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An alternative approach to approximating the moments of least squares estimators

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  • Liu-Evans, Gareth
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    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.

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    File URL: http://mpra.ub.uni-muenchen.de/26550/
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    File URL: http://mpra.ub.uni-muenchen.de/26600/
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    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 26550.

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    Date of creation: 09 Nov 2010
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    Handle: RePEc:pra:mprapa:26550

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    Keywords: moment approximation; bias; finite sample;

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    1. 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.
    2. 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(01), pages 62-80, January.
    3. 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.
    4. 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.
    5. 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 229-38, January.
    6. 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.
    7. 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.
    8. 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(05), pages 1013-1021, October.
    9. 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.
    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. Sargan, J D, 1974. "The Validity of Nagar's Expansion for the Moments of Econometric Estimators," Econometrica, Econometric Society, vol. 42(1), pages 169-76, January.
    12. Magnus, J.R. & Neudecker, H., 1979. "The commutation matrix: Some properties and applications," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153207, Tilburg University.
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