In the absence of unobserved confounders, matching and weighting methods arewidely used to estimate causal quantities including the Average TreatmentEffect on the Treated (ATT). Unfortunately, these methods do not necessarilyachieve their goal of making the multivariate distribution of covariates forthe control group identical to that of the treated, leaving some (potentiallymultivariate) functions of the covariates with different means between the twogroups. When these "imbalanced" functions influence the non-treatment potentialoutcome, the conditioning on observed covariates fails, and ATT estimates maybe biased. Kernel balancing, introduced here, targets a weaker requirement forunbiased ATT estimation, specifically, that the expected non-treatmentpotential outcome for the treatment and control groups are equal. Theconditional expectation of the non-treatment potential outcome is assumed tofall in the space of functions associated with a choice of kernel, implying aset of basis functions in which this regression surface is linear. Weights arethen chosen on the control units such that the treated and control group haveequal means on these basis functions. As a result, the expectation of thenon-treatment potential outcome must also be equal for the treated and controlgroups after weighting, allowing unbiased ATT estimation by subsequentdifference in means or an outcome model using these weights. Moreover, theweights produced are (1) precisely those that equalize a particularkernel-based approximation of the multivariate distribution of covariates forthe treated and control, and (2) equivalent to a form of stabilized inversepropensity score weighting, though it does not require assuming any model ofthe treatment assignment mechanism. An R package, KBAL, is provided toimplement this approach.
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