A Powerful Subvector Anderson Rubin Test in Linear Instrumental Variables Regression with Conditional Heteroskedasticity

TL;DR

This paper develops a robust subvector Anderson-Rubin test for linear IV regression that maintains size control under heteroskedasticity and improves power by adaptively choosing between a structured and a fully robust approach.

Contribution

It extends the GKM19 subvector AR test to handle arbitrary conditional heteroskedasticity using an adaptive procedure based on covariance structure.

Findings

The new test controls size asymptotically under heteroskedasticity.

It shows improved power over fully robust tests in simulations.

The adaptive method performs well when the covariance matrix is close to the AKP structure.

Abstract

We introduce a new test for a two-sided hypothesis involving a subset of the structural parameter vector in the linear instrumental variables (IVs) model. Guggenberger et al. (2019), GKM19 from now on, introduce a subvector Anderson-Rubin (AR) test with data-dependent critical values that has asymptotic size equal to nominal size for a parameter space that allows for arbitrary strength or weakness of the IVs and has uniformly nonsmaller power than the projected AR test studied in Guggenberger et al. (2012). However, GKM19 imposes the restrictive assumption of conditional homoskedasticity. The main contribution here is to robustify the procedure in GKM19 to arbitrary forms of conditional heteroskedasticity. We first adapt the method in GKM19 to a setup where a certain covariance matrix has an approximate Kronecker product (AKP) structure which nests conditional homoskedasticity. The new test equals this adaption when the data is consistent with AKP structure as decided by a model selection procedure. Otherwise the test equals the AR/AR test in Andrews (2017) that is fully robust to conditional heteroskedasticity but less powerful than the adapted method. We show theoretically that the new test has asymptotic size bounded by the nominal size and document improved power relative to the AR/AR test in a wide array of Monte Carlo simulations when the covariance matrix is not too far from AKP.