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Higher-order asymptotic expansions of the least-squares estimation bias in first-order dynamic regression models

  • Kiviet, Jan F.
  • Phillips, Garry D.A.

An approximation to order T−2 is obtained for the bias of the full vector of least-squares estimates obtained from a sample of size T in general stable but not necessarily stationary ARX(1) models with normal disturbances. This yields generalizations, allowing for various forms of initial conditions, of Kendall’s and White’s classic results for stationary AR(1) models. The accuracy of various alternative approximations is examined and compared by simulation for particular parameterizations of AR(1) and ARX(1) models. The results show that often the second-order approximation is considerably better than its first-order counterpart and hence opens up perspectives for improved bias correction. However, order T−2 approximations are also found to be more vulnerable in the near unit root case than the much simpler order T−1 approximations.

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Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 56 (2012)
Issue (Month): 11 ()
Pages: 3705-3729

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Handle: RePEc:eee:csdana:v:56:y:2012:i:11:p:3705-3729
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  19. 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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  21. 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.
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  26. 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.
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