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Quasi ML estimation of the panel AR(1) model with arbitrary initial conditions

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  • Kruiniger, Hugo

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 and possibly time-series heteroskedasticity even when the error components are drawn from heterogeneous distributions. We investigate both analytically and by means of Monte Carlo simulations the properties of the QML estimators for ρ. The RE(Q)MLE for ρ is asymptotically at least as robust to individual heterogeneity and, when the data are i.i.d. and normal, at least as efficient as the FE(Q)MLE for ρ. Furthermore, the QML estimators for ρ only suffer from a ‘weak moment conditions’ problem when ρ is close to one if the cross-sectional average of the variances of the errors is (almost) constant over time, e.g. under time-series homoskedasticity. However, in this case the QML estimators for ρ are still consistent when ρ is local to or equal to one although they converge to a non-normal possibly asymmetric distribution at a rate that is lower than N1/2 but at least N1/4. 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

  • Kruiniger, Hugo, 2013. "Quasi ML estimation of the panel AR(1) model with arbitrary initial conditions," Journal of Econometrics, Elsevier, vol. 173(2), pages 175-188.
  • Handle: RePEc:eee:econom:v:173:y:2013:i:2:p:175-188 DOI: 10.1016/j.jeconom.2012.11.004
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    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. repec:bla:obuest:v:79:y:2017:i:4:p:463-494 is not listed on IDEAS
    5. 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, pages 463-494.
    6. 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.
    7. 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.
    8. Zhenlin Yang, 2014. "Initial-Condition Free Estimation of Fixed Effects Dynamic Panel Data Models," Working Papers 16-2014, Singapore Management University, School of Economics.
    9. 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.
    10. 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; Fixed effects; Quasi Maximum Likelihood (QML); Singular information matrix; Generalized Method of Moments (GMM); Weak moment conditions; Local-to-zero asymptotics; Rate of convergence;

    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

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