Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curves

TL;DR

This paper introduces kernel ridge regression estimators for nonparametric causal functions, providing theoretical guarantees and demonstrating superior performance in simulations and policy evaluation.

Contribution

It develops simple closed-form kernel ridge estimators for various causal functions with uniform consistency proofs and extensions to counterfactuals and causal identification.

Findings

State-of-the-art performance in nonlinear simulations

Consistent estimators with finite sample rates

Effective policy evaluation of US Job Corps program

Abstract

We propose estimators based on kernel ridge regression for nonparametric causal functions such as dose, heterogeneous, and incremental response curves. Treatment and covariates may be discrete or continuous in general spaces. Due to a decomposition property specific to the RKHS, our estimators have simple closed form solutions. We prove uniform consistency with finite sample rates via original analysis of generalized kernel ridge regression. We extend our main results to counterfactual distributions and to causal functions identified by front and back door criteria. We achieve state-of-the-art performance in nonlinear simulations with many covariates, and conduct a policy evaluation of the US Job Corps training program for disadvantaged youths.