SMABS 2004 Jena University
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European Association of Methodology

Department of methodology and evaluation research

Jena University

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Contributions: Abstract

Estimating causal effects using matching with multiple control groups

Elizabeth Stuart Donald Rubin
Harvard University

When estimating causal effects using observational data, it is desirable toreplicate a randomized experiment as closely as possible by obtaining treated and control groups with similar covariate distributions. This is often done by choosing well-matched samples of the original treated and control groups, thereby reducing bias due to the covariates. Since exact matches on all of the covariates are rarely feasible, multivariate matching methods such as using propensity scores or Mahalanobis matching are often utilized to select these well-matched treated and control groups.

However, sometimes the originally chosen control units cannot provide adequate matches for the treated units. In these cases, it may be desirable to obtain matched controls from multiple control groups. Multiple control groups have been used to test for hidden biases in causal inference; however, little work has been done on their use in matching or adjustment for these biases.

We provide a theoretical basis and practical guidelines for this new approach, based on affinely invariant matching methods with mixtures of ellipsoidally symmetric distributions. The method is applied to the evaluation of a school dropout prevention program, where the original treated and control students were significantly different from each other. We examine the use of a second source of control students to supplement the original control group.