Order Statistics Approaches to Unobserved Heterogeneity in Auctions

TL;DR

This paper introduces a nonparametric method using order statistics to identify and estimate unobserved heterogeneity in auction models, demonstrating its practical benefits through judicial auction data in China.

Contribution

It develops a novel nonparametric identification approach and sieve maximum likelihood estimators for auction models with unobserved heterogeneity, applied to real-world data.

Findings

Accounting for unobserved heterogeneity improves reserve price setting.

Using appraisal value as reserve price nearly maximizes revenue.

Method provides substantial revenue gains in judicial auctions.

Abstract

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.