Structural analysis of auction data with an unknown number of bidders

My dissertation develops and applies new methods for analyzing auctions in which the number of potential bidders is unknown. That number is unknown in many real-world auctions, among which the popular eBay auction is a representative example.; The first chapter presents a new identification result and proposes an estimation method for an eBay auction model with an application. In particular, I show that within the symmetric independent private values (IPV) model, observation of any two order statistics of valuations nonparametrically identifies the bidders' underlying value distribution. In contrast to the results of previous studies, one does not need to know the number of potential bidders. It is sufficient to know two valuations with their rankings from the top (for example, the second- and third-highest valuations). I then propose a consistent estimator using the semi-nonparametric maximum likelihood estimation method. Monte Carlo experiments show that the proposed estimator performs well. I apply the proposed method to university yearbook sales on eBay. Using the estimate of bidders' value distribution, I explore the effects of sellers' ratings on bidders' value distribution; compute consumers' surplus; and check whether a regularity assumption that is often made in the mechanism design literature is satisfied.; The second chapter extends the first-chapter result to a first-price auction model with an uncertain number of bidders. There the first- and second-highest bids identify the bidders' value distribution and the distribution of the number of potential bidders within the symmetric IPV model. I then propose a consistent estimator of the bidders' value distribution. Again, unlike previous results, one need not know the number of potential bidders.; The third chapter develops new methods for structural analysis of auctions in which only winning bids are available. While I maintain a nonparametric approach with regard to the distribution of bidders' valuations, I assume that the number of potential bidders follows a Poisson distribution. The methods in the chapter are particularly useful for empirical study of descending and ascending auctions. In descending auctions, only winning bids are made. In ascending auctions, the interpretation of losing bids is often controversial.