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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, even though this estimator is not consistent. Since large sample inferential techniques are not adequate in our setting, we provide inferential procedures based on the theory of randomization tests under approximate symmetry. We show that these tests are asymptotically valid when the number treated observations is fixed and the number of control observations goes to infinity. Our simulation results suggest that our inference methods provide better size and power when compared to existing alternatives even when the number of control observations is not large.

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