Abstract: Matching and weighting methods are widely used to estimate causal effects when needing to adjust for a set of observables. Matching is appealing for its nonparametric nature, but with continuous variables, is not guaranteed to remove bias. Weighting techniques choose weights on units to ensure that prespecified functions of the covariates have equal (weighted) means for the treated and control groups. This ensures an unbiased effect estimate only when the potential outcomes are linear in those prespecified functions of the observables. Kernel balancing begins by assuming that the expectation of the nontreatment potential outcome, conditional on the covariates, falls in a large, flexible space of functions associated with a kernel. It then constructs linear bases for this function space, and achieves approximate balance on these bases. A worst-case bound on the bias due to this approximation is given and minimized. Relative to current practice, kernel balancing offers a reasonable solution to the long-standing question of which functions of the covariates investigators should balance. Furthermore, these weights are also those that would make the estimated multivariate density of covariates approximately the same for the treated and control groups, when the same choice of kernel is used to estimate those densities. The approach is fully automated, given the user's choice of kernel and smoothing parameter, for which default options and guidelines are provided. An R package, kbal, implements this approach.

Key words and phrases: Causal inference, covariate balance, matching, statistical learning, weighting.