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- 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 0 20 40 60 80 100 120 140 160 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 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
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