Are There Exploitable
Market Inefficiencies
in Online Auctions?
Mark R. Jahn

1
I. INTRODUCTION
Online auctions bear a close resemblance to the perfectly competitive markets of
economic theory, yet online auction prices for similar items seem to vary a great deal as
shown in Figure 1. Since online auctions are a relatively new phenomenon, there have
been few systematic attempts to study the puzzling behavior of online auction prices, the
most notable of which are the various studies by David Lucking-Reiley. The main focus
of this paper will be whether choices made by the seller which theoretically should not
affect price, such as the time that the auction ends, actually influence the price. If
statistically significant exploitable market inefficiencies are found, it would be of obvious
practical interest to participants in online auctions and show how online auctions differ
from theoretical perfectly competitive markets. Since this study is somewhat limited,
sweeping conclusions about the entire online auction market cannot be drawn. However,
exploitable inefficiencies can be found in particular markets, indicating that further
research is justified and suggesting future directions for investigation.
Figure 1: V oodoo 3 3000 B id P rices on eB ay
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O bservation
BidPriceinU.S.Dollars

2
II. FRAMEWORK
Given the size of the online auction market, it is inherently difficult to make
measurements that will be econometrically useful. The approach of this paper will be to
study several items that are auctioned online and attempt to draw some conclusions based
on those items. There are several restrictions that must be placed on the items that are
studied so that regressions may be performed. The items to be studied must be somewhat
homogeneous, and there must be a reasonably large number of auctions. Fortunately, the
conditions needed for regressions are also the same conditions that are needed for a
competitive market to exist.
The question of what items will be studied now arises and must be answered
somewhat carefully because the conclusions drawn from the data are likely to depend
heavily on the choice of items. The first item to be studied will be the Voodoo 3 3000
video card because it was one of the most homogenous items sold in large quantities.
Some Voodoo 3 3000’s use the AGP port, while others use the PCI bus, and most
retailers charged the same price for the two models. Other than that, all Voodoo 3 3000’s
are identical and were manufactured by the company, thus greatly reducing the problems
caused by unobserved factors in a regression. Not all items auctioned online are so
homogenous, so the other items to be studied should be more heterogeneous to see if the
conclusions drawn from the first regression are robust to heterogeneity in the market. The
other items that will be studied are hard drives and VCR’s, which are clearly definable
markets even though features may differ somewhat between models and there are
numerous different manufacturers.

3
In the online auction literature, there is always concern over whether a private values
framework or a common values framework is appropriate. In a private values framework,
individuals choose their bids based on the benefits that they anticipate from owning the
item. In a common values framework, bidders are interested in the item as an asset that
they can resell, so they choose their bids based on what they believe others think the item
is worth. Naturally, a common values framework is much more difficult to model.
Fortunately, all the items being considered for this study are technological items that tend
to depreciate rather rapidly. It is therefore logical to assume that people are not interested
in the asset value of Voodoo 3’s, hard drives, and VCR’s, which allows us to use a
private values framework.
The final conceptual question to be dealt with is what will be taken as evidence of an
exploitable market inefficiency. To qualify as exploitable, a market inefficiency must be
something that sellers can change for a given auction. For example, a glance at some
auction results may show that when several items are auctioned on a given day, the items
auctioned first receive higher bids. This may be an inefficiency, but a seller cannot force
other sellers to auction their items later. On the other hand, sellers can choose when their
own auctions end, so this would be exploitable. A market inefficiency will be defined as
a factor which theoretically should not affect the bid price, but which actually affects the
bid price in a statistically and practically significant way. The difficult part of this
definition is obviously “should”, so I will explain why each of the variables being studied
should not affect the bid price. The first and most obvious variable to test is the starting
price set by the seller. According to economic theory, the item will eventually be bid up
to the market price if the starting price is below the market price and the item will not sell

4
if its starting price is above the market price. The first part of this theory is very easy to
test. However, the second part cannot be tested since this study is limited to items that
have actually been sold. Another obvious test of efficient markets is the shipping price.
According to economic theory, the buyer should care only about the total price that he or
she pays for an item. In an efficient market, one would therefore expect that if the
shipping price were raised, the bid price would fall by an equal amount so that the total
price paid by the buyer remains constant. How long an item is up for sale has no obvious
effect on the buyer, so auction length should have no effect on the bid price in an efficient
market.
The final variables to be considered are the day of the week and the time of day when
the auction ends, which will require much more extensive justification. I will have to get
slightly ahead of myself to explain why this should not affect the bid price. The data is
collected from eBay, which uses proxy bidding. Through proxy bidding, buyers initially
specify the maximum amount that they are willing to pay for an item and their bids are
raised up to that amount to meet other bids. This allows buyers to bid on, and if they bid
high enough win, items that are sold several days after their bids are placed. It is
reasonable to believe that most bidders do not place a high value on receiving their items
slightly earlier. If they did, they would not be bidding on auctions because retail and
online stores are a much better way to receive an item rapidly. More empirically, I
auctioned seven items myself in 1999 and every bidder chose the slowest and least
expensive shipping over faster and more expensive types of shipping. Given proxy
bidding and the low value placed on receiving items quickly, one would expect that the
time of the auction would have no effect in an efficient market.

5
Left unsaid so far is which variables should be used as controls. Controls vary
somewhat from item to item, and there are a large number of them, so most of this is best
left for later sections. For now, it is enough to note generally what some of the controls
are. Obviously, the reputation of the seller (see sellrep in Table A1 in the appendix for a
definition), methods of payment allowed, and whether or not the item is new could be
useful controls. For hard drives and VCR’s, brand dummies could prove useful. There
will also be capacity dummies for the hard drives.

6
III. MODELS AND METHODS
All the models will be presented here, so it is probably a good time to note that
definitions of all the variables are listed in Table A1 in the appendix.
For the Voodoo 3 3000s,
(1) bidprice = 0 + 1laucleng + 2strtprce + 3rsv + 4shipprce + 5shipsqrd +
6actship + 7time + 8timesqrd + 9wtime + 10wtimesq + 11,..,16(day dummies) +
17modrep + 18check +19cc + 20new + 21pic + u
For the hard drives,
(2) bidprice = 0 + 1laucleng + 2strtprce + 3rsv + 4shipprce + 5shipsqrd +
6actship + 7time + 8timesqrd + 9wtime + 10wtimesq + 11,..,16(day dummies) +
17modrep + 18check + 19cc + 20new + 21pic + 22gig6 + 23gig8 +
24,..,k(brand dummies) + u
For the VCR’s,
(3) bidprice = 0 + 1laucleng + 2strtprce + 3rsv + 4shipprce + 5shipsqrd +
6actship + 7time + 8timesqrd + 9wtime + 10wtimesq + 11,..,16(day dummies) +
17modrep + 18check + 19cc + 20new + 21pic + 22search2 +
23,..,k(brand dummies) + u
The modeling of bidprice and strtprce must be justified. The variable bidprice is not
modeled as a natural log, which would have some advantages, because that would make
it difficult to form a null hypothesis about the effect of shipping. Since bidprice is
modeled as a level, it seems sensible that strtprce should be left as a level as well.
Although there are too few instances of reserve price auctions to expect rsv to differ

7
significantly from zero, rsv should be included to correct for the influence of having a
reserve price on the effect (if any) of strtprce on bidprce.
The variable laucleng requires further explanation. The variable laucleng is the
natural log of the auction length. If auction length influences bidprice, it will do so in a
decreasing fashion and the natural log is a simple way to model this effect. If the effect of
auction length on bidprice were constant and nonzero, sellers would want the auction
length to be arbitrarily short or extremely long. Most of eBay’s profits come from taking
a percentage of each sale, so it is clear that eBay would offer sellers the option of
auctions shorter than three days or longer than ten days if these were profitable options
for sellers.
Another modeling choice requiring explanation is the modeling of shipping. The
coefficient on shipping should be equal to negative one under the null hypothesis of
efficient markets for reasons explained earlier. However, the alternative hypothesis
should not be that the coefficient is some constant greater than negative one. If most
sellers charge five dollars shipping for an item, then offering free shipping might not
increase bidprice because potential bidders would not notice this until they read the
description. However, a seller charging 25 dollars for shipping the same item would
almost certainly receive a lower bidprice because actual bidders would reduce their bids
to compensate, and potential bidders might take the overstated shipping charge as a signal
that the seller is untrustworthy. The quadratic form for shipping given by shipprce and
shipsqrd is the simplest way to model this effect. Additionally, there is a dummy
variable, actship, which is equal to one if the seller chooses to have the buyer pay the
actual shipping cost instead of a fixed shipping cost. It is difficult to form a null

8
hypothesis about actship given the evidence that buyers are risk averse, but it must be
included in the regression so that the zeros entered for shipping when the seller charges
actual shipping do not distort the effect of fixed shipping on bidprice.
The modeling of time requires further explanation. The time of day that the auction
ends is modeled as a quadratic equation for the obvious reason that if bidprice increased
or decreased linearly with the time of day, it would imply a sharp and extremely irrational
discontinuity in bidder behavior at midnight everyday. In a more debatable move, I also
created separate time variables, wtime and wtimesq, that take on the same values as time
and timesqrd for weekend auctions and equal zero otherwise. This is done under the
assumption that if bidprice varies based on time of day, it is likely to do so differently on
weekends because many people will be able to bid during times that they would be
working during the week.
The variable modrep is equal to sellrep1/6, and this functional form is used because it
is more likely to capture the effect of seller reputation on bidprce. Obviously a sellrep
equal to 1000 will not yield a substantially higher bidprice than a sellrep equal to 100.
Natural logs are a poor choice for functional form because the log of zero is undefined,
which makes it difficult to model the substantial difference between a sellrep equal to
zero and a sellrep equal to one. The specific choice of sellrep1/6 as modrep is only an
approximation of the correct functional form based on my own perceptions and is not
derived from running regressions.
As most of the other modeling methods and variable choices should be non-
controversial, the only modeling task remaining is the choice of estimation method.
Particularly in (3), there could be some endogeneity problems with strtprce. Suppose that

9
a VCR includes a special feature not captured by the regression. This may lead the seller
to set strtprce higher and may also cause bidprce to be higher. This would cause a
positive bias in the OLS estimated coefficient on strtprce. Ideally, one could use IV
estimation to correct for this bias. Unfortunately, every variable that I have data on is
either a control that would effect bidprice in an efficient market or a potential market
inefficiency that I am attempting to test. For this reason, OLS must be used instead. This
is not necessarily a great detriment to this study, as under the null hypothesis strtprce has
no effect on bidprice. If OLS estimates a positive coefficient on strtprce that is not
statistically significant, the failure to reject the null hypothesis is not diminished in any
way because the expected bias is positive.
Although normally distributed errors are not a requirement for using OLS, it is
extremely useful to argue that the errors are normally distributed when the sample size is
small. Fortunately, there is a reasonable argument for the approximate normality of the
errors in (1), (2), and (3). Suppose that we knew with certainty the effects of all the
control variables and potential market inefficiencies. There would still be some
unexplained variation in bidprice based on the different values that different bidders
placed on the items being auctioned. Conditional on the dependent variables, one would
expect that each auction item receives a random sample of bidders from the vast pool of
potential bidders. Hence, the central limit theorem applies and it is reasonable to suppose
that the errors are approximately normally distributed. Since there is some heterogeneity
in both the hard drive and VCR markets, testing for heteroskedasticity will be necessary.
However, weighted least square estimates that correct for heteroskedasticity are likely to

10
be biased because of the small sample size. Therefore, OLS with heteroskedasticity
robust standard errors will be used if evidence of heteroskedasticity is found.

11
IV. LITERATURE REVIEW
There are a number of interesting studies of online auctions that, while not directly
related to the topic at hand, will nonetheless be instructive to consider. Lucking-Reiley
(2000) provides a good overview of online auction sites, formats, and associated terms.
Lucking-Reiley (1999) is an interesting study in large part because it consists of a
controlled field experiment, quite a rarity in economics, in which the author auctions
Magic: the Gathering cards in newsgroups and via email to test if different auction
formats yield different returns. More directly relevant to this study is a follow up working
paper, Lucking-Reiley (2000a), that uses different starting prices for Magic cards
auctioned by the author in a similar field experiment. Lucking-Reiley initially
hypothesized that there was an optimum starting price, which naturally implies that
strtprce should have been modeled as a quadratic equation. However, he found that a
number of bidders systematically bid higher for items with higher starting prices and
concluded that bids are a multi-peaked function of starting price. The fact some bidders
use starting price as a signal for higher quality should reinforce previous concerns about
the potential endogeneity of strtprice. The other key findings of Lucking-Reiley (2000a)
were that items with higher starting prices attract fewer bidders, are more likely to remain
unsold, and ultimately sell for higher prices if they are actually sold.
The Lucking-Reiley et al. working paper on Indian-head pennies sold on eBay is the
most interesting study of online auctions to date. Lucking-Reiley et al. (1999) assumes a
private values framework, just as this paper does. It is important to note that Lucking-
Reiley et al. take a different approach to dealing with possible heterogeneity within the
market. Instead of using qualitative dummies, they use the estimated book value of the

12
Indian-head pennies. The obvious objection to this method is that there is error inherent
in estimating the book value of something like Indian-head pennies, and errors in
measuring dependent variables can cause severe problems in estimation. On the other
hand, the choice of qualitative dummies can be somewhat subjective and leads to serious
problems when mistakes are made, as will be seen later. Although Lucking-Reiley et al.
collected over 20,000 observations, only 461 of these are used in most regressions so that
book value can be included, and of these approximately 30% received no bids.
Having covered the preliminaries, we can now turn to the results of Lucking-Reiley
et al. (1999). The treatment of eBay user feedback ratings is much more sophisticated in
Lucking-Reiley et al. than in this paper. They divide sellrep into its positive and negative
feedback components and find that negative feedbacks have a greater effect on the bid
price than positive feedbacks, calling into question both eBay’s method of computing
overall feedback ratings and this study’s method of dealing with eBay user feedback.
Lucking-Reiley et al. found that the estimated coefficient on sellrep was not significant
and that when it was broken down into its components, the number of negative feedbacks
had a significant negative effect on the bid price, while the number of positive feedbacks
remained insignificant. Lucking-Reiley et al. did not model the time that the auction ends
as thoroughly as this paper does. They created a dummy variable for auctions that end on
the weekend and found that it did not have a statistically significant effect on the bid
price. Another key finding was that the auction length, whether modeled as qualitative
dummies or as a natural log, has a significant positive effect on the bid price. The most
interesting aspect of Lucking-Reiley et al.’s treatment of the number of bidders is that
they run separate regressions to find out how the number of bidders affects the estimated

13
coefficient on strtprce. The estimated coefficient is insignificant when no restrictions are
imposed, significantly positive when only auctions with one or more bids are considered,
and insignificant when the sample is restricted to auctions with two or more bids.
The Bajari and Hortacsu working paper on eBay auctions of U.S. coin proof sets is
another valuable source for insights into online auctions. Bajari and Hortacsu (2000),
alone among online auction studies, concludes that a common values framework is
appropriate. Bajari and Hortacsu use book value to control for possible heterogeneity, but
they often divide the bid price by the book value instead of using book value as a
dependent variable. This procedure eliminates the problems caused by potential
measurement error in an independent variable while introducing concerns about the
normality of the errors. The most interesting part of the paper deals with endogenous
bidder entry. According to Bajari and Hortacsu, the decision of bidders to consider
bidding on a particular online auction item is influenced by many of the independent
variables that determine the bid price, and therefore the standard auction assumption of a
fixed number of potential bidders cannot be maintained. Endogenous bidder entry could
also prove to be a useful explanation for any exploitable market inefficiencies that are
found. Given that the number of bidders now appears so interesting, it is natural to ask
why data was not collected on the number of bidders for this paper. The number of
bidders should not affect bidprice, but a seller cannot directly control the number of
bidders. Hence, the number of bidders cannot be an exploitable market inefficiency.

14
V. THE DATA
Some fairly general observations about the data sets are in order. The first thing to
note about the data is that the appendix contains variable definitions in Table A1 and
summary statistics for each model’s data set in Tables A2, A3, and A4. The data sets
were collected during most of November of 1999 and should be considered cross-
sectional data. All data was collected by searching eBay’s list of completed auctions and
typing or pasting the results into Excel. The data sets contain id numbers for each
auction, but the id numbers are too old to be used to locate the auctions on eBay. Money
orders were accepted as a method of payment in nearly all auctions, so this can generally
be assumed to be the only method of payment when check and cc are both zero. During
the data collection process, it became apparent that that nearly all VCR auctions included
pictures and virtually no Voodoo 3 cards offered credit cards as a method of payment.
Therefore, data on pic was not collected for VCR’s and data on cc was not collected for
Voodoo 3’s. 60 observations were collected on the Voodoo 3 3000, 62 observations were
collected on hard drives, and 90 observations were collected on VCR’s, although only 77
will be used for reasons explained in part VI. Hard drives were restricted to being
standard IDE hard drives with capacities of 4.3, 6.4, or 8.4 gigabytes. All VCR’s in the
data set are VHS VCR’s with 4 heads and hi-fi stereo.
There were numerous reasons that various potential observations were not collected
for these data sets. Auctions could not be ended prematurely, fixed shipping auctions had
to specify the fixed shipping cost, the starting price had to be met, and the reserve price
had to be met for reserve price auctions (see strtprce and rsv in Table A1 for definitions).

15
There is also another type of auction, which eBay calls a Dutch auction1, where several
items of the same type are sold simultaneously and all winning bidders pay the same
price as the lowest winning bid. When only a few items are sold this way, the results are
generally similar to normal auctions, so these were counted. Each Dutch auction included
in a data set was counted as only one observation, in part because this was bound to
happen accidentally much of the time anyway and in part because these auctions do not
reflect market forces as well as normal auctions. Large Dutch auctions on eBay often
specify a somewhat low price and sell only a fraction of the quantity for sale because the
market cannot absorb this many units at once. I therefore decided not to include large
Dutch auctions. In retrospect, this was a mistake because the large Dutch auctions might
depress the prices of other auction items that are sold at the same time and I now have no
way of controlling for the resulting error.
For all basic variables except sellrep, I had access to exactly the same information
that the bidders used to make their decisions. Unfortunately, eBay lists the current
reputation of the seller with the completed auctions instead of the reputation of the seller
at the time the auction was completed, which means there is some error inherent in this
measurement. However, the reputations of small sellers do not change as often as the
reputations of large sellers and modrep is a concave and increasing function of sellrep,
which will tend to reduce the effects of this measurement error.
1
See Lucking-Reiley (2000) for the standard definition of a Dutch auction, which differs from eBay’s

16
VI. RESULTS
Most of the results section will focus on the failure to reject or the rejection of the
null hypotheses suggested by the efficient markets hypothesis, at least after some
preliminaries are taken care of. Only when a null hypothesis is rejected will the
magnitudes of the coefficients need to be discussed. However, the estimated coefficients,
standard errors, R2, and other typical statistics for each of the regressions can be found in
the appendix in Tables A5, A6, and A7.
There are several reasons why I avoided repeatedly dropping statistically
insignificant variables. The first is that the null hypothesis is that there are no exploitable
market inefficiencies, not that that all the coefficients are zero. For example, it is not
really justifiable to drop new from a regression if it has a positive but statistically
insignificant coefficient because an efficient market is likely place some value on an item
being new. The other main reason to avoid dropping insignificant variables and
estimating the model again is that most of the variables being tested are not significant in
any given regression. Hence, dropping insignificant variables would result in separate
models for each test variable, thus greatly increasing the number of regressions while also
increasing the difficulty of making comparisons. That said, I must nonetheless make
some minor adjustments to the models.
The models must be altered somewhat based on the data and some of the early
results. As noted previously, cc was dropped from (1) and pic was dropped from (3)
because of a lack of variation in the actual data. Additionally, wtime and wtimesq will be
dropped from all three equations for two main reasons. The first reason is that the
inclusion of these variables tends to make the day dummies absurdly large and difficult to

17
interpret. The second and related reason is that the inclusion of wtime and wtimesq makes
it impossible to test time of day and the day of the week dummies separately. Suppose
that the only time related effect is that auctions held on Saturday and Sunday have a
higher bidprice. Then wtime and wtimesq may pickup this effect, possibly leading to an
unwarranted rejection of the hypothesis that the time of day has no effect on bidprice or a
spurious failure to reject the hypothesis that the day of the week has no effect on
bidprice. It also appears necessary to drop all of the Sony VCR’s from the VCR
regression in order to avoid possible misspecification. The revised models are presented
below.
Note: the day dummies used in all models are sun, mon, tue, wed, thur, fri
For the Voodoo 3 3000s,
(4) bidprice = 0 + 1laucleng + 2strtprce + 3rsv + 4shipprce + 5shipsqrd +
6actship + 7time + 8timesqrd + 9,..,14(day dummies) + 15modrep +
16check + 17new + 18pic + u
For the hard drives,
(5) bidprice = 0 + 1laucleng + 2strtprce + 3rsv + 4shipprce + 5shipsqrd +
6actship + 7time + 8timesqrd + 9,..,14(day dummies) + 15modrep + 16check +
17cc + 18new + 19pic + 20gig6 + 21gig8 + 22,..,26(brand dummies) + u
where the brand dummies are fujitsu, ibmseag, maxtor, quantum, wd
For the VCR’s,
(6) bidprice = 0 + 1laucleng + 2strtprce + 3rsv + 4shipprce + 5shipsqrd +
6actship + 7time + 8timesqrd + 9,..,14(day dummies) + 15modrep + 16check +
17cc + 18new + 19search2 + 20,..,26 or 27(brand dummies) + u
where the brand dummies are jvc, korean, mitbishi, pansonic,
sanyo, toshiba, western, and sony where noted

18
For reasons explained in part III, the errors in the regressions were expected to be
approximately normally distributed with some potential for heteroskedasticity. However,
the skewness and kurtosis test for nonnormality has revealed that this null hypothesis
should be rejected in the VCR case, as can be seen in the OLS w/ Sony row in Table 1
below. The skewness and kurtosis joint test p-values for the Voodoo 3 and hard drive
regressions are 0.7966 and 0.7169, respectively, and therefore need not concern us
further. Naturally, one must ask if the nonnormality detected in the VCR regression
residuals is simply a result of heteroskedasticity. The way to answer this question is to
use weighted least squares (WLS) to correct for heteroskedasticity, and then test the WLS
residuals for nonnormality. The WLS estimates are computed according to the method
described in Wooldridge (1999) on page 267. Table 1 shows that while WLS corrects for
skewness, the distribution of the residuals continues to display excess kurtosis. As a
result, the null hypothesis that the errors are normally distributed is still rejected at the
five percent level.
Table 1:
H0: errors in the VCR model are normally distributed
Model
Skewness Test
p-value
Kurtosis Test
p-value
Joint Test
p-value
OLS w/ Sony 0.060 0.008 0.0098
WLS w/ Sony 0.941 0.010 0.0439
OLS w/o Sony 0.062 0.331 0.1057
WLS w/o Sony 0.770 0.372 0.6364
Since the errors are not normally distributed, an explanation and a remedy must be
found. While I was entering the data, I noticed that several of the Sony VCR’s with very
high values for bidprice where advertised as having advanced features, such as a jog dial
on the remote. This potential difference in the values of Sony VCR’s would not have

19
created any problems if I had taken the book value approach. As it is, I no longer have the
original auction information and cannot distinguish between the different types of Sony
VCR’s. The only remedy available is to drop all Sony VCR’s from the regression (13 of
the 90 observations). Fortunately, this remedy appears to work. Table 1 shows that
without the Sony observations, it is reasonable to assume that the errors in the VCR
regression are normally distributed with potential heteroskedasticity. Furthermore, the
RESET test for misspecification gives a much higher p-value for the model without the
Sony VCR’s, as illustrated below in Table 2. Now that the possibility of misspecification
has been dealt with, we can turn our attention to heteroskedasticity.
Table 2:
H0: VCR model is correctly specified
Model F-statistic p-value
OLS w/ Sony 2.63 0.0582
OLS w/o Sony 0.73 0.5396
Table 3
H0: no heteroskedasticity
Model
Special Case White Test
p-value
Breusch-Pagan Test
p-value
Voodoo 3 3000 (4) 0.9759 0.8859
hard drive (5) 0.4602 0.1705
VCR w/o Sony (6) 0.1777 0.0263
As shown in Table 3, the tests for heteroskedasticity return vastly different results for
the different models. The failure to reject the null hypothesis of no heteroskedasticity is
especially strong in the Voodoo 3 3000 regression (4). In the hard drive regression (5),
the special case White test fails to reject the null hypothesis of no heteroskedasticity by a
substantial margin, while the Breusch-Pagan test also fails to reject the null hypothesis,
albeit by a smaller margin. Note that the special case of the White test,
(7) 2 2
0 1 2
ˆ ˆ ˆ ,u y y error     

20
is used because the White test consumes too many degrees of freedom for the limited
number of observations available for these models. It is not clear if there is
heteroskedasticity in the VCR case because the Breusch-Pagan and special case White
tests give different results. Given the mixed evidence and the fact that robust standard
errors can be unreliable in models with small sample sizes, both robust and non-robust
standard errors will be provided for the VCR regression (6). Now without further ado, the
results:
Table 4
H0: the coefficient on shiprce=-1 and the coefficient on shipsqrd=0
Model F-statistic p-value
Voodoo 3 3000 (4) 4.35 0.0193
hard drive (5) 1.04 0.3650
VCR w/o Sony (6) 4.05 0.0235
VCR w/o Sony robust (6) 4.25 0.0197
Table 4 shows that shipping charges are likely to be an exploitable market
inefficiency in online auctions. Although the null hypothesis holds up fairly well in the
hard drive case, the VCR and the Voodoo 3 3000 regressions provide clear evidence
against the null hypothesis. This exploitable market inefficiency exists in large part
because the current bidprice of an eBay auction item is prominently displayed for easy
comparison, while shipping information is often buried in the item description.
Since we now know that shipping has a statistically significant effect, the practical
significance of these results should be considered in the Voodoo 3 and VCR cases.
Unfortunately, the estimated coefficient on shipsqrd in the VCR case, 0.0802, does not
have a logical interpretation. If taken literally, it implies that bidprice can be made
arbitrarily high by raising shipping charges. A more likely explanation is that the true
coefficient on shipsqrd is very small and negative instead of very small and positive, but

21
this hypothesis can only be tested by collecting more observations. On the face of it, the
estimated coefficients on shipprce and shipsqrd in the Voodoo 3 case, approximately
9.21 and -0.766 respectively, also seem difficult to believe. However, this is just a typical
result of OLS estimation being more accurate near the mean value. Most sellers realize
that free shipping is less profitable than charging a modest fee for shipping and therefore
there are few observations with shipping equal to zero, which leads to the seemingly
strange OLS estimates. If you take the derivative of the estimated equation for bidprice
with respect to shipprce and set it equal to –1 (for the same reason as the null hypothesis),
the resulting optimal shipping price is approximately $6.67. Interestingly enough, the
mean value of shipprce for Voodoo 3 3000 auctions given actship is equal to zero, which
is more relevant in this case than the unconditional mean listed in the appendix, is equal
to about $7.08. Not only does an exploitable market inefficiency exist, many sellers are
already taking advantage of it. This is quite likely to be true in other online auction
markets as well, so this result has clear practical significance.
Table 5
H0: the coefficient on laucleng=0
Model t-statistic p-value
Voodoo 3 3000 (4) -1.386 0.173
hard drive (5) 3.104 0.004
VCR w/o Sony (6) 1.07 0.290
VCR w/o Sony robust (6) 1.07 0.291
As Table 5 shows, the results on auction length are decidedly mixed. Auction length
clearly does not affect bidprice for VCR’s in a statistically significant way. Although the
evidence is not quite strong enough for rejection, the results suggest that further
investigation may reveal a negative relationship between auction length and bidprice for

22
Voodoo 3’s. However, the null hypothesis is strongly rejected in the hard drive case in
favor of a positive relationship between bidprice for hard drives and auction length.
Not only is the relationship between bidprice and laucleng statistically significant for
hard drives, it is practically significant as well. The coefficient on laucleng is
approximately equal to 9, so the difference in the predicted bidprice for an auction of the
maximum length, 10 days, and the minimum length, 3 days, is equal to about $11, a
substantial amount relative to the typical bidprice for a hard drive. This constitutes clear
evidence of an exploitable market inefficiency in a particular market. However, the
results for the other regressions strongly suggest that this market inefficiency does not
exist in all markets. Since this market inefficiency may not always work in the same
direction when it does exist, it will be difficult to decide on a course of action in a given
market without running a new regression.
Table 6
H0: the coefficients on time, timesqrd=0
Model F-statistic p-value
Voodoo 3 3000 (4) 0.14 0.8680
hard drive (5) 0.03 0.9708
VCR w/o Sony (6) 0.22 0.8022
VCR w/o Sony robust (6) 0.24 0.7894
Table 7
H0: the coefficients on sun, mon, tue, wed, thur, fri=0
Model F-statistic p-value
Voodoo 3 3000 (4) 1.34 0.2620
hard drive (5) 0.60 0.7279
VCR w/o Sony (6) 1.35 0.2517
VCR w/o Sony robust (6) 0.90 0.5032
All the models seem to be sending the same message on the time of day and the day
of the week when the auction is completed: they don’t affect bidprice. In Tables 6 and 7,
the null hypothesis is generally vindicated by an ample margin. The conclusion to be

23
drawn from this is that those looking for exploitable market inefficiencies in online
auctions would generally be well advised to look elsewhere.
Table 8
H0: the coefficient on strtprce=0
Model t-statistic p-value
Voodoo 3 3000 (4) 0.703 0.486
hard drive (5) -1.187 0.243
VCR w/ Sony (6) 1.766 0.082
VCR w/ Sony robust (6) 1.831 0.072
VCR w/o Sony (6) -0.26 0.796
VCR w/o Sony robust (6) -0.22 0.824
There is very little evidence that strtprce influences bidprice. However, the results in
Table 8 and the potential endogeneity of strtprce can be used to support the decision to
drop Sony VCR’s from the VCR regression. It was argued earlier that a variable that
influences bidprice is very likely to affect the strtprce set by the seller, which would
create an endogeneity problem if the variable in question is not included in the
regression. If the correct specification of the model includes a separate dummy for Sony
VCR’s with special features and that dummy is not included, one would expect that the
estimated coefficient on strtprce would be positively biased. This appears to be exactly
what happens in the VCR regression when the Sony VCR’s are included, as can be seen
above in Table 8.

24
VI. CONCLUSION
The main conclusion of this paper is that there are some exploitable market
inefficiencies in online auctions, and therefore further research in this area is clearly
warranted. This study was limited to only three different items and no more than 77
observations per item, and yet some significant exploitable market inefficiencies were
found. Larger studies would allow more sweeping conclusions to be drawn about the
entire online auction market. The other important conclusion that can be drawn from this
paper is which of the numerous test variables are more promising for future study. This
study clearly showed that there are exploitable market inefficiencies in online auctions
related to shipping price and auction length, and future research could show how
widespread these inefficiencies are. The time that the auction ends, whether it is the day
of the week or the time of day, is a less promising area for future research. If a way is
found to control for the potential endogeneity, the starting price may also be a useful
variable to investigate.
A particularly promising explanation for the existence of these exploitable market
inefficiencies is the possibility of endogenous bidder entry. It seems possible, even likely,
that attracting more bidders increases the probability that two or more bidders will place a
higher than normal value on the item, causing the bid price to be higher than normal as
well. Obviously, an item that is auctioned for a longer amount of time is likely to attract
more bidders. Less obviously, an item with a higher shipping charge may appear less
expensive than an identical item that has an equal total cost, so a higher shipping charge
may increase the number of bidders as well. Only a new study that investigates the effects
of shipping and auction length on the number of bidders can provide a definitive answer.

APPENDIX
25
Table A1
Variable Definition
actship a dummy variable equal to one if the buyer pays actual shipping and zero otherwise
aucleng the amount of time that an auction lasts, which may equal 3, 5, 7, or 10 days
bidprice
the price in U.S. dollars that the winning bidder pays for an item up for auction, which is
only recorded when the starting price is met or the reserve price is met for a reserve price
auction (see rsv for further description of reserve price auctions or strtprce for a further
description of the starting price)
cc
a dummy variable equal to one if the seller accepts credit cards as a method of payment
and zero otherwise
check
a dummy variable equal to one if the seller accepts personal checks as a method of
payment and zero otherwise
fri a dummy variable equal to one if the auction ends on a Friday and zero otherwise
fujitsu a dummy variable equal to one if the manufacturer is Fujitsu and zero otherwise
gig4
a dummy variable equal zero if a hard drive has a capacity equal to 4.3 gigabytes and
zero otherwise
gig6
a dummy variable equal zero if a hard drive has a capacity equal to 6.4 gigabytes and
zero otherwise
gig8
a dummy variable equal zero if a hard drive has a capacity equal to 8.4 gigabytes and
zero otherwise
ibm a dummy variable equal to one if the manufacturer is IBM and zero otherwise
ibmseag
a dummy variable equal to one if the manufacturer is IBM or Seagate and zero otherwise,
an artifical construction created because there were too few hard drives manufactured by
either company to justify separate dummies
id
a unique identification number assigned to each eBay auction, id can be used to locate
the auctions in this data set on eBay's web site by searching by id number
jvc a dummy variable equal to one if the manufacturer is JVC and zero otherwise
korean
a dummy variable equal to one if the manufacturer is Korean (Sharp or Samsung) and
zero otherwise
laucleng
is equal to the natural log aucleng and better represents the effect of auction length on
bidprice than aucleng
maxtor a dummy variable equal to one if the manufacturer is Maxtor and zero otherwise
mitbishi a dummy variable equal to one if the manufacturer is Mitsubishi and zero otherwise
modrep
sellrep to the 1/6th power, this modification better represents the way that seller
reputation influences bidprice than sellrep
mon a dummy variable equal to one if the auction ends on a Monday and zero otherwise
new
a dummy variable equal to one if the item is advertised as new in the auction title and
zero otherwise
pansonic a dummy variable equal to one if the manufacturer is Panasonic and zero otherwise
pic
a dummy variable equal to one if the item description includes a picture and zero
otherwise
quantum a dummy variable equal to one if the manufacturer is Quantum and zero otherwise
rsv
a dummy variable equal to one if the auction is a reserve price auction and zero
otherwise, where a reserve price auction is an auction where the seller has specified a
price, higher than the starting price and hidden from bidders until it is met, below which
winning bids are nonbinding for both buyers and sellers
samsung a dummy variable equal to one if the manufacturer is Samsung and zero otherwise
sanyo a dummy variable equal to one if the manufacturer is Sanyo and zero otherwise
sat a dummy variable equal to one if the auction ends on a Saturday and zero otherwise
seagate a dummy variable equal to one if the manufacturer is Seagate and zero otherwise

APPENDIX
26
Variable Definition
search2
a dummy variable equal to one if the item was located on eBay using the search words
"vcr 4 hifi" instead of "vcr 4 fi" and zero otherwise
sellrep
the reputation of a seller on eBay, where reputation is an integer value calculated as the
number of positive feedbacks that a user has received minus the number of negative
feedbacks that a user has received and each user may leave only one feedback on any
other user
shipprce
is equal to the price of shipping in U.S. dollars when the seller charges a fixed shipping
cost and equal to zero when the seller pays shipping or the buyer pays actual shipping
(the dummy variable actship prevents this from distorting the regression)
shipsqrd is equal to shipprce squared
sony a dummy variable equal to one if the manufacturer is Sony and zero otherwise
strtprce
the price in U.S. dollars at which bidding on an auction item begins, the starting price is
set by the seller
sun a dummy variable equal to one if the auction ends on a Sunday and zero otherwise
t
a variable that measures the time that the auction was completed as the number days,
which can be fractions, since 12:00 AM on 10/14/99, t can be used to sort the auctions
chronologically
thur a dummy variable equal to one if the auction ends on a Thursday and zero otherwise
time is equal to the time that the auction ends (where time is measured as a fraction of a day)
timesqrd is equal time squared
toshiba a dummy variable equal to one if the manufacturer is Toshiba and zero otherwise
tue a dummy variable equal to one if the auction ends on a Tuesday and zero otherwise
wd a dummy variable equal to one if the manufacturer is Western Digital and zero otherwise
wed a dummy variable equal to one if the auction ends on a Wednesday and zero otherwise
western
a dummy variable equal to one if the manufacturer is western (RCA, Phillips/Magnavox,
GE, or Zenith) and zero otherwise
wtime
is equal to the time of day (where time is measured as a fraction of a day) that the auction
ends if the auction ends on a weekend and zero otherwise where time is measured as a
fraction of a day
wtimesq is equal to wtime squared

APPENDIX
27
Table A2
Voodoo 3 3000 Data: 60 observations
Variable Mean Standard Deviation Minimum Maximum
actship 0.283333 0.4544196 0 1
aucleng 6.416667 2.157303 3 10
bidprice 114.6323 14.80117 75 150
check 0.616667 0.4903014 0 1
fri 0.2 0.4033756 0 1
laucleng 1.796369 0.3706995 1.098612 2.302585
modrep 1.345033 0.7427155 0 2.447596
mon 0.15 0.3600847 0 1
new 0.5 0.5042195 0 1
pic 0.55 0.5016921 0 1
rsv 0.133333 0.3428033 0 1
sat 0.116667 0.3237318 0 1
sellrep 39.58333 66.07707 0 215
shipprce 5.078333 3.857464 0 10
shipsqrd 40.4215 36.83158 0 100
strtprce 25.09833 29.41645 0.01 99
sun 0.166667 0.375823 0 1
thur 0.15 0.3600847 0 1
time 0.637661 0.2087001 0.109109 0.953183
timesqrd 0.449441 0.2632467 0.011905 0.908558
tue 0.05 0.2197842 0 1
wed 0.166667 0.375823 0 1
wtime 0.177552 0.3066799 0 0.921863
wtimesq 0.12401 0.2369626 0 0.849832

APPENDIX
28
Table A3
Hard Drive Data: 62 observations
Variable Mean Standard Deviation Minimum Maximum
actship 0.403226 0.4945499 0 1
aucleng 6.177419 2.004292 3 10
bidprice 82.05452 9.816491 56 103.5
cc 0.129032 0.3379723 0 1
check 0.5 0.5040817 0 1
fri 0.112903 0.319058 0 1
fujitsu 0.129032 0.3379723 0 1
gig4 0.532258 0.5030315 0 1
gig6 0.258065 0.4411417 0 1
gig8 0.209677 0.4104015 0 1
ibm 0.032258 0.178127 0 1
ibmseag 0.080645 0.2745122 0 1
laucleng 1.762687 0.3575806 1.098612 2.302585
maxtor 0.129032 0.3379723 0 1
modrep 1.533309 0.4644302 0 2.854519
mon 0.16129 0.370801 0 1
new 0.419355 0.4974818 0 1
pic 0.241936 0.4317514 0 1
quantum 0.209677 0.4104015 0 1
rsv 0.193548 0.3983042 0 1
samsung 0.048387 0.2163345 0 1
sat 0.16129 0.370801 0 1
seagate 0.048387 0.2163345 0 1
sellrep 36.12903 79.39329 0 541
shipprce 3.664516 3.617267 0 12
shipsqrd 26.30226 33.13932 0 144
strtprce 19.56065 25.19483 0.01 99
sun 0.145161 0.355139 0 1
thur 0.177419 0.3851418 0 1
time 0.645219 0.2090172 0.158241 0.968889
timesqrd 0.459291 0.2453393 0.02504 0.938746
tue 0.080645 0.2745122 0 1
wd 0.33871 0.4771345 0 1
wed 0.16129 0.370801 0 1
wtime 0.196078 0.3216756 0 0.943206
wtimesq 0.140253 0.256771 0 0.889638

APPENDIX
29
Table A4
VCR Data: 77 observations
Variable Mean Standard Deviation Minimum Maximum
actship 0.3376623 0.4760139 0 1
aucleng 5.779221 2.13753 3 10
bidprice 95.16896 19.7898 53 159
cc 0.3896104 0.4908597 0 1
check 0.4155844 0.4960542 0 1
fri 0.1688312 0.3770592 0 1
jvc 0.1168831 0.3233877 0 1
korean 0.1558442 0.365086 0 1
laucleng 1.676916 0.4109666 1.098612 2.302585
mitbishi 0.0519481 0.2233774 0 1
modrep 2.068707 0.9394927 0 3.181995
mon 0.1428571 0.3522217 0 1
new 0.5194805 0.5028966 0 1
pansonic 0.1428571 0.3522217 0 1
rsv 0.1298701 0.3383649 0 1
sanyo 0.0649351 0.2480271 0 1
sat 0.1948052 0.3986477 0 1
search2 0.1688312 0.3770592 0 1
sellrep 319.987 385.2704 0 1038
shipprce 7.693506 6.134348 0 19
shipsqrd 96.33156 91.64519 0 361
strtprce 30.06558 36.19545 0.01 110
sun 0.1298701 0.3383649 0 1
thur 0.1038961 0.3071266 0 1
time 0.6501804 0.1694035 0.2758565 0.9885648
timesqrd 0.4510594 0.2215782 0.0760968 0.9772604
toshiba 0.2337662 0.4260005 0 1
tue 0.1428571 0.3522217 0 1
wed 0.1168831 0.3233877 0 1
western 0.1688312 0.3770592 0 1
wtime 0.2167947 0.3259791 0 0.9656019
wtimesq 0.1518823 0.2469952 0 0.9323869

APPENDIX
30
Table A5
Voodoo 3
3000 Results
Number of obs = 60
F( 18, 41) = 1.47
Prob > F = 0.1526
R-squared = 0.3919
Adj R-squared = 0.1250
Root MSE = 13.845
Variable Coefficient
Standard
Error
t-stat vs.
Coef.=0
p-val vs.
Coef.=0
_cons 104.5283 22.7485 4.59 0
actship 15.87463 11.7712 1.35 0.185
check 1.853765 4.331702 0.43 0.671
fri -3.81594 7.311944 -0.52 0.605
laucleng -7.82281 5.644697 -1.39 0.173
modrep 2.934219 3.090257 0.95 0.348
mon 4.010365 8.271285 0.48 0.63
new 6.35348 4.720968 1.35 0.186
pic 5.353747 4.628905 1.16 0.254
rsv 4.058164 6.267009 0.65 0.521
shipprce 9.212315 3.461341 2.66 0.011
shipsqrd -0.76612 0.271165 -2.83 0.007
strtprce 0.054054 0.076882 0.7 0.486
sun -6.9898 8.629377 -0.81 0.423
thur 5.819057 8.232322 0.71 0.484
time -32.5335 64.87168 -0.5 0.619
timesqrd 27.78538 53.08651 0.52 0.604
tue 11.92419 11.35099 1.05 0.3
wed -6.90232 8.678985 -0.8 0.431

APPENDIX
31
Table A6
Hard Drive
Results
Number of obs = 62
F( 26, 35) = 4.49
Prob > F = 0.0000
R-squared = 0.7695
Adj R-squared = 0.5982
Root MSE = 6.2224
Variable Coefficient
Standard
Error
t-stat vs.
Coef.=0
p-val vs.
Coef.=0
_cons 66.99473 10.20539 6.565 0
actship -12.15947 6.637816 -1.832 0.075
cc 0.7892394 3.695769 0.214 0.832
check 1.141036 2.632554 0.433 0.667
fri 0.4047268 4.066983 0.1 0.921
fujitsu 8.334609 5.041594 1.653 0.107
gig6 12.96589 3.465709 3.741 0.001
gig8 24.68965 4.672654 5.284 0
ibmseag 8.240517 5.139604 1.603 0.118
laucleng 9.134536 2.942838 3.104 0.004
maxtor 5.153925 3.881836 1.328 0.193
modrep -4.870166 2.373008 -2.052 0.048
mon -1.090563 3.895352 -0.28 0.781
new 6.88036 2.369279 2.904 0.006
pic -0.683302 2.688112 -0.254 0.801
quantum 0.7774004 3.791328 0.205 0.839
rsv -0.310757 2.699447 -0.115 0.909
shipprce -3.436327 1.978184 -1.737 0.091
shipsqrd 0.2129634 0.1529276 1.393 0.173
strtprce -0.067585 0.0569442 -1.187 0.243
sun 1.449873 4.071097 0.356 0.724
thur -2.458341 3.604366 -0.682 0.5
time 2.080268 25.29683 0.082 0.935
timesqrd -0.800864 22.01827 -0.036 0.971
tue 2.757128 4.096819 0.673 0.505
wd 11.40292 3.764361 3.029 0.005
wed 3.197668 3.564766 0.897 0.376

APPENDIX
32
Table A7
VCR
Results
Number of obs = 77
F( 26, 50) = 2.47
Prob > F = 0.0030
R-squared = 0.5621
Adj R-squared = 0.3343
Root MSE = 16.146
Robust F(26,50)= 4.49
Robust Prob > F= 0.0000
Variable Coefficient
Standard
Error
t-stat vs.
Coef.=0
p-val vs.
Coef.=0
Robust
S.E.
Robust
t-stat
Robust
p-value
_cons 61.00705 37.44222 1.63 0.11 40.84164 1.49 0.142
actship 12.64186 17.38496 0.73 0.471 12.77257 0.99 0.327
cc 6.805372 5.785907 1.18 0.245 5.811371 1.17 0.247
check -4.02457 5.316919 -0.76 0.453 5.973571 -0.67 0.504
fri -19.329 7.30315 -2.65 0.011 8.600891 -2.25 0.029
jvc 28.94373 11.24533 2.57 0.013 16.11117 1.8 0.078
korean 14.08509 9.919328 1.42 0.162 10.0137 1.41 0.166
laucleng 8.701281 8.134123 1.07 0.29 8.147261 1.07 0.291
mitbishi 13.15508 13.71335 0.96 0.342 10.60261 1.24 0.22
modrep 1.236535 3.390686 0.36 0.717 4.723271 0.26 0.795
mon -11.9455 7.319958 -1.63 0.109 7.608973 -1.57 0.123
new 13.35233 6.912129 1.93 0.059 6.852637 1.95 0.057
pansonic 31.4019 9.60217 3.27 0.002 9.907073 3.17 0.003
rsv 14.76914 7.432406 1.99 0.052 10.25432 1.44 0.156
sanyo 36.53502 12.18903 3 0.004 13.26466 2.75 0.008
search2 -5.93602 7.08578 -0.84 0.406 8.278112 -0.72 0.477
shipprce -0.0574 3.123585 -0.02 0.985 2.284358 -0.03 0.98
shipsqrd 0.080231 0.145673 0.55 0.584 0.121127 0.66 0.511
strtprce -0.01956 0.075256 -0.26 0.796 0.087577 -0.22 0.824
sun -6.76518 7.774641 -0.87 0.388 9.112666 -0.74 0.461
thur -10.808 8.046637 -1.34 0.185 6.870899 -1.57 0.122
time -46.4216 86.08891 -0.54 0.592 87.77844 -0.53 0.599
timesqrd 38.83829 65.66827 0.59 0.557 66.35055 0.59 0.561
toshiba 27.07407 12.4453 2.18 0.034 11.7814 2.3 0.026
tue -12.9122 7.175322 -1.8 0.078 8.104997 -1.59 0.117
wed -11.1051 8.621557 -1.29 0.204 8.928681 -1.24 0.219
western 3.215591 9.352314 0.34 0.732 9.718282 0.33 0.742

33
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