# Nonparametric Identification of a Binary Random Factor in Cross Section Data

*Yingying Dong* and
*Arthur Lewbel* ()

No 707, Boston College Working Papers in Economics from Boston College Department of Economics

**Abstract:**
Suppose V and U are two independent mean zero random variables, where V has an asymmetric distribution with two mass points and U has a symmetric distribution. We show that the distributions of V and U are nonparametrically identified just from observing the sum V+U, and provide a rate root n estimator. We apply these results to the world income distribution to measure the extent of convergence over time, where the values V can take on correspond to country types, i.e., wealthy versus poor countries. We also extend our results to include covariates X, showing that we can nonparametrically identify and estimate cross section regression models of the form Y=g(X,D*)+U, where D* is an unobserved binary regressor.

**Keywords:** Mixture model; Random effects; Binary; Unobserved factor; Unobserved regressor; Nonparametric identification; Deconvolution; Treatment (search for similar items in EconPapers)

**JEL-codes:** C25 C21 (search for similar items in EconPapers)

**Date:** 2009-06-16, Revised 2010-07-01

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**Related works:**

Journal Article: Nonparametric identification of a binary random factor in cross section data (2011)

Working Paper: Nonparametric identification of a binary random factor in cross section data (2009)

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**Persistent link:** https://EconPapers.repec.org/RePEc:boc:bocoec:707

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