Kernel Balancing: A flexible non-parametric weighting procedure for estimating causal effects

TL;DR

Kernel balancing is a non-parametric weighting method that ensures unbiased estimation of causal effects by aligning the distributions of covariate functions between treated and control groups without relying on parametric models.

Contribution

This paper introduces kernel balancing, a novel non-parametric weighting procedure that achieves unbiased causal effect estimation by matching covariate function expectations, without assuming treatment assignment models.

Findings

Kernel balancing produces weights that equalize covariate function means.

It achieves unbiased ATT estimation without modeling treatment assignment.

The method is implemented in the KBAL R package.

Abstract

In the absence of unobserved confounders, matching and weighting methods are widely used to estimate causal quantities including the Average Treatment Effect on the Treated (ATT). Unfortunately, these methods do not necessarily achieve their goal of making the multivariate distribution of covariates for the control group identical to that of the treated, leaving some (potentially multivariate) functions of the covariates with different means between the two groups. When these "imbalanced" functions influence the non-treatment potential outcome, the conditioning on observed covariates fails, and ATT estimates may be biased. Kernel balancing, introduced here, targets a weaker requirement for unbiased ATT estimation, specifically, that the expected non-treatment potential outcome for the treatment and control groups are equal. The conditional expectation of the non-treatment potential outcome is assumed to fall in the space of functions associated with a choice of kernel, implying a set of basis functions in which this regression surface is linear. Weights are then chosen on the control units such that the treated and control group have equal means on these basis functions. As a result, the expectation of the non-treatment potential outcome must also be equal for the treated and control groups after weighting, allowing unbiased ATT estimation by subsequent difference in means or an outcome model using these weights. Moreover, the weights produced are (1) precisely those that equalize a particular kernel-based approximation of the multivariate distribution of covariates for the treated and control, and (2) equivalent to a form of stabilized inverse propensity score weighting, though it does not require assuming any model of the treatment assignment mechanism. An R package, KBAL, is provided to implement this approach.