Inference with Many Weak Instruments. (24th December 2021)

• Record Type: Journal Article
• Authors: Mikusheva, Anna; Sun, Liyang
• Is Part Of: Review of economic studies. Volume 89:Number 5(2022)
• Page Start: 2663
• Page End: 2686
• Publication Date: 2021-12-24
• Subjects: Instrumental variables -- Weak identification -- Dimensionality asymptotics; C12 -- C36 -- C55; Economics -- Periodicals; 330
• DOI: 10.1093/restud/rdab097
• Languages: English
• ISSNs: 0034-6527

Abstract

Abstract: We develop a concept of weak identification in linear instrumental variable models in which the number of instruments can grow at the same rate or slower than the sample size. We propose a jackknifed version of the classical weak identification-robust Anderson–Rubin (AR) test statistic. Large-sample inference based on the jackknifed AR is valid under heteroscedasticity and weak identification. The feasible version of this statistic uses a novel variance estimator. The test has uniformly correct size and good power properties. We also develop a pre-test for weak identification that is related to the size property of a Wald test based on the Jackknife Instrumental Variable Estimator. This new pre-test is valid under heteroscedasticity and with many instruments.