Kernel Balancing: A Balancing Method to Equalize Multivariate Densities and Reduce Bias without a Specification Search

Matching and weighting estimators are often used to adjust for differences between treated and control groups on observed characteristics. These methods require the user to choose what functions of the covariates to include in balancing procedures, and do not ensure equal multivariate densities of the treated and control groups. As a result, functions of the covariates that influence the outcome may remain imbalanced, biasing treatment effect estimates. This talk introduces kernel balancing, a method designed to reduce or eliminate such bias, without relying on specification searches or balance tests. The weights derived by kernel balancing (1) achieve approximate mean balance on a large set of smooth functions of the covariates, and (2) approximately equalize the multivariate densities of the treated and controls. In an empirical application, I reanalyze a widely cited study finding that democracies are as likely as non-democracies to successfully defeat insurgencies, contrary to prior theoretical and empirical evidence. Kernel balancing shows that this result is likely due to insufficient balance achieved by matching estimates. When democracies and non-democracies are compared on more similar cases, democracies are substantively and statistically less likely to defeat insurgencies.