Generalized Kernel Ridge Regression for Causal Inference with Missing-at-Random Sample Selection

TL;DR

This paper introduces kernel ridge regression estimators for nonparametric causal inference in settings with missing-at-random sample selection, accommodating complex covariate and treatment structures.

Contribution

It extends kernel ridge regression methods to handle non-random sample selection with covariates that may cause or be caused by treatment, providing closed-form estimators and theoretical guarantees.

Findings

Proposes closed-form kernel ridge estimators for causal effects.

Establishes uniform consistency for continuous treatments.

Achieves root-n consistency and efficiency for discrete treatments.

Abstract

I propose kernel ridge regression estimators for nonparametric dose response curves and semiparametric treatment effects in the setting where an analyst has access to a selected sample rather than a random sample; only for select observations, the outcome is observed. I assume selection is as good as random conditional on treatment and a sufficiently rich set of observed covariates, where the covariates are allowed to cause treatment or be caused by treatment -- an extension of missingness-at-random (MAR). I propose estimators of means, increments, and distributions of counterfactual outcomes with closed form solutions in terms of kernel matrix operations, allowing treatment and covariates to be discrete or continuous, and low, high, or infinite dimensional. For the continuous treatment case, I prove uniform consistency with finite sample rates. For the discrete treatment case, I prove root-n consistency, Gaussian approximation, and semiparametric efficiency.