Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-16T16:26:59.041Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

This article was originally published with a missing reference. A notice detailing this has been published, and the reference added to the online PDF and HTML versions.

References

REFERENCES

Ahn, S. C. & Schmidt, P. (1995) Efficient estimation of models for dynamic panel data. Journal of Econometrics 68, 5–27. CrossRefGoogle Scholar
Ahn, S.C. & G.M. Thomas (2006) Likehood Based Inference for Dynamic Panel Data Models. Unpublished manuscript.Google Scholar
Alvarez, J. & Arellano, M. (2004) Robust Likelihood Estimation of Dynamic Panel Data Models. CEMFI Working Paper No. 0421. Google Scholar
Anderson, T. W. & Hsiao, C. (1981) Estimation of dynamic models with error components. Journal of the American Statistical Association 76, 598–606.CrossRefGoogle Scholar
Anderson, T. W. & Hsiao, C. (1982) Formulation and estimation of dynamic models using panel data. Journal of Econometrics 18, 47–82.CrossRefGoogle Scholar
Anderson, T. W. & Rubin, H. (1949) Estimation of the parameters of a single equation in a complete set of stochastic equations. The Annals of Mathematical Statistics 21, 570–582.CrossRefGoogle Scholar
Andrews, D. W. K., Moreira, M. J. & Stock, J. H. (2006) Optimal two-sided invariant similar tests for instrumental variables regression. Econometrica 74, 715–752.CrossRefGoogle Scholar
Andrews, I. (2016) Conditional linear combination tests for weakly identified models. Econometrica 84, 2155–2182.CrossRefGoogle Scholar
Andrews, I. & Mikusheva, A. (2016) Conditional inference with a functional nuisance parameter. Econometrica 84, 1571–1612.CrossRefGoogle Scholar
Arellano, M. & Bond, S. (1991) Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies 58, 277–297.CrossRefGoogle Scholar
Arellano, M. & Bover, O. (1995) Another look at the instrumental variable estimation of error-components models. Journal of Econometrics 68, 29–51.CrossRefGoogle Scholar
Blundell, R. & Bond, S. (1998) Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics 87, 115–143.CrossRefGoogle Scholar
Bond, S., Nauges, C., & Windmeijer, F. (2005) Unit Roots: Identification and Testing in Micro Panels. CEMMAP Working paper CWP07/05, Centre for microdata methods and practice, University College, London. CrossRefGoogle Scholar
Bond, S. & Windmeijer, F. (2005) Reliable inference for GMM estimators? Finite sample properties of alternative test procedures in linear panel data models. Econometric Reviews 24, 1–37.CrossRefGoogle Scholar
Bun, M. J. G. & Windmeijer, F. (2010) The weak instrument problem of the system GMM estimator in dynamic panel data models. Econometrics Journal 13, 95–126.CrossRefGoogle Scholar
Davidson, R. & MacKinnon, J.G. (2002) Graphical methods for investigating the size and power of hypothesis tests. The Manchester School 66, 1–26.CrossRefGoogle Scholar
Dhaene, G. & Jochmans, K. (2016) Likelihood inference in an autoregression with fixed effects. Econometric Theory 31, 1178–1215.CrossRefGoogle Scholar
Dovonon, P. & Hall, A. R. (2018) The asymptotic properties of GMM and indirect inference under second-order identification. Journal of Econometrics 205, 76–111.CrossRefGoogle Scholar
Dovonon, P., Hall, A. R. & Kleibergen, F. (2020) Inference in second-order identified models. Journal of Econometrics 218, 346–372.CrossRefGoogle Scholar
Dovonon, P. & Renault, E. (2013) Testing for common conditionally heteroskedastic factors. Econometrica 81, 2561–2586.Google Scholar
Dufour, J. M. (1997) Some impossibility theorems in econometrics with applications to structural and dynamic models. Econometrica 65, 1365–1388.CrossRefGoogle Scholar
Dufour, J. M. & Taamouti, M. (2005) Projection-based statistical inference in linear structural models with possibly weak instruments. Econometrica 73, 1351–1365. CrossRefGoogle Scholar
Engle, R. F. & Granger, C. W. J. (1987) Co-integration and error correction: Representation, estimation and testing. Econometrica 55, 251–276.CrossRefGoogle Scholar
Guggenberger, P., Kleibergen, F. & Mavroeidis, S. (2019) A more powerful Anderson–Rubin test in linear instrumental variables regression. Quantitative Economics 10, 487–526.CrossRefGoogle Scholar
Guggenberger, P., Kleibergen, F., Mavroeidis, S. & Chen, L. (2012) On the asymptotic sizes of subset Anderson–Rubin and Lagrange multiplier tests in linear instrumental variables regression. Econometrica 80, 2649–2666.Google Scholar
Hahn, J., Hausman, J. & Kuersteiner, G. (2007) Long difference instrumental variable estimation for dynamic panel models with fixed effects. Journal of Econometrics 140, 574–617.CrossRefGoogle Scholar
Han, C. & Phillips, P. C. B. (2010) GMM estimation for dynamic panels with fixed effects and strong instruments at unity. Econometric Theory 26, 119–151.CrossRefGoogle Scholar
Hansen, L. P. (1982) Large sample properties of generalized method moments estimators. Econometrica 50, 1029–1054.CrossRefGoogle Scholar
Hansen, L. P., Heaton, J. & Yaron, A. (1996) Finite sample properties of some alternative GMM estimators. Journal of Business and Economic Statistics 14, 262–280.CrossRefGoogle Scholar
Hsiao, C., Pesaran, M. H. & Tahmiscioglu, A. K. (2002) Maximum likelihood estimation of fixed effects dynamic panel data models covering short time periods. Journal of Econometrics 109, 107–150.CrossRefGoogle Scholar
Johansen, S. (1991) Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59, 1551–1580.CrossRefGoogle Scholar
Kleibergen, F. (2005) Testing parameters in GMM without assuming that they are identified. Econometrica 73, 1103–1124.CrossRefGoogle Scholar
Kleibergen, F. (2021) Efficient size correct subset inference in homoskedastic linear instrumental variables regression. Journal of Econometrics 221, 78–96.CrossRefGoogle Scholar
Kleibergen, F., Kong, L., & Zhan, Z. (2020) Identification Robust Testing of Risk Premia in Finite Samples. Journal of Financial Econometrics, Forthcoming.Google Scholar
Kleibergen, F. & Zhan, Z. (2020) Robust inference for consumption-based asset pricing. Journal of Finance 75, 507–550.CrossRefGoogle Scholar
Kruiniger, H. (2002) On the Estimation of Panel Regression Models with Fixed Effects. Manuscript, Queen Mary University.CrossRefGoogle Scholar
Kruiniger, H. (2009) GMM estimation and inference in dynamic panel data models with persistent data. Econometric Theory 25, 1348–1391.CrossRefGoogle Scholar
Kruiniger, H. (2013) Quasi ML estimation of the panel AR(1) model with arbitrary initial conditions. Journal of econometrics 173, 175–188.CrossRefGoogle Scholar
Madsen, E. (2003) GMM Estimators and Unit Root Tests in the AR(1) Panel Data Model. Centre for Applied Micro Econometrics Working paper 2003-11, University of Copenhagen.Google Scholar
Moreira, M. J. (2003) A conditional likelihood ratio test for structural models. Econometrica 71, 1027–1048.CrossRefGoogle Scholar
Newey, W. K. & Windmeijer, F. (2009) Generalized method of moments with many weak moment conditions. Econometrica 77, 687–719.Google Scholar
Nickell, S. J. (1981) Biases in dynamic models with fixed effects. Econometrica 49, 1417–1426.CrossRefGoogle Scholar
Phillips, P. C. B. (1989) Partially identified econometric models. Econometric Theory 5, 181–240.CrossRefGoogle Scholar
Phillips, P. C. B. (2018) Dynamic panel Anderson–Hsiao estimation with roots near unity. Econometric Theory 34, 253–276.CrossRefGoogle Scholar
Staiger, D. & Stock, J. H. (1997) Instrumental variables regression with weak instruments. Econometrica 65, 557–586.CrossRefGoogle Scholar
Stock, J. H. & Wright, J. H. (2000) GMM with weak identification. Econometrica 68, 1055–1096.CrossRefGoogle Scholar