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

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Author Info

  • 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.

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Bibliographic Info

Paper provided by Exeter University, Department of Economics in its series Discussion Papers with number 9903.

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Length: 52 pages
Date of creation: 1999
Date of revision:
Handle: RePEc:exe:wpaper:9903

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Postal: Streatham Court, Rennes Drive, Exeter EX4 4PU
Phone: (01392) 263218
Fax: (01392) 263242
Web page: http://business-school.exeter.ac.uk/about/departments/economics/
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Related research

Keywords: UNIT ROOTS ; REGRESSION ANALYSIS ; ECONOMETRICS;

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References

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  1. 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.
  2. Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-69, September.
  3. Dufour, J.M. & Kiviet, J.F., 1995. "Exact Tests in Single Equation Autoregressive Distributed Lag Models," Cahiers de recherche 9549, Universite de Montreal, Departement de sciences economiques.
  4. 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.
  5. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May.
  6. MacKinnon, James G. & Smith Jr., Anthony A., 1998. "Approximate bias correction in econometrics," Journal of Econometrics, Elsevier, vol. 85(2), pages 205-230, August.
  7. Glenn D. Rudebusch, 1990. "Trends and random walks in macroeconomic time series: a re-examination," Finance and Economics Discussion Series 139, Board of Governors of the Federal Reserve System (U.S.).
  8. Broda, Simon & Paolella, Marc S. & Carstensen, Kai, 2007. "Bias-adjusted estimation in the ARX(1) model," Munich Reprints in Economics 19992, University of Munich, Department of Economics.
  9. Vinod, H.D. & Shenton, L.R., 1996. "Exact Moments for Autor1egressive and Random walk Models for a Zero or Stationary Initial Value," Econometric Theory, Cambridge University Press, vol. 12(03), pages 481-499, August.
  10. Maekawa, Koichi, 1983. "An Approximation to the Distribution of the Least Squares Estimator in an Autoregressive Model with Exogenous Variables," Econometrica, Econometric Society, vol. 51(1), pages 229-38, January.
  11. Kadane, Joseph B, 1971. "Comparison of k-Class Estimators when the Disturbances are Small," Econometrica, Econometric Society, vol. 39(5), pages 723-37, September.
  12. 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.
  13. 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.
  14. 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.
  15. repec:fth:exetec:99/06 is not listed on IDEAS
  16. 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.
  17. Tanaka, Katsuto, 1983. "Asymptotic Expansions Associated with the AR(1) Model with Unknown Mean," Econometrica, Econometric Society, vol. 51(4), pages 1221-31, July.
  18. Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, edition 1, number 9780198774488, September.
  19. Magnus, J.R., 1978. "The moments of products of quadratic forms in normal variables," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153205, Tilburg University.
  20. 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.
  21. Tsui, Albert K. & Ali, Mukhtar M., 1994. "Exact distributions, density functions and moments of the last squares estimator in a first-order autoregressive model," Computational Statistics & Data Analysis, Elsevier, vol. 17(4), pages 433-454, May.
  22. 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.
  23. Hadri, K. & Phillips, G.D.A., 1999. "The Accuracy of the Higher Order Bias Approximation for the 2SLS Estimator," Discussion Papers 9906, Exeter University, Department of Economics.
  24. Russell Davidson & James G. MacKinnon, 1985. "Testing Linear and Loglinear Regressions against Box-Cox Alternatives," Canadian Journal of Economics, Canadian Economics Association, vol. 18(3), pages 499-517, August.
  25. Nankervis, J. C. & Savin, N. E., 1988. "The exact moments of the least-squares estimator for the autoregressive model corrections and extensions," Journal of Econometrics, Elsevier, vol. 37(3), pages 381-388, March.
  26. 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.
  27. Tanizaki, Hisashi, 2000. "Bias correction of OLSE in the regression model with lagged dependent variables," Computational Statistics & Data Analysis, Elsevier, vol. 34(4), pages 495-511, October.
  28. Emma M. Iglesias & Garry D. A. Phillips, 2008. "Finite Sample Theory of QMLE in ARCH Models with Dynamics in the Mean Equation," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(4), pages 719-737, 07.
  29. 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.
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Citations

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Cited by:
  1. 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.
  2. Liu-Evans, Gareth, 2010. "An alternative approach to approximating the moments of least squares estimators," MPRA Paper 26550, University Library of Munich, Germany.
  3. 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.

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