  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.
