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

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Kazuhiko Hayakawa

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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.

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Paper provided by Institute of Economic Research, Hitotsubashi University in its series Hi-Stat Discussion Paper Series with number d05-130.

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Date of creation: Jan 2006
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Handle: RePEc:hst:hstdps:d05-130

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Related research
Keywords: Dynamic panel data; many instruments; generalized method of moments estimator; unobservable large heterogeneity;

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Find related papers by JEL classification:
C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Bun, Maurice J.G. & Kiviet, Jan F., 2006. "The effects of dynamic feedbacks on LS and MM estimator accuracy in panel data models," Journal of Econometrics, Elsevier, vol. 132(2), pages 409-444, June. [Downloadable!] (restricted)
    Other versions:
  2. Alvarez, J. & Arellano, M., 1998. "The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators," Papers 9808, Centro de Estudios Monetarios Y Financieros-.
    Other versions:
  3. Arellano, Manuel & Bond, Stephen, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," Review of Economic Studies, Blackwell Publishing, vol. 58(2), pages 277-97, April. [Downloadable!] (restricted)
  4. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, vol. 69(5), pages 1161-91, September.
  5. Theodore W. Anderson & Naoto Kunijtomo & Yukitoshi Matsushita, 2005. "A New Light from Old Wisdoms : Alternative Estimation Methods of Simultaneous Equations and Microeconometric Models," CIRJE F-Series CIRJE-F-321, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  6. Hahn, Jinyong, 2002. "Optimal Inference With Many Instruments," Econometric Theory, Cambridge University Press, vol. 18(01), pages 140-168, February. [Downloadable!]
  7. Bover, Olympia & Watson, Nadine, 2001. "Are there Economies of Scale in the Demand for Money by Firms? Some Panel Data Estimates," CEPR Discussion Papers 2818, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  8. Angrist, Joshua D & Krueger, Alan B, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, MIT Press, vol. 106(4), pages 979-1014, November. [Downloadable!] (restricted)
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  9. Angrist, J D & Imbens, G W & Krueger, A B, 1999. "Jackknife Instrumental Variables Estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 57-67, Jan.-Feb.. [Downloadable!]
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  10. Breusch, Trevor & Qian, Hailong & Schmidt, Peter & Wyhowski, Donald, 1999. "Redundancy of moment conditions," Journal of Econometrics, Elsevier, vol. 91(1), pages 89-111, July. [Downloadable!] (restricted)
  11. Jinyong Hahn & Atsushi Inoue, 2002. "A Monte Carlo Comparison Of Various Asymptotic Approximations To The Distribution Of Instrumental Variables Estimators," Econometric Reviews, Taylor and Francis Journals, vol. 21(3), pages 309-336. [Downloadable!] (restricted)
  12. Hayakawa, Kazuhiko, 2007. "Small sample bias properties of the system GMM estimator in dynamic panel data models," Economics Letters, Elsevier, vol. 95(1), pages 32-38, April. [Downloadable!] (restricted)
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  13. Jinyong Hahn & Guido Kuersteiner, 2002. "Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects when Both "n" and "T" Are Large," Econometrica, Econometric Society, vol. 70(4), pages 1639-1657, July. [Downloadable!] (restricted)
  14. Manuel Arellano, 2003. "Modelling Optimal Instrumental Variables For Dynamic Panel Data Models," Working Papers wp2003_0310, CEMFI. [Downloadable!]
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  16. Donald W.K. Andrews & James H. Stock, 2005. "Inference with Weak Instruments," NBER Technical Working Papers 0313, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  17. Wooldridge, Jeffrey M., 2005. "Instrumental Variables Estimation With Panel Data," Econometric Theory, Cambridge University Press, vol. 21(04), pages 865-869, August. [Downloadable!]
  18. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2005. "Bias Corrected Instrumental Variables Estimation for Dynamic Panel Models with Fixed E¤ects," Boston University - Department of Economics - Working Papers Series WP2005-024, Boston University - Department of Economics. [Downloadable!]
  19. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, 09. [Downloadable!] (restricted)
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  20. 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. [Downloadable!]
  21. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May. [Downloadable!] (restricted)
  22. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2004. "Estimation with weak instruments: Accuracy of higher-order bias and MSE approximations," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 272-306, 06. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Hiroaki Chigira & Taku Yamamoto, 2006. "A Bias-Corrected Estimation for Dynamic Panel Models in Small Samples," Hi-Stat Discussion Paper Series d06-177, Institute of Economic Research, Hitotsubashi University. [Downloadable!]
  2. 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. [Downloadable!]
  3. 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. [Downloadable!]
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