Deconvolution From Two Order Statistics

Abstract

Economic data are often truncated by ranking and contaminated by measurement errors. We study the identification of the distributions of a latent variable of interest and its measurement errors using a subvector of order statistics of repeated measurements. Kotlarski's lemma is inapplicable due to dependence in the order statistics of measurement errors. Exploiting the ratio of characteristic functions of order statistics, we show observing two order statistics are sufficient to identify the underlying distributions nonparametrically. We adapt an existing simulated sieve estimator to our setting and illustrate its performance in finite samples.

Keywords: Measurement Error, Order Statistics, Nonparametric Identification, Spacing, Cross-Sum

JEL Classification: C14, D44