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Higher-Order Asymptotic Expansions of the Least-Squares Estimation Bias in First-Order Dynamic Regression Models

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  • Kiviet, J.F.
  • Phillips, G.D.A.

Abstract

An approximation to order T-2 is obtained for the bias of the least-squares estimator in the stationary ARX model which yields generalisations of Kendall's and White's classic results for particular variants of AR(1) models. The results show that generally the second-order approximation is considerably better than its first-order counterpart in ARX models. This is also largely true for AR(1) models except that in such models second-order approximations may be vulnerable in the near unit root case.

Suggested Citation

  • 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, University of Exeter, Department of Economics.
    • Handle: RePEc:exe:wpaper:9903
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    as
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    23. repec:exe:wpaper:99/06 is not listed on IDEAS
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    Citations

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    Cited by:

    1. Gareth Liu-Evans, 2021. "Improving the Estimation and Predictions of Small Time Series Models," Working Papers 202106, University of Liverpool, Department of Economics.
    2. Jacob Boudoukh & Ronen Israel & Matthew P. Richardson, 2020. "Biases in Long-Horizon Predictive Regressions," NBER Working Papers 27410, National Bureau of Economic Research, Inc.
    3. Kiviet, Jan, 2019. "Instrument-free inference under confined regressor endogeneity; derivations and applications," MPRA Paper 96839, University Library of Munich, Germany.
    4. Kruse, Robinson & Kaufmann, Hendrik & Wegener, Christoph, 2018. "Bias-corrected estimation for speculative bubbles in stock prices," Economic Modelling, Elsevier, vol. 73(C), pages 354-364.
    5. Liu-Evans Gareth D. & Phillips Garry D. A., 2012. "Bootstrap, Jackknife and COLS: Bias and Mean Squared Error in Estimation of Autoregressive Models," Journal of Time Series Econometrics, De Gruyter, vol. 4(2), pages 1-35, November.
    6. 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.
    7. Liu-Evans, Gareth, 2014. "A note on approximating moments of least squares estimators," MPRA Paper 57543, University Library of Munich, Germany.
    8. Quintana Carapia, Gustavo & Markovsky, Ivan & Pintelon, Rik & Csurcsia, Péter Zoltán & Verbeke, Dieter, 2020. "Bias and covariance of the least squares estimate in a structured errors-in-variables problem," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    9. Boudoukh, Jacob & Israel, Ronen & Richardson, Matthew, 2022. "Biases in long-horizon predictive regressions," Journal of Financial Economics, Elsevier, vol. 145(3), pages 937-969.
    10. Atukorala, Ranjani & Sriananthakumar, Sivagowry, 2015. "A comparison of the accuracy of asymptotic approximations in the dynamic regression model using Kullback-Leibler information," Economic Modelling, Elsevier, vol. 45(C), pages 169-174.
    11. Liu-Evans, Gareth, 2010. "An alternative approach to approximating the moments of least squares estimators," MPRA Paper 26550, University Library of Munich, Germany.
    12. Kiviet, Jan F., 2023. "Instrument-free inference under confined regressor endogeneity and mild regularity," Econometrics and Statistics, Elsevier, vol. 25(C), pages 1-22.
    13. 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.
    14. van Giersbergen, Noud P.A., 2016. "The ability to correct the bias in the stable AD(1,1) model with a feedback effect," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 186-204.

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    More about this item

    Keywords

    UNIT ROOTS ; REGRESSION ANALYSIS ; ECONOMETRICS;
    All these keywords.

    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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