On the Asymptotic Optimality of the LIML Estimator with Possibly Many Instruments
AbstractWe consider the estimation of the coefficients of a linear structural equation in a simultaneous equation system when there are many instrumental variables. We derive some asymptotic properties of the limited information maximum likelihood (LIML) estimator when the number of instruments is large; some of these results are new and we relate them to results in some recent studies. We have found that the variance of the LIML estimator and its modifications often attain the asymptotic lower bound when the number of instruments is large and the disturbance terms are not necessarily normally distributed, that is, for the micro-econometric models with many instruments.
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Bibliographic InfoPaper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-542.
Length: 46 pages
Date of creation: Jan 2008
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- T. W. Anderson & Naoto Kunitomo & Yukitoshi Matsushita, 2006. "A New Light from Old Wisdoms : Alternative Estimation Methods of Simultaneous Equations with Possibly Many Instruments," CIRJE F-Series CIRJE-F-399, CIRJE, Faculty of Economics, University of Tokyo.
- Yukitoshi Matsushita, 2007. "t-Tests in a Structural Equation with Many Instruments," CIRJE F-Series CIRJE-F-467, CIRJE, Faculty of Economics, University of Tokyo.
- Anderson, T.W., 2005. "Origins of the limited information maximum likelihood and two-stage least squares estimators," Journal of Econometrics, Elsevier, vol. 127(1), pages 1-16, July.
- 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.
- 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.
- Kentaro Akashi & Naoto Kunitomo, 2010.
"Some Properties of the LIML Estimator in a Dynamic Panel Structural Equation,"
CIRJE-F-707, CIRJE, Faculty of Economics, University of Tokyo.
- 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.
- Naoto Kunitomo, 2012. "An optimal modification of the LIML estimation for many instruments and persistent heteroscedasticity," Annals of the Institute of Statistical Mathematics, Springer, vol. 64(5), pages 881-910, October.
- Guy Tchuente & Marine Carrasco, 2013. "Regularized LIML for many instruments," CIRANO Working Papers 2013s-20, CIRANO.
- 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.
- 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.
- Michal Kolesár & Raj Chetty & John N. Friedman & Edward L. Glaeser & Guido W. Imbens, 2011. "Identification and Inference with Many Invalid Instruments," NBER Working Papers 17519, National Bureau of Economic Research, Inc.
- 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.
- 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.
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