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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 the number of treated observations is fixed while the number of treated 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. We also provide a test based on the theory of randomization tests under approximate symmetry developed in Canay et al. (2014) that is asymptotically valid when the number of control observations goes to infinity. This is important because large sample inferential techniques developed in Abadie and Imbens (2006) would not be valid in this setting.

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  • Ferman, Bruno, 2017. "Matching Estimators with Few Treated and Many Control Observations," MPRA Paper 78940, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:78940
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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 Laura Molnár, 2023. "Accident-induced absence from work and wage ladders," IFS Working Papers W23/30, Institute for Fiscal Studies.
    3. Ferman, Bruno, 2021. "Matching estimators with few treated and many control observations," Journal of Econometrics, Elsevier, vol. 225(2), pages 295-307.
    4. Bruno Ferman, 2019. "Assessing Inference Methods," Papers 1912.08772, arXiv.org, revised Oct 2022.
    5. Luis Alvarez & Bruno Ferman & Raoni Oliveira, 2022. "Randomization Inference Tests for Shift-Share Designs," Papers 2206.00999, arXiv.org.
    6. 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.
    7. Raluca Maran, 2023. "Drivers of sovereign catastrophe bond issuance: an empirical analysis," SN Business & Economics, Springer, vol. 3(6), pages 1-20, June.
    8. 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.
    9. 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.

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    More about this item

    Keywords

    matching estimator; treatment effect; hypothesis testing; randomization inference;
    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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