IDEAS home Printed from https://ideas.repec.org/p/qmw/qmwecw/wp582.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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.

Suggested Citation

  • Hugo Kruiniger, 2006. "Quasi ML Estimation of the Panel AR(1) Model with Arbitrary Initial Conditions," Working Papers 582, Queen Mary University of London, School of Economics and Finance.
  • Handle: RePEc:qmw:qmwecw:wp582
    as

    Download full text from publisher

    File URL: http://www.econ.qmul.ac.uk/media/econ/research/workingpapers/archive/wp582.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Javier Alvarez & Manuel Arellano, 2004. "Robust Likelihood Estimation Of Dynamic Panel Data Models," Working Papers wp2004_0421, CEMFI.
    2. 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.
    3. 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.
    4. 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, February.
    5. 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, July.
    6. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, April.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, April.
    12. 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.
    13. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
    14. 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.
    15. 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.
    16. 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.
    17. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-1426, November.
    18. Stephen 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. Gary Chamberlain, 1980. "Analysis of Covariance with Qualitative Data," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 225-238.
    24. 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.
    25. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Arturas Juodis, 2013. "Cointegration Testing in Panel VAR Models Under Partial Identification and Spatial Dependence," UvA-Econometrics Working Papers 13-08, Universiteit van Amsterdam, Dept. of Econometrics.
    2. Juodis, Arturas & Sarafidis, Vasilis, 2014. "Fixed T Dynamic Panel Data Estimators with Multi-Factor Errors," MPRA Paper 57659, University Library of Munich, Germany.
    3. 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.
    4. Prosper Donovon & Alastair R. Hall, 2017. "The Asymptotic Properties of GMM and Indirect Inference under Second Inference," The School of Economics Discussion Paper Series 1705, Economics, The University of Manchester.
    5. repec:bla:obuest:v:79:y:2017:i:4:p:463-494 is not listed on IDEAS
    6. Maurice J.G. Bun & Martin A. Carree & Artūras Juodis, 2017. "On Maximum Likelihood Estimation of Dynamic Panel Data Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(4), pages 463-494, August.
    7. Arturas Juodis, 2015. "Iterative Bias Correction Procedures Revisited: A Small Scale Monte Carlo Study," UvA-Econometrics Working Papers 15-02, Universiteit van Amsterdam, Dept. of Econometrics.
    8. Robert F. Phillips, 2014. "Quasi Maximum-Likelihood Estimation Of Dynamic Panel Data Models For Short Time Series," Working Papers 2014-006, The George Washington University, Department of Economics, Research Program on Forecasting.
    9. Zhenlin Yang, 2014. "Initial-Condition Free Estimation of Fixed Effects Dynamic Panel Data Models," Working Papers 16-2014, Singapore Management University, School of Economics.
    10. 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.
    11. Hayakawa, Kazuhiko & Pesaran, M. Hashem, 2015. "Robust standard errors in transformed likelihood estimation of dynamic panel data models with cross-sectional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 188(1), pages 111-134.

    More about this item

    Keywords

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

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:qmw:qmwecw:wp582. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Nicholas Owen). General contact details of provider: http://edirc.repec.org/data/deqmwuk.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.