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An alternative approach to approximating the moments of least squares estimators

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  • Liu-Evans, Gareth

Abstract

A new methodology is presented for approximating the moments of least squares coefficient estimators in situations where endogeneity and dynamics are present. The OLS estimator is the focus here, but the method, which is valid under a simple set of smoothness and moment conditions, can be applied to related estimators. An O(T−1) approximation is presented for the bias in OLS estimation of a general ARX(p) model.

Suggested Citation

  • Liu-Evans, Gareth, 2010. "An alternative approach to approximating the moments of least squares estimators," MPRA Paper 26550, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:26550
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    References listed on IDEAS

    as
    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. Kiviet, Jan F. & Phillips, Garry D. A., 1996. "The bias of the ordinary least squares estimator in simultaneous equation models," Economics Letters, Elsevier, vol. 53(2), pages 161-167, November.
    3. 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.
    4. 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(5), pages 1013-1021, October.
    5. 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.
    6. 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 229-238, January.
    7. 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.
    8. Sargan, J D, 1974. "The Validity of Nagar's Expansion for the Moments of Econometric Estimators," Econometrica, Econometric Society, vol. 42(1), pages 169-176, January.
    9. Rilstone, Paul & Srivastava, V. K. & Ullah, Aman, 1996. "The second-order bias and mean squared error of nonlinear estimators," Journal of Econometrics, Elsevier, vol. 75(2), pages 369-395, December.
    10. 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.
    11. 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(1), pages 62-80, January.
    12. Phillips, Garry D. A., 2000. "An alternative approach to obtaining Nagar-type moment approximations in simultaneous equation models," Journal of Econometrics, Elsevier, vol. 97(2), pages 345-364, August.
    13. Magnus, J.R. & Neudecker, H., 1979. "The commutation matrix : Some properties and applications," Other publications TiSEM d0b1e779-7795-4676-ac98-1, Tilburg University, School of Economics and Management.
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    More about this item

    Keywords

    moment approximation; bias; finite sample;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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