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

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Author Info
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.

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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-577.

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Length: 34 pages
Date of creation: Jul 2008
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Handle: RePEc:tky:fseres:2008cf577

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  1. 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 503-33, October. [Downloadable!] (restricted)
  2. Angrist, Joshua D & Krueger, Alan B, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, MIT Press, vol. 106(4), pages 979-1014, November. [Downloadable!] (restricted)
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  3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  4. Ron Mittelhammer & George Judge & Ron Schoenberg, 2003. "Empirical Evidence Concerning the Finite Sample Performance of EL-Type Structural Equation Estimation and Inference Methods," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series 945, Department of Agricultural & Resource Economics, UC Berkeley. [Downloadable!]
  5. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
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  6. Morimune, Kimio, 1989. "Test in a Structural Equation," Econometrica, Econometric Society, vol. 57(6), pages 1341-60, November. [Downloadable!] (restricted)
  7. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, 09. [Downloadable!] (restricted)
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  8. Anderson, T W & Kunitomo, Naoto & Sawa, Takamitsu, 1982. "Evaluation of the Distribution Function of the Limited Information Maximum Likelihood Estimator," Econometrica, Econometric Society, vol. 50(4), pages 1009-27, July. [Downloadable!] (restricted)
  9. Fujikoshi, Yasunori & Morimune, Kimio & Kunitomo, Naoto & Taniguchi, Masanobu, 1982. "Asymptotic expansions of the distributions of the estimates of coefficients in a simultaneous equation system," Journal of Econometrics, Elsevier, vol. 18(2), pages 191-205, February. [Downloadable!] (restricted)
  10. 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. [Downloadable!]
  11. 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, 01. [Downloadable!] (restricted)
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  12. 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. [Downloadable!] (restricted)
  13. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(01), pages 232-261, February. [Downloadable!]
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  1. 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. [Downloadable!]
  2. 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. [Downloadable!]
  3. Naoto Kunitomo & Yukitoshi Matsushita, 2009. "Asymptotic Expansions and Higher Order Properties of Semi-Parametric Estimators in a System of Simultaneous Equations," CIRJE F-Series CIRJE-F-611, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
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