Achieving Optimal Covariate Balance Under General Treatment Regimes

Balancing covariates across treatment levels provides an effective and increasingly popular strategy for conducting causal inference in observational studies. Matching procedures, as a means of achieving balance, pre-process the data through identifying a subset of control observations with similar background characteristics to the treated observations. Inference in a matched sample is unbiased and robust to model specification. The proposed method adapts the support vector machine (SVM) classifier to the matching problem. The SVM separates easy to classify observations from hard to classify observations, and only uses the hard to classify cases in estimating a decision boundary between two classes. The treatment levels for these hard to classify observations are estimated with some uncertainty, the hallmark of random assignment. A series of lemmas prove that these hard to classify observations are balanced, for both binary and continuous treatment regimes. Unlike existing methods, the proposed method maximizes balance across all covariates simultaneously, rather than along a summary measure of balance. The method accommodates both binary and continuous treatment regimes. The proposed method is applied to four prominent social science datasets: the effect of a job training program on income, the effect of UN interventions on conflict duration, the effect of changes in foreign aid on domestic insurgent conflict, and the effect of education on political participation. The method is shown to recover an experimental benchmark, retain more observations than its competitors, and avoid dichotomization of a continuous treatment. ∗I thank Kosuke Imai for continued support throughout this project. I also thank participants at Yale’s ISPS Experiments Lunch seminar for useful comments and feedback.