Do auction formats matter in eBay auctions ?

The proliferation of Internet auction elicits many interesting research questions for researchers engaging in this area. This study applies the empirical model to test whether the prices generated from different auction formats in eBay are equivalent. The daily observations in each format from eBay auctions are employed, and the empirical findings give rise to an important implication for internet auctions. The prices generated from different auction formats would be likely to converge except for the combination of the fixed-price listings with the best-offer option and the auction-style listings with the buy-it-now price. Therefore, the sellers’ expected revenues would be equal even they specify their auctions with different formats.


INTRODUCTION
Online auction is very interesting and attractive because varieties of auction formats are offered and conducted sequentially or even in parallel.
The studies that investigate in the relationship between the auction formats and the seller's revenue (or transaction price) have appeared in large numbers in recent years (Bajari and Hortacsu (2004) and Ockenfels et al. (2006) and Hasker and Sickles (2010)).These studies are based on cross sectional analysis that could not provide a longterm view between these auction formats.Haruvy et al. (2008) and Haruvy and Popkowski Leszczyc (2009), however, mentioned that competition is ordinary in online auctions, and we believe that this scene may be mapped Corresponding author.E-mail: yingtang.huang@gmail.com , Tel: +886-933-255532.by long-term relationship between auctions. 2Therefore, this study would like to explore and examine the relationship by using eBay auctions.
In the previous studies about online auctions, buyout prices in online auctions may be the most interesting mechanism and attract many researchers to investigate.From Budish and Takeyama (2001), Mathews and Katzman (2006), to Reynolds and Wooders (2009), Shunda (2009), Inami (2011), Che (2011), Malmendier and Lee (2011), and Shahriar and Wooders (2011), they all try to explain the bidders' behavior when the sellers provide or not provide buyout price in online auctions.Otherwise, the ending rules in online auctions also draw much attention.Roth and Ockenfels (2002), Ariely et al. (2005), and Ockenfels and Roth (2006) are the pioneering in this topic, and then Tsuchihashi (2012) and Damiano et al. (2012) follow the pioneer and go a step further in this issue.
However, these previous studies lack dynamic view point may be arisen from two main reasons.First, their data cannot be transferred to time-series data, and it is difficult for them to apply any dynamic model.Otherwise, it may be difficult and almost impossible to process auctions by using two or more formats at the same time conventionally.However, the auctions in eBay take place when identical items are proceeding simultaneously.
In eBay auctions, either sellers or buyers could retrieve the results of completed auctions, either result in a sale or not, without any charge.
3 That is, it is possible for the agents to retrieve records of completed auctions when planning current transaction son the Internet auction sites defines a learning scheme that has been examined by Sonsino and Ivanova-Stenzel (2006).Therefore, the prices of the items in the same category may be correlated.Sonsino and Ivanova-Stenzel (2006)'s results suggest that the contents of samples retrieved from public databases may significantly affect the behavior of sampling agents.Since the price generation would be affected by the behavior(i.e., information retrieval) of the participants, the effects of records of completed auctions on the price generations in eBay should be expected.Other than the agents' behavior (both buyers and sellers) may be influenced by retrieving the information via the history records in eBay, there are still reasons for investigating in the relationship between auction formats using a time-series model.First, auctions on eBay are conducted sequentially or even in parallel (overlapped).Thus, the current highest prices and the current highest bids in eBay may be affected by the other auctions that are conducted at the same time.
4 Therefore, serial correlations between prices exist in eBay would be expected.Meanwhile, the other current prices from other auctions with similar (or even identical) items may affect the buyers' valuations for their items.Therefore, exploring the eBay auctions' results by using time series model should be reasonable.
In the light of the aforementioned concerns, the purpose of this paper is to empirically examine whether the transaction prices under different auction formats are likely to converge.A dynamic model proposed by Ravallion (1986) can visit in the issue of prices generation by using eBay as a target, and the new insight is also highlighted due to eBay auctions offering formats that differ from conventional auctions.Based on Ravallion (1986)'s model, the test results show that the transaction prices will not converge in the short run, but they are likely to converge in the long run in eBay auctions.The most related work to our study would be Li et al., (2006) which studied the final price prediction by collecting large amounts of historical exchange data from Each net in China.Their prediction was made by traditional statis-4 The difference between "the current highest price" and "the current highest bid"is depended on which bidding way is used by the buyer in eBay.One can refer to the following link: http://pages.ebay.com/help/buy/formats.htmlHuang et al. 11313 tical methods to forecast the final prices of auction items, but they ignored the possible correlation between the current auctions and the past auctions' records.The remainder of this article is organized as follows.Section 2 outlines the econometric model and hypotheses that are derived from Ravallion (1986).The empirical data and specifications are illustrated in Section 3. Section 4 describes and analyzes the empirical results.The concluding remarks and implications are provided in Section 5. Ravallion (1986) has proposed an empirical model to test spatial market integration.However, the 'markets' will be replaced by 'formats' in the following section while the purpose will be to test whether the prices from two different auction formats are equal.Hence, the static pattern of price formation among N formats can be represented as follows:

RAVALLION MODEL AND HYPOTHESES
) is a vector of other exogenous variables which might influence price formation in format i, and P i and P j are the prices of the ith and jth formats, respectively.The functions f i (i = 1,...,N) can be thought of as solutions to the appropriate conditions for the equilibrium of format i, taking into account the main spatial choices and the costs of adjustment facing traders when deciding where to sell.The econometric version of the above static pattern of price formation should embody a suitable dynamic structure; as is well known, dynamic effects can arise from a number of conditions in the underlying behavioral relations, including expectations formation and adjustment costs (Ravallion, 1986).
In combining these considerations, the following econometric model of a T-period series of prices for 2 formats is specified as follows: (1) Where P it and P jt indicate the prices of theith and jthformats at time t, respectively.P it-h and P jt-k respectively display the lagged terms of theith and jth formats, while a ih and b jk are their corresponding coefficients.X' it is the vector of other predetermined variables that could affect the price of the ith format, and c i is its vector of coefficients.e it is a white noise process or suitable error process.
In terms of the parameters of equation ( 1), for every two auction formats, one is the ith format and the other is the jth format.Ravallion (1986) proposed the following four testable hypotheses: H 01 : Formats are segmented Suppose the expected equilibrium price in the ith format is indicated by E(P it ), and that E(P jt ) illustrates the expected equilibrium price in the jth format.Then the following two equations can display the expectation for each format: Equations ( 2) and ( 3) respectively indicate that the expected transaction prices for the ith or jth auction format in each period are equal.One can say that the auction formats are segmented if the following relationship holds: By means of equations ( 2), (3), and (4), the first null hypothesis H 01 can be expressed as: If H 01 is rejected, this implies that the price in the jth auction format may influence the pricein theith auction format.However, the price convergence is still not resolved before testing the other three hypotheses.
H 02 : Strong form short-run price convergence Ravallion (1986) demonstrates that strong form short-run price convergence is the effect of a price increase in thejth auction format that will be immediately passed on to the ith auction format price.That is, it implies that the prices in the two auction formats will instantaneously adjust to the same expected value as follows: By contrast, when the price in the jth format is integrated with that in the ith format within one time period, the lagged effectof both theith and jth formats cannot affect the future price in theith auction format.Thus, the following two equations exhibit the relationships: Hence, by combining equations ( 6), ( 7), and ( 8), the null hypothesis may be presented as follows: H 02 : b j0 = 1, and a ih = b jk = 0, h = 1…m, and k = 0, 1…n.
If this null hypothesis is not rejected, then one can say that the price in the ith format will be integrated with the price in the jth format within one period.That is, the prices in the two different formats will instantaneously adjust to the same expected value.
H 03 : Weak form short-run price convergence The hypothesis of weak form short-run price convergence will also be tested.It allows the aggregate effects of both lagged prices (the ith and jth formats) on the future price of the ith format to only vanish on average when compared with the strong form short-run price convergence.Ravallion (1986) explains that the lagged variable may still have an impact on the future prices unless the lagged effects (both the ith and jth formats) aggregate to zero.Then, the null hypothesis can be expressed as follows: H 03 : b j0 =1, and . If H 03 is not rejected, the aggregated effect of lagged prices (which combines the effects of the ith and jth formats) on the future price in the ith format may be zero and the short-run price convergence between the ith and jth formats will be achieved.

H 04 : Long-run price convergence
A long-run equilibrium is one in which market prices are constant over time, undisturbed by any stochastic effects (Ravallion, 1986).Assume that equation (1) takes the form P it =P * =P jt , and that e it =0 for all t; then equation ( 9) which follows demonstrates this expectation: By substituting the expectations into equation (1), we can then obtain the following equation ( 10): Moreover, when the prices in the ith and jth formats are convergent, the effect of other characteristics, X it , on the prices of the ith format will vanish, That is, the coefficients of X it will not be significant.Equation (10) can then be documented as follows: All the four null hypotheses proposed by Ravallion (1986) can be applied to test price convergence between the two auction formats.Hence, this study will estimate the price generating process suggested by equation (1) for each auction format and will then apply the above documentation to test the four hypotheses.

Data collections and descriptions 5
The empirical data were collected on eBay finished auctions, similar to that described in Li (2010) and Lucking-Reiley (1999). 6To avoid the heterogeneous quality by different manufacturers (or brands), we collected the auction data for a single manufacturer (or brand).
The authors followed Roth and Ockenfels (2002) and did not restrict the data to a particular subset of auctions.This is partly to avoid the danger that the data are dominated by a typical behavior patterns.
In the sample category, there are at least 1,500 auctions processed on eBay sites every day during our sample period, but the proportion of auctions that succeed is less than 30%. 7Fortunately, four auction formats are simultaneously observed on eBay and collected by us.Thus, this paper can test whether the prices generations are getting equalized among the four formats.The pooled daily transaction prices for each auction format were applied in the empirical estimations.
The auction formats in eBay can be roughly classified into two types, which are fixed-price listings and auction-style listings (that is, ascending price auctions), and Figure 1 simply depicts their relationship.There is no ascending bidding process under fixedprice listings since the seller wants to sell the item only for a fixedprice.Recently (from 2005), eBay auction sites provide a new option for the sellers, namely, the best-offer, under fixed-price listings.That is, if the seller adopts the best-offer in his fixed-price listing, he/she gives buyers chances to negotiate the price with him/her.And then, the seller may reply to accept or reject the price offered by the buyer within the next 48 hours, or the offer price will expire.Therefore, PF (the 1 st format) represents the transaction prices series under fixed-price listings without the best offer in each period, and (the 2 nd format) denotes the transaction prices series when the best-offer is provided by the sellers under fixedprice listings.
The other two auction formats are both based on auction-style listings, and one of them provides a buy-it-now price.An auctionstyle listing needs to provide a minimum-bid (that is, starting-bid) for the buyer to start the ascending or competitive bidding process.However, if a seller provides a buy-it-now price in his auction-style listing, a buyer can avoid competition with other potential buyers by bidding the buy-it-now price to be the winner in the auction. 8ence, PA_buy (the 3 rd format) indicates the transaction prices when the buy-it-now price is available and also the transaction price in the listings.Otherwise, PA (the 4 th format) denotes the transaction prices of auction-style listings when it is ended by the second highest bid plus the minimum increment.The relationship between these four auction formats is depicted in Figure 1.
For the period from Feb. 8, 2008 to Apr.21, 2008, data on 14,352 completed auctions on eBay auction sites were collected.There were 4,289 auctions that were successful, and each auction received at least one bid that was at least higher than the reserve price set by the seller. 9Therefore, this paper divides these 4,289 observations into the four auction formats mentioned above.Finally, there are 74 daily observations from Feb. 8 to Apr.21, 2008 for each auction format, for which can be conducted the empirical estimations and tests.Table 1 display the summary statistics, and Figure 2 shows the time-series plots of the four different types of auction.In Figure 2, though the transaction prices series of fixed-9 On eBay, the reserve price can be meant to be the 'starting bid (minimum bid)' or 'secret reserve price'.Among these 4,289 auctions, there are 107 auctions based on the 1 st format, 468 on the 2 nd format, 695 on the 3 rd format, and 3,019 on the 4 th format.
price listings, that is, PF more volatile than the other three price series, the four prices series may co-integrate by eyeball test.
In what follows, we will describe the empirical steps and methodology.

Augmented Dickey-Fuller tests
We seek to make sure that the stationarity of each series is a necessary condition for estimating an empirical model with time series data, or else the non-stationary series may lead to spurious regressions (Enders, 2004).To avoid the possibility of a spurious relationship, the well-known ADF (augmented Dickey-Fuller, henceforth ADF) test Dickey andFuller (1979, 1981) can be used to certify the stationarity of the series.The ADF test statistics for the four series are shown in Table 2.We can observe that all sequences in the sample set are stationary, and can conclude that the estimation of the model can avoid the possibility of spurious regression.
Q3, Q6, and Q9 are diagnostic tests of data generation process, and their results may guarantee the error term (eit) at each model is white noise.***The critical values of 1%, 5%, and 10% are -3.521,-2.901, and -2.588 respectively.

Empirical model estimations
In order to develop a more precise data generating process, equation ( 1), the econometric package in E-Views, is applied.For convenience, we limit the largest lagged price series in the estimation for both the ith and jth formats to 7. On the other hand, too many lag terms in the estimations may lack degrees of freedom and lead to inefficient estimations.All the possible lag-combinations of each of the two formats are included in the estimations and the results of the estimations are shown in Table 3. the error term when estimating equation ( 1) is required to be a white-noise process, in which the error term sequence has a mean of zero, a constant variance, and is serially uncorrelated.That is, well-known diagnostic tests are performed following the estimations.Hence, the following two conditions are necessary in searching for a suitable data process (Enders, 2004): To ensure the estimated coefficients are unbiased, the test statistics for Q3, Q6, and Q9 in Table 4 are used to perform the diagnostic tests.These three statistics reject the serial correlation in the error term, which is generated when estimating equation (1).Hence, the estimated coefficients of equation ( 1) are unbiased due to its error term being white noise.After ensuring that the estimations are unbiased, the parsimonious model is confirmed by SBIC (Schwarz Bayesian Information Criterion), that the estimation with the smallest SBIC was applied in the following analysis.Finally, these estimated coefficients of the models are used to test the four hypotheses that are discussed in Section 2. Based on the Wald-test, the test statistics for the four hypotheses, H01, H02, H03, and H04, are displayed in the right four columns of Table 4, and are further summarized in Table 4.In the next section we discuss the test results.

RESULTS AND DISCUSSION
The test results are summarized in Table 4, where "Rejected" indicates that the null hypothesis is rejected and "Not rejected" signifies that the opposite conclusion has been reached.
One can find that both hypotheses of H 02 and H 03 are rejected.This would imply that the prices of different auction formats cannot immediately adjust to the same expected value in one day, even though the price information may be transmitted quickly through internet auction sites. 10We then go a step further to examine the results of testing H 01 (formats are segmented) and H 04 (long-run convergence).
Notice that the results of testing H 01 and H 04 can be compared at the same time.That is, if H 01 is rejected, then H 04 will not be expected to be rejected.Or, in other words, when the two transaction price sequences exhibit a relationship over the long run (that is, fail to reject H 04 ), H 01 should be rejected to indicate that the two formats are not segmented.From Table 4, almost all the tests report that the H 01 s are rejected and the H 04 s are not rejected, except for the estimation of the regressions for the fixed price auctions with the best offer being P it and the ascending auctions with the buy-it-now price being P jt .
11 Hence, we note that none of the test results is paradoxical, and in what follows we give some explanations for these results.To our knowledge, both theoretical and empirical studies conclude that different auction formats may give rise to different levels of revenue among sellers, especially auction-style listing with a buy-it-now or buyout price (Ockenfels et al., 2006).However, eBay auctions are simultaneously and sequentially proceeding.Otherwise under open auctions, 12 buyers can monitor whether the prices is higher than the other auctions in real time, and then decide if they should participate in the auction, revise their bids or drop out of the auction (e.g., by not raising their bids above the prevailing market-clearing bids) (Koh et al., 2007).This might be the reason why the transaction prices for different auction formats will eventually converge to the same expected value.
**Each model is selected by SBIC (Schwarz Bayesian information criterion).Q3, Q6, and Q9 are diagnostic tests of data generation process, and their results may guarantee that the error term (eit) at each Ravallion estimation is white noise.*** H01: prices are uncorrelated under different mechanism; H02: strong form short-run price convergence; H03: weak form short-run price convergence; H04: long-run price convergence.enables the registered users to trace back the statuses of the auctions that have been completed during the past 14 days, that is information retrievals. 14Either buyers or sellers in eBay auctions could refer to the records of the completed auctions if necessary, and this could also induce more informational transparency in eBay auction sites.The winning bidder may retrieve the information of completed auctions, and then bid accordingly.Therefore, the prices between formats are insignificantly different from each other.Otherwise based on our data, the proportion of auctions that were successful was less than thirty percent (29.88%), so that more than 70% were unsuccessful.Therefore, the proportion of unsuccessful auctions might be significantly higher than the proportion of successful ones.The authors have therefore carefully checked the whole data set and have found that the reserve prices 14 Yahoo auction sites do not provide this specific service for users of their site.
(that is, the seller's minimum willingness to accept) of the unsuccessful auctions are significantly higher than the transaction prices of the successful auctions.Hence, consumers in eBay auction markets might have greater power to determine the transaction price, regardless of which format a seller would like to offer.
Most test results (more than 83%) show that the transaction prices would converge.Hencein eBay, the transaction prices might be expected to converge even though the sellers may wish to make more revenue by offering different formats, and the revenue equivalence theorem is found to hold in eBay auctions.

Conclusion
The study attempts to investigate whether the auction formats matter by the prices in eBay auctions.Unlike the previous studies that consider the prices generations between formats by static that may bias the conclusion due to such as information retrieval by the participants in eBay (Sonsino and Ivanova-Stenzel, 2006).This study goes a step further to estimate the prices generation process by a dynamic model by using transaction prices for different formats in eBay.The 74 daily observations from February 8 to August 21 in 2008 on eBay auction sites are examined to test whether the transaction prices between different formats are equivalent.
The test results show that the transaction prices (also the seller's revenue) for different auction formats cannot immediately adjust to the same expected value, that is, the tests for short-run convergence are rejected.Furthermore, except for P F_best which is P it and P A_buy which is P jt in Ravallion (1986)'s estimation, the other results from testing H 01 show that neither of the two formats is segmented, and the hypotheses of long-run price convergence (H 04 s) are not rejected.
Hence, we expect that the prices would converge even though the seller might expect higher revenue by offering a specific format (for example, auctions with a buy-it-now price).Therefore, our empirical results may provide new insights for online auctions.That is, the price series will be converged even under different auction formats.
In addition, common value element may be existed in eBay auctions which are with repeated and simultaneous objects.Under these phenomenon, the prices could converge to the same value, and then the bidders may decide whether they should participate in the auction, and revise their bids or drop out of the auction (e.g., by not raising their bids above the prevailing market-clearing bids) (Koh et al., 2007).
There is still one test result (P F_best on P A_buy ), however, that leads to the rejection of the prices will converge to the same value.The short time length of the data set may be the reason for this, and may be an issue that should become the focus of future research.In addition, the empirical results can enable us to more precisely estimate whether the empirical data can be examined further to avoid the possible effects of heterogeneity.In other words, this paper, among others, has to provide new insights into testing the prices generation process in the context of online auctions.However, when more convincing data become available, we can re-estimate the related empirical model and obtain more promising results.
As an exploratory study, the regression results of this study imply the prices will be equivalent.In the future, we wish to shed more light on possible strategies used by buyers and sellers if more regression results are obtained in the future study are reliable, or on more detailed characteristics of the different auction formats that might lead them to generate different prices.Other wise, using a time series econometric model does not involve considering the endogenous choice of auction formats that result from the seller choosing which auction format to adopt (Hansen, 1986).This is indeed an important Huang et al. 11319 limitation of the econometric model estimations in this study, and we therefore hope that this shortcoming can also be resolved in the future.
statistics are estimated by this research.*The superscript ' ', and ' b ' denote the statistic is fail to be rejected at 5% and 10% significant level respectively.**The superscript ' c denotes the statistic is to be rejected at 5% significant level.

Table 1 .
The time series plots of price of the four formats.Periods of above four figures are all from Feb. 8 to Apr.21, 2008.The vertical axis implies the transaction prices, and the horizontal axis implies the days.Variable Descriptions.
Figure 2. Source: All statistics are estimated by this research.

Table 3 .
Ravallion Model Estimations and Tests (p-values are in the parentheses).

Table 4 .
Summary of Ravallion Model Tests.