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Matching Estimators with Few Treated and Many Control Observations

Ferman, Bruno (2017): Matching Estimators with Few Treated and Many Control Observations.

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Abstract

We analyze the properties of matching estimators when the number of treated observations is fixed and the number of control observations is large. We show that, under standard assumptions, the nearest neighbor matching estimator for the average treatment effect on the treated is asymptotically unbiased. However, the estimator is not consistent, and it is generally not asymptotically normal. Since large-sample inferential techniques are inadequate in our setting, we provide alternative inferential procedures based on the theory of randomization tests under approximate symmetry. These tests are asymptotically valid when the number of treated observations is fixed and the number of control observations goes to infinity. Simulations show that our inference methods provide better size and power when compared to existing alternatives. We explore the validity of matching estimators, and of our inferential methods, in the estimation of the effects of an educational program in Brazil that provides a setting with few treated and many control schools.

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