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A POWERFUL SUBVECTOR ANDERSON–RUBIN TEST IN LINEAR INSTRUMENTAL VARIABLES REGRESSION WITH CONDITIONAL HETEROSKEDASTICITY

Published online by Cambridge University Press:  14 April 2023

Patrik Guggenberger ,
Frank Kleibergen  and
Sophocles Mavroeidis
Patrik Guggenberger
Affiliation:
Pennsylvania State University
Frank Kleibergen*
Affiliation:
University of Amsterdam
Sophocles Mavroeidis
Affiliation:
University of Oxford
*
Address correspondence to Frank Kleibergen, Department of Quantitative Economics, University of Amsterdam, Amsterdam, Netherlands; e-mail: f.r.kleibergen@uva.nl.
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Abstract

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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, Kleibergen, and Mavroeidis (2019, Quantitative Economics, 10, 487–526; hereafter GKM19) 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, Econometrica, 80(6), 2649–2666). However, GKM19 imposes the restrictive assumption of conditional homoskedasticity (CHOM). 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 CHOM. The new test equals this adaptation when the data are consistent with AKP structure as decided by a model selection procedure. Otherwise, the test equals the AR/AR test in Andrews (2017, Identification-Robust Subvector Inference, Cowles Foundation Discussion Papers 3005, Yale University) 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.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 40 , Issue 5 , October 2024 , pp. 957 - 1002
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Footnotes

We would like to thank the Editor (Peter Phillips), the Co-Editor (Michael Jansson), and two referees for very helpful comments. Guggenberger thanks the European University Institute for its hospitality while parts of this paper were drafted. Mavroeidis gratefully acknowledges the research support of the European Research Council via Consolidator grant number 647152. We would also like to thank Donald Andrews for detailed comments and for providing his Gauss code of, and explanations about, Andrews (2017) and Lixiong Li for outstanding research assistance for the Monte Carlo study. We would also like to thank seminar participants in Amsterdam, Bologna, Bristol, Florence (EUI), Indiana, Konstanz, Manchester, Mannheim, Paris (PSE), Pompeu Fabra, Regensburg, Rotterdam, Singapore (NUS and SMU), Tilburg, Toulouse, Tübingen, and Zurich, and conference participants at the Institute for Fiscal Studies (London) for helpful comments.

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