A powerful subvector anderson rubin test in linear instrumental variables regression with conditional heteroskedasticity
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 asympt...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Cambridge University Press
2023
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| Summary: | 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. |
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