A conditional linear combination test with many weak instruments

• Main Authors: LIM, Dennis, WANG, Wenjie, ZHANG, Yichong
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2024
• Subjects: Many instruments; power; size; weak identification; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/2618; https://ink.library.smu.edu.sg/context/soe_research/article/3617/viewcontent/ConditionalLinearComb_Weak_2023_sv.pdf
• Institution: Singapore Management University

We consider a linear combination of jackknife Anderson-Rubin (AR) and orthogonalized Lagrangian multiplier (LM) tests for inference in IV regressions with many weak instruments and heteroskedasticity. We choose the weight in the linear combination based on a decision-theoretic rule that is adaptive to the identification strength. Under both weak and strong identifications, the proposed linear combination test controls asymptotic size and is admissible. Under strong identification, we further show that our linear combination test is the uniformly most powerful test against local alternatives among all tests that are constructed based on the jackknife AR and LM tests only and invariant to sign changes.