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Matching Estimators with Few Treated and Many Control Observations

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  • Bruno Ferman

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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  • Bruno Ferman, 2019. "Matching Estimators with Few Treated and Many Control Observations," Papers 1909.05093, arXiv.org, revised Mar 2021.
  • Handle: RePEc:arx:papers:1909.05093
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    Cited by:

    1. Zhexiao Lin & Peng Ding & Fang Han, 2023. "Estimation Based on Nearest Neighbor Matching: From Density Ratio to Average Treatment Effect," Econometrica, Econometric Society, vol. 91(6), pages 2187-2217, November.
    2. Anikó Bíró & Márta Bisztray & João G. da Fonseca & Tímea Molnár, 2023. "Accident-Induced Absence from Work and Wage Ladders," CERS-IE WORKING PAPERS 2321, Institute of Economics, Centre for Economic and Regional Studies.
    3. Luis Alvarez & Bruno Ferman & Raoni Oliveira, 2022. "Randomization Inference Tests for Shift-Share Designs," Papers 2206.00999, arXiv.org.
    4. Bruno Ferman, 2019. "Assessing Inference Methods," Papers 1912.08772, arXiv.org, revised Oct 2022.
    5. Raluca Maran, 2023. "Drivers of sovereign catastrophe bond issuance: an empirical analysis," SN Business & Economics, Springer, vol. 3(6), pages 1-20, June.
    6. Ferman, Bruno, 2021. "Matching estimators with few treated and many control observations," Journal of Econometrics, Elsevier, vol. 225(2), pages 295-307.
    7. Heinrich, Victor, 2023. "Private Equity Transactions: Value Creation through Operational Engineering – Evidence from Europe," Junior Management Science (JUMS), Junior Management Science e. V., vol. 8(3), pages 634-657.
    8. Xin Su & Shengwen Wang, 2024. "Impact of China’s free trade zones on the innovation performance of firms: evidence from a quasi-natural experiment," Palgrave Communications, Palgrave Macmillan, vol. 11(1), pages 1-17, December.
    9. Brantly Callaway & Tong Li, 2020. "Evaluating Policies Early in a Pandemic: Bounding Policy Effects with Nonrandomly Missing Data," Papers 2005.09605, arXiv.org, revised Jan 2023.

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    More about this item

    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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