Ulric B. and Evelyn L. Bray Social Sciences Seminar
Identification of auctions with incomplete bid data in the presence of unobserved heterogeneity
Abstract: This paper derives novel nonparametric identification results for auction models with in-complete bid data and finite unobserved heterogeneity (UH). By exploiting the Markov property of order statistics, I show that the joint distribution of bidders' valuations and the UH is point identified from an incomplete set of bids. The result holds if the econometrician either observes (any) five order statistics of the bids in each auction or only three along with an instrument, and without imposing any functional form restriction on how the UH affects valuations. This data structure is encountered in many empirical settings, such as ascending auctions in which the winner's bid is usually not observed. I establish these results under weak distributional assumptions. For second price auctions, the result holds generically over the space of possible distributions of valuations and UH, and for first-price auctions, it holds when the conditional distribution of valuations varies monotonically with the UH in the reverse hazard rate order. I show that identification can be extended to settings where the number of potential bidders is unobserved, as is often the case in online auctions. Finally, I provide easily implementable nonparametric estimation procedures, and simulation results show that they perform well for samples of moderate size.
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