A Conditional Linear Combination Test with Many Weak Instruments

TL;DR

This paper introduces a new adaptive linear combination test for IV regressions with many weak instruments, controlling size and optimizing power under various identification strengths.

Contribution

It proposes a novel adaptive linear combination test that integrates multiple jackknife-based tests for better inference in weak instrument scenarios.

Findings

Controls asymptotic size under weak and strong identification

Achieves optimal power against local alternatives under strong identification

Demonstrates good power properties through simulations and empirical data

Abstract

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.