Econometrica

Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Nov, 2023, Volume 91, Issue 6

Estimation Based on Nearest Neighbor Matching: from Density Ratio to Average Treatment Effect

https://doi.org/10.3982/ECTA20598
p. 2187-2217

Zhexiao Lin, Peng Ding, Fang Han

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.


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Supplemental Material

Supplement to "Estimation Based on Nearest Neighbor Matching: from Density Ratio to Average Treatment Effect"

Zhexiao Lin, Peng Ding, and Fang Han

This online appendix contains material not found within the manuscript.

Supplement to "Estimation Based on Nearest Neighbor Matching: from Density Ratio to Average Treatment Effect"

Zhexiao Lin, Peng Ding, and Fang Han

The replication package for this paper is available at https://doi.org/10.5281/zenodo.8322609. The authors were granted an exemption to publish parts of their data because either access to these data is restricted or the authors do not have the right to republish them. Therefore, the replication package only includes the codes and the parts of the data that are not subject to the exemption. However, the authors provided the Journal with (or assisted the Journal to obtain) temporary access to the restricted data. The Journal checked the provided and restricted data and the codes for their ability to reproduce the results in the paper and approved online appendices.