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Quasi ML Estimation of the Panel AR(1) Model with Arbitrary Initial Conditions

  • Hugo Kruiniger

    (Queen Mary, University of London)

In this paper we show that the Quasi ML estimation method yields consistent Random and Fixed Effects estimators for the autoregression parameter ρ in the panel AR(1) model with arbitrary initial conditions even when the errors are drawn from heterogenous distributions. We compare both analytically and by means of Monte Carlo simulations the QML estimators with the GMM estimator proposed by Arellano and Bond (1991) [AB], which ignores some of the moment conditions implied by the model. Unlike the AB GMM estimator, the QML estimators for ρ only suffer from a weak instruments problem when ρ is close to one if the cross-sectional average of the variances of the errors is constant over time, e.g. under time-series homoskedasticity. However, even in this case the QML estimators are still consistent when ρ is equal to one and they display only a relatively small bias when ρ is close to one. In contrast, the AB GMM estimator is inconsistent when ρ is equal to one, and is severly biased when ρ is close to one. Finally, we study the finite sample properties of two types of estimators for the standard errors of the QML estimators for ρ, and the bounds of QML based confidence intervals for ρ.

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File URL: http://www.econ.qmul.ac.uk/papers/doc/wp582.pdf
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Paper provided by Queen Mary University of London, School of Economics and Finance in its series Working Papers with number 582.

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Date of creation: Dec 2006
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Handle: RePEc:qmw:qmwecw:wp582
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  1. Ahn, Seung C. & Schmidt, Peter, 1997. "Efficient estimation of dynamic panel data models: Alternative assumptions and simplified estimation," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 309-321.
  2. Kazuhiko Hayakawa, 2005. "Small Sample Bias Propreties of the System GMM Estimator in Dynamic Panel Data Models," Hi-Stat Discussion Paper Series d05-82, Institute of Economic Research, Hitotsubashi University.
  3. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-26, November.
  4. Richard Blundell & Steve Bond, 1999. "GMM estimation with persistent panel data: an application to production functions," IFS Working Papers W99/04, Institute for Fiscal Studies.
  5. Hsaio, Cheng & Pesaran, M. Hashem & Tahmiscioglu, A. Kamil, 1998. "Maximum Likelihood Estimation of Fixed Effects Dynamic Panel Data Models Covering Short Time Periods," Cambridge Working Papers in Economics 9826, Faculty of Economics, University of Cambridge.
  6. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, November.
  7. Gary Chamberlain, 1980. "Analysis of Covariance with Qualitative Data," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 225-238.
  8. Kruiniger, Hugo, 2008. "Maximum likelihood estimation and inference methods for the covariance stationary panel AR(1)/unit root model," Journal of Econometrics, Elsevier, vol. 144(2), pages 447-464, June.
  9. Blundell, Richard & Bond, Stephen, 1998. "Initial conditions and moment restrictions in dynamic panel data models," Journal of Econometrics, Elsevier, vol. 87(1), pages 115-143, August.
  10. Anderson, T. W. & Hsiao, Cheng, 1982. "Formulation and estimation of dynamic models using panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 47-82, January.
  11. Hugo Kruiniger, 2002. "On the Estimation of Panel Regression Models with Fixed Effects," Working Papers 450, Queen Mary University of London, School of Economics and Finance.
  12. Javier Alvarez & Manuel Arellano, 2004. "Robust Likelihood Estimation Of Dynamic Panel Data Models," Working Papers wp2004_0421, CEMFI.
  13. Steve Bond & Céline Nauges & Frank Windmeijer, 2005. "Unit roots: identification and testing in micro panels," CeMMAP working papers CWP07/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  14. Alonso-Borrego, César & Arrellano, Manuel, 1996. "Symmetrically normalized instrumental-variable estimation using panel data," UC3M Working papers. Economics 4098, Universidad Carlos III de Madrid. Departamento de Economía.
  15. Maurice J.G. Bun & Frank Windmeijer, 2009. "The Weak Instrument Problem of the System GMM Estimator in Dynamic Panel Data Models," Tinbergen Institute Discussion Papers 09-086/4, Tinbergen Institute.
  16. Kruiniger, Hugo, 2007. "An Efficient Linear Gmm Estimator For The Covariance Stationary Ar(1)/Unit Root Model For Panel Data," Econometric Theory, Cambridge University Press, vol. 23(03), pages 519-535, June.
  17. Manuel Arellano & Stephen Bond, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 277-297.
  18. Javier Alvarez & Manuel Arellano, 2003. "The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators," Econometrica, Econometric Society, vol. 71(4), pages 1121-1159, 07.
  19. Ahn, Seung C. & Schmidt, Peter, 1995. "Efficient estimation of models for dynamic panel data," Journal of Econometrics, Elsevier, vol. 68(1), pages 5-27, July.
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  21. Kruiniger, Hugo, 2009. "Gmm Estimation And Inference In Dynamic Panel Data Models With Persistent Data," Econometric Theory, Cambridge University Press, vol. 25(05), pages 1348-1391, October.
  22. Arellano, Manuel & Bover, Olympia, 1995. "Another look at the instrumental variable estimation of error-components models," Journal of Econometrics, Elsevier, vol. 68(1), pages 29-51, July.
  23. Windmeijer, Frank, 2005. "A finite sample correction for the variance of linear efficient two-step GMM estimators," Journal of Econometrics, Elsevier, vol. 126(1), pages 25-51, May.
  24. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, November.
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