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

IF 6.6 1区经济学 Q1 ECONOMICS Econometrica Pub Date : 2023-12-07 DOI:10.3982/ECTA20598

Zhexiao Lin, Peng Ding, Fang Han

引用次数: 0

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.

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基于近邻匹配的估算：从密度比到平均治疗效果

近邻匹配（NN）被广泛应用于因果效应的观察研究中。Abadie 和 Imbens（2006 年）首次对近邻匹配进行了大样本分析。他们的理论侧重于近邻数量 M 固定的情况。我们从他们的研究中发现了一些新的东西，并证明一旦允许 M 随样本量的变化而变化，他们分析中的一个固有统计量就构成了对治疗组和对照组协变量密度比的一致估计。因此，在 M 发散的情况下，使用 Abadie 和 Imbens（2011 年）的偏差校正进行 NN 匹配，可以得到平均治疗效果的双重稳健估计值，而且如果密度函数足够平滑且结果模型的估计结果一致，则该估计值具有半参数效率。因此，可以将其视为双重机器学习估计器的前身。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Econometrica 社会科学-数学跨学科应用

CiteScore

11.00

自引率

3.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Econometrica publishes original articles in all branches of economics - theoretical and empirical, abstract and applied, providing wide-ranging coverage across the subject area. It promotes studies that aim at the unification of the theoretical-quantitative and the empirical-quantitative approach to economic problems and that are penetrated by constructive and rigorous thinking. It explores a unique range of topics each year - from the frontier of theoretical developments in many new and important areas, to research on current and applied economic problems, to methodologically innovative, theoretical and applied studies in econometrics. Econometrica maintains a long tradition that submitted articles are refereed carefully and that detailed and thoughtful referee reports are provided to the author as an aid to scientific research, thus ensuring the high calibre of papers found in Econometrica. An international board of editors, together with the referees it has selected, has succeeded in substantially reducing editorial turnaround time, thereby encouraging submissions of the highest quality. We strongly encourage recent Ph. D. graduates to submit their work to Econometrica. Our policy is to take into account the fact that recent graduates are less experienced in the process of writing and submitting papers.

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