A conditional linear combination test with many weak instruments

A conditional linear combination test with many weak instruments

We consider a linear combination of jackknife Anderson-Rubin (AR), jackknife Lagrangian multiplier (LM), and orthogonalized jackknife LM tests for inference in IV regressions with many weak instruments and heteroskedasticity. Following I.Andrews (2016), we choose the weights in the linear combinatio...

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Bibliographic Details
Main Authors: Lim, Dennis, Wang, Wenjie, Zhang, Yichong
Other Authors: School of Social Sciences
Format: Article
Language:English
Published: 2024
Subjects:
Social sciences::Economic theory
Many Instruments
Weak Identification
Online Access:https://hdl.handle.net/10356/173316
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Institution: Nanyang Technological University
Language: English
Description
Summary:We consider a linear combination of jackknife Anderson-Rubin (AR), jackknife Lagrangian multiplier (LM), and orthogonalized jackknife LM tests for inference in IV regressions with many weak instruments and heteroskedasticity. Following I.Andrews (2016), we choose the weights 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 test controls asymptotic size and is admissible among certain class of tests. Under strong identification, our linear combination test has optimal power against local alternatives among the class of invariant or unbiased tests which are constructed based on jackknife AR and LM tests. Simulations and an empirical application to Angrist and Krueger's (1991) dataset confirm the good power properties of our test.

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