Order Statistics Approaches to Unobserved Heterogeneity in Auctions

We establish nonparametric identification of auction models with continuous unobserved heterogeneity using either three consecutive order statistics of bids or two with an instrument. We then propose sieve maximum likelihood estimators for the joint distribution of unobserved heterogeneity and private value, as well as their conditional and marginal distributions. Lastly, we apply our methodology to a novel dataset from judicial auctions in China. Our estimates suggest substantial gains from accounting for unobserved heterogeneity when setting reserve prices. We propose a simple scheme that achieves nearly optimal revenue by using the appraisal value as the reserve price.