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Comparing Single-Equation Estimators in a Simultaneous Equation System

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  • Anderson, T. W.
  • Kunitomo, Naoto
  • Morimune, Kimio

Abstract

Comparisons of estimators are made on the basis of their mean squared errors and their concentrations of probability computed by means of asymptotic expansions of their distributions when the disturbance variance tends to zero and alternatively when the sample size increases indefinitely. The estimators include k-class estimators (limited information maximum likelihood, two-stage least squares, and ordinary least squares) and linear combinations of them as well as modifications of the limited information maximum likelihood estimator and several Bayes' estimators. Many inequalities between the asymptotic mean squared errors and concentrations of probability are given. Among medianunbiasedestimators, the limited information maximum likelihood estimator dominates the median-unbiased fixed k-class estimator.

Suggested Citation

  • Anderson, T. W. & Kunitomo, Naoto & Morimune, Kimio, 1986. "Comparing Single-Equation Estimators in a Simultaneous Equation System," Econometric Theory, Cambridge University Press, vol. 2(1), pages 1-32, April.
    • Handle: RePEc:cup:etheor:v:2:y:1986:i:01:p:1-32_01
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    Cited by:

    1. Anderson, T.W. & Kunitomo, Naoto & Matsushita, Yukitoshi, 2011. "On finite sample properties of alternative estimators of coefficients in a structural equation with many instruments," Journal of Econometrics, Elsevier, vol. 165(1), pages 58-69.
    2. YUEH, Linda, 2009. "Self-employment in urban China: Networking in a transition economy," China Economic Review, Elsevier, vol. 20(3), pages 471-484, September.
    3. Kleibergen, Frank & Zivot, Eric, 2003. "Bayesian and classical approaches to instrumental variable regression," Journal of Econometrics, Elsevier, vol. 114(1), pages 29-72, May.
    4. 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.
    5. Naoto Kunitomo, 2002. "Improving Small Sample Properties of the Empirical Likelihood Estimation," CIRJE F-Series CIRJE-F-184, CIRJE, Faculty of Economics, University of Tokyo.
    6. 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.
    7. Ali Mehrabani, 2024. "Stein-Like Shrinkage Estimators for Coefficients of a Single-Equation in Simultaneous Equation Systems," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202414, University of Kansas, Department of Economics.
    8. 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.
    9. Liu-Evans, Gareth & Phillips, Garry D.A., 2018. "On the use of higher order bias approximations for 2SLS and k-class estimators with non-normal disturbances and many instruments," Econometrics and Statistics, Elsevier, vol. 6(C), pages 90-105.
    10. Matsushita, Yukitoshi & Otsu, Taisuke, 2023. "Second-order refinements for t-ratios with many instruments," Journal of Econometrics, Elsevier, vol. 232(2), pages 346-366.
    11. Phillips, Garry D.A. & Liu-Evans, Gareth, 2011. "The Robustness of the Higher-Order 2SLS and General k-Class Bias Approximations to Non-Normal Disturbances," Cardiff Economics Working Papers E2011/20, Cardiff University, Cardiff Business School, Economics Section.
    12. Matsushita, Yukitoshi & Otsu, Taisuke, 2023. "Second-order refinements for t-ratios with many instruments," LSE Research Online Documents on Economics 111065, London School of Economics and Political Science, LSE Library.
    13. Oberhelman, Dennis & Rao Kadiyala, K., 2000. "Asymptotic probability concentrations and finite sample properties of modified LIML estimators for equations with more than two endogenous variables," Journal of Econometrics, Elsevier, vol. 98(1), pages 163-185, September.
    14. 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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