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Moment Approximation for Least Squares Estimators in Dynamic Regression Models with a Unit Root

Author

Listed:
  • Jan F. Kiviet

    (University of Amsterdam)

  • Garry D.A. Phillips

    (Cardiff Business School, Cardiff, Wales, UK)

Abstract

This discussion paper led to a publication in 'The Econometrics Journal' . Asymptotic expansions are employed in a dynamic regression model with a unit root inorder to find approximations for the bias, the variance and for the mean squared error of theleast-squares estimator of all coefficients. It is found that in this particular context suchexpansions exist only when the autoregressive model contains at least one non-redundant exogenousexplanatory variable and that local to zero asymptotic approaches are here without avail.Surprisingly the large sample and small disturbance asymptotic techniques give closely relatedresults, which is not the case in stable dynamic regression models. The expressions for momentapproximations are specialized to the random walk with (trend in) drift model and their accuracyis examined in Monte Carlo experiments.

Suggested Citation

  • Jan F. Kiviet & Garry D.A. Phillips, 2001. "Moment Approximation for Least Squares Estimators in Dynamic Regression Models with a Unit Root," Tinbergen Institute Discussion Papers 01-118/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20010118
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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. Pesaran, M. Hashem & Timmermann, Allan, 2005. "Small sample properties of forecasts from autoregressive models under structural breaks," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 183-217.
    3. Chevillon, Guillaume, 2007. "Inference in the Presence of Stochastic and Deterministic Trends," ESSEC Working Papers DR 07021, ESSEC Research Center, ESSEC Business School.
    4. Liu-Evans, Gareth, 2010. "An alternative approach to approximating the moments of least squares estimators," MPRA Paper 26550, University Library of Munich, Germany.

    More about this item

    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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