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

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  • 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.

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Bibliographic Info

Paper provided by Nanyang Technolgical University, School of Humanities and Social Sciences, Economic Growth centre in its series Economic Growth centre Working Paper Series with number 1206.

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Length: 47 pages
Date of creation: Jun 2012
Date of revision:
Handle: RePEc:nan:wpaper:1206

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

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  1. Glenn D. Rudebusch, 1990. "Trends and random walks in macroeconomic time series: a re-examination," Working Paper Series / Economic Activity Section 105, Board of Governors of the Federal Reserve System (U.S.).
  2. Phillips, G.D.A., 1999. "An Alternative Approach to Obtaining Nagar-Type Moment Approximations in Sumultaneous Equation Models," Discussion Papers 9905, Exeter University, Department of Economics.
  3. Rudebusch, Glenn D, 1993. "The Uncertain Unit Root in Real GNP," American Economic Review, American Economic Association, vol. 83(1), pages 264-72, March.
  4. Karim Abadir & Kaddour Hadri & Elias Tzavalis, . "The Influence of VAR Dimensions on Estimator Biases," Discussion Papers 96/14, Department of Economics, University of York.
  5. Sargan, J D, 1976. "Econometric Estimators and the Edgeworth Approximation," Econometrica, Econometric Society, vol. 44(3), pages 421-48, May.
  6. 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.
  7. 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.
  8. Kiviet, J.F. & Phillips, G.D.A., 1999. "The Bias of the 2SLS Variance Estimator," Discussion Papers 9904, Exeter University, Department of Economics.
  9. Kiviet, J.F. & Phillips, G.D.A., 1999. "Higher-Order Asymptotic Expansions of the Least-Squares Estimation Bias in First-Order Dynamic Regression Models," Discussion Papers 9903, Exeter University, Department of Economics.
  10. 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.
  11. 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.
  12. 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, 07.
  13. Sawa, Takamitsu, 1978. "The exact moments of the least squares estimator for the autoregressive model," Journal of Econometrics, Elsevier, vol. 8(2), pages 159-172, October.
  14. 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.
  15. 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.
  16. 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.
  17. MacKinnon, James G. & Smith Jr., Anthony A., 1998. "Approximate bias correction in econometrics," Journal of Econometrics, Elsevier, vol. 85(2), pages 205-230, August.
  18. Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, edition 1, number 9780198774488.
  19. Orcutt, Guy H & Winokur, Herbert S, Jr, 1969. "First Order Autoregression: Inference, Estimation, and Prediction," Econometrica, Econometric Society, vol. 37(1), pages 1-14, January.
  20. 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.
  21. 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.
  22. Anindya Roy & Barry Falk & Wayne A. Fuller, 2004. "Testing for Trend in the Presence of Autoregressive Error," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1082-1091, December.
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