Estimating First-Price Auctions with Unknown Number of Bidders: A Misclassification Approach

In this paper, we consider nonparametric identification and estimation of first-price auction models when N∗, the number of potential bidders, is unknown to the researcher. Exploiting results from the recent econometric literature on models with misclassification error, we develop a nonparametric procedure for recovering the distribution of bids conditional on unobserved N∗. Monte Carlo results illustrate that the procedure works well in practice. We present evidence from a dataset of procurement auctions, which shows that accounting for the unobservability of N ∗ can lead to meaningful differences in the estimates of bidders’ profit margins. In many auction applications, researchers do not observe N ∗, the number of bidders in the auction. (In the parlance of the literature, N ∗ is the “number of potential bidders”, a terminology we adopt in the remainder of the paper.) The most common scenario obtains under binding reserve prices. When reserve prices bind, the number of potential bidders N∗, which is observed by auction participants and influences their bidding behavior, differs from the observed number of bidders A (≤ N ∗), which is the number of auction participants whose bids exceed the reserve price. Other scenarios which would cause the true level of The authors can be reached at [email protected] and [email protected]. We thank Ken Hendricks, Harry Paarsch, Isabelle Perrigne, Jean-Marc Robin, Quang Vuong, and seminar participants at Brown, Caltech, UC-Irvine, Iowa, NC State, and SITE (Stanford) for helpful comments. Guofang Huang provided exceptional research assistance.