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ON GMM INFERENCE: PARTIAL IDENTIFICATION, IDENTIFICATION STRENGTH, AND NONSTANDARD ASYMPTOTICS

Published online by Cambridge University Press:  18 September 2023

Donald S. Poskitt
Donald S. Poskitt*
Affiliation:
Monash University
*
Address correspondence to Donald S. Poskitt, Department of Econometrics and Business Statistics, Monash University, Clayton, VIC 3800, Australia; e-mail: Donald.Poskitt@monash.edu.au
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Abstract

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This paper analyses aspects of generalized method of moments (GMM) inference in moment equality models in settings where standard regularity conditions may break down. Explicit analytic formulations for the asymptotic distributions of estimable functions of the GMM estimator and statistics based on the GMM criterion function are derived under relatively mild assumptions. The moment Jacobian is allowed to be rank deficient, so first order identification may fail, the values of the Jacobian singular values are not constrained, thereby allowing for varying levels of identification strength, the long-run variance of the moment conditions can be singular, and the GMM criterion function weighting matrix may also be chosen sub-optimally. The large-sample properties are derived without imposing a specific structure on the functional form of the moment conditions. Closed-form expressions for the distributions are presented that can be evaluated using standard software without recourse to bootstrap or simulation methods. The practical operation of the results is illustrated via examples involving instrumental variables estimation of a structural equation with endogenous regressors and a common CH features model.

Type
ARTICLES
Information
Econometric Theory , Volume 40 , Issue 4 , August 2024 , pp. 875 - 925
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

I am grateful to two anonymous referees for valuable comments which helped to improve the paper. I am indebted to the Co-Editor (Patrik Guggenberger) for insightful and constructive criticism and for helpful suggestions on the content and presentation of the paper. I am also grateful to the Editor (Peter C.B. Phillips) for correcting errors, directing my attention to related extant literature, and editorial assistance. This research has been supported by the Australian Research Council (ARC) Discovery Grant DP120102344.

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