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  .
This paper provides tests for detecting sample selection in nonparametric conditional quantile functions. 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, we suggest a second test to provide supporting evidence 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. Importantly, neither of the two tests requires parametric assumptions on the selection equation nor a continuous exclusion restriction. Data-driven bandwidth procedures are proposed, and Monte Carlo evidence suggests a good finite sample performance in particular of the first test. Finally, we also derive an extension of the first test to nonparametric conditional mean functions, and apply our procedure to test for selection in log hourly wages using UK Family Expenditure Survey data as \mbox{%DIFAUXCMD AB2017 .
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Our testing strategy consists of a two-step procedure: the
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since the differentiation of the two causes has implications for nonparametric (point) identification and estimation of the conditional quantile function(s),
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identify
provide supporting evidence
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Our testing procedure does not require any
Importantly, neither of the two tests requires
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, and all our results hold uniformly across quantile ranks in a compact set. We
nor a continuous exclusion restriction. Data-driven bandwidth procedures are proposed, and Monte Carlo evidence suggests a good finite sample performance in particular of the first test. Finally, we also derive an extension of the first test to nonparametric conditional mean functions, and
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as \mbox{%DIFAUXCMD AB2017