2021/03/21 by Patrik Guggenberger, Guggenberger, Patrik, Frank Kleibergen +3 · 3 citations
Mathematics · #Econometrics (econ.EM) #FOS: Economics and business #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2103.11371
openalex publication_date 2021/03/21 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We introduce a new test for a two-sided hypothesis involving a subset of the\nstructural parameter vector in the linear instrumental variables (IVs) model.\nGuggenberger et al. (2019), GKM19 from now on, introduce a subvector\nAnderson-Rubin (AR) test with data-dependent critical values that has\nasymptotic size equal to nominal size for a parameter space that allows for\narbitrary strength or weakness of the IVs and has uniformly nonsmaller power\nthan the projected AR test studied in Guggenberger et al. (2012). However,\nGKM19 imposes the restrictive assumption of conditional homoskedasticity. The\nmain contribution here is to robustify the procedure in GKM19 to arbitrary\nforms of conditional heteroskedasticity. We first adapt the method in GKM19 to\na setup where a certain covariance matrix has an approximate Kronecker product\n(AKP) structure which nests conditional homoskedasticity. The new test equals\nthis adaption when the data is consistent with AKP structure as decided by a\nmodel selection procedure. Otherwise the test equals the AR/AR test in Andrews\n(2017) that is fully robust to conditional heteroskedasticity but less powerful\nthan the adapted method. We show theoretically that the new test has asymptotic\nsize bounded by the nominal size and document improved power relative to the\nAR/AR test in a wide array of Monte Carlo simulations when the covariance\nmatrix is not too far from AKP.\n