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The optimality of non-optimal GMM estimation of parameters of interest and the partial asymptotic efficiency of 2SLS estimation

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  • Heather L. Bednarek

    (Saint Louis University)

  • Hailong Qian

    (Saint Louis University)

Abstract

In this paper, we first derive a necessary and sufficient condition for generalized method of moments (GMM) estimation of a subset of parameters using a non-optimal weighting matrix to be asymptotically as efficient as the optimal GMM estimation. We then apply our result to simultaneous equations models and derive a necessary and sufficient condition for 2SLS estimation of a subset of regression coefficients to be asymptotically as efficient as the 3SLS estimation applied to the whole system. Our condition for the partial asymptotic efficiency of 2SLS estimation encompasses many existing results for the numerical equality of 2SLS and 3SLS estimation of all regression coefficients.

Suggested Citation

  • Heather L. Bednarek & Hailong Qian, 2016. "The optimality of non-optimal GMM estimation of parameters of interest and the partial asymptotic efficiency of 2SLS estimation," Economics Bulletin, AccessEcon, vol. 36(3), pages 1636-1649.
    • Handle: RePEc:ebl:ecbull:eb-15-00727
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    References listed on IDEAS

    as
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    5. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, April.
    6. Hailong Qian & Heather L. Bednarek, 2015. "Partial efficient estimation of SUR models," Economics Bulletin, AccessEcon, vol. 35(1), pages 338-348.
    7. Baltagi, Badi H., 1988. "The Efficiency of OLS in a Seemingly Unrelated Regressions Model," Econometric Theory, Cambridge University Press, vol. 4(03), pages 536-537, December.
    8. Srivastava, V K & Tiwari, Ramji, 1978. "Efficiency of Two-Stage and Three-Stage Least Squares Estimators," Econometrica, Econometric Society, vol. 46(6), pages 1495-1498, November.
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    More about this item

    Keywords

    GMM estimation; Parameters of interest; Partial asymptotic efficiency; 2SLS estimation; 3SLS estimation; simultaneous equations models;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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