A powerful subvector Anderson Rubin test in linear instrumental variables regression with conditional heteroskedasticity

Working paper

We introduce a new test for a two-sided hypothesis involving a subset of the struc tural 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 ho moskedasticity. 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 se lection 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.

Authors: Guggenberge, P; Kleibergen, F; Mavroeidis, S

• Publication status: Published
• Publisher: University of Oxford
• Article number: 960
• Series: Department of Economics Discussion Paper Series
• Publication date: 2021-05-04
• Paper number: 960
• Language: English
• Keywords: weak instruments; conditional heteroskedasticity; Kronecker product; subvector inference; Asymptotic size; linear IV regression