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Degrees of freedom adjustment for disturbance variance estimators in dynamic regression models

Author

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  • JAN F. KIVIET
  • GARRY D.A. PHILLIPS

Abstract

In the classical regression model with fixed regressors the statistic S 2 , i.e. the sum of squared residuals (SSR) divided by the number of degrees of freedom, is an unbiased estimator of the variance of the disturbances. If the model is dynamic and contains lagged-dependent explanatory variables, then the least-squares coefficient estimators are biased in finite samples, and so is S 2 . By deriving the expectation of the initial terms in an expansion of the expression for SSR in the case of an autoregressive regression model, we prove that the bias in the degrees of freedom adjusted estimator is of smaller order in T , the sample size, than the bias of the unadjusted maximum-likelihood estimator. We also indicate how a further decrease in the bias can be achieved, and what the consequences are for estimating s. Insight is provided into the relative numerical magnitude of the bias for various estimators of s 2 in some relevant particular cases of this class of model by Monte Carlo simulation.

Suggested Citation

  • 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.
    • Handle: RePEc:ect:emjrnl:v:1:y:1998:i:regularpapers:p:44-70
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    Citations

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    Cited by:

    1. Martin Browning & Mette Ejrnæs & Javier Alvarez, 2010. "Modelling Income Processes with Lots of Heterogeneity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(4), pages 1353-1381.
    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. Rault, Christophe, 2000. "Non-causality in VAR-ECM models with purely exogenous long-run paths," Economics Letters, Elsevier, vol. 66(1), pages 7-15, January.
    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. 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.
    6. Doornik Jurgen A & Ooms Marius, 2004. "Inference and Forecasting for ARFIMA Models With an Application to US and UK Inflation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-25, May.

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