This paper provides a unified approach for detecting sample selection in nonparametric conditional quantile 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 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.
This paper provides a testing approach for detecting sample selection in nonparametric conditional quantile functions. Our testing strategy consists of a two-step procedure: the first test is an omitted predictor test with the propensity score as the omitted variable. As with any omnibus test, in the case of rejection we cannot distinguish between rejection due to genuine selection or to misspecification. Thus, since the differentiation of the two causes has implications for nonparametric (point) identification and estimation of the conditional quantile function (s), we suggest a second test to identify whether the cause for rejection at the first stage was solely due to selection or not . Using only individuals with propensity score close to one, this second test relies on an `identification at infinity' argument, but accommodates cases of irregular identification. Our testing procedure does not require any parametric assumptions on the selection equation, and all our results 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.
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unified
testing
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and
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mean
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the
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This test has power against \sqrt{n
As with
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in the case of rejection we cannot
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Since
Thus, since the
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latter
two causes
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, our second test is designed to detect misspecification
(s), we suggest a second test to identify whether the cause for rejection at the first stage was solely due to selection or not
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second
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Finally, our
Our
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in the quantile case