Estimation And Inferences For Partially Conditional Quantile Treatment Effects

In the last decades,an increasing number of literature in economics and other social sciences has been focusing on the identification of the causal effect of a treatment or policy on economic and other outcomes of interest and a large fraction of this literature focuses on the mean treatment effects.Although the mean treatment effects are very important in measuring a treatment or policy's effect,they might not provide sufficient information about the impact of the treatment or policy on the entire distribution of outcomes.In many contexts,researchers may be more interested in the heterogeneously distributional effects of a treatment or policy on outcomes.To characterize the heterogeneous effects along with the outcome distribution,quantile treatment effect(QTE)provides an effective and intuitive tool to document such heterogeneity.However,it is generally recognized in program evaluation literature that treatment effects can be heterogeneous across different individuals.Therefore,except for the quantile treatment effect for the entire population,researchers may also be interested in estimating the quantile effect of a treatment or policy on outcome of interest in various sub-populations defined by the possible values of some covariates.To this end,in this dissertation,we propose the partially conditional quantile treatment effect model to capture the heterogeneously distributional impacts of treatment participation across different sub-populations.In addition,note that the unconfoundedness assumption plays a central role in identifying the parameters of treatment effect and there are only a few of procedures available in the literature to test it,so we try to propose an alternative method to test whether it is true.In summary,the main body of the dissertation consists of three parts.In the first part,we consider the partially conditional quantile treatment effect(PCQTE)model under the identifying restriction that selection to treatment is based on observable characteristics.First,we show that the PCQTE parameter is nonparametrically identified,which leads to an estimation procedure with two steps:(i)nonparametric or parametric estimation of the propensity score function and(ii)computation of the difference between the solutions of two separate minimization problems.Under some regularity conditions,we then show consistency and asymptotic normality of the proposed fully nonparametric and semiparametric estimator.In addition,to test whether there exits heterogeneity for PCQTE across sub-populations,we propose a consistent test based on Cramer-von Mises criterion and derive the asymptotic properties of the proposed test,including consistency and asymptotic normality.Finally,the performance of the proposed methods is illustrated through Monte-Carlo experiments and an empirical example,estimating the effect of the first-time mother's smoking during pregnancy on the baby's birth weight conditional on mother's age and testing whether the partially conditional quantile treatment effect is equal to the corresponding unconditional quantile treatment effect or varies across different mother's age.In the second part,we propose an alternative test procedure for testing the unconfoundedness assumption which is an important identification condition commonly imposed in the literature of program analysis and policy evaluation.We transform the unconfoundedness test to a nonparametric conditional moment test using an auxiliary variable which is independent of the treatment assignment variable conditional on potential outcomes and observable covariates.The proposed test statistic is shown to have a limiting normal distribution under null hypotheses of unconfoundedness.Monte Carlo simulations are conducted to examine the finite sample performances of the proposed test statistics.Finally,the proposed test method is applied to test the unconfoundedness in real examples:the 401(k)participation program and return to college education.In the third part,we extend the model framework considered in the first part to estimate the partially conditional quantile treatment effect under the framework of selection on unobservables.In this setting,to identify meaningful treatment parameters,instrumental variable(?)is needed and it provides a powerful tool to address this problem.We show that the partially conditional quantile treatment effect is nonparametrically identified when ? satisfies some conditions,which leads to an estimation procedure with two steps:(?)nonparametric or parametric estimation of the instrument propensity score function and(?)computation of the difference between the solutions of two separate minimization problems.Under some regular conditions,the(point-wise)consistency and asymptotic normality of the proposed estimate are derived.Finally,the usefulness of the proposed estimation procedure is illustrated via Monte Carlo experiments and an application to the effects of 401(k)eligibility and 401(k)participation on measures of accumulated assets conditional on age or income.