Generalized Kernel Ridge Regression for Long Term Causal Inference: Treatment Effects, Dose Responses, and Counterfactual Distributions

Abstract

I propose kernel ridge regression estimators for long term causal inference, where a short term experimental data set containing randomized treatment and short term surrogates is fused with a long term observational data set containing short term surrogates and long term outcomes. I propose estimators of treatment effects, dose responses, and counterfactual distributions with closed form solutions in terms of kernel matrix operations. I allow covariates, treatment, and surrogates to be discrete or continuous, and low, high, or infinite dimensional. For long term treatment effects, I prove √ n consistency, Gaussian approximation, and semiparametric efficiency. For long term dose responses, I prove uniform consistency with finite sample rates. For long term counterfactual distributions, I prove convergence in distribution.Preprint. Under review.

Long-term Causal Inference Under Persistent Confounding via Data Combination

“…Chen and Ritzwoller [2021] derive the efficiency lower bound for average longterm treatment effect in settings of Athey et al [2019] and Athey et al [2020]. Singh [2021Singh [ , 2022 further develop debiased estimators based on machine learning nuisance estimation. In contrast, Kallus and Mao [2020], Cai et al [2021a] combine two datasets that both satisfy unconfoundedness.…”