Estimating first-price auctions with an 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, but observed by bidders. 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 the unknown N ∗ . Monte Carlo results illustrate that the procedure works well in practice. We present illustrative evidence from a dataset of procurement auctions, which shows that accounting for the unobservability of N ∗ can lead to economically meaningful differences in the estimates of bidders’ profit margins.