Deconvolution from two order statistics

Abstract

Economic data are often contaminated by measurement errors and truncated by ranking. This paper shows that the classical measurement error model with independent and additive measurement errors is identified nonparametrically using only two order statistics of repeated measurements. The identification result confirms a hypothesis by Athey and Haile (2002) for a symmetric ascending auction model with unobserved heterogeneity. Extensions allow for heterogeneous measurement errors, broadening the applicability to additional empirical settings, including asymmetric auctions and wage offer models. We adapt an existing simulated sieve estimator and illustrate its performance in finite samples.