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Testing for Sample Selection

Valentina Corradi and Daniel Gutknecht

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Abstract: This paper provides a unified approach for detecting sample selection in nonparametric conditional quantile \textit{and} mean functions. Our testing strategy consists of a two-step procedure: the first test is an omitted predictor test with the propensity score as omitted variable. This test has power against $\sqrt{n}-$alternatives. While failure to reject the null implies no selection, we cannot, as any omnibus test, distinguish between rejection due to genuine selection or to misspecification. Since differentiation of the latter has implications for nonparametric (point) identification and estimation of the conditional quantile function, our second test is designed to detect misspecification. Using only individuals with propensity score close to one, this test relies on an `identification at infinity' argument, but accommodates cases of irregular identification. Finally, our testing procedure does not require any parametric assumptions on the selection equation, and all our results in the quantile case hold uniformly across quantile ranks in a compact set. We apply our procedure to test for selection in log hourly wages using UK Family Expenditure Survey data.

New Economics Papers: this item is included in nep-ecm
Date: 2019-07, Revised 2019-08
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