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Register a new userTreatment Effects Estimation by Uniform Transformer
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Added by
Shulei Wang
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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In observational studies, balancing covariates in different treatment groups is essential to estimate treatment effects. One of the most commonly used methods for such purposes is weighting. The performance of this class of methods usually depends on strong regularity conditions for the underlying model, which might not hold in practice. In this paper, we investigate weighting methods from a functional estimation perspective and argue that the weights needed for covariate balancing could differ from those needed for treatment effects estimation under low regularity conditions. Motivated by this observation, we introduce a new framework of weighting that directly targets the treatment effects estimation. Unlike existing methods, the resulting estimator for a treatment effect under this new framework is a simple kernel-based $U$-statistic after applying a data-driven transformation to the observed covariates. We characterize the theoretical properties of the new estimators of treatment effects under a nonparametric setting and show that they are able to work robustly under low regularity conditions. The new framework is also applied to several numerical examples to demonstrate its practical merits.
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We extend balloon and sample-smoothing estimators, two types of variable-bandwidth kernel density estimators, by a shift parameter and derive their asymptotic properties. Our approach facilitates the unified study of a wide range of density estimators which are subsumed under these two general classes of kernel density estimators. We demonstrate our method by deriving the asymptotic bias, variance, and mean (integrated) squared error of density estimators with gamma, log-normal, Birnbaum-Saunders, inverse Gaussian and reciprocal inverse Gaussian kernels. We propose two new density estimators for positive random variables that yield properly-normalised density estimates. Plugin expressions for bandwidth estimation are provided to facilitate easy exploratory data analysis.
The empirical literature on program evaluation limits its scope almost exclusively to models where treatment effects are homogenous for observationally identical individuals. This paper considers a treatment effect model in which treatment effects may be heterogeneous, even among observationally identical individuals. Specifically, extending the classical instrumental variables (IV) model with an endogenous binary treatment and a binary instrument, we allow the heteroskedasticity of the error disturbance to also depend upon the treatment variable so that treatment has both mean and variance effects on the outcome. In this endogenous heteroskedasticity IV (EHIV) model with heterogeneous individual treatment effects, the standard IV estimator can be inconsistent and lead to incorrect inference. After showing identification of the mean and variance treatment effects in a nonparametric version of the EHIV model, we provide closed-form estimators for the linear EHIV for the mean and variance treatment effects and the individual treatment effects (ITE). Asymptotic properties of the estimators are provided. A Monte Carlo simulation investigates the performance of the proposed approach, and an empirical application regarding the effects of fertility on female labor supply is considered.
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