Matching estimators with few treated and many control observationsJournal of Econometrics, 2021, vol. 225, issue 2, 295-307 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. Keywords: Matching estimators; Treatment effects; Hypothesis testing; Randomization inference; Synthetic control estimator (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:225:y:2021:i:2:p:295-307 DOI: 10.1016/j.jeconom.2021.07.005 Access Statistics for this article Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson More articles in Journal of Econometrics from Elsevier |
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