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Improved Variance Estimation of Maximum Likelihood Estimators in Stable First-Order Dynamic Regression Models

Author

Listed:
  • Jan F. KIVIET

    (Division of Economics, Nanyang Technological University, Singapore 637332, Singapore)

  • Garry D.A. PHILLIPS

    (Cardiff Business School, Aberconway Building, Colum Drive, CF10 3EU, Cardiff, Wales, UK)

Abstract

In dynamic regression models conditional maximum likelihood (least-squares) coefficient and variance estimators are biased. From expansions of the coefficient variance and its estimator we obtain an approximation to the bias in variance es- timation and a bias corrected variance estimator, for both the standard and a bias corrected coefficient estimator. These enable a comparison of their mean squared errors to second order. We formally derive sufficient conditions for admissibility of these approximations. Illustrative numerical and simulation results are presented on bias reduction of coefficient and variance estimation for three relevant classes of ?rst-order autoregressive models, supplemented by e¤ects on mean squared er- rors, test size and size corrected power. These indicate that substantial biases do occur in moderately large samples, but these can be mitigated substantially and may also yield mean squared error reduction. Crude asymptotic tests are cursed by huge size distortions. However, operational bias corrections of both the esti- mates of coefficients and their estimated variance are shown to curb type I errors reasonably well.

Suggested Citation

  • Jan F. KIVIET & Garry D.A. PHILLIPS, 2012. "Improved Variance Estimation of Maximum Likelihood Estimators in Stable First-Order Dynamic Regression Models," Economic Growth Centre Working Paper Series 1206, Nanyang Technological University, School of Social Sciences, Economic Growth Centre.
  • Handle: RePEc:nan:wpaper:1206
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    References listed on IDEAS

    as
    1. Kiviet, J.F. & Phillips, G.D.A., 1999. "The Bias of the 2SLS Variance Estimator," Discussion Papers 9904, Exeter University, Department of Economics.
    2. Bao, Yong & Ullah, Aman, 2007. "The second-order bias and mean squared error of estimators in time-series models," Journal of Econometrics, Elsevier, vol. 140(2), pages 650-669, October.
    3. Jan F. Kiviet & Garry D.A. Phillips, 1998. "Degrees of freedom adjustment for disturbance variance estimators in dynamic regression models," Econometrics Journal, Royal Economic Society, vol. 1(RegularPa), pages 44-70.
    4. Kiviet, Jan F. & Phillips, Garry D.A., 2012. "Higher-order asymptotic expansions of the least-squares estimation bias in first-order dynamic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3705-3729.
    5. Grubb, David & Symons, James, 1987. "Bias in Regressions With a Lagged Dependent Variable," Econometric Theory, Cambridge University Press, vol. 3(03), pages 371-386, June.
    6. Sargan, J D, 1976. "Econometric Estimators and the Edgeworth Approximation," Econometrica, Econometric Society, vol. 44(3), pages 421-448, May.
    7. Jan F. Kiviet & Garry D. A. Phillips, 2000. "Improved Coefficient and Variance Estimation in Stable First-Order Dynamic Regression Models," Econometric Society World Congress 2000 Contributed Papers 0631, Econometric Society.
    8. Kiviet, Jan F. & Phillips, Garry D. A. & Schipp, Bernhard, 1995. "The bias of OLS, GLS, and ZEF estimators in dynamic seemingly unrelated regression models," Journal of Econometrics, Elsevier, vol. 69(1), pages 241-266, September.
    9. Bao, Yong, 2007. "The Approximate Moments Of The Least Squares Estimator For The Stationary Autoregressive Model Under A General Error Distribution," Econometric Theory, Cambridge University Press, vol. 23(05), pages 1013-1021, October.
    10. Rudebusch, Glenn D, 1993. "The Uncertain Unit Root in Real GNP," American Economic Review, American Economic Association, vol. 83(1), pages 264-272, March.
    11. Rudebusch, Glenn D, 1992. "Trends and Random Walks in Macroeconomic Time Series: A Re-examination," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(3), pages 661-680, August.
    12. Yang, Zhenlin, 2015. "A general method for third-order bias and variance corrections on a nonlinear estimator," Journal of Econometrics, Elsevier, vol. 186(1), pages 178-200.
    13. Jan F. Kiviet & Garry D. A. Phillips, 2005. "Moment approximation for least-squares estimators in dynamic regression models with a unit root *," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 115-142, July.
    14. MacKinnon, James G. & Smith Jr., Anthony A., 1998. "Approximate bias correction in econometrics," Journal of Econometrics, Elsevier, vol. 85(2), pages 205-230, August.
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    17. Kiviet, Jan F., 2012. "Monte Carlo Simulation for Econometricians," Foundations and Trends(R) in Econometrics, now publishers, vol. 5(1–2), pages 1-181, March.
    18. Kiviet, Jan F. & Phillips, Garry D. A., 1994. "Bias assessment and reduction in linear error-correction models," Journal of Econometrics, Elsevier, vol. 63(1), pages 215-243, July.
    19. Kiviet, Jan F. & Phillips, Garry D.A., 1993. "Alternative Bias Approximations in Regressions with a Lagged-Dependent Variable," Econometric Theory, Cambridge University Press, vol. 9(01), pages 62-80, January.
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    Citations

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    Cited by:

    1. Phillip, Garry & Xu, Yongdeng, 2016. "Almost Unbiased Variance Estimation in Simultaneous Equation Models," Cardiff Economics Working Papers E2016/10, Cardiff University, Cardiff Business School, Economics Section.
    2. Liu-Evans, Gareth, 2014. "A note on approximating moments of least squares estimators," MPRA Paper 57543, University Library of Munich, Germany.

    More about this item

    Keywords

    higher-order asymptotic expansions; bias correction; efficiency gains; lagged dependent variables; finite sample moments; size improvement;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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