because other auctions that have LNBAD log (number of neutral and negative 1.14 lower minimum bids may offer better chances to obtain the reports 1) (1.12) same item for a lower price. To capture this effect, I identify Other Variables Affecting Participation Decision the other auctions of Firesole irons that either were active at the time an auction ended or ended on the same day, find the MINBID Minimum-allowable bid (chosen by seller) 234.30 average minimum bid used in those auctions (MBMEAN), (185.44) MBMEAN Average minimum bid among other 213.04 and calculate the difference between an auction’s minimum auctions that were either active at the (51.50) bid and this average (MBDIFF). Auctions are then catego- time the auction ended or ended on the rized by this difference: those that use minimum bids that same day MBDIFF Difference between MINBID and 21.26 are less than the average minimum bid used by competitors, MBMEAN (180.10) and those that use minimum bids that are at least as high as MBDL1 0-1 dummy variable that equals 1 if 0.23 the average used by competitors. These categories are fur- MBDIFF is less than $153.13 (0.42) MBDL2 0-1 dummy variable that equals 1 if 0.23 ther divided at the category median minimum bid differ- MBDIFF is at least $153.13 but less (0.42) ence. MBDL1 equals 1 if the difference is less than than 0 $153.13, MBDL2 equals 1 if the difference is at least MBDH1 0-1 dummy variable that equals 1 if 0.27 MBDIFF is at least 0 but less than (0.45) $153.13 but less than $0, MBDH1 equals 1 if the differ- $167.50 ence is at least $0 but less than $167.50, and MBDH2 equals MBDH2 0-1 dummy variable that equals 1 if 0.27 1 if the difference is at least $167.50. MBDIFF is at least $167.50 (0.44) Previous work controls for other differences among the Controls for Auction, Item, or Market Heterogeneity auctions. I include these variables to make the analysis as comparable as possible to this work. If more auctions of COMPET Number of other auctions of the same good 33.84 in progress at the time the auction ended (9.85) Firesole irons are in progress at the time the auction ends, CC 0-1 dummy variable that equals 1 if the 0.52 the added competition may draw bidders away and drive the seller allows payment by credit card (0.50) market price down. COMPET is the number of other auc- LATE 0-1 dummy variable that equals 1 if the 0.01 auction ends between midnight and (0.12) tions of Firesole irons that either were active at the time the 4:00 A.M. Pacific time auction ended, or ended on the same day. Allowing buyers PRIME 0-1 dummy variable that equals 1 if the 0.17 to pay by credit card makes payments instantaneous, so the auction ends between 3:00 P.M. and (0.38) 7:00 P.M. Pacific time 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. 7. HOW VALUABLE IS A GOOD REPUTATION? 459 payment by credit card. Auctions that end in late hours of w* 1 p tv t M 0. As discussed, this decision may be the day may not receive as much activity. LATE equals 1 if more complicated than described by our simple model that the auction ends between midnight and four o’clock A.M. auctions do not actually occur in isolation. The bidder’s Pacific Daylight Time. Similarly, auctions that end in prime optimal bid and the level of the minimum bid will play a shopping hours may receive more activity. PRIME equals 1 role, but other factors may come into play when a bidder if the auction ends between three and seven o’clock P.M. decides whether to participate. To try to capture the influ- Pacific Daylight Time.16 Auctions that end on the weekend ence of some of these factors, w * is now assumed to be a 1 may also receive more activity. WEEKEND equals 1 for linear function of observed variables z, where the vector z auctions that end on a weekend. Finally, sellers can run includes 1, POS1, POS2, POS3, POS4, NNRATIO, COM- auctions that last either 3, 5, 7, or 10 days. More bidders PET, CC, LATE, PRIME, WEEKEND, LENGTH5, may observe and participate in auctions that run longer, so LENGTH7, LENGTH10, RETAIL, NEW, LEFT, SENIOR, the winning bid may be higher. LENGTH3, LENGTH5, LADIES, MBDL2, MBDH1, MBDH2, and SECRES. LENGTH7, and LENGTH10 equal 1 if the auction lasts 3, 5, The model has the form 7, or 10 days, respectively. Finally, sellers can set a secret reserve price, as well as the minimum bid level. Bidders w* 1j zj εj , j 1, 2, . . . , n, (11) know whether a secret reserve price is being used, but they do not know what the price is. SECRES equals 1 if the and w 1i is defined as follows: auction uses a secret reserve price. Firesole irons vary along a few observable characteristics. 1 if w* 1j 0, Data are collected on these differences. The retail price of w 1j 0 if w* 0, j 1, 2, . . . , n. (12) 1j the clubs (RETAIL) captures several differences that affect the value of the clubs.17 NEW takes a value of 1 if the set of The probability that at least one bid is placed in auction j is clubs is new, not used. New clubs have more value than used clubs. Also, the market may be segmented in that some prob w1j 1 prob εj zj golfers have different characteristics, and some submarkets (13) may be thinner than others. Dummy variables indicate 1 zj zj , whether the clubs are left-handed (LEFT), senior (SENIOR), or ladies clubs (LADIES). where ε j is N(0,1) and is the cumulative distribution function of the standard normal distribution. V. Effect of a Seller’s Reputation on Bidders’ The results of estimating this model are presented in Participation Decisions column 1 of table 2. Positive reports have statistically and economically significant effects on the chance that a bidder Are bidders more willing to place a bid if a seller has a participates in a seller’s auction, but the first few reports good reputation? The model predicts that an individual have a much larger effect on this probability than later bidder is more likely to place a bid if the seller has more reports do. The probability that a bid is placed is 0.034 positive reports. Therefore, the probability that a seller higher if the seller has from 1 to 25 positive reports than in receives any bids, as well as the probability that the seller’s auctions with sellers who have yet to receive a positive auction results in a sale, should increase as he gains addi- report. This probability is 0.046 higher for auctions where the tional positive reports. However, at some point there should seller has from 26 to 175 positive reports, 0.051 higher where be severely decreasing marginal returns to additional posi- the seller has from 176 to 672 positive reports, and 0.087 tive reports. higher where the seller has more than 672 positive reports, than To test these hypotheses, I estimate the relationships as to the probability for auctions where the seller has no positive probit models. According to the theoretical model presented reports. To put these effects in perspective, in the sample, the above, at least one bid will be placed if the optimal bid of observed probability of receiving a bid is 0.85 across all the bidder with the highest valuation exceeds the minimum auctions. The returns to reports are severely decreasing. allowable bid. Let w * represent the unobserved expected i Column 1 of table 3 presents likelihood ratio tests of the difference between the high bidder’s optimal bid and M. hypotheses that higher quartiles of positive reports have an Assume bidder i has the highest valuation. Then according additional effect on the probability that at least one bid is to our theoretical model, a bid should be received if received. They show that the estimated coefficients on the first three positive-report-quartile dummy variables are not 16 Previous studies, such as McDonald and Slawson (2002), also based statistically significantly different from each other, suggest- the coding of these variables on Pacific time. 17 These differences include the type of shaft the club has (graphite, ing that after the first 25 reports have been received, the next SensiCore, or steel), and the number of clubs included in the set. A large several hundred reports have no effect on the chance that at majority of the sets include a pitching wedge through a 3-iron, but a seller least one bidder places a bid. The coefficient on the fourth 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 quartile of positive reports received is significantly different extra items any time one was included. from the coefficients on the other three quartiles, however.
  8. 8. 460 THE REVIEW OF ECONOMICS AND STATISTICS TABLE 2.—MARGINAL EFFECTS OF POSITIVE REPORTS TABLE 3.—DO HIGHER POSITIVE REPORT QUARTILES HAVE ADDITIONAL ON PARTICIPATION DECISION EFFECTS ON PARTICIPATION DECISIONS? Independent Pr(at Least One Bid Received) Pr(Sale) Pr(at Least One Variable (1) (2) Bid Received) Pr(Sale) (1) (2) POS1 0.034** 0.209*** (0.014) (0.049) LR p- LR p- POS2 0.046*** 0.175*** Null Hypothesis Statistic Value Statistic Value (0.015) (0.056) POS3 0.051*** 0.294*** Quartile 1 coeff. quartile 2 coeff. 0.83 0.363 1.06 0.302 (0.016) (0.047) Quartile 1 coeff. quartile 3 coeff. 1.79 0.180 3.99 0.046 POS4 0.087*** 0.240*** Quartile 1 coeff. quartile 4 coeff. 16.55 0.000 0.33 0.565 (0.020) (0.052) Quartile 2 coeff. quartile 3 coeff. 0.32 0.573 11.05 0.001 NNRATIO 0.148* 0.005 Quartile 2 coeff. quartile 4 coeff. 13.15 0.000 2.94 0.087 (0.084) (0.263) Quartile 3 coeff. quartile 4 coeff. 10.33 0.001 2.41 0.121 COMPET 0.001 0.002 Coefficients on first 3 quartiles are equal 1.83 0.400 11.18 0.004 (0.001) (0.002) Coefficients on all quartiles are equal 18.05 0.000 11.24 0.011 CC 0.024* 0.159*** (0.014) (0.035) LATE 0.003 0.010 (0.055) (0.137) PRIME 0.024 0.035 inclusion of time effects in the model.19 There is little (0.020) (0.042) WEEKEND 0.006 0.017 change in the results if different specifications that exclude (0.013) (0.039) some of the controls are used. LENGTH5 0.009 0.118** The effect of reputation on a seller’s expected returns (0.019) (0.057) LENGTH7 0.026 0.242*** depends on whether sellers who have better reputations are (0.017) (0.042) more likely to have their auctions result in a sale. Auctions LENGTH10 0.030 0.232*** may receive bids but not result in a sale if the seller sets a (0.039) (0.086) RETAIL 0.00003 0.00001 secret reserve price R that is not met. In the terms of our (0.00008) (0.0002) theoretical model, an auction will result in a sale if p t v i NEW 0.029* 0.105*** max(M, R) for at least one bidder. A probit model that is (0.016) (0.040) LEFT 0.071 0.079 similar to the one specified above can also be estimated. (0.093) (0.119) These results are reported in column 2 of table 2. Sellers in SENIOR 0.255* 0.033 the first quartile of positive reports received are 21 percent- (0.132) (0.100) LADIES 0.024 0.025 age points more likely than sellers with zero positive reports (0.064) (0.128) to successfully sell their goods, sellers in the second quartile SECRES 0.072*** 0.300*** are 18 percentage points more likely, sellers in the third (0.020) (0.039) MBDL2 0.043 0.053 quartile are 29 percentage points more likely, and sellers in (0.053) (0.049) the fourth quartile are 24 percentage points more likely. MBDH1 0.210*** 0.203*** Relative to the mean of 68% of auctions that resulted in a (0.074) (0.054) MBDH2 0.422*** 0.313*** sale, these are large effects. But again, although the first few (0.091) (0.056) positive reports have a large impact on the probability that N 861 861 an auction results in a sale, there is strong evidence that the Pseudo R 2 0.39 0.14 marginal returns to additional positive reports are severely Standard errors in parentheses. decreasing. Column 2 of table 3 presents likelihood ratio * Significant at 10%; ** significant at 5%; *** significant at 1%. 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 Still, these results suggest that there are returns of approx- quartile dummies are the same is rejected, we cannot reject imately 3.4 percentage points to just the first 1 to 25 reports, the null hypotheses that the coefficient on quartile 1 is no but several hundred more reports must be received before different from the coefficient on quartile 2, quartile 3, or the chance of receiving a bid goes up by another 5.3 quartile 4, implying that reports beyond the first 25 have no percentage points, so the marginal return for each individual report beyond the first 25 must be extremely small. The 26 to 50 reports, 51 to 100 reports, or more than 100 reports were qualitative results of these estimates are robust to changes in received; and dummy variables indicating the quartile of positive reports the definitions of the positive report categories,18 and to the 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 18 I tried specifications that categorized the positive reports in many specification mentioned, even the first positive report appears to have a different ways, each time using auctions where no positive reports were large effect on the probability of sale and the winning bid amount. received as the reference group. Some of the specifications I tried include 19 If dummy variables indicating the week in which the auction was held dummy variables indicating the deciles of positive reports; dummy vari- are included in this regression, the estimates of the marginal effects of ables indicating whether 1 to 5 reports, 6 to 10 reports, 11 to 25 reports, POS1–POS4 are 0.029, 0.042, 0.040, and 0.064, respectively.
  9. 9. HOW VALUABLE IS A GOOD REPUTATION? 461 additional impact on the probability of sale.20 Again, these The previous section shows that bids may not be placed results are not sensitive to changes in how the positive if the seller has yet to establish a reputation or if the reports are categorized or to the exclusion of controls from minimum bid level is set too high. In eBay auctions, the the specification, and they are robust to the inclusion of time winner pays an amount equal to the second highest bid effects.21 received, so the recorded amount of the second highest bid Two other parameters are of interest. A larger percentage is equal to the minimum bid if either no bids or one bid is of neutral or negative reports reduces the probability that at placed. Therefore, the amount of the second highest bid is least one bid is received (the test is significant at the 10% censored when fewer than two bids are placed. Models that level), but appears to have no effect on the probability that do not control for this fact will produce biased estimates of the auction results in a sale. The difference between the the effect of reputation. Some previous studies of reputation minimum bid and the average minimum bid used by other in Internet auctions, including Eaton (2002), Kaufman and active auctions of the same item, which is to be used as an Wood (2001a, 2001b), McDonald and Slawson (2002), and exclusion restriction in the sample selection model of the Resnick and Zeckhauser (2002) use models that do not address amount of the winning bid that follows, has a significant this problem. To demonstrate the bias that results from not effect on both the probability that a bid is received and the probability that the auction results in a sale. I argued controlling for this problem, I estimate the relationship be- previously that auctions that use high minimum bids relative tween positive reports and the winning bid amount by OLS, to other auctions of the same item will receive fewer bids, using only observations where at least two bids were re- because bidders may take their business to the auctions that ceived.22 OLS estimates of this relationship will be biased appear to offer a better chance of obtaining the good for a because observations where the seller has few positive reports lower price. This argument is supported by the data. In the will only have data on the bid level if some unobserved factor sample, at least one bid was placed in 99% of the auctions pushes at least two bidders’ optimal bids above the minimum where the minimum bid was less than the average minimum bid, so that two or more bids are placed. Other observations, bid used by competitors, but in only 73% of auctions where where the seller has a weak reputation but no such factor the minimum bid was more than the average used by boosted the bids, will not have data on the bid level. Hence, competitors. This effect is also seen in the regressions. within the sample of observations, the number of positive Auctions that used minimum bids that were more than the reports is inversely correlated with the error term, so OLS average used by competitors were much less likely to estimates of the effect of reputation will be downward biased.23 receive a bid than auctions that used minimum bids that For reasons that will be discussed shortly, to eliminate were more than $150.13 below average. If the minimum bid this bias, the problem is treated as an incidental truncation is at least as high as the average among competitors but less problem rather than a censoring problem, so a sample than $167.50 more, the auction is 21 percentage points less selection model is estimated. The sample selection model is likely to receive a bid. If the minimum bid is at least $167.50 specified as follows. Let b * be the recorded amount of the j more than the average, the auction is 42 percentage points less second highest bid in auction j. Then b * is assumed to be a j likely to receive a bid. Relative minimum bids had a similar linear function of observed variables x, where the vector x effect on the chance that an auction results in a sale. includes 1, POS1, POS2, POS3, POS4, NNRATIO, COMPET, CC, LATE, PRIME, WEEKEND, LENGTH5, LENGTH7, VI. Effect of a Seller’s Reputation on the Decision LENGTH10, RETAIL, NEW, LEFT, SENIOR, and LADIES. of How Much to Bid The model has the form A seller’s expected returns depend not only on the prob- ability that his auction results in a sale, but also upon the b*j xj uj , amount of the winning bid, given that a sale occurs. The w* zj vj , (14) 2j theoretical model presented earlier predicts that an individ- ual bidder will place a larger bid if the seller has more b* if w* j 2j Mj , bj Mj if w* Mj , j 1, 2, . . . , n, positive reports. Therefore, the winning bid (which is equal 2j to the second highest bid) should also increase if the seller 22 To be clear, this regression uses all observations where at least two gains additional positive reports, although there should be bids were received, regardless of whether the auction resulted in a sale. So severely decreasing returns to these reports. 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 20 However, as an anonymous referee points out, we would expect these reserve price. results to be more noisy than the results on whether a bid is received, 23 Relative to models that do take account of the censoring problem, because whether a sale occurs depends upon whether at least one bid OLS will underestimate the effect of reputation, because the observations exceeds the secret reserve price, which we do not observe. We only that are not used by the OLS estimator, but are used by models that control observe whether one is in use. for censoring, have lower numbers of positive reports as well as more 21 If dummy variables indicating the week in which the auction was held negative error terms, so there is less opportunity to observe the larger are included in this regression, the estimates of the marginal effects of winning bids that result from additional positive reports. I thank an POS1–POS4 are 0.212, 0.196, 0.279, and 0.219, respectively. anonymous referee for pointing this out.
  10. 10. 462 THE REVIEW OF ECONOMICS AND STATISTICS where w * represents the value of placing a bid to the bidder 2j TABLE 4.—MARGINAL EFFECT OF POSITIVE REPORTS ON SECOND HIGHEST BID with the second highest valuation, z is as previously de- Sample Selection Model fined,24 M j is the minimum bid used in auction j, and (u j , v j ) Bid Amount Selection are i.i.d. draws from a bivariate normal distribution with Independent OLS Tobit Equation Equation Variable (1) (2) (3) (4) zero mean, variances 2 and 2 , covariance uv, and cor- u v relation . As noted by Amemiya (1985), setting b j equal to POS1 18.14 14.99 20.42* 0.27 (11.19) (11.75) (10.96) (0.24) M j when it is censored has no effect on the likelihood POS2 24.27** 28.66** 31.78*** 0.50** function, and merely signifies the event w * 2j M j . 25 (10.91) (11.45) (10.75) (0.24) Studies such as Lucking-Reiley et al. (2000), Melnik and POS3 28.21*** 30.38*** 37.18*** 0.48** (10.89) (11.54) (10.74) (0.24) Alm (2002), and Resnick et al. (2002) do address the sample POS4 31.77*** 39.35*** 42.82*** 0.95*** selection problem using tobit models, treating the minimum (10.89) (11.63) (10.84) (0.27) bid as a censoring point below which the true winning bid NNRATIO 0.57 41.39 2.92 0.62 (42.93) (41.54) (42.61) (1.04) would fall.26 The tobit model is a special case of the sample COMPET 0.46* 0.36 0.49* 0.01 selection model that constrains the selection equation to be (0.25) (0.27) (0.25) (0.01) CC 7.46 7.85 7.41 0.20 identical to the equation of interest. When u v, 1, (5.15) (5.55) (5.10) (0.13) x z, and , the sample selection model is equivalent LATE 4.70 52.62** 17.06 1.10** to the tobit model (Bockstael et al., 1990). If any of these (22.60) (22.25) (22.11) (0.45) PRIME 0.63 4.21 0.11 0.07 conditions does not hold, then the sample selection model (6.51) (6.86) (6.43) (0.16) should be used instead of tobit. These conditions will hold WEEKEND 1.61 3.83 2.06 0.17 if bidders do decide whether to participate in an auction (5.77) (6.06) (5.68) (0.13) LENGTH5 2.69 22.05*** 8.55 0.55*** purely according to whether their optimal bids exceed the (7.32) (7.66) (7.40) (0.18) minimum bid, as suggested by our theoretical model. How- LENGTH7 7.30 17.49*** 4.73 0.48*** (6.30) (6.41) (6.39) (0.15) ever, their decisions are likely more complex than indicated LENGTH10 14.60 35.63*** 26.44** 0.62** by our simple model, so the true selection equation might be (11.30) (11.78) (11.26) (0.28) quite different from the true bid amount equation. First, RETAIL 0.41*** 0.36*** 0.40*** 0.001 (0.03) (0.03) (0.03) (0.001) there may be unobserved factors that affect the participation NEW 81.50*** 82.79*** 83.05*** 0.02 decision, but do not affect the bid amount decision, so (5.50) (5.82) (5.42) (0.14) may be less than 1. Second, the minimum bid should affect LEFT 58.33*** 49.78*** 58.04*** 0.15 (16.19) (17.77) (16.07) (0.43) the selection equation but not the winning bid amount SENIOR 0.33 44.17*** 6.68 1.13*** equation, so z and x may not be identical. As argued (16.85) (16.80) (16.65) (0.41) LADIES 44.86** 47.46** 42.59** 0.33 previously, higher minimum bids may drive bidders away to (18.27) (19.71) (18.11) (0.48) other auctions of the same item that are also accepting bids. SECRES 16.41*** 4.59 5.86 0.92*** Accordingly, the selection equation should control for this (5.33) (5.73) (5.52) (0.16) MBDL2 1.15** possible effect. However, the minimum bid should not (0.48) appear in the bid amount equation, for bid amounts theo- MBDH1 2.22*** retically do not vary with publicly known reserve prices. (0.40) MBDH2 3.44*** The tobit model does not allow for this specification. Be- (0.40) cause there may be both unobserved and observed factors Intercept 35.40 26.12 11.17 0.51 (29.38) (31.63) (29.21) (0.90) that affect the selection equation but not the bid amount equation, the constraints of the tobit model may result in N 615 861 861 861 biased estimates of the return to reputation. R2 0.52 The sample selection model is estimated using full- Standard errors in parentheses. * Significant at 10%; ** significant at 5%; *** significant at 1%. information maximum likelihood (FIML). The parameters of the model can be estimated by maximizing the following likelihood function: L P w* 2j Mj f bj w* 2j Mj P w* 2j 0. (15) bj Mj bj b* j 24 Recall that z includes MBDL2, MBDH1, and MBDH2 as exclusion The results of the estimation are presented in table 4. restrictions, because we expect that the minimum bid level will effect the selection equation, but it theoretically has no effect on bid amounts. Column 3 reports the results of the estimation of the bid 25 Note carefully that an observation is not incidentally truncated if no amount equation, and column 4 reports the results of the sale occurs, so long as at least two bids are received. Even if the secret estimation of the selection equation.27 On average, sellers 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. 27 The results from the selection equation are also interesting. The 26 Houser and Wooders (2001) have a small data set of 94 observations selection equation examines the probability that an auction receives at where at least one bid was placed in each auction, so they argue that the least two bids. The effects that positive reports have on this probability are sample selection issue is not relevant for their data. similar to the effects they have on the probability that at least one bid is

×