{"title":"The robust F-statistic as a test for weak instruments","authors":"Frank Windmeijer","doi":"10.1016/j.jeconom.2025.105951","DOIUrl":null,"url":null,"abstract":"<div><div>For the linear model with a single endogenous variable, (Montiel Olea and Pflueger 2013) proposed the effective F-statistic as a test for weak instruments in terms of the Nagar bias of the two-stage least squares (2SLS) or limited information maximum likelihood (LIML) estimator relative to a benchmark worst-case bias. We show that their methodology for the 2SLS estimator applies to a class of linear generalized method of moments (GMM) estimators with an associated class of generalized effective F-statistics. The standard robust F-statistic is a member of this class. The associated GMMf estimator, with the extension “f” for first-stage, has the weight matrix based on the first-stage residuals. In the grouped-data IV designs of Andrews (2018) with moderate and high levels of endogeneity and where the robust F-statistic is large but the effective F-statistic is small, the GMMf estimator is shown to behave much better in terms of bias than the 2SLS estimator.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"247 ","pages":"Article 105951"},"PeriodicalIF":9.9000,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Econometrics","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0304407625000053","RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 0
Abstract
For the linear model with a single endogenous variable, (Montiel Olea and Pflueger 2013) proposed the effective F-statistic as a test for weak instruments in terms of the Nagar bias of the two-stage least squares (2SLS) or limited information maximum likelihood (LIML) estimator relative to a benchmark worst-case bias. We show that their methodology for the 2SLS estimator applies to a class of linear generalized method of moments (GMM) estimators with an associated class of generalized effective F-statistics. The standard robust F-statistic is a member of this class. The associated GMMf estimator, with the extension “f” for first-stage, has the weight matrix based on the first-stage residuals. In the grouped-data IV designs of Andrews (2018) with moderate and high levels of endogeneity and where the robust F-statistic is large but the effective F-statistic is small, the GMMf estimator is shown to behave much better in terms of bias than the 2SLS estimator.
对于单一内生变量的线性模型,(Montiel Olea 和 Pflueger,2013 年)提出了有效 F 统计量,作为两阶段最小二乘(2SLS)或有限信息最大似然(LIML)估计器相对于基准最坏情况偏差的纳加尔偏差的弱工具检验。我们表明,他们针对 2SLS 估计器的方法适用于一类线性广义矩法 (GMM) 估计器,以及相关的一类广义有效 F 统计量。标准稳健 F 统计量就是这一类的成员。相关的 GMMf 估计器(扩展名为 "f "表示第一阶段)的权重矩阵基于第一阶段的残差。在 Andrews(2018)的分组数据 IV 设计中,具有中等和高等程度的内生性,且稳健 F 统计量较大但有效 F 统计量较小,GMMf 估计器在偏差方面的表现比 2SLS 估计器要好得多。
期刊介绍:
The Journal of Econometrics serves as an outlet for important, high quality, new research in both theoretical and applied econometrics. The scope of the Journal includes papers dealing with identification, estimation, testing, decision, and prediction issues encountered in economic research. Classical Bayesian statistics, and machine learning methods, are decidedly within the range of the Journal''s interests. The Annals of Econometrics is a supplement to the Journal of Econometrics.