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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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    Citations

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    Cited by:

    1. 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.
    2. Kiviet, Jan F., 2023. "Instrument-free inference under confined regressor endogeneity and mild regularity," Econometrics and Statistics, Elsevier, vol. 25(C), pages 1-22.
    3. Jacob Boudoukh & Ronen Israel & Matthew P. Richardson, 2020. "Biases in Long-Horizon Predictive Regressions," NBER Working Papers 27410, National Bureau of Economic Research, Inc.
    4. Liu-Evans, Gareth, 2010. "An alternative approach to approximating the moments of least squares estimators," MPRA Paper 26550, University Library of Munich, Germany.
    5. Gareth Liu-Evans, 2021. "Improving the Estimation and Predictions of Small Time Series Models," Working Papers 202106, University of Liverpool, Department of Economics.
    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. 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.
    10. Boudoukh, Jacob & Israel, Ronen & Richardson, Matthew, 2022. "Biases in long-horizon predictive regressions," Journal of Financial Economics, Elsevier, vol. 145(3), pages 937-969.
    11. Kiviet, Jan, 2019. "Instrument-free inference under confined regressor endogeneity; derivations and applications," MPRA Paper 96839, University Library of Munich, Germany.
    12. 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.
    13. 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.
    14. 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.

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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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