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Improved Coefficient and Variance Estimation in Stable First-Order Dynamic Regression Models

Author

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  • Jan F. Kiviet

    (University of Amsterdam)

  • Garry D. A. Phillips

    (University of Exeter)

Abstract

In dynamic regression models the least-squares coefficient estimators are biased in finite samples, and so are the usual estimators for the disturbance variance and for the variance of the coefficient estimators. By deriving the expectation of the initial terms in an expansion of the usual expression for the asymptotic coefficient variance estimator and by comparing these with an approximation to the true variance we find an approximation to the bias in variance estimation from which a bias corrected estimator for the variance readily follows. This is also achieved for a bias corrected coefficient estimator and allows to compare analytically the second-order approximation to the mean squared error of the least-squares estimator and its counterpart for the first-order bias corrected coefficient estimator. Two rather strong results on efficiency gains through bias correction for AR(1) models follow. Illustrative simulation results on the magnitude of bias in coefficient and variance estimation and on the scope for effective bias correction and efficiency improvement are presented for some relevant particular cases of the ARX(1) class of models.

Suggested Citation

  • 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.
  • Handle: RePEc:ecm:wc2000:0631
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    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. 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.
    7. 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.
    8. 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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    Cited by:

    1. Pesaran, M. Hashem & Timmermann, Allan, 2005. "Small sample properties of forecasts from autoregressive models under structural breaks," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 183-217.
    2. Kiviet, Jan F. & Phillips, Garry D.A., 2014. "Improved variance estimation of maximum likelihood estimators in stable first-order dynamic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 424-448.
    3. Kiviet, Jan F. & Niemczyk, Jerzy, 2007. "The asymptotic and finite sample distributions of OLS and simple IV in simultaneous equations," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3296-3318, April.
    4. Chiquoine, Benjamin & Hjalmarsson, Erik, 2009. "Jackknifing stock return predictions," Journal of Empirical Finance, Elsevier, vol. 16(5), pages 793-803, December.

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