Competition, endogeneity and the winning bid: An empirical analysis of eBay auctions

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Highlights

  • We estimate the effect of the number of bidders on the winning bid in eBay auctions.

  • The observed number of bidders is endogenous.

  • We use instrumental variables techniques and introduce a novel instrumental variable.

  • We show existence of a sizeable bias when endogeneity is not accounted for.

Abstract

Using a dataset of Texas Instruments (TI) calculator auctions on eBay, we estimate the impact of the number of bidders on the winning bid. We highlight the possible endogeneity associated with using the number of observed bidders. We tackle this problem by employing approaches involving instrumental variables. We introduce a novel instrumental variable, the closing interval between successive auctions. Estimates from the two-stage least squares (2SLS) regression are over three times those from an ordinary least squares (OLS) regression.

Introduction

This paper estimates the impact of the number of bidders on the winning bid using a sample of eBay auctions for Texas Instrument TI-83 graphing calculators. Because the bidding decision is costly, the number of bidders is likely to be endogenous to auction characteristics. A substantial literature tackles this endogeneity problem both theoretically and empirically, often with structural approaches. The contribution of this paper is to account for this endogeneity using a novel instrument for the number of bidders, the closing interval between successive auctions. Because data on auction timing is typically readily available, the approach has potential applications in many settings. An instrumental variables regression of the number of bidders on the winning bid produces estimates over three times those obtained from an ordinary least squares approach.

There is ample evidence in the literature to suggest that bidding is a costly activity. Reiley (2005) uses field-experiments to assess the entry costs for bidders in online auctions and consistently finds evidence that bidders’ participation decisions are endogenous. Bajari and Hortaçsu (2003) examine eBay collectible coin auctions to analyze determinants of bidder and seller behavior. They develop a structural econometric model of bidding in eBay auctions and use parameter estimates from this model to estimate, among other things, entry costs for bidders. They find that a low minimum bid and a high book value appear to attract more bidders, a finding that is consistent with costly participation. In their survey paper on internet auctions (Bajari and Hortaçsu, 2004), the same authors also advocate models of bidding in auctions that endogenize the number of participants.

Our paper is similar to that of Bajari and Hortaçsu (2003) in regard to the analysis of increased competition on the winning bid. Like them, we treat the observed number of bidders as endogenous. Unlike them, we use a reduced-form approach in estimating this relationship. We utilize methods based on instrumental variables, to control for the endogenous regressor and employ statistical tests to show the validity and effectiveness of our instruments.

Online auction data are usually easily accessible and relatively clean. However, they comprise information on a limited number of variables. Researchers generally use information on auction characteristics as instruments for endogenous regressors. In the context of our particular research question, several papers have used the initial or starting bid, scaled by the book value of the item, as an instrumental variable (IV) for the realized number of bidders in the auction.1 However, not all items sold in online auctions have a book value. In such cases, there is a concern that bidders may update values based on the seller’s reservation price.

For items with no recorded book values, the starting bid could provide a strong signal of the underlying worth of the item. This implies that this variable does not satisfy the criteria for a good IV for our purpose; a higher starting price may directly contribute to a higher final price, in addition to lowering the probability of an auction finding a buyer. Given this challenge, our particular contribution is the construct of a new instrumental variable – the closing interval between successive auctions – to correct for the endogenous regressor. We define this variable in Section 2. The information required to define this variable is also available in other online auction sites and this variable can inform aspects of online auctions other than the one we study in this paper. Moreover, it can be used to study conventional auctions as well. As such, this variable can potentially enrich future research on auctions.

Our results from an OLS specification suggest that an increase in the number of bidders increases the winning bid on average. When we treat the former variable as endogenous and use two-stage least squares (2SLS) specification, the magnitude of the coefficient is over three times the OLS estimate. Our results underscore the importance of addressing the endogeneity of the realized number of bidders in online auction settings.

The rest of the article is organized as follows: Section 2 describes our sample data from TI-83 graphing calculator auctions on eBay. We present the empirical strategy in Section 3 and results in Section 4. Section 5 concludes.

Section snippets

Data and descriptives

Our dataset consists of information collected on all auctions (including those that did not attract any bids) of Texas Instruments TI-83 graphing calculator auctions featured on eBay between 15 June 2003 and 30 July 2003. We exclude private auctions, ‘Dutch auctions’ of multiple units as well as ‘Buy-It-Now’ auctions, in which a buyer can pre-empt the auction by paying a posted price selected by the seller.

Empirical strategy

We examine the impact of the number of bidders in an auction on the winning bid, by estimating the following linear model:ln(WinningBid)i=Niβ1+Xiβ2+μi,where Ni is the number of bidders in auction i, and X is a vector of auction characteristics. The coefficient of interest is β1, the effect of an additional bidder on the (log of) the winning bid.

At first glance, the ordinary least squares (OLS) method would appear to be the natural candidate for estimating the above relationship. However, for

Results

Table 3 presents coefficient estimates from our 2SLS regressions. To gauge the magnitude of the endogeneity bias, we also present estimates from OLS regressions. In column (2) of Table 3, we present the 2SLS estimates. We observe that the coefficient for number of bidders increases the winning bid by about 11.53%, implying an average increase of $6.70 relative to the mean winning bid of $57.89. The implied elasticity is 0.84 for the winning bid with respect to the number of bidders. A

Conclusions

In this paper, we study the effect of increased competition among bidders on the winning bid, using a sample of TI-83 calculator auctions from eBay. We tackle the endogenity arising from using the observed number of bidders, N, by using instrumental-variable (IV) techniques. One of the instruments used in the analysis – the closing interval between auctions – is a hitherto underutilized variable in auction research. Our results underline the importance of treating N as an endogenous variable.

Acknowledgement

The authors thank Adam Loch, Steven Stillman and Matthew Wennersten for comments and suggestions. They retain sole responsibility for any remaining errors and omissions.

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