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A New Light from Old Wisdoms : Alternative Estimation Methods of Simultaneous Equations with Possibly Many Instruments

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  • T. W. Anderson

    (Department of Statistics and Department of Economics, Stanford University)

  • Naoto Kunitomo

    (Faculty of Economics, University of Tokyo)

  • Yukitoshi Matsushita

    (Graduate School of Economics, University of Tokyo)

Abstract

We compare four dffierent estimation methods for a coefficient of a linear structural equation with instrumental variables. As the classical methods we consider the limited information maximum likelihood (LIML) estimator and the two-stage least squares (TSLS) estimator, and as the semi-parametric estimation methods we consider the maximum emirical likelihood (MEL) estimator and the generalized method of moments (GMM) (or the estimating equation) estimator. We prove several theorems on the asymptotic optimality of the LIML estimator when the number of instruments is large, which are new as well as old, and we relate them to the results in some recent studies. Tables and figures of the distribution functions of four estimators are given for enough values of the parameters to cover most of interest. We have found that the LIML estimator has good performance when the number of instruments is large, that is, the micro-econometric models with many instruments in the terminology of recent econometric literature.

Suggested Citation

  • T. W. Anderson & Naoto Kunitomo & Yukitoshi Matsushita, 2006. "A New Light from Old Wisdoms : Alternative Estimation Methods of Simultaneous Equations with Possibly Many Instruments," CIRJE F-Series CIRJE-F-399, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2006cf399
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2006/2006cf399.pdf
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    References listed on IDEAS

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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    3. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-681, May.
    4. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    5. Naoto Kunitomo & Yukitoshi Matsushita, 2003. "On Finite Sample Distributions of the Empirical Likelihood Estimator and the GMM Estimator," CIRJE F-Series CIRJE-F-200, CIRJE, Faculty of Economics, University of Tokyo.
    6. Naoto Kunitomo & Yukitoshi Matsushita, 2003. "Asymptotic Expansions of the Distributions of Semi-Parametric Estimators in a Linear Simultaneous Equations System," CIRJE F-Series CIRJE-F-237, CIRJE, Faculty of Economics, University of Tokyo.
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    Cited by:

    1. T. W. Anderson & Naoto Kunitomo & Yukitoshi Matsushita, 2008. "On the Asymptotic Optimality of the LIML Estimator with Possibly Many Instruments," CIRJE F-Series CIRJE-F-542, CIRJE, Faculty of Economics, University of Tokyo.
    2. Naoto Kunitomo, 2012. "An optimal modification of the LIML estimation for many instruments and persistent heteroscedasticity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 881-910, October.
    3. Anderson, T.W. & Kunitomo, Naoto & Matsushita, Yukitoshi, 2010. "On the asymptotic optimality of the LIML estimator with possibly many instruments," Journal of Econometrics, Elsevier, vol. 157(2), pages 191-204, August.
    4. Naoto Kunitomo, 2008. "An Optimal Modification of the LIML Estimation for Many Instruments and Persistent Heteroscedasticity," CIRJE F-Series CIRJE-F-576, CIRJE, Faculty of Economics, University of Tokyo.
    5. Akashi, Kentaro & Kunitomo, Naoto, 2012. "Some properties of the LIML estimator in a dynamic panel structural equation," Journal of Econometrics, Elsevier, vol. 166(2), pages 167-183.
    6. Naoto Kunitomo & Kentaro Akashi, 2007. "The Conditional Limited Information Maximum Likelihood Approach to Dynamic Panel Structural Equations," CIRJE F-Series CIRJE-F-503, CIRJE, Faculty of Economics, University of Tokyo.
    7. Kentaro Akashi & Naoto Kunitomo, 2010. "The Limited Information Maximum Likelihood Approach to Dynamic Panel Structural Equations," CIRJE F-Series CIRJE-F-708, CIRJE, Faculty of Economics, University of Tokyo.

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