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IDENTIFICATION ROBUST INFERENCE FOR MOMENTS-BASED ANALYSIS OF LINEAR DYNAMIC PANEL DATA MODELS

Published online by Cambridge University Press:  11 June 2021

Maurice J.G. Bun  and
Frank Kleibergen
Maurice J.G. Bun
Affiliation:
De Nederlandsche Bank University of Amsterdam
Frank Kleibergen*
Affiliation:
University of Amsterdam
*
Address correspondence to Frank Kleibergen, Amsterdam School of Economics, University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands; e-mail: f.r.kleibergen@uva.nl.
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Abstract

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We use identification robust tests to show that difference (Dif), level (Lev), and nonlinear (NL) moment conditions, as proposed by Arellano and Bond (1991, Review of Economic Studies 58, 277–297), Ahn and Schmidt (1995, Journal of Econometrics 68, 5–27), Arellano and Bover (1995, Journal of Econometrics 68, 29–51), and Blundell and Bond (1998, Journal of Econometrics 87, 115–143) for the linear dynamic panel data model, do not separately identify the autoregressive parameter when its true value is close to one and the variance of the initial observations is large. We prove that combinations of these moment conditions, however, do so when there are more than three time series observations. This identification then solely results from a set of, so-called, robust moment conditions. These robust moments are spanned by the combined Dif, Lev, and NL moment conditions and only depend on differenced data. We show that, when only the robust moments contain identifying information on the autoregressive parameter, the discriminatory power of the Kleibergen (2005, Econometrica 73, 1103–1124) Lagrange multiplier (KLM) test using the combined moments is identical to the largest rejection frequencies that can be obtained from solely using the robust moments. This shows that the KLM test implicitly uses the robust moments when only they contain information on the autoregressive parameter.

Type
ARTICLES
Information
Econometric Theory , Volume 38 , Issue 4 , August 2022 , pp. 689 - 751
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 (http://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), 2021. Published by Cambridge University Press

Footnotes

The research of the first author has been funded by the NWO Vernieuwingsimpuls research grant “Causal Inference with Panel Data.” We thank the Editor, Peter Phillips, the Co-Editor, Guido Kuersteiner, two anonymous referees, Manuel Arellano, Richard Blundell, Steve Bond, Peter Boswijk, Geert Dhaene, Frank Windmeijer, and participants of seminars at Bristol, CEMFI, and CORE, the Cowles Summer Conference at Yale, the EC2 Meeting in Maastricht, Groningen, Leuven, and Monash, and the 19th International Conference on Panel Data in London and Oxford, the Tinbergen Institute in Amsterdam and Toulouse, and UCL for helpful comments and discussion.

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