Matching With Multiple Control Groups With Adjustment for Group Differences

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Abstract
When estimating causal effects from observational data, it is desirable to approximate a randomized experiment as closely as possible. This goal can often be achieved by choosing a subsample from the original control group that matches the treatment group on the distribution of the observed covariates. However, sometimes the original control group cannot provide adequate matches for the treatment group. This article presents a method to obtain matches from multiple control groups. In addition to adjusting for differences in observed covariates between the groups, the method adjusts for a group effect that distinguishes between the control groups. This group effect captures the additional otherwise unobserved differences between the control groups, beyond that accounted for by the observed covariates. The method is illustrated and evaluated using data from an evaluation of a school drop-out prevention program that uses matches from both local and nonlocal control groups.