Best Feasible Conditional Critical Values for a More Powerful Subvector Anderson-Rubin Test

TL;DR

This paper proposes a new data-dependent critical value method for the subvector Anderson-Rubin test in instrumental variables models, improving power especially when testing multiple parameters under weak identification conditions.

Contribution

It introduces a critical value function based on the second-smallest eigenvalue, enhancing power over existing methods when testing multiple parameters.

Findings

The new critical value function maintains correct size.

It achieves higher power than the GKM test with multiple parameters.

Applicable to models with heteroskedasticity and weak instruments.

Abstract

For subvector inference in the linear instrumental variables model under homoskedasticity but allowing for weak instruments, Guggenberger, Kleibergen, and Mavroeidis (2019) (GKM) propose a conditional subvector Anderson and Rubin (1949) (AR) test that uses data-dependent critical values that adapt to the strength of the parameters not under test. This test has correct size and strictly higher power than the test that uses standard asymptotic chi-square critical values. The subvector AR test is the minimum eigenvalue of a data dependent matrix. The GKM critical value function conditions on the largest eigenvalue of this matrix. We consider instead the data dependent critical value function conditioning on the second-smallest eigenvalue, as this eigenvalue is the appropriate indicator for weak identification. We find that the data dependent critical value function of GKM also applies to this conditioning and show that this test has correct size and power strictly higher than the GKM test when the number of parameters not under test is larger than one. Our proposed procedure further applies to the subvector AR test statistic that is robust to an approximate kronecker product structure of conditional heteroskedasticity as proposed by Guggenberger, Kleibergen, and Mavroeidis (2024), carrying over its power advantage to this setting as well.