  We establish nonparametric identification of auction models with continuous
and nonseparable unobserved heterogeneity using three consecutive order
statistics of bids. We then propose sieve maximum likelihood estimators for the
joint distribution of unobserved heterogeneity and the 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.
