Nonparametric Identication of a Binary Random Factor in Cross Section Data
نویسندگان
چکیده
Suppose V and U are two independent mean zero random variables, where V has an asymmetric distribution with two mass points and U has some zero odd moments (having a symmetric distribution su¢ ces). We show that the distributions of V and U are nonparametrically identi ed just from observing the sum V + U , and provide a rate root n estimator. This can permit point identi cation of average treatment e¤ects when the econometrician does not observe who was treated. We 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: C25, C21 Keywords: Mixture model, Random e¤ects, Binary, Unobserved factor, Unobserved regressor, Nonparametric identi cation, Deconvolution, Treatment
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Nonparametric Identification of a Binary Random Factor in Cross Section Data
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