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

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