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Matching estimators with few treated and many control observations

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  • Ferman, Bruno

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.

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  • Ferman, Bruno, 2021. "Matching estimators with few treated and many control observations," Journal of Econometrics, Elsevier, vol. 225(2), pages 295-307.
  • Handle: RePEc:eee:econom:v:225:y:2021:i:2:p:295-307
    DOI: 10.1016/j.jeconom.2021.07.005
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    2. Ferman, Bruno, 2021. "Matching estimators with few treated and many control observations," Journal of Econometrics, Elsevier, vol. 225(2), pages 295-307.
    3. Bruno Ferman, 2019. "Assessing Inference Methods," Papers 1912.08772, arXiv.org, revised Oct 2022.
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    More about this item

    Keywords

    Matching estimators; Treatment effects; Hypothesis testing; Randomization inference; Synthetic control estimator;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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