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Efficient GMM Estimation of Dynamic Panel Data Models Where Large Heterogeneity May Be Present

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  • Kazuhiko Hayakawa

Abstract

This paper addresses the many instruments problem, i.e. (1) the trade-off between the bias and the efficiency of the GMM estimator, and (2) inaccuracy of inference, in dynamic panel data models where unobservable heterogeneity may be large. We find that if we use all the instruments in levels, although the GMM estimator is robust to large heterogeneity, inference is inaccurate. In contrast, if we use the minimum number of instruments in levels in the sense that we use only one instrument for each period, the performance of the GMM estimator is heavily affected by the degree of heterogeneity, that is, both the asymptotic bias and the variance are proportional to the magnitude of heterogeneity. To address this problem, we propose a new form of instruments that are obtained from the so-called backward orthogonal deviation transformation. The asymptotic analysis shows that the GMM estimator with the minimum number of new instruments has smaller asymptotic bias than the estimators typically used such as the GMM estimator with all instruments in levels, the LIML estimators and the within-groups estimators, while the asymptotic variance of the proposed estimator is equal to the lower bound. Thus both the asymptotic bias and the variance of the proposed estimators become small simultaneously. Simulation results show that our new GMM estimator outperforms the conventional GMM estimator with all instruments in levels in term of the RMSE and in terms of accuracy of inference. An empirical application with Spanish firm data is also provided.

Suggested Citation

  • Kazuhiko Hayakawa, 2006. "Efficient GMM Estimation of Dynamic Panel Data Models Where Large Heterogeneity May Be Present," Hi-Stat Discussion Paper Series d05-130, Institute of Economic Research, Hitotsubashi University.
  • Handle: RePEc:hst:hstdps:d05-130
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    File URL: http://hi-stat.ier.hit-u.ac.jp/research/discussion/2005/pdf/D05-130.pdf
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    References listed on IDEAS

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    Cited by:

    1. Kazuhiko Hayakawa, 2006. "The Asymptotic Properties of the System GMM Estimator in Dynamic Panel Data Models When Both N and T are Large," Hi-Stat Discussion Paper Series d05-129, Institute of Economic Research, Hitotsubashi University.
    2. Blessing Chiripanhura & Miguel Niño‐Zarazúa, 2015. "Aid, Political Business Cycles and Growth in Africa," Journal of International Development, John Wiley & Sons, Ltd., vol. 27(8), pages 1387-1421, November.
    3. Naoto Kunitomo & Kentaro Akashi, 2010. "An Aysmptotically Optimal Modification of the Panel LIML Estimation for Individual Heteroscedasticity," CIRJE F-Series CIRJE-F-780, CIRJE, Faculty of Economics, University of Tokyo.
    4. Kentaro Akashi & Naoto Kunitomo, 2015. "The limited information maximum likelihood approach to dynamic panel structural equation models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 39-73, February.
    5. Gebregziabher, Fiseha & Nino-Zarazua, Miguel, 2014. "Social spending and aggregate welfare in developing and transition economies," WIDER Working Paper Series 082, World Institute for Development Economic Research (UNU-WIDER).
    6. Naoto Kunitomo & Kentaro Akashi, 2007. "The Conditional Limited Information Maximum Likelihood Approach to Dynamic Panel Structural Equations," CIRJE F-Series CIRJE-F-503, CIRJE, Faculty of Economics, University of Tokyo.
    7. Kentaro Akashi & Naoto Kunitomo, 2010. "The Limited Information Maximum Likelihood Approach to Dynamic Panel Structural Equations," CIRJE F-Series CIRJE-F-708, CIRJE, Faculty of Economics, University of Tokyo.

    More about this item

    Keywords

    Dynamic panel data; many instruments; generalized method of moments estimator; unobservable large heterogeneity;

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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