Estimation of Standard Auction Models

Estimating value and/or bid distributions from an observed sequence of auctions is a fundamental challenge in Econometrics with direct practical applic ations. For example, these fundamentals allow one to analyze the performance of an auction and make co unterfactual predictions about alternatives. The difficulty of this problem depends on the fo rmat of the auctions and the structure of the observed information from each one, as well as how the fundamentals of bidders are interrelated and vary across the sequence of observations. In this paper, we study a basic version of the afore-describe d estimation challenge, wherein the auction format and the bidder distributions stay fixed across observations, and the bidders have independent private values (which are independently resam pled across different observations). The auction formats that we consider are first-and second-pri ce auctions, as well as Dutch and English auctions. What will make our problem challenging is that (i) our bidders are ex ante asymmetric, drawing their independent private values from different distributions; (ii) we will make no parametric assumptions about these distributions; and (iii) we will only be observing the 1 identity of the winner and the price they paid but not the losi ng bids. Under this observational model and our independent private values assumption above, we can focus our attention on first-and second-price auctions, and our results automatically e xtend to Dutch and English auctions. In the above settings, we give computationally and sample ef ficient methods for estimating all agents' bid distributions and (under equilibrium assumpti ons) value distributions: In the case of first-price auctions, we provide finite-sample es timation guarantees under L evy, Kolmogorov and T otal V ariation distance with minimal assumptions. Under (a condition weaker than) a lower bound on the density of the bid dis tributions (although we actually do not need existence of densities), Theorem 2.2 shows that the bid distributions can be estimated to within ε in L evy distance, using 1/ ε