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An alternative approach to obtaining Nagar-type moment approximations in simultaneous equation models

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  • Phillips, Garry D. A.

Abstract

The paper examines asymptotic expansions for estimation errors expressed explicitly as functions of unferlying random variables. Taylor series expansions are obtained from which first and secomd moment approximationc are derived. While the expansions are essentially equivalent to the traditional Nagar-tupe, the terms are expressed in a form which enables moment approximations to be obtained in a particular straightforward way, once the partial derivatives have been found. The approach is illustrated by considering the k-class estimators in a static simultaneous equation model where the distrubances are non-spherical.
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Suggested Citation

  • 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.
  • Handle: RePEc:eee:econom:v:97:y:2000:i:2:p:345-364
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    References listed on IDEAS

    as
    1. Kiviet, J.F. & Phillips, G.D.A., 1999. "The Bias of the 2SLS Variance Estimator," Discussion Papers 9904, Exeter University, Department of Economics.
    2. repec:exe:wpaper:99/04 is not listed on IDEAS
    3. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(02), pages 181-240, August.
    4. Buse, A, 1992. "The Bias of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 60(1), pages 173-180, January.
    5. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
    6. Sargan, J D, 1976. "Econometric Estimators and the Edgeworth Approximation," Econometrica, Econometric Society, vol. 44(3), pages 421-448, May.
    7. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    8. repec:exe:wpaper:99/05 is not listed on IDEAS
    9. Kinal, Terrence W, 1980. "The Existence of Moments of k-Class Estimators," Econometrica, Econometric Society, vol. 48(1), pages 241-249, January.
    10. 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.
    11. Kadane, Joseph B, 1971. "Comparison of k-Class Estimators when the Disturbances are Small," Econometrica, Econometric Society, vol. 39(5), pages 723-737, September.
    12. Harvey, A C & Phillips, G D A, 1980. "Testing for Serial Correlation in Simultaneous Equation Models," Econometrica, Econometric Society, vol. 48(3), pages 747-759, April.
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    Cited by:

    1. Symeonides Spyridon D. & Karavias Yiannis & Tzavalis Elias, 2017. "Size corrected Significance Tests in Seemingly Unrelated Regressions with Autocorrelated Errors," Journal of Time Series Econometrics, De Gruyter, vol. 9(1), pages 1-41, January.
    2. Iglesias, Emma M. & Phillips, Garry D.A., 2011. "Almost Unbiased Estimation in Simultaneous Equations Models with Strong and / or Weak Instruments," Cardiff Economics Working Papers E2011/19, Cardiff University, Cardiff Business School, Economics Section.
    3. Phillip, Garry & Xu, Yongdeng, 2016. "Almost Unbiased Variance Estimation in Simultaneous Equation Models," Cardiff Economics Working Papers E2016/10, Cardiff University, Cardiff Business School, Economics Section.
    4. 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.
    5. Liu-Evans, Gareth, 2014. "A note on approximating moments of least squares estimators," MPRA Paper 57543, University Library of Munich, Germany.
    6. Liu-Evans, Gareth, 2010. "An alternative approach to approximating the moments of least squares estimators," MPRA Paper 26550, University Library of Munich, Germany.
    7. Phillips, Garry D.A. & Liu-Evans, Gareth, 2016. "Approximating and reducing bias in 2SLS estimation of dynamic simultaneous equation models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 734-762.
    8. Phillips, Garry D.A. & Liu-Evans, Gareth, 2011. "The Robustness of the Higher-Order 2SLS and General k-Class Bias Approximations to Non-Normal Disturbances," Cardiff Economics Working Papers E2011/20, Cardiff University, Cardiff Business School, Economics Section.

    More about this item

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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