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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
Contact details of provider: Postal: London E1 4NS
Phone: +44 (0) 20 7882 5096
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Web page: http://www.econ.qmul.ac.uk

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  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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, Wiley Blackwell, vol. 58(2), pages 277-97, April.
  6. 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.
  7. Maurice J. G. Bun & Frank Windmeijer, 2010. "The weak instrument problem of the system GMM estimator in dynamic panel data models," Econometrics Journal, Royal Economic Society, vol. 13(1), pages 95-126, 02.
  8. Hugo Kruiniger, 2006. "GMM Estimation and Inference in Dynamic Panel Data Models with Persistent Data," Working Papers 560, Queen Mary University of London, School of Economics and Finance.
  9. 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.
  10. Richard Blundell & Stephen Bond, 2000. "GMM Estimation with persistent panel data: an application to production functions," Econometric Reviews, Taylor & Francis Journals, vol. 19(3), pages 321-340.
  11. 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.
  12. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
  13. Javier Alvarez & Manuel Arellano, 2004. "Robust Likelihood Estimation Of Dynamic Panel Data Models," Working Papers wp2004_0421, CEMFI.
  14. repec:cup:cbooks:9780521252805 is not listed on IDEAS
  15. Sims, Christopher A., 2000. "Using a likelihood perspective to sharpen econometric discourse: Three examples," Journal of Econometrics, Elsevier, vol. 95(2), pages 443-462, April.
  16. M Arellano & O Bover, 1990. "Another Look at the Instrumental Variable Estimation of Error-Components Models," CEP Discussion Papers dp0007, Centre for Economic Performance, LSE.
  17. Blundell, R. & Bond, S., 1995. "Initial Conditions and Moment Restrictions in Dynamic Panel Data Models," Economics Papers 104, Economics Group, Nuffield College, University of Oxford.
  18. 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.
  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.
  20. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-26, November.
  21. 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.
  22. Chamberlain, Gary, 1980. "Analysis of Covariance with Qualitative Data," Review of Economic Studies, Wiley Blackwell, vol. 47(1), pages 225-38, January.
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  24. Alonso-Borrego, Cesar & Arellano, Manuel, 1999. "Symmetrically Normalized Instrumental-Variable Estimation Using Panel Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 36-49, January.
  25. 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.
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