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Abstract:
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Individuals do not only differ in their innate characteristics, but also in how they respond to a particular treatment or intervention. Quantile regression, which models the effect of covariates on the conditional distribution of the response variable, provides a natural approach to studying such heterogeneous treatment effects. We propose a framework for uniform inference of the entire conditional quantile treatment function in the presence of high-dimensional covariates. Our estimation method combines a de-biased L1-penalized regression adjustment with a quantile-specific balancing scheme. We obtain weak convergence of the proposed estimator to a Gaussian process whose covariance operator can be estimated consistently under mild conditions. This theoretical result has immediate practical implications for testing hypotheses about functionals of the quantile treatment effect function, such as the individual conditional quantile treatment effect itself, robustified average treatment effects, and conditional quantile treatment effects for subgroups. We discuss the merits of our approach and provide finite-sample performances in a variety of settings.
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