Kernel Balancing: A Flexible Non-Parametric Weighting Procedure for Estimating Causal Effects
Hazlett, C. (2020). Kernel balancing: a flexible non-parametric weighting procedure for estimating causal effects. Statistica Sinica, 30, 1155-1189.
35 Pages Posted: 14 Mar 2016 Last revised: 28 Mar 2021
Date Written: August 30, 2018
Methods such as matching and weighting for causal effect estimation attempt to adjust the joint distribution of observed covariates for treated and control units to be the same. However, they often cannot fully achieve this goal, leaving potential for bias in average treatment effect on the treated (ATT) estimates. Kernel balancing targets a weaker condition: that the expected non-treatment potential outcome for the treatment and control groups are equal. This can be achieved under mild smoothness assumptions on the regression surface for the non-treatment potential outcome with respect to the covariates. It works by establishing equal means for the treatment and control groups not on the original covariates, but on a feature expansion of the covariates implied by a choice of kernel. Despite this different motivation, I show that the weights produced by kernel balancing are also interpretable as (1) those that ensure a particular approximation of the multivariate distribution of the covariates is the same for the treated and controls, and (2) a form of stabilized inverse propensity score weights that does not require a model of the treatment assignment mechanism. I provide an R package, KBAL, implementing this approach.
Keywords: causal inference, machine learning
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