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Moment approximation for least-squares estimators in dynamic regression models with a unit root *

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

Abstract

To find approximations for bias, variance and mean-squared error of least-squares estimators for all coefficients in a linear dynamic regression model with a unit root, we derive asymptotic expansions and examine their accuracy by simulation. It is found that in this particular context useful expansions exist only when the autoregressive model contains at least one non-redundant exogenous explanatory variable. Surprisingly, the large-sample and small-disturbance asymptotic techniques give closely related results, which is not the case in stable dynamic regression models. We specialize our general expressions for moment approximations to the case of the random walk with drift model and find that they are unsatisfactory when the drift is small. Therefore, we develop what we call small-drift asymptotics which proves to be very accurate, especially when the sample size is very small. Copyright 2005 Royal Economic Society

Suggested Citation

  • 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, July.
  • Handle: RePEc:ect:emjrnl:v:8:y:2005:i:2:p:115-142
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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. Aman Ullah & Yong Bao & Ru Zhang, 2014. "Moment Approximation for Unit Root Models with Nonnormal Errors," Working Papers 201401, University of California at Riverside, Department of Economics.
    3. Chiquoine, Benjamin & Hjalmarsson, Erik, 2009. "Jackknifing stock return predictions," Journal of Empirical Finance, Elsevier, vol. 16(5), pages 793-803, December.
    4. Lawford, Steve & Stamatogiannis, Michalis P., 2009. "The finite-sample effects of VAR dimensions on OLS bias, OLS variance, and minimum MSE estimators," Journal of Econometrics, Elsevier, vol. 148(2), pages 124-130, February.
    5. 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.
    6. Liu-Evans, Gareth, 2014. "A note on approximating moments of least squares estimators," MPRA Paper 57543, University Library of Munich, Germany.

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