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On Finite Sample Properties of Alternative Estimators of Coefficients in a Structural Equation with Many Instruments

Author

Listed:
  • 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 different estimation methods for the coefficients 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 empirical likelihood (MEL) estimator and the generalized method of moments (GMM) (or the estimating equation) estimator. Tables and figures of the distribution functions of four estimators are given for enough values of the parameters to cover most linear models of interest and we include some heteroscedastic cases and nonlinear cases. We have found that the LIML estimator has good performance in terms of the bounded loss functions and probabilities 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, 2008. "On Finite Sample Properties of Alternative Estimators of Coefficients in a Structural Equation with Many Instruments," CIRJE F-Series CIRJE-F-577, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2008cf577
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2008/2008cf577.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. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    4. Theodore W. Anderson & Naoto Kunijtomo & Yukitoshi Matsushita, 2005. "A New Light from Old Wisdoms : Alternative Estimation Methods of Simultaneous Equations and Microeconometric Models," CIRJE F-Series CIRJE-F-321, CIRJE, Faculty of Economics, University of Tokyo.
    5. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(01), pages 232-261, February.
    6. Anderson, T W & Sawa, Takamitsu, 1973. "Distributions of Estimates of Coefficients of a Single Equation in a Simultaneous System and Their Asymptotic Expansions," Econometrica, Econometric Society, vol. 41(4), pages 683-714, July.
    7. 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.
    8. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-681, May.
    9. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    10. Anderson, T. W. & Kunitomo, Naoto & Morimune, Kimio, 1986. "Comparing Single-Equation Estimators in a Simultaneous Equation System," Econometric Theory, Cambridge University Press, vol. 2(01), pages 1-32, April.
    11. Mariano, Roberto S, 1982. "Analytical Small-Sample Distribution Theory in Econometrics: The Simultaneous-Equations Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(3), pages 503-533, October.
    12. Morimune, Kimio, 1989. "Test in a Structural Equation," Econometrica, Econometric Society, vol. 57(6), pages 1341-1360, November.
    13. 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. Kunitomo, Naoto & Matsushita, Yukitoshi, 2009. "Asymptotic expansions and higher order properties of semi-parametric estimators in a system of simultaneous equations," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1727-1751, September.
    2. 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.
    3. Naoto Kunitomo & Michael McAleer & Yoshihiko Nishiyama, 2010. "Moment Restriction-based Econometric Methods: An Overview," Working Papers in Economics 10/65, University of Canterbury, Department of Economics and Finance.
    4. Naoto Kunitomo & Yukitoshi Matsushita, 2008. "Improving the Rank-Adjusted Anderson-Rubin Test with Many Instruments and Persistent Heteroscedasticity," CIRJE F-Series CIRJE-F-588, CIRJE, Faculty of Economics, University of Tokyo.
    5. Okui, Ryo, 2011. "Instrumental variable estimation in the presence of many moment conditions," Journal of Econometrics, Elsevier, vol. 165(1), pages 70-86.
    6. 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.
    7. T. W. Anderson & Naoto Kunitomo & Yukitoshi Matsushita, 2009. "The Limited Information Maximum Likelihood Estimator as an Angle," CIRJE F-Series CIRJE-F-619, CIRJE, Faculty of Economics, University of Tokyo.
    8. Naoto Kunitomo & Kentaro Akashi, 2010. "An Aysmptotically Optimal Modification of the Panel LIML Estimation for Individual Heteroscedasticity," CIRJE F-Series CIRJE-F-780, CIRJE, Faculty of Economics, University of Tokyo.
    9. Mieno, Taro & Brozovic, Nicholas, 2012. "Unraveling deterrence effects of regulatory activities under Clean Water Act," 2012 Annual Meeting, August 12-14, 2012, Seattle, Washington 124612, Agricultural and Applied Economics Association.
    10. 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.

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