Identification in most sample selection models depends on the independence of the regressors and the error terms conditional on the selection probability. All quantile and mean functions are parallel in these models; this implies that quantile estimators cannot reveal any - per assumption non-existing - heterogeneity. Quantile estimators are nevertheless useful for testing the conditional independence assumption because they are consistent under the null hypothesis. We propose tests of the Kolmogorov-Smirnov type based on the conditional quantile regression process. Monte Carlo simulations show that their size is satisfactory and their power sufficient to detect deviations under plausible data generating processes. We apply our procedures to female wage data from the 2011 Current Population Survey and show that homogeneity is clearly rejected.
This paper proposes bootstrap tests for the validity of instrumental variables (IV) in just identified treatment effect models with endogeneity. We demonstrate that the IV assumptions required for the identification of the local average treatment effect (LATE) allow us to both point identify and bound the mean potential outcomes (i) of the always takers (those treated irrespective of the instrument) under treatment and (ii) of the never takers (never treated irrespective of the instrument) under non-treatment. The point identified means must lie within their respective bounds, which provides four testable inequality moment constraints for IV validity. Furthermore, we present simulations on the finite sample behavior of various tests and empirical applications to labor market and economic development data. Finally, we show how to increase testing power by imposing mean dominance assumptions and propose a method to check for effect homogeneity across subpopulations
Standard sample selection models with non-randomly censored outcomes assume (i) an exclusion restriction (i.e., a variable affecting selection, but not the outcome) and (ii) additive separability of the errors in the selection process. This paper proposes tests for the joint satisfaction of these assumptions by applying the approach of Huber and Mellace (2011) (for testing instrument validity under treatment endogeneity) to the sample selection framework. We show that the exclusion restriction and additive separability imply two testable inequality constraints that come from both point identifying and bounding the outcome distribution of the subpopulation that is always selected/observed. We apply the tests to two variables for which the exclusion restriction is frequently invoked in female wage regressions: non-wife/husband's income and the number of (young) children. Considering eight empirical applications, our results suggest that the identifying assumptions are likely violated for the former variable, but cannot be refuted for the latter on statistical grounds.
In many empirical problems, the evaluation of treatment effects is complicated by sample selection so that the outcome is only observed for a non-random subpopulation. In the absence of instruments and/or tight parametric assumptions, treatment effects are not point identified, but can be bounded under mild restrictions. Previous work on partial identification has primarily focused on the "always observed'' (whose outcomes are observed irrespective of the treatment). This paper complements those studies by considering further populations, namely the "compliers'' (whose outcomes are observed if they are treated) and the observed population. We derive sharp bounds under various assumptions (monotonicity and stochastic dominance) and provide an empirical application to a school voucher experiment.
