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Estimation based on nearest neighbor matching: from density ratio to average treatment effect

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  • Zhexiao Lin
  • Peng Ding
  • Fang Han

Abstract

Nearest neighbor (NN) matching as a tool to align data sampled from different groups is both conceptually natural and practically well-used. In a landmark paper, Abadie and Imbens (2006) provided the first large-sample analysis of NN matching under, however, a crucial assumption that the number of NNs, $M$, is fixed. This manuscript reveals something new out of their study and shows that, once allowing $M$ to diverge with the sample size, an intrinsic statistic in their analysis actually constitutes a consistent estimator of the density ratio. Furthermore, through selecting a suitable $M$, this statistic can attain the minimax lower bound of estimation over a Lipschitz density function class. Consequently, with a diverging $M$, the NN matching provably yields a doubly robust estimator of the average treatment effect and is semiparametrically efficient if the density functions are sufficiently smooth and the outcome model is appropriately specified. It can thus be viewed as a precursor of double machine learning estimators.

Suggested Citation

  • Zhexiao Lin & Peng Ding & Fang Han, 2021. "Estimation based on nearest neighbor matching: from density ratio to average treatment effect," Papers 2112.13506, arXiv.org.
    • Handle: RePEc:arx:papers:2112.13506
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    References listed on IDEAS

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    1. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    2. Alberto Abadie & Guido W. Imbens, 2011. "Bias-Corrected Matching Estimators for Average Treatment Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 1-11, January.
    3. Alberto Abadie & Guido W. Imbens, 2008. "On the Failure of the Bootstrap for Matching Estimators," Econometrica, Econometric Society, vol. 76(6), pages 1537-1557, November.
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    5. Alberto Abadie & Guido W. Imbens, 2012. "A Martingale Representation for Matching Estimators," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 833-843, June.
    6. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    7. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, vol. 66(2), pages 315-332, March.
    8. Heejung Bang & James M. Robins, 2005. "Doubly Robust Estimation in Missing Data and Causal Inference Models," Biometrics, The International Biometric Society, vol. 61(4), pages 962-973, December.
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    11. Ho, Daniel E. & Imai, Kosuke & King, Gary & Stuart, Elizabeth A., 2007. "Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference," Political Analysis, Cambridge University Press, vol. 15(3), pages 199-236, July.
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    Cited by:

    1. Zhexiao Lin & Fang Han, 2022. "On regression-adjusted imputation estimators of the average treatment effect," Papers 2212.05424, arXiv.org, revised Jan 2023.

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