Flexible Bayesian analysis of first price auctions using simulated likelihood. Chapter 2, unpublished

Current nonparametric methods often conduct inference based on estimated bid dis-tributions that cannot be generated by an equilibrium. Then, the analysis results, e.g., policy recommendations, may be suspicious. This actually happens for the sample from the OCS auctions that has been widely used. To provide more reliable inference, we develop a Bayesian method satisfying the equilibrium implications: (i) bidding mono-tonicity and (ii) density affiliation. We obtain (i) by directly parametrizing the valuation density and (ii) by putting zero prior on every non-affiliated density. Our method allows for a very flexible specification. To handle this highly parametrized model, we use a sim-ulated likelihood. We re-analyze the sample from OCS auctions. Our approach gives significantly different implications for auction design than preivous methods. Since the sample is small, the additional equilibrium information would have a large contribution. ∗I am greatly indebted to Keisuke Hirano, my advisor, for his guidance, patience, and encouragement. I am grateful to my professors, Jonah Gelbach, Gautam Gowrisankaran, John Wooders, and Mo Xiao for their invaluable advices and suggestions. I would also like to thank Tong Li for providing me with the data