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Matching Estimators with Few Treated and Many Control Observations

Bruno Ferman

arXiv 11 Sep 2019 · Econometrics · publishedJournal of Econometrics (2021) · 10 citations (OpenAlex)

arXiv:1909.05093 · PDF · DOI · OpenAlex · Extracted main text

Abstract

We analyze the properties of matching estimators when there are few treated, but many control observations. We show that, under standard assumptions, the nearest neighbor matching estimator for the average treatment effect on the treated is asymptotically unbiased in this framework. However, when the number of treated observations is fixed, the estimator is not consistent, and it is generally not asymptotically normal. Since standard inference methods are inadequate, we propose alternative inference methods, based on the theory of randomization tests under approximate symmetry, that are asymptotically valid in this framework. We show that these tests are valid under relatively strong assumptions when the number of treated observations is fixed, and under weaker assumptions when the number of treated observations increases, but at a lower rate relative to the number of control observations.

Citation extraction

45
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Otsu, T. and Rai, Y (2017) Bootstrap inference of matching estimators for average treatment effects0.8435460%
2Canay, I. A., Romano, J. P., and Shaikh, A. M (2017) Randomization tests under an approximate symmetry assumption0.8307457%
3Heckman, J. J., Ichimura, H., and Todd, P. E (1997) Matching as an econometric evaluation estimator: Evidence from evaluating a job training programme0.64422100%
4Conley, T. G. and Taber, C. R (2011) Inference with Difference in Differences with a Small Number of Policy Changes0.5114225%
5Huber, M., Lechner, M., and Wunsch, C (2013) The performance of estimators based on the propensity score0.5112250%
6Smith, J. A. and Todd, P. E (2001) Reconciling conflicting evidence on the performance of propensity-score matching methods0.51121100%
7Abadie, A. and Imbens, G. W (2011) Bias-corrected matching estimators for average treatment effects0.51121100%
8Abadie, A., Diamond, A., and Hainmueller, J (2010) Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California's Tobacco Control Program0.51121100%
9Imbens, G. and Wooldridge, J (2009) Recent developments in the econometrics of program evaluation0.51121100%
10Armstrong, T. B. and Kolesár, M (2021) Finite-sample optimal estimation and inference on average treatment effects under unconfoundedness0.51121100%

Showing the top 10 of 45 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Inference with few treated units0.69361
2Randomization Inference Tests for Shift-Share Designs0.40511