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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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    Cited by:

    1. Songliang Chen & Fang Han, 2024. "On the limiting variance of matching estimators," Papers 2411.05758, arXiv.org.
    2. Ziming Lin & Fang Han, 2024. "On the consistency of bootstrap for matching estimators," Papers 2410.23525, arXiv.org, revised Nov 2024.
    3. Zhexiao Lin & Pablo Crespo, 2024. "Variance reduction combining pre-experiment and in-experiment data," Papers 2410.09027, arXiv.org.
    4. 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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