What Attracts Bidders to Online Auctions and What is
Their Price Impact?
Michaël Dewally*
Louis Ederington**
June 2006
Initial Draft: June 2004
*Assistant Professor of Finance
Marquette University
College of Business Administration
Straz Hall, 318
P.O. Box 1881
Milwaukee, WI 53201-1881
Tel: (414) 288-1442
Fax: (414) 288-5756
[email protected]
**Micheal F. Price Professor of Finance
University of Oklahoma
Price College of Business
Adams Hall, 205
Norman, OK 73019-4005
Tel: (405) 325-5591
Fax: (405) 325-7688
[email protected]
What Attracts Bidders to Online Auctions and What is Their Incremental Price Impact?
Abstract
Based on eBay auctions of classic comic books, we explore what attracts bidders to
individual online auctions. Seventy percent of the variation in the number of bidders across
auctions is predictable based on characteristics of the item for sale, the seller, and the auction
design. Not surprisingly, high minimum bids discourage bidders while longer auctions attract
slightly more. We also find that the presence of a secret reserve price sharply reduces the number
of bidders while third party certification attracts more. Seller reputation as measured by
feedback ratings has a statistically significant impact on the number of bidders. Overall, our
results support the hypotheses that bidding is fairly costly and that bidders value transparency.
Holding issue, seller, and auction characteristics constant, an additional bidder is associated with
a price increase of between 2.3% and 4.3%. While secret reserve prices sharply reduce the
number of bidders, they have little impact on what individual bidders are willing to bid while
third party certification of the auctioned item increases both the number and level of bids. On the
other hand, the condition of the item being auctioned has a relatively minor impact on the
number of bidders but strongly impacts their bids.
What Attracts Bidders to Online Auctions and What is Their Price Impact?
1. Introduction
Online auctions play an increasing role in the United States economy. According to a 2003 ISM /
Forrester Research report, 72% of business respondents purchased goods or services on the Internet and
25% did so through an Internet auction. 42% of firms buying more than $100 million per year used online
auctions for some purchases. Sales on eBay totaled almost $21.5 billion in the first half of 2005.
Based on a sample of over 5000 eBay auctions of classic comic books, this paper explores what
attracts bidders to a specific on-line auction and the impact on the price received by the seller of an
additional bidder. The number of bidders varies widely in comic book auctions. In our data set 20.4% of
the auctions fail to attract a single bidder while 21.8% attract eight or more. We find that over seventy
percent of the variation in the number of bidders across individual auctions is predictable based on
characteristics of the comic, the seller, and the auction design. Not surprisingly, high minimum bids
discourage bidders. In addition, the presence of a secret reserve price strongly discourages bidding.1 All
other things equal, we find that the number of bidders is sharply lower on auctions with reserve prices - by
about 1.6 bidders on average. While secret reserve prices scare off bidders, we find they have little impact
on what individual bidders are willing to bid. The claimed condition or grade of the comic has a significant
impact on the number of bidders but a much larger impact on what they are willing to bid. On the other
hand, certification of the claimed grade by a rating agency strongly impacts both the number of bidders
(attracting roughly one more bidder on average) and their individual bids. Both the number of bidders and
their bid amounts are significantly impacted by the reputation of the seller as reflected in feedback ratings.
Money back guarantees attract slightly more bidders (roughly .3) while failure to provide a scan discourages
bidders (roughly .5). Not surprisingly, longer auctions attract more bidders with a 10 day auction attracting
about .7 more bidders than a ten day auction.
Overall, our results support the hypothesis that bidding is costly since bidders seem to restrict their
bidding to auctions in which the likelihood of success is higher. As evidenced by the fact that they avoid
1
auctions with secret reserve prices and flock to auctions where the claimed condition or grade of the comic
is certified by a third party, bidders also appear to strongly prefer fully transparent auctions.
Holding issue, seller, and auction characteristics constant, we find that the arrival of an additional
bidder is associated with an increase in the final price of between 2.3% and 4.2%. In common value
auctions, if bidders fully adjust for winners’ curse and the number of competing bidders is known, then an
increase in the number of bidders (beyond two) should not impact the price since existing bidders should
reduce their bids to adjust for the increased likelihood that the winning bidder has over-estimated the value
of the item. Our finding that the price increases with the number of bidders suggest that either 1) comics are
partially a private value item, 2) bidders do not fully adjust for bidders curse, and/or 3) bidders cannot fully
predict the number of competing bidders.
The remainder of the paper is organized as follows. In the next section, we briefly describe the
comic book market and eBay auctions and review the relevant literature. In section 3, we describe our data.
In 4, we develop our empirical tests of the determinants of the number of bidders. Results are presented in
section 5. In 6 we explore the impact of the number of bidders on the price. Section 7 concludes the paper.
2. Collectible Comics and eBay Auctions.
2.1 The Market for Collectible Comic Books.
This paper investigates bidder behavior in the on-line auction market for collectible comics books
from what is generally referred to as comics’ “Silver Age”, the period from 1956-1969 when super heroes,
such as Spider-Man, ruled supreme. This is the most active collectible comics market. For instance, on
August 16, 2004, eBay had 17,176 auctions underway in Silver Age comics, versus 5,409 for comics
published before 1956 and 14,216 for comics published from 1970-1980. Since the comic’s condition is a
major determinant of its price, the marketplace has established a grading structure recognizing 24 grades
according to such characteristics as tears, creases, paper condition, cover gloss and condition of the spine.
Major grades are: Poor, Fair, Good, Very Good, Fine, Very Fine, Near Mint and Mint. Such intermediate
2
grades as Fine+, Fine-, and Fine/Very Fine round out the 24 grades. Traditionally, dealers price Good and
Fine comic books at roughly 10% and 25% respectively of the price of a Near Mint book.
In an Internet auction (or mail order sale) the would-be-buyer is obviously at a greater informational
disadvantage than in a dealer’s shop since distance prevents the buyer from personally inspecting the book.
Hence, bidders must rely on some combination of the seller’s reputation, possible warranties, scans and/or
third party certification to resolve the quality uncertainty and avoid a lemons problem. As described in
Dewally and Ederington (2006), for a fee which ranges from $20 to $55, Comics Guarantee LLC (CGC) will
grade and certify a comic. To maintain the integrity of its certification, CGC encases the comic in plastic.
Opening the casing invalidates the certification.
2.2 eBay Auctions.
The growth of the Internet, and eBay in particular, has transformed the markets for collectibles
including classic comic books. On August 16, 2004 when over 17,000 Silver Age comic books were up for
auction on eBay, Amazon’s Silver Age category had 2,413 listings and Yahoo! 374 auctions. In designing
an eBay auction, the seller sets four parameters: (1) the starting time and length of the auction (3,5,7 or 10
days), (2) the minimum acceptable bid, (3) the acceptable means of payment (money order, credit card,
personal check), and (4) shipping charges if any. The seller can also include scans of the comic book, offer
a money back guarantee, and/or set a secret reserve price (for a fee).
eBay auctions are variations of Vickrey’s second price sealed bid auction in that the winner pays the
second highest bid plus a set increment. Bidders choose a reservation price, and the eBay computer then
enters the minimum bid (below this reservation price) which will lead the bidding. For example, suppose a
seller posts an item with a minimum acceptable bid of $100. Suppose the first bidder, A, enters a
reservation price of $110. The eBay computer posts A as the highest bidder at $100.00. If bidder B enters
the bidding with a reservation price of $125, she becomes the high bidder at $112.50 – A’s reservation price
plus the preset $2.50 increment. If B had instead set a maximum of $105, A would have remained the high
bidder at $107.50 – B’s limit plus $2.50. Hence, the winner pays the reservation price of the second highest
3
bidder plus a small increment. Given this pricing scheme, minimum bids and reserve prices essentially
introduce an additional bidder into the process.
2.3 Previous Research.
Online auctions have been the subject of considerable research in recent years, (for excellent
reviews see Bajari and Hortaçsu, 2004, and Anandalingam et al, 2005). While most have focused on the
impact of seller and auction characteristics on the price received, most relevant for our study are those
exploring determinants of the number of bidders. McDonald and Slawson (2002) (Barbie dolls), LuckingReiley et al (2000) (coins), Bajari and Hortaçsu (2003) (coins) and Livingston (forthcoming) (golf clubs) all
find evidence that sellers with positive feedback ratings attract slightly more bidders, though Livingston
finds that after a couple of positive feedback ratings additional positive feedbacks have little incremental
impact. While McDonald and Slawson and Lucking-Reiley et al find that high minimum bids discourage
bidders, results are mixed on the impact of a secret reserve price. Livingston finds that the propensity to bid
is significantly higher when a reserve price is present. In Lucking-Reiley et al the estimated impact of a
secret reserve on the number of bidders is positive but insignificant while in Bajari and Hortaçsu, it is
negative but insignificant. This is surprising since our evidence indicates a very strong negative impact.
Evidence is also mixed on whether longer auctions attract more bidders. Lucking-Reiley et al find that they
do while McDonald and Slawson find no significant difference. To our knowledge, no one has examined
whether third-party certification or money-back guarantee’s attract more bidders or how the number of
bidders varies with the claimed condition or grade and the predicted price.
An issue has been whether on-line bidding is costly. While there are no explicit costs to bidding on
eBay, there could well be considerable time costs in researching the item and seller and dealing with sellers.
If costs are very low, then we should observe bidders entering all auctions in which the current high bid is
below what they are willing to pay. If costly, they should only enter where the chance of success is
reasonably high. Livingston’s evidence supports the latter hypothesis.
4
A second issue we consider is how the entry of an additional bidder impacts the price received. This
depends on both the nature of the item being auctioned and whether bidders fully adjust for winners curse.
If 1) the item being auctioned is a public value item (meaning that its value to all bidders is its market
value), 2) bidders fully adjust for winner’s curse, and 3) bidders know how many competitors they are
bidding against, then the entry of a new bidder should not impact the final price. Briefly the reason is that as
the number of bidders increases, the likelihood that the winning bidder over-estimates the value of the item
rises. Thus, rational bidders should lower their bids as the number of competitors rises.
Winners curse has received considerable attention in the literature. Based on a structural
econometric model, Bajari and Hortaçsu (2003) estimate that bidders bid 10% below their ex-ante estimate
of the value of the collectible coin for sale. Consistent with adjustment for winner’s curse, they estimate
that the expectation of one additional bidder causes existing bidders to lower their bids by about 3.2%. Yin
(2004) finds that successful eBay bidders paid more than the estimated value in only 9% of the auctions
indicating that participants in computer auctions on eBay adjust for the winner’s curse. Consistent with the
other two studies, Jin and Kato (2002) find that in baseball card auctions bidders adjust their bids in an
effort to avoid the winner’s curse. Contrary to the other authors though, they conclude that this adjustment is
insufficient to prevent winners from overpaying.
While extant empirical studies focus on whether individual bidders adjust their bids for winner’s
curse, we examine how the final auction price varies as the number of bidders increases. In common value
auctions, as the number of bidders increases, existing bidders should lower their individual bids leaving the
expected selling price unchanged. A finding that the price increases with the number of bidders indicates
that either (1) the auctioned item has a private value component, (2) some bidders fail to fully adjust for
winner’s curse, or (3) bidders do not know when an additional bidder enters so fail to fully adjust.
5
3. Data
Data were collected on Ebay auctions of the 30 Silver Age comic books listed in Table 1 over two
periods: January 12, 2001-June 23, 2001 and June 1, 2002 to July 25, 2002 eliminating books sold through
eBay’s buy-it-now option, comics identified as restored, and auctions with incomplete data.2 Figures on the
number of bidders and bids could not be obtained on auctions issues in the 2001 sample leaving us with a
sample of 5275 actions of which 3584 were from the 2001 sample and 1691 from the 2002 sample.
Characteristics of the 30 comics are reported in Table 1.
The average price (which is based on the high bid if the secret reserve price is not met and excludes
auctions with no bidders) is $390 but varies considerably as indicated by the standard deviation of $1143. In
28.4% of the auctions, the claimed quality of the comic is certified by Comics Guaranty Corporation. 15.3%
include a money-back guarantee and 96.6% include a scan of the comic. In 29.4%, the seller sets a secret
reserve price. 79.6% of the auctions attract at least one bidder and 61.9% result in a successful sale.
4. Bids and Bidders.
4.1 Descriptive Data.
In our sample the number of bids and bidders varies widely. The number of bidders averages 5.05
per auction and the median is 4. As shown in Table 2, there is substantial variation. There are no bidders in
20.4% of the auctions and only 1 in 8.1%. On the other hand, there are ten or more bidders in 16.5% of the
observed auctions and more than fifteen in 2.1%. Obviously a bidder may bid more than once. In our
sample the mean number of bids is 8.27 and the median is 7. The bid distribution is also documented in
Table 2. The correlation between bids and bidders is .895.
4.2 Bidders and Auction Design.
We seek to determine what influences the number of bidders for an issue by regressing the number
of bidders on characteristics of the auction, comic, and signals by the seller. The number of bidders and bids
should be dependent on the minimum bid set by the seller. If on the same item, seller A sets a minimum bid
6
of $10 and seller B a minimum bid of $100, a number of bids would normally be required to raise the going
bid for A to the starting point for B. Hence it is important to control for the relationship between the
minimum bid and the number of bidders before examining more interesting possible determinants. What
should matter is the minimum bid as a fraction of the expected value of the comic. In our sample, the price
ranges from a minimum of $1.62 to a maximum of $55,000.00. Much of this price variation is predictable
based on the issue and the comic’s condition. Books graded “near mint” sell for many times the price of
similar books graded lower. As shown in Table 1, price also varies considerably across our 30 comic books
with the first issue of Spider-Man selling for many times the price of the 41st issue.
We estimate an approximate value of each comic based on the issue and claimed grade and then
express the minimum bid as a fraction of this estimated value. For this, we regress the log of the comic’s
auction price (plus 1.0 to avoid negative log values) on zero-one dummies for each of the 30 comics and 22
of the 24 grades (“poor” is the left out group and we observe only one “mint” condition comic so it is
removed). We also include a dummy to designate observations from the 2001 sample. The sample is
restricted to issues which sold. Coefficients of the grade dummies are reported in Table 3. As shown there,
the price increases monotonically with the claimed grade and the estimated price differences are substantial
with “near mint” books selling for over 200 times the price of those in “poor” condition. Prices tend to be
about 14% higher in the 2002 sample. With an adjusted R2 of .928, it is clear that most price differentials
are explained by the issue and the book’s claimed grade.
Using the estimated values of each comic from this regression, we then form the ratio of the seller’s
minimum bid to this estimated value resulting in the RELATIVE_MIN_BID variable. This ratio averages
58.9% and the median is 39.8%. There is considerable variation. In almost one third of the auctions
(32.6%) the minimum bid is 10% or less of the estimated value while in 11.9% the minimum bid exceeds the
estimated value (69% of the later failed to sell). Not surprisingly, since a secret reserve price represents a
secret minimum bid, the public minimum bid is much lower when the auction includes a secret reserve price.
The average minimum bid on issues with a reserve price is 20.1% of the predicted price versus 75.0% on
issues without a secret reserve price. In general, we expect the number of bidders to fall as
7
RELATIVE_MIN_BID increases but we also include the square and cube of this term to capture likely nonlinearities.3
In addition to setting a minimum bid, sellers in an eBay auction may for a small fee also set a secret
reserve price. Both the theoretical and empirical literatures are mixed on how such reserve prices impact the
price received. According to Vincent (1995), a secret reserve price essentially injects an additional bidder
and (as opposed to a public minimum bid) has the advantage of not revealing to bidders the seller’s
evaluation of the asset’s value thus resulting in a higher price. On the other hand, Li and Tan (2000) predict
that in an independent private value framework, it should make no difference whether the seller’s reserve
price is known or not. Empirically, Bajari and Hortaçsu (2003) conclude that reserve prices raise the price
received in eBay coin auctions causing them to wonder why more sellers don’t use them. In contrast
Dewally and Ederington (2006) and Katkar and Lucking-Reiley (2000) find that secret reserve prices lower
the price. As noted above, Livingston (forthcoming) finds that the propensity to bid is significantly higher
when a reserve price is present while Lucking-Reiley et al (2000) and Bajari and Hortaçsu (2003) find no
significant impact.
Despite the previous evidence that reserve prices either increase or have little impact on the number
of bidders, we see a couple of reasons secret reserve prices might discourage bidders. First, questions of
trust and disclosure are important in this market due to the information asymmetry. A seller’s failure to
fully disclose their reserve price may be taken by potential buyers as a signal that they are likely withholding
other information as well. Second, sellers with no intention of selling may run an auction with a very high
secret reserve to gauge the market and estimate the comic’s value. After observing the bids received, the
sellers can then decide whether they want to run a second auction with a more reasonable minimum.
Although Ebay seeks to prohibit such behavior,4 the seller may also contact the highest bidder directly and
attempt to negotiate a higher price. Fearing such behavior, bidders may decide that it is not worth the time
and expense to formulate a bid when they see a secret reserve price. Since there are thousands of comics
and 24 quality grades, estimating the value of a comic and formulating a bid consumes time. When there is
a secret reserve price, a prospective bidder may decide bidding is not worth the effort and turn to auctions
8
without secret reserve prices. To test for such behavior, we include a zero-one dummy, RESERVE, in our
bidder regressions expecting a negative coefficient.
When setting up an auction on eBay, the seller can choose to run the auction for 3, 5, 7 or 10 days.
While intuitively longer auctions should attract more bidders, much bidding occurs in the final hours and
minutes. Indeed, neither Houser and Wooders (2006) nor McDonald and Slawson, Jr. (2002) find any
evidence the auction length impacts the price. However, both Lucking-Reiley et al. (2000) and Dewally and
Ederington (2006) find that longer auctions result in higher prices. Even if they wait until the end to
actually bid, the number of potential bidders who are aware of the auction should be an increasing function
of the auction length. To test for this, we include zero-one dummies, D5, D7, and D10 to designate 5, 7, and
10 day auctions respectively so 3 day auctions are the left-out category. We expect D10's coefficient to
exceed D7's which should exceed D5's.
4.3 Bidders and Signaling.
We also expect the number of bidders to depend on signals of the issue’s quality and the seller’s
reliability. It is often claimed that a big reason for eBay’s success is their feedback system. Obviously
information asymmetry is a problem in online markets since buyers are buying from strangers and cannot
personally examine the items. Online buyers may well wonder whether the item is of the quality claimed
and whether the seller will follow through particularly given the frequent charges of internet fraud. By
constructing a system in which sellers and buyers rate their satisfaction with the counter party’s
performance, eBay both provides a means for bidders to judge the seller’s reputation and an incentive for
sellers to provide good, honest service.
The impact of these feedback ratings on the price is one of the most studied topics in the online
auction literature. Studies fairly consistently find that, ceteris paribus, sellers with established, positive
reputations receive higher prices than those without but estimates of the impact of feedback ratings on the
price vary widely and in several it is slight (Bajari and Hortaçsu, 2004). However, as Melnik and Alm
(2005) point out, in most studies the item being auctioned is fairly homogeneous and of known quality.
9
They find that when there is more uncertainty about the condition of the item up for sale (as is the case
here), reputation matters more.
Feedback ratings have limitations. Since sellers can start over with a different identity, they have
an incentive to defraud customers after building up positive ratings. Consistent with this, Bolton et al (2004)
find that buyers put less trust in feedback ratings from strangers than in their own experience with sellers.
An unsettled question is whether these feedback ratings affect the willingness of potential buyers to
bid or just the price they are willing to pay when they do bid. If bidding entails time and effort, buyers may
decide not to bid if the seller has a poor or meager feedback rating. If bidding is costless, they may lower
their bids but go ahead and bid. Accordingly, we test whether the number of bidders is related to the
feedback rating of the seller. While most price studies include the numbers of positive and negative
feedbacks as separate independent variables, we follow Dewally and Ederington (2006) in separating the
impact of the feedback numbers into measures of 1) how much bidders know about the seller and 2) whether
what they know is good or bad. To measure whether a seller’s reputation is good or bad, we use the percent
of negative feedbacks. Specifically, NEG_PCT = (the number negative feedbacks) / (n+1) where n is the
total number of positive and negative feedbacks.5 The 1 is added to the denominator to avoid dividing by
zero in the case of first time sellers. By this measure, a large majority of sellers have quite positive
reputations. NEG_PCT averages only .54% in our sample and is zero for more than half. To measure how
much bidders know about the seller, we include a proxy for the standard deviation of NEG_PCT. For a
given population of bad experiences, the standard deviation of the sample proportion is roughly proportional
to the reciprocal of the square root of the number of feedbacks (Dewally and Ederington, 2006).
Consequently our proxy for how established the seller’s reputation is is STD_DEV = [1/(n+1)].5 . Based on
the predictions of Bolton et al (2004), we expect the number of bidders to be negatively related to both
NEG_PCT and STD_DEV.
One finding of Bolton et al (2004) is that buyers put more weight on personal experience with
sellers than they do on feedback ratings from strangers. However, building personal experiences with the
thousands of sellers on sites such as eBay is impractical. Third-party certification of the quality of the item
10
is a possible partial solution. Unlike the sellers, certification agencies have no incentive to lie about an
item’s quality and the costs to their reputation are serious. Certifying agencies are common in financial
markets where auditors, investment bankers, and bond rating agencies all perform this role and are now
becoming common in online markets. In the comic book market Comics Guaranty LLC (hereafter CGC)
grades and certifies comic books for fees ranging from $20 to $55.6 However, it is important to note that
CGC only certifies the quality of the comic book. A seller could still fail to deliver. Dewally and
Ederington (2006) estimate that on average certified comics sell for approximately 50% more than noncertified with the same claimed grade with the certification premium rising with the claimed grade. To test
whether certification impacts the number willing to bid for an item, we define CERTIFICATION = 1 if the
comic is certified by CGC (28.4% of our sample) and 0 if not. The hypothesis that certification attracts
more bidders implies a positive coefficient.
Sellers may also attempt to attract bidders by offering buyers a money back guarantee if dissatisfied.
However, Dewally and Ederington (2006) find that such warranties have no discernible impact on the price
and hypothesize that this is because potential buyers view the warranties as costly or impossible to enforce.
Nonetheless we test for a possible impact on the number of bidders by including the dummy
WARRANTY=1 if a money back offer is included (15.3% of our sample) and 0 if not. We also include the
variable NOSCAN if the seller fails to provide a scan of the issue (3.4%). We anticipate a positive
coefficient for WARRANTY and a negative coefficient for NOSCAN.
4.4. Other Variables.
We also anticipate that the number of bidders could depend on the expected price of the comic.
Given the relatively fixed costs of bidding in terms of time and the fixed costs of shipping in terms of
money, we expect less interest in low price/value comics. On the other hand, many collectors may simply be
financially unable to enter market for very expensive comics. In 9.48% of our auctions, the predicted price
based on the issue/grade regression in Table 3 exceeds $1000. We expect interest in such issues to be
limited. Consequently we expect the number of bidders to be a humped function of the predicted price - first
11
rising with the predicted price and then falling. To test this, we include both PREDICTED_PRICE, which is
the estimated price based on the regression in Table 3, and PREDICTED_PRICE2 as independent variables.
Since bidding interest may change over time, we include a zero-one dummy, 2001_SAMPLE, to
designate observations from the earlier, i.e., 2001. sample. Finally, there may simply be more buyer interest
in some issues than others, e.g., more interest in Spider-man than Silver Surfer. To test this, we include
zero-one dummies to represent each of the 30 issues listed in Table 1. The regressions are run both with and
without these 30 dummies.
4.5 Estimation Procedures.
The regressions are estimated using both ordinary least squares and the Poisson count regression
model. Ordinary least squares results have the advantage of easy interpretation, e.g., a coefficient of 1.2 on
a zero-one dummy variable implies that, ceteris paribus, an average of 1.2 more bidders are observed when
this variable takes a value of one. However, since the number of bidders takes only integer values, the
normality assumption does not hold. Consequently, we also estimate a Poisson count maximum likelihood
model, which maximizes the likelihood that the number of bidders is equal to the number actually observed
assuming a Poisson distribution.
5. Bidder Results.
Results are presented in Table 4. As shown there, although the scales differ, the results of the OLS
and Poisson count regressions are quite similar. Since the results of the OLS regressions are easier to
interpret, we focus most of our discussion on those. Adjusted R2 s vary from .67 for the OLS regression
without issue dummies to .71 for the Poisson regression with issue dummies.
According to the estimates in Table 4, the presence of a secret reserve price lowers the number of
bidders by approximately 1.5 to 1.6. Since the mean number of bidders is only 5.05, this represents a
substantial reduction. As explained above, we see two possible explanations. One, this is a market which
relies on trust and transparency. Potential buyers may suspect that if the seller is withholding information
12
about what price she will accept, she is likely withholding information about the comic’s quality or
condition as well. Two, potential bidders may suspect that sellers are conducting a sham auction to gather
information on demand for the item by setting a very high secret reserve price. Since it is possible the item
will not be sold, given the time costs of formulating and submitting a bid, potential bidders may decide it is
not worth the effort.
Bajari and Hortaçsu (2004) question why more sellers don’t set secret reserve prices. Our finding
that they scare away bidders provides an explanation. Indeed, combined with the price results in Dewally
and Ederington (2006), our results raise the question why so many (29.4% in our sample) do. Of course, one
possibility is that they do not recognize that secret reserves scare away bidders. Another, is that, as just
hypothesized, many sellers are using this mechanism to test the market, i.e., they set a very high reserve and
after viewing the results decide to 1) contact the highest bidder and negotiate a higher price, 2) re-auction
the comic with a more reasonable reserve price, or 3) keep in their collection.
Signals sent by the seller also impact the number of bidders. Obtaining certification of the claimed
grade by CGC adds an average of .89 bidders according to the regression without issue dummies and 1.1
according to the regression with issue dummies. Clearly certification by a respected third party affects
buyers’ willingness to bid as well as what they are willing to pay as documented by Dewally and Ederington
(2006).
The number of bidders is also significantly related to how much buyers know about the seller as
measured by the estimated standard deviation of the negative feedback percentage and whether what they
know is good or bad as measured by the percentage of negative feedbacks. Both have significant negative
coefficients as hypothesized indicating that buyers are reluctant to bid if a seller has few feedback ratings
from previous customers and also reluctant if the percentage of negative feedbacks is high. The OLS
regression estimates in Table 4 imply that a rise in the percentage of negative feedbacks from 0% to 3%
(3.8% of the sample have negative feedback percentages 3% or higher) leads to an estimated decrease in the
number of bidders of between .15 and .18. Assuming no negative feedbacks, a increase in the number of
positive feedbacks from zero to ten leads to an estimated increase of .20 to .23 additional bidders and a
13
further increase in positive feedbacks to one hundred adds about .06 to .07 more bidders. So while
statistically significant, the impact of seller reputation on the number of bidders is relatively modest. Of
course this may be partially due to the fact that very few sellers in our sample have poor reputations. For
example only 1.3% have negative feedback ratios above 5%. Failure to provide a scan scares away an
average of about .5 bidders while offering a money back guarantee tends to attract .23 to .35 additional
bidders.
Our evidence indicates that longer auctions attract more bidders. Although only the dummy for ten
day auctions is individually significant at the .01 level, the coefficients increase monotonically as one moves
from 3 day to 5 day to 7 day and finally to 10 day auctions and the three are significant as a group at the .01
level. Ten day auctions tend to attract an average of about .6-.7 more bidders than three day auctions. Thus
although bidding tends to be concentrated in the last few hours and minutes, a longer auction does seem to
have the advantage of causing the item to be noticed by more potential buyers.
As expected, the number of bidders is strongly related to the minimum bid. Over reasonable values
of RELATIVE_MIN_BID (e.g. between 0 and 1.5) the implication is that the number of bidders declines as
the relative minimum bid is increased. Results for PREDICTED_PRICE and PREDICTED_PRICE_SQ
depend on whether or not issue dummies are included in the regression. When issue dummies are excluded,
these variables are significant and imply that the number of bidders increases with the expected price until
the price reaches about $20,000. However these coefficients are small and insignificant once issue dummies
are included suggesting that they are proxying for buyer interest in particular issues. Coefficients of the
issue dummies are not reported in Table 4. The estimated difference between the issue attracting the most
bidders, Amazing Adult Fantasy 15, a key Silver Age issue in which Spider-Man makes his first
appearance, and the issue attracting the least, Silver Surfer 2, is about 3.5 bidders.
In summary, there is strong evidence that adding a secret reserve price discourages bidders while
obtaining third party certification attracts more bidders. There is also evidence that sellers with established
positive reputations attract more bidders than sellers with nascent or negative reputations and evidence that
longer auctions attract more bidders. The finding that reserve prices scare away bidders and that third party
14
certification attracts them, indicates that bidders strongly prefer fully transparent auctions in which all
parameters are known.
6. Bidders and Prices.
Next we explore how the entry of an additional bidder impacts the price received by the seller. As
explained above, if (1) comics book auctions are common value auctions, (2) bidders know how many other
bidders they are bidding against, and (3) bidders recognize and adjust for bidder’s curse, then the final
auction price should not vary with the number of bidders as long as there is at least one competing bidder. If
in a common value auction, individual bidders do not adjust their bids as the number of bidders increases,
then the expected value of the high bid will increase with the number of bidders since it is being drawn from
a larger sample. However, the likelihood that an individual bidder has overestimated the value of the item
given that they win the bidding also increases with the number of bidders. If bidders recognize this winner’s
curse effect, then they should lower their individual bids as the number of bidders increases, offsetting the
impact of the additional bidder on the expected winning bid price.
Violation of any of the three assumptions listed above could cause the number of bidders to
positively impact the price. Comic books could have a private value component. If for instance, a collector
specializes in Silver Surfer comics and a copy of issue #4 would complete his collection, then that comic
may be more valuable to that collector than to the mass of collectors and traders. In this case, an increase in
the number of bidders increases the expected price since it increases the sample of private values from
which the highest is drawn. Likewise, if comics are common value items but bidders fail to recognize and
adjust for winner’s curse, then the price will rise as the number of bidders increases.
A third possibility is that comic books are common value items and bidders recognize and try to
adjust for winner’s curse but do not have full information. In an online auction, It is difficult for a bidder to
determine the number of competing bidders. Some bidders wait until the final minutes of the bidding to
submit their bids in order to keep this information from competitors. Specifically, about 50% of sampled
eBay auctions receive bids in the last 5 minutes and 37% in the last minute. Bidders sometimes hire a
15
service to submit their bids seconds from the auction close. Moreover, early bidders may drop out once the
price has risen. In this situation, we hypothesize that individual bidders will make their winner’s curse
adjustment based on the expected number of competing bidders. An unexpectedly higher (or lower) number
of bidders should then cause the price to rise (fall).
6.1 Structure of the regressions.
We test the impact of additional bidders on the price received by regressing the price received in
online comic auctions on the number of bidders, BIDDERS, and on a series of variables which we
hypothesize should influence what individual bidders are willing to pay. A variable might influence the
price received by the seller either: 1) by impacting the number of bidders and/or 2) by impacting what
individual bidders are willing to pay. Since the number of bidders is one of the independent variables in our
price regression, (assuming our specification is correct) the coefficients of the other independent variables
should estimate their impact on the price holding the number of bidders constant, i.e., their impact on what
individual bidders are willing to bid. We would expect many variables which were included in the bidder
regressions in Table 4 to also impact what individual bidders are willing to pay. For instance, if issue A is
more sought after or popular than issue B, we would expect both the number of bidders and what bidders are
willing to bid to be higher for A. Likewise we would expect third-party certification, which as we have seen
attracts more bidders, to also impact what individual bidders are willing to bid. On the other hand, we
would expect the length of the auction to impact only the number of bidders. And we would expect the
claimed grade to have more impact on the level of individual bids than on the number of bidders.
As in Table 3, our dependent variable is the log of the price (or the highest bid when the item fails to
sell due to a secret reserve price) and, as in the Table 3 regressions, we include the 30 issue dummies and
the 22 dummy variables for the claimed grade. For other independent variables, we draw on the results in
Dewally and Ederington (2006). The CERTIFICATION dummy is included to designate issues whose
claimed quality grade is certified by Comics Guaranty LLC. Since third party certification should mean
more if the claimed grade is high, we also include an interaction dummy CERT_GRADE which is equal to
16
the coefficient of the claimed grade from Table 3 if the issue is certified by CGC and zero otherwise. The
hypothesis that bidders are willing to pay more for certified comics regardless of the claimed grade implies a
positive coefficient for CERTIFICATION while the hypothesis that they are willing to pay more for
certification when the claimed grade is high implies a positive coefficient for CERT_GRADE.
We include the two reputation variables NEG_PCT and STD_DEV. The hypothesis that bidders are
willing to bid more for comics offered by sellers with positive reputations implies a negative coefficient for
NEG_PCT . The hypothesis that bidders are willing to pay more the more certain they are of the seller’s
reputation (whether positive or negative) implies a negative coefficient for STD_DEV.
We include the WARRANTY variable to test the hypothesis that bidders are willing to pay more if
the seller offers a money back guarantee. A positive coefficient is predicted. The variable NOSCAN is
included to test the hypothesis that bidders reduce the price they are willing to pay in those rare instances
when a scan is not provided which implies a negative coefficient. Finally, we include the variable
RESERVE to designate issues on which the seller sets a secret reserve price. By essentially adding an
additional bidder (to those measured by our BIDDERS variable), reserve prices might achieve higher prices
all other things equal. On the other hand, it is conceivable that because they dislike the lack of transparency,
bidders might lower what they are willing to bid on auctions with secret reserve prices. If so, then the
presence of a secret reserve price might impact what bidders are willing to pay as well as their willingness to
bid implying a negative coefficient. Finally we include a dummy, 2001_SAMPLE, to denote observations
from the 2001 sample since prices might rise or fall between the two sample periods.
6.2 Sample Selection Issues
Testing how the price depends on the number of bidders, the reputation variables, and such seller
controlled variables as RESERVE and WARRANTY, is complicated by the fact that some auctions do not
result in a sale either because no one was willing to bid above the public minimum bid price or because none
of the bids exceeded the secret reserve price. The standard procedure in the literature for dealing with these
sample selection issues is two staged. First, when the issue did not sell because no bid exceeded the secret
17
reserve price, the dependent variable is calculated as what the winning bid would have been absent the
reserve price, i.e., the second highest bid plus the standard increment. Second, there may be no sale and no
bids because no one is willing to bid above the specified minimum bid. Because the minimum bid (unlike
the reserve price) is observed, this is handled by estimating a Tobit regression with the minimum bid as the
censoring variable. This is the standard procedure in the literature and that followed here.
7. Results: Bidders and Prices.
Results are presented in Table 5 in the column labeled “Model 1.” To focus on the variables of
interest, we do not report the coefficients of the 23 grade dummies and 30 issue dummies - most of which
are significant. The coefficient of the number of bidders, BIDDERS, is highly significant indicating that
each additional bidder is associated with an increase in the price received of approximately 2.3%. This is a
considerable impact - particularly considering that many of the observed bidders may have only bid early
when the price was low and withdrawn in the final stages of the bidding. These results indicate that either
1) comic book auctions are partially private value auctions, 2) that bidders fail to adjust for winner’s curse,
or 3) that bidders do not know how many competitors they are bidding against. It is also possible that
BIDDERS is proxying for unobserved variables which influence the attractiveness of particular comics.
Results for some of the other variables are also interesting. As noted above, since BIDDERS is
included in the regression, their coefficients should measure their impact on the price holding the number of
bidders constant, i.e., their impact on what individual bidders are willing to bid.
The dummy for the presence of a secret reserve price is small and insignificant. This is interesting
since, as we have seen, the presence of a secret reserve price sharply reduces the number of bidders. We
argued above that the finding that a secret reserve price scares off bidders could be due to either of two
causes: 1) that potential bidders fear the seller is simply using the auction to judge the market so has set an
unreasonably high reserve, or 2) that potential bidders interpret a secret reserve price as indicating that it is
likely that the seller is withholding other information about the comics value as well. The insignificance of
the RESERVE variable in the price regression seems more consistent with the former interpretation. If the
18
presence of a reserve price causes bidders to suspect that the seller is withholding other pertinent
information, we would expect it to lower what individual bidders are willing to pay as well as their
willingness to bid, so a negative coefficient would be expected. On the other hand if bidders fear that the
seller is using a sham auction to judge the market, they would likely be unwilling to entail the cost of
researching the value of the comic and formulating a bid. But, once they have researched the issue and
formulated a bid, these sunk costs should not impact their bid price, so RESERVE should be insignificant in
the price regression. The indirect impact of a secret reserve price on the auction price is substantial.
According to the regressions in Table 4, a secret reserve scares off about 1.5 to 1.6 bidders which combined
with the BIDDERS coefficient of .0232 implies a price reduction of about 3.5%.
While the CERTIFICATION dummy variable is insignificant, the variable CERT_GRADE
representing the interaction of certification and grade is highly significant. The implication is that
certification does not impact the price of a comic if the certified grade of poor or fair but does as the claimed
grade rises. Specifically, the Model 1 estimates imply that certification raises the price of comics graded
good by 17%, those graded very good by 28%, fine by 40%, very fine by 56%, and near mint by 89%.
Although certification attracts more bidders, most of the impact of certification on the price is due to its
impact on what individual bidders are willing to pay. Both reputation variables are significant at the .01
level indicating that these variables impact the prices individual bidders are willing to bid as well as their
willingness to bid. This confirms the finding of Melnik and Alm (2005) that seller reputation is particularly
important when there is uncertainty about the quality or condition of the item for sale.
Turning to the remaining variables, the WARRANTY variable is insignificant. Failure to provide a
scan tends to reduce what bidders are willing to pay by about 13% according to our estimates and prices
were significantly lower in the 2001 period.
In the column labeled “Model 2" we change the measure of the number of bidders. Here we use the
residual from the Poisson count model estimation in Table 4 to measure the number of “unexpected bidders”
given the characteristics of the issue which we label UNEXP_BIDDERS. The estimated coefficient of
UNEXP_BIDDERS is even larger imply each additional bidder raises the price about 4.25%.
19
In summary, our results indicate that the price in an auction varies significantly with the number of
bidders. We find that variables such as certification and reputation impact both potential bidders’
willingness to bid and the prices they are willing to bid if they do but that their major impact on the price is
due to their impact on the latter - the prices individual bidders are willing to bid. However, a secret reserve
price has the opposite pattern, that is, it strongly reduces the number of bidders but has little impact on what
each is willing to bid.
8. Conclusions
Using data from eBay auctions of classic comic books, we have explored what attracts bidders to
online auctions and the impact of additional bidders on the price. We find that over 70% of the variation in
the number of bidders across different auctions is predictable based on characteristics of the issue, the seller,
and the auction design. Not surprisingly, high minimum bids discourage more bidders and longer auctions
attract more.
Importantly we find that the presence of a secret reserve price tends to reduce the number of bidders
in an online auction by about 1.5 to 1.6 bidders, we propose two possible explanations. The first is that
potential buyers fear that the seller has likely set an unreasonably high reserve price in order to gather
information on the item’s market value with no intention of selling so reason that it is not worth the cost of
researching the likely value of the comic and formulating a bid. The second is that potential bidders
interpret a seller’s unwillingness to make his minimum bid public as a signal that the seller is likely
withholding other important information about the comic as well so again are reluctant to bid.
We further find that obtaining third party certification of the claimed grade attracts roughly one
additional bidder on average and that a positive well-established seller reputation attracts more bidders.
We find that each additional bidder tends to increase the auction price by about 2.3% to 4.2%
suggesting that either: 1) comic books have different values to different bidders, i.e., a private value
component, 2) comics books are common value items but some bidders fail to recognize and adjust for
20
winners curse, and 3) bidders try to adjust for winners curse but cannot accurately estimate the number of
bidders.
Finally we find that while variables such as third party certification and seller reputation impact both
how many bidders bid in an auction and how much individual bidders are willing to bid, their major impact
on the price is via their impact on how much individual bidders are willing to bid. The presence of a secret
reserve price is the exception to this rule. It impacts the number of bidders but not what individual bidders
are willing to bid. This is consistent with the hypothesis that there is a cost to researching the value of a
comic and formulating a bid so that if potential bidders fear a reserve price is likely unreasonably high they
may choose not to bid. However, once they have incurred the cost of formulating a bid, this cost is sunk so
does not impact the bid price.
21
REFERENCES
Anandalingam, G., Robert Day, and S. Raghavan, 2005, ‘The Landscape of Electronic Market Design’,
Management Science, vol 51, n3 (March), pp 316-327.
Bajari, Patrick and Ali Hortaçsu, 2003, ‘The Winner’s Curse, Reserve Prices and Endogenous Entry:
Empirical Insights from eBay Auctions’, Rand Journal of Economics, vol. 34, no .2, pp. 329-355.
Bajari, Patrick and Ali Hortaçsu, 2004, ‘Economic Insights from Internet Auctions’, Journal of Economic
Literature, vol. 42, no . 2, pp. 457-486.
Bolton, Gary E., Elena Katok, and Axel Ockenfels, 2004, ‘How Effective Are Electronic Reputation
Mechanisms? An Empirical Investigation,’ Management Science, vol. 50, n11(November), pp.
1587-1602.
Dewally, Michaël and Louis Ederington, 2006, ‘Reputation, Certification, Warranties, and Information
Asymmetries: Lessons from the On-Line Comic Book Market’, Journal of Business, vol 79, n.2
(March), pp 693-729.
eBay, 10Q, May 5, 2004.
Houser, Dan and John Wooders, 2006, ‘Reputation in Auctions: Theory and Evidence from eBay’, Journal
of Economics and Management Strategy, vol 15, n2 (summer), pp 353-369.
ISM/Forrester Report on Technology in Supply Management: Q3 2003, October 2003, by Andrew Bartels,
with Ryan Hudson and Tom Pohlmann.
Jin, Ginger and Andrew Kato, 2002, ‘Blind Trust Online: Experimental Evidence from Baseball Cards’,
working paper, University of Maryland.
Katkar, Rama and David Lucking-Reiley, 2000, ‘Public versus Secret Reserve Prices in eBay Auctions:
Results from a Pokémon Field Experiment’, working paper,University of Arizona.
Livingston, Jeffrey, forthcoming, “What Attracts a Bidder to a Particular Internet Auction, “ Advances in
Applied Microeconomics vol 12: Organizing the New Industrial Economy, Michael Bayne, ed.,
Lucking-Reiley, David, Doug Bryan, Naghi Prasad and Daniel Reeves, 2000, ‘Pennies from eBay: the
Determinants of Price in Online Auctions, working paper, University of Arizona.
22
Melnik, Mikhail and James Alm, 2005, “Seller Reputation, Information Signals, and Prices for
Heterogeneous Coins on eBay,” Southern Economic Journal, vol 72, n.4, pp 305-328.
McDonald, Cynthia and V. Carlos Slawson, Jr., 2002, ‘Reputation in an Internet Auction Market’, Economic
Inquiry, vol. 40, no. 4, Oct. 2002, pp. 633-650.
United States Department of Commerce, Retail E-Commerce Sales, May 21, 2004.
Vincent, Daniel, 1995, ‘Bidding Off the Wall: Why Reserve Prices May Be Kept Secret’, Journal of
Economic Theory, vol. 65, no .2, pp. 575-584.
Yin, Pai-Ling, 2004, ‘Information Dispersion and Auction Prices’, working paper, Harvard Business School.
23
Table 1 - Descriptive Statistics - Ebay Auctions of 30 Classic Comic Books
Statistics for eBay auctions of 30 classic comics from January 12, 2001-June 23, 2001 and June 1, 2002 to
July 25, 2002 are presented. Price figures are based on the sale price or the highest bid (if the minimum bid
or reserve price is not met) and on those auctions attracting a bidder. Grade abbreviations are: Poor: P, Fair:
Fr, Good: G, Very Good: VG, Fine: Fn, Very Fine: VF and Near Mint: NM.
Price
Issue
Auctions
Mean
Median
Median
Grade
Median
Bidders
Median
Bids
Amaz. Adult Fantasy 15
106
$1883
$1425
VG-
8
12.5
Amazing Spider-Man 1
170
$1881
$1125
VG-
7
12
Amazing Spider-Man 14
239
$427
$265
VG+
6
10
Amazing Spider-Man 19
218
$102
$51
VG/Fn
4
6
Amazing Spider-Man 2
111
$485
$311
VG
6
11
Amazing Spider-Man 41
188
$43
$26
VG+
3
4
Amazing Spider-Man 5
150
$281
$129
VG
5.5
9
Avengers 1
159
$397
$224
VG
6
10
Avengers 11
97
$64
$37
Fn-
4
6
Avengers 4
230
$336
$203
Fn-
5
7
Captain America 100
294
$112
$54
Fn
3
5.5
Daredevil 1
179
$597
$294
VG+
7
12
Doctor Strange 169
187
$94
$34
Fn/VF
2
3
Fantastic Four 1
83
$1059
$875
G/VG
7
11
Fantastic Four 3
71
$356
$275
VG/Fn
6
9
Fantastic Four 48
359
$296
$128
Fn
6
9
Incredible Hulk 1
56
$1303
$700
G/VG
8
12.5
Incredible Hulk 6
96
$187
$148
VG
5
7
Iron Man 1
357
$200
$100
Fn/VF
4
7
Iron Man & Sub-Mariner 1
245
$60
$28
Fn
3
5
19
$1889
$1025
VG
7
14
Silver Surfer 1
271
$200
$82
Fn+
4
6
Silver Surfer 2
272
$82
$35
Fn+
1
1
Silver Surfer 4
164
$223
$103
Fn/VF
4
6
Sub-Mariner 1
243
$91
$39
Fn/VF
3
5
Tales of Suspense 39
83
$808
$455
VG+
7
12
The Brave & the Bold 28
91
$357
$313
VG
4
6
X-Men 1
218
$1046
$510
VG
7
11
X-Men 16
140
$42
$27
Fn-
3
4
X-Men 2
179
$319
$163
VG+
4
8
All
5275
$390
$129
VG/Fn
4
7
Showcase 4
Table 2 - Bids and Bidders
Statistics on the number of bids and bidders in eBay auctions of 30 classic comic books over the periods
January 12, 2001-June 23, 2001 and June 1, 2002 to July 25, 2002 are reported.
Bidders
Number
Percent
Cumulative
Percent
Bids
Percent
Cumulative
Percent
0
20.38
20.38
20.38
20.38
1
8.08
28.45
7.41
27.79
2
7.37
35.83
4.32
32.11
3
8.00
43.83
4.53
36.64
4
7.34
51.17
3.91
40.55
5
6.77
57.93
4.08
44.63
6
7.51
65.44
3.55
48.17
7
7.26
72.70
4.45
52.63
8
5.50
78.20
4.06
56.68
9
5.25
83.45
4.40
61.08
10
4.09
87.55
4.15
65.23
11
3.34
90.88
4.15
69.38
12
2.62
93.50
3.24
72.63
13
1.86
95.36
3.68
76.30
14
1.38
96.74
3.37
79.68
15
1.12
97.86
2.75
82.43
16 to 20
1.89
99.75
9.80
92.23
21 to 25
.21
99.96
5.68
96.91
26 to 30
.04
100.00
2.05
98.96
100.00
1.04
100.00
> 30
Table 3 - Basic Price Regression
The log of the sale price in eBay auctions of classic comic books, January 12, 2001June 23, 2001 and June 1, 2002 to July 25, 2002 is regressed on dummies for 23
claimed grades, dummies for 29 comics (coefficients not reported), and a dummy for
observations in the 2001 sample.
Grade Dummy
Coefficient
Standard Error
Fair
.0452
.0620
Fair/Good
.7083
.0691
Good -
.7475
.0694
Good
.9954
.0573
Good +
1.1327
.0639
Good / Very Good
1.2783
.0601
Very Good -
1.3407
.0638
Very Good
1.4776
.0564
Very Good +
1.5977
.0593
Very Good / Fine
1.7747
.0592
Fine -
1.9025
.0643
Fine
1.9611
.0585
Fine +
2.1405
.0607
Fine / Very Fine
2.3425
.0613
Very Fine -
2.6145
.0649
Very Fine
2.6816
.0601
Very Fine +
2.9868
.0639
Very Fine / Near Mint
3.3536
.0633
Near Mint -
3.7678
.0665
Near Mint
4.0665
.0686
Near Mint +
4.7303
.0796
Near Mint / Mint
5.5429
.1913
2001 Sample
-.1404
.0138
Adjusted R2
.9285
Table 4 - Bidder Regressions
The number of bidders in on-line auctions of classic comic book is regressed on characteristics of the
comic book and auction using ordinary least squares and Poisson Count regressions. Regressions both
with and without dummies for the 30 different comics are reported. Standard errors are reported in
parentheses below the coefficient estimates. * and ** denote coefficients which are significantly
different from zero at the .05 and .01 levels respectively. The left out auction length group is three
days.
OLS Regressions
Variable
Intercept
Secret reserve price dummy
(RESERVE)
Without Issue
Dummies
With Issue
Dummies
9.729**
(.104)
Poisson Count Regressions
Without Issue
Dummies
With Issue
Dummies
2.251**
(.016)
-1.518**
(.093)
-1.579**
(.091)
-.243**
(.014)
-.256**
(.014)
0.882**
(.084)
1.096**
(.083)
.185**
(.014)
.213**
(.014)
Percent negative feedbacks
(NEG_PCT)
-5.131**
(1.879)
-6.142**
(1.840)
-.657*
(.308)
-.849**
(.317)
Std. deviation of feedback
percentage (STD_DEV)
-0.297*
(.146)
-.336*
(.143)
-.070*
(.027)
-.088**
(.027)
No scan dummy
(NO_SCAN)
-0.504*
(.204)
-.563**
(.199)
-.175**
(.044)
-.162**
(.044)
Warranty dummy
(WARRANTY)
.234*
(.100)
.350**
(.098)
.065**
(.018)
.078**
(.018)
5 day auctions (D5)
.169
(.233)
.252
(.227)
.053
(.047)
.045
(.047)
7 day auctions (D7)
.351
(.200)
.358
(.195)
.107**
(.041)
.090*
(.041)
10 day auctions (D10)
.688**
(.212)
.650**
(.208)
.153**
(.043)
.123**
(.043)
-15.177**
(.453)
-12.152**
(.196)
-1.628**
(.071)
-1.464**
(.067)
8.135**
(.631)
3.747**
(.110)
-.272**
(.103)
-.419**
(.089)
-1.562**
(.223)
.0002
(.001)
-.068
(.040)
-.040
(.031)
Predicted price ($000)
(PREDICTED_PRICE)
1.159**
(.083)
.040
(.109)
.191**
(.013)
.033*
(.016)
Predicted price squared
(PREDICTED_PRICE2 )
-.076**
(.011)
.009
(.012)
-.013**
(.002)
-.0009
(.001)
2001 sample dummy
(2001_SAMPLE)
-.554**
(.198)
-.545**
(.195)
-.135**
(.041)
-.120**
(.041)
Certification dummy
(CERTIFICATION)
Relative minimum bid
(RELATIVE_MIN_BID)
Relative minimum bid squared
(RELATIVE_MIN_BID2 )
Relative minimum bid cubed
(RELATIVE_MIN_BID3 )
Adjusted R2
.668
.686
.677
.713
Table 5 - Price Regressions
The log of the auction price (or highest bid if a secret reserve was not met) is regressed on
characteristics of the comic book, seller, and auction using a Tobit estimation procedure with the log
of the minimum bid as the censoring variable. Standard errors are reported in parentheses below the
coefficient estimates. * and ** denote coefficients which are significantly different from zero at the
.05 and .01 levels respectively. Not shown are coefficients for dummies for the 23 claimed grades
listed in Table 3 and the 30 issues listed in Table 4.
Variable
Number of bidders (BIDDERS)
Model 1
Coefficients
Model 2
Coefficients
.0232**
(.0015)
Number of unexpected bidders
(UNEXP_BIDDERS)
.0425**
(.0021)
Certification dummy
(CERTIFICATION)
-.0606
(.0376)
.0052
(.0365)
Certification-Grade interaction (CERT_GRADE)
.2328**
(.0159)
.2136**
(.0155)
Percent negative feedbacks on Seller
(NEG_PCT)
-.8684**
(.2736)
-.9020**
(.2650)
Std. deviation of seller’s feedback percentage
(STD_DEV)
-.0769**
(.0241)
-.1036**
(.0233)
Secret reserve price dummy (RESERVE)
.0034
(.0128)
.01560
(.0124)
No scan dummy
(NO_SCAN)
-.1263**
(.0348)
-.1582**
(.0336)
Warranty dummy
(WARRANTY)
.0226
(.0155)
.0220
(.0150)
2001 sample dummy
(2001_SAMPLE)
-.1220**
(.0118)
-.1312**
(.0114)
Adjusted R2
.9522
.9524
ENDNOTES
1. In all eBay auctions, the seller sets a public minimum bid. They may also set a reserve price
which functions as a secret minimum bid. While potential bidders cannot see the level of the
reserve price, they are notified if one is present and whether the current high bid exceeds the
reserve price.
2. The thirty issues are those with the most on-going or expired auctions on eBay in January
2001.
3. In a few cases, the minimum bid was set prohibitively high. Since we would expect the level
of the minimum bid to matter little once it is far above the likely price, in the regressions,
MIN_BID_PCT was set equal to 2.0 (200%) for all cases when MIN_BID_PCT > 2.0.
Consequently, the maximums of the squared and cubed terms are 4.0 and 8.0 respectively.
4. According to eBay policies, solicitation of off-sites sales is prohibited. Disciplinary actions
for reported violations of this policy may range from a formal warning up to indefinite
suspension of a user’s account.
5. We ignore neutral feed backs which are quite rare.
6. CGC encases the certified comic in plastic. Consequently the buyer cannot enjoy the comic
without opening the case invalidating the certification.