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Asymptotic Expansions and Higher Order Properties of Semi-Parametric Estimators in a System of Simultaneous Equations

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  • Naoto Kunitomo

    (Faculty of Economics, University of Tokyo)

  • Yukitoshi Matsushita

    (JSPS and Graduate School of Economics, University of Tokyo)

Abstract
Asymptotic expansions are made for the distributions of the Maximum Empirical Likelihood (MEL) estimator and the Estimating Equation (EE) estimator (or the Generalized Method of Moments (GMM) in econometrics) for the coefficients of a single structural equation in a system of linear simultaneous equations, which corresponds to a reduced rank regression model. The expansions in terms of the sample size, when the non-centrality parameters increase proportionally, are carried out to O(n-1). Comparisons of the distributions of the MEL and GMM estimators are made. Also we relate the asymptotic expansions of the distributions of the MEL and GMM estimators to the corresponding expansions for the Limited Information Maximum Likelihood (LIML) and the Two-Stage Least Squares (TSLS) estimators. We give useful information on the higher order properties of alternative estimators including the semi-parametric inefficiency factor under the homoscedasticity assumption.

Suggested Citation

  • 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.
    • Handle: RePEc:tky:fseres:2009cf611
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    References listed on IDEAS

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    6. 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.
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    12. Mittelhammer, Ronald C. & Judge, George G. & Schoenberg, Ron, 2003. "Empirical Evidence Concerning the Finite Sample Performance of EL-Type Structural Equation Estimation and Inference Methods," CUDARE Working Papers 25090, University of California, Berkeley, Department of Agricultural and Resource Economics.
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    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. 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.

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