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

  • 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)

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.

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File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2006/2006cf399.pdf
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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-399.

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Length: 52pages
Date of creation: Feb 2006
Date of revision:
Handle: RePEc:tky:fseres:2006cf399
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  1. Whitney Newey & Richard Smith, 2003. "Higher order properties of GMM and generalised empirical likelihood estimators," CeMMAP working papers CWP04/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  3. 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.
  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. "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.
  6. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
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