De-biased Inference on Heterogeneous Quantile Treatment Effects in High Dimensions

Understanding treatment effect heterogeneity in observational studies is of great practical importance since the same treatment may affect different individuals differently. Quantile regression provides a natural framework for modeling such heterogeneity. In this talk, I propose a new estimator for quantile treatment effects in the presence of high-dimensional covariates. The estimator combines a de-biased L1-penalized regression adjustment with a novel quantile-specific covariate balancing scheme. Conceptually, this approach differs from classical de-biasing approaches as the proposed bias correction directly targets the conditional quantile function and not the high-dimensional regression vector. I present a comprehensive study of the theoretical properties of the estimator, including weak convergence of the quantile treatment effect process. The key finding is that the estimator is semi-parametric efficient. I illustrate its finite-sample performance through Monte Carlo experiments and an empirical example, dealing with the differential effect of mothers’ education on infant birth weight.