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.
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.
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.
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.
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.
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.
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.
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.
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
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