Nonparametric Identification of a Binary Random Factor in Cross Section Data

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 illustrate the results with an empirical example looking at possible convergence over time in the world income distribution. 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. JEL Codes: C35