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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 is widely used in observational studies for causal effects. Abadie and Imbens (2006) provided the first large‐sample analysis of NN matching. Their theory focuses on the case with the number of NNs, M fixed. We reveal something new out of their study and show that once allowing M to diverge with the sample size an intrinsic statistic in their analysis constitutes a consistent estimator of the density ratio with regard to covariates across the treated and control groups. Consequently, with a diverging M, the NN matching with Abadie and Imbens' (2011) bias correction 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 consistently estimated. It can thus be viewed as a precursor of the double machine learning estimators.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:emetrp:v:91:y:2023:i:6:p:2187-2217
    DOI: 10.3982/ECTA20598
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    References listed on IDEAS

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    1. Masashi Sugiyama & Taiji Suzuki & Shinichi Nakajima & Hisashi Kashima & Paul Bünau & Motoaki Kawanabe, 2008. "Direct importance estimation for covariate shift adaptation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(4), pages 699-746, December.
    2. Timothy B. Armstrong & Michal Kolesár, 2021. "Finite‐Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness," Econometrica, Econometric Society, vol. 89(3), pages 1141-1177, May.
    3. Farrell, Max H., 2015. "Robust inference on average treatment effects with possibly more covariates than observations," Journal of Econometrics, Elsevier, vol. 189(1), pages 1-23.
    4. Chen, Xiaohong & Christensen, Timothy M., 2015. "Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions," Journal of Econometrics, Elsevier, vol. 188(2), pages 447-465.
    5. Shadish, William R. & Clark, M. H. & Steiner, Peter M., 2008. "Can Nonrandomized Experiments Yield Accurate Answers? A Randomized Experiment Comparing Random and Nonrandom Assignments," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1334-1344.
    6. Rosenbaum, Paul R., 2010. "Design Sensitivity and Efficiency in Observational Studies," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 692-702.
    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. Ferman, Bruno, 2021. "Matching estimators with few treated and many control observations," Journal of Econometrics, Elsevier, vol. 225(2), pages 295-307.
    9. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    10. 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.
    11. Taisuke Otsu & Yoshiyasu Rai, 2017. "Bootstrap Inference of Matching Estimators for Average Treatment Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1720-1732, October.
    12. Ben B. Hansen, 2008. "The prognostic analogue of the propensity score," Biometrika, Biometrika Trust, vol. 95(2), pages 481-488.
    13. Bhaswar B. Bhattacharya, 2019. "A general asymptotic framework for distribution‐free graph‐based two‐sample tests," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(3), pages 575-602, July.
    14. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881.
    15. 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. Matias D. Cattaneo & Fang Han & Zhexiao Lin, 2023. "On Rosenbaum's Rank-based Matching Estimator," Papers 2312.07683, arXiv.org, revised Jan 2024.

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