This paper develops a doubly robust procedure for estimating the quantile treatment effect under the identifying restriction that selection to treatment is determined by observable characteristics. Unlike other estimators, the suggested estimator is consistent if either (but not necessarily both) a propensity score model or outcome regression working models are correctly specified. Additionally, it is shown that when the working models are appropriately specified, the suggested estimator achieves the semiparametric efficiency bound, and is asymptotically normally distributed under some mild conditions. A real data application and Monte Carlo simulations are also used to illustrate the finite-sample performance of the proposed estimator.

This paper develops an empirical balancing approach for the estimation of treatment effects under the framework of outcomes being suffered from missing. We first represent the parameter of interest as a weighted expectation of the observed outcome by introducing two auxiliary binary variables and then estimate the weighting functions using covariate balancing methods. By tailoring the loss function for the weighting functions, the resulting treatment effect estimates are automatically weight-normalized and exhibit both low bias and reduced variance in finite samples when compared to conventional inverse probability weighting methods. Under some regularity conditions, we show that the proposed estimator is consistent, asymptotically normally distributed with the asymptotic variance achieving the semiparametric efficiency bound. Finite-sample performance of the proposed method is evaluated via Monte Carlo simulations.

In this paper, we propose a new procedure to test conditional independence assumption in studying casual inference for time series data. The conditional independence assumption is transformed to a nonparametric conditional moment test with the help of auxiliary variables which are allowed to affect policy choice but the dependence can be fully captured by potential outcomes and observable controls. When the policy choice is binary, a nonparametric statistic test is developed further for testing the conditional independence assumption conditional on policy propensity score. Under some regular conditions, we show that the proposed test statistics are asymptotically normal under the null hypotheses for time series data. In addition, the performances of the proposed methods are illustrated through Monte Carlo simulations and a real example considered in Angrist and Kuersteiner (2011).

This paper proposes a nonparametric test to assess whether there exist heterogeneous quantile treatment effects (QTEs) of an intervention on the outcome of interest across different sub-populations defined by covariates of interest. Specifically, a consistent test statistic based on the Cramér–von Mises type criterion is developed to test if the treatment has a constant quantile effect for all sub-populations defined by covariates of interest. Under some regularity conditions, the asymptotic behaviors of the proposed test statistic are investigated under both the null and alternative hypotheses. Furthermore, a nonparametric Bootstrap procedure is suggested to approximate the finite-sample null distribution of the proposed test; then, the asymptotic validity of the proposed Bootstrap test is theoretically justified. Through Monte Carlo simulations, we demonstrate the power properties of the test in finite samples. Finally, the proposed testing approach is applied to investigate whether there exists heterogeneity for the QTE of maternal smoking during pregnancy on infant birth weight across different age groups of mothers.

This paper develops an empirical likelihood approach to construct the confidence interval for the average treatment effect on the treated under the difference-in-differences framework. The empirical likelihood function is constructed based on a doubly robust moment function of the parameter of interest. Under some regularity conditions, we show that the proposed method retains the nonparametric Wilks property of empirical likelihood.

This paper proposes a new model, termed as the partially conditional quantile treatment effect model, to characterize the heterogeneity of treatment effect conditional on some predetermined variable(s). We show that this partially conditional quantile treatment effect is identified under the assumption of selection on observables, which leads to a semiparametric estimation procedure in two steps: first, parametric estimation of the propensity score function and then, nonparametric estimation of conditional quantile treatment effects. Under some regularity conditions, the consistency and asymptotic normality of the proposed semiparametric estimator are derived. Furthermore, the finite sample performance of the proposed method is illustrated through Monte Carlo experiments. Finally, we apply our methods to estimate the quantile treatment effects of a first-time motherOs smoking during the pregnancy on the babyOs weight as a function of the motherOs age, and our empirical results show substantial heterogeneity across different motherOs ages with a significant negative effect of smoking on infant birth weight across all motherOs ages and quantiles considered.

In this paper, we propose a new procedure to test conditional independence assumption for macroeconomic policy evaluation in a time series context. The unconfoundedness assumption is transformed to a nonparametric conditional moment test using auxiliary variables which are allowed to affect potential outcomes but the dependence can be fully captured by potential outcomes and observable controls. When the policy choice is binary, a nonparametric statistic test is developed further for testing the unconfoundedness assumption conditional on policy propensity score. The proposed test statistics are shown to have the limiting normal distribution under the null hypotheses for time series data. Monte Carlo simulations are conducted to examine the finite sample performances of the proposed test statistics. Finally, the proposed test method is applied to testing the conditional unconfoundedness in a real example as considered in Angrist and Kuersteiner (2011).

This paper proposes a new quantile regression model to characterize the heterogeneity for distributional effects of maternal smoking during pregnancy on infant birth weight across different the mother's age. By imposing a parametric restriction on the quantile functions of the potential outcome distributions conditional on the mother's age, we estimate the quantile treatment effects of maternal smoking during pregnancy on her baby's birth weight across different age groups of mothers. The results show strongly that the quantile effects of maternal smoking on low infant birth weight are negative and substantially heterogenous across different ages.

This paper proposes an alternative test procedure for testing the conditional unconfoundedness assumption which is an important identification condition commonly imposed in the literature of program analysis and policy evaluation. We transform the conditional 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 the null hypothesis of conditional independence. 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 conditional unconfoundedness in the real example of the return to college education.

This paper proposes a new quantile regression model to characterize the heterogeneity for distributional effects of maternal smoking during pregnancy on infant birth weight across different sub-populations denfied by the mother's age. By imposing a parametric restriction on the quantile functions of the potential outcome distributions conditional on the mother's age, we estimate the quantile treatment effects of maternal smoking during pregnancy on her baby's birth weight across different age groups of mothers. The results show strongly that the quantile effects of maternal smoking on infant birth weight are negative and substantially heterogenous across different ages.

In this paper, a new model, termed as the partially conditional quantile treatment effect (PCQTE) model, is proposed to characterize the heterogeneity of treatment effect conditional on some predetermined variable(s). We show that the partially conditional quantile treatment effect is identified under the assumption of selection on observables, which leads to a semiparametric estimation procedure in two steps: First, parametric estimation of the propensity score function and then, nonparametric estimation of conditional quantile treatment effect. Under some regularity conditions, the consistency and asymptotic normality of the proposed semiparametric estimator are derived. In addition, a specification test is seminally proposed in quantile regression literature, to test whether there exits heterogeneity for PCQTE across sub-populations, a consistent test, based on the Cramer-von Mises type criterion. The asymptotic properties of the proposed test statistic are investigated, including consistency and asymptotic normality. Finally, the performance of the proposed methods is illustrated through Monte Carlo experiments and an empirical application on 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 varies across different mother's age.

This paper provides a selective review of the recent developments on economet-ric/statistical modeling in quantile treatment effects under both selection on observables and on unobservables.First,we discuss identification,estimation and inference of quantile treatment effects under the framework of selection on observables.Then,we consider the case where the treatment variable is endogenous or self-selected,for which an instrumental variable method provides a powerful tool to tackle this problem.Finally,some extensions are discussed to the data-rich environments,to the regression discontinuity design,and some other approaches to identify quantile treatment effects are also discussed.In particular,some future research works in this area are addressed.

In the article, we provide the Schur, Schur multiplicative, and Schur harmonic convexities properties for the symmetry function Fnx,r=Fnx1,x2,⋯,xn;r=∏1≤i1

Four inequalities associated with two n-dimensional simplexes are given,so they have generalized and improved the results in some related paper.

A new proof of an inequality in Hilbert space was given by using algebraic method.Sufficient and necessary condition for equality in the inequality was presented.As application,the Hadamard’s inequality was obtained.