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

Author

Listed:
  • Kiviet, J.F.
  • Phillips, G.D.A.

Abstract

Asymptotic expansions are employed in a dynamic regression model with a unit root in order to find approximations for the bias, the variance and for the mean squared error of the least-squares estimator. For this purpose such expansions are shown to be useful only when the autoregressive model contains at least one non-redundant exogenous explanatory variable. It is found that large sample and small disturbance asymptotic techniques give closely related results in this model, which is not the case in stable dynamic regression models. The results are specialised to the random walk with drift model, where it is seen that the ratio of the standard deviation of the disturbance tot he drift term plays a crucial role. The random walk to the model with drift plus a linear trend is also examined. The accuracy of the approximations are checked in the context of these models making use of a set of Monte Carlo experiments to estimate the true moments.

Suggested Citation

  • Kiviet, J.F. & Phillips, G.D.A., 1998. "Moment Approximation for Least Squares Estimators in Dynamic Regression Models with a Unit Root," Discussion Papers 9909, University of Exeter, Department of Economics.
    • Handle: RePEc:exe:wpaper:9909
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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. Liu-Evans, Gareth, 2010. "An alternative approach to approximating the moments of least squares estimators," MPRA Paper 26550, University Library of Munich, Germany.
    3. 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.
    4. Chevillon, Guillaume, 2007. "Inference in the Presence of Stochastic and Deterministic Trends," ESSEC Working Papers DR 07021, ESSEC Research Center, ESSEC Business School.

    More about this item

    Keywords

    ESTIMATOR ; TIME SERIES ; REGRESSION ANALYSIS;
    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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