Nonparametric estimation of causal heterogeneity under high-dimensional confounding

By Michael Zimmert, M. Lechner. 2019

61 citations recorded by the source corpus.

This paper considers the practically important case of nonparametrically estimating heterogeneous average treatment effects that vary with a limited number of discrete and continuous covariates in a selection-on-observables framework where the number of possible confounders is very large. We propose a two-step estimator for which the first step is estimated by machine learning. We show that this estimator has desirable statistical properties like consistency, asymptotic normality and rate double robustness. In particular, we derive the coupled convergence conditions between the nonparametric and the machine learning steps. We also show that estimating population average treatment effects by averaging the estimated heterogeneous effects is semi-parametrically efficient. The new estimator is an empirical example of the effects of mothers' smoking during pregnancy on the resulting birth weight.

Subfields: Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

Citations in the corpus

Double/De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers (2018, background): “Independently and contemporaneously to the present version of the paper, Fan et al. (2019) and Zimmert and Lechner (2019) define and study perfectly localized average treatment effects with high-dimensional confounders.”
Towards optimal doubly robust estimation of heterogeneous causal effects (2020, background): “…noted in the dose-response estimation problem by Kennedy et al. [2017], and is in contrast with the error bounds given in Nie and Wager [2021] and Zimmert and Lechner [2019], which required ATE-like conditions for oracle efficiency of CATE estimators, via n − 1 / 4 or faster rates on the…”
Estimation and Inference about Heterogeneous Treatment Effects in High-Dimensional Dynamic Panels. (2017, background): “Going a step further, Semenova and Chernozhukov (2018), Colangelo and Lee (2019), Jacob et al. (2019), Fan et al. (2019), Oprescu et al. (2019), Zimmert and Lechner (2019), among many others, represent heterogeneous treatment effects via a nonparametric function that is assumed to depend on a small…”
Estimation of Conditional Average Treatment Effects With High-Dimensional Data (2019, background): “In a related article, Zimmert and Lechner (2019) considered the local constant estimation of CATE in the highdimensional setting but only provide pointwise asymptotic results.”
Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments (2019, unknown): “Heuristically the rate condition (a) uses the bounded kernel, resulting in a penalty h − d T / 2 in the loose bound, as in Zimmert and Lechner (2019).”