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

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  • Hugo Kruiniger

    (Queen Mary, University of London)

Abstract

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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Bibliographic Info

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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Keywords: Dynamic panel data; Initial conditions; Quasi ML; GMM; Weak moment conditions; Local-to-zero asymptotics;

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References

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  1. 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.
  2. 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.
  3. 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.
  4. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-26, November.
  5. Richard Blundell & Steve Bond, 1995. "Initial conditions and moment restrictions in dynamic panel data models," IFS Working Papers W95/17, Institute for Fiscal Studies.
  6. Hugo Kruiniger, 2002. "On the estimation of panel regression models with fixed effects," 10th International Conference on Panel Data, Berlin, July 5-6, 2002 C6-2, International Conferences on Panel Data.
  7. 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.
  8. 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.
  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. 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.
  11. 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.
  12. 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.
  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. Hsiao, Cheng & Hashem Pesaran, M. & Kamil Tahmiscioglu, A., 2002. "Maximum likelihood estimation of fixed effects dynamic panel data models covering short time periods," Journal of Econometrics, Elsevier, vol. 109(1), pages 107-150, July.
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  16. 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.
  17. 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.
  18. 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.
  19. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, October.
  20. Javier Alvarez & Manuel Arellano, 2004. "Robust Likelihood Estimation Of Dynamic Panel Data Models," Working Papers wp2004_0421, CEMFI.
  21. 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.
  22. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
  23. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, October.
  24. 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.
  25. 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.
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Cited by:
  1. Arturas Juodis, 2013. "First Difference Transformation in Panel VAR models: Robustness, Estimation and Inference," UvA-Econometrics Working Papers 13-06, Universiteit van Amsterdam, Dept. of Econometrics.
  2. Robertson, Donald & Sarafidis, Vasilis & Westerlund, Joakim, 2014. "GMM Unit Root Inference in Generally Trending and Cross-Correlated Dynamic Panels," MPRA Paper 53419, University Library of Munich, Germany.

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