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On the Asymptotic Optimality of the LIML Estimator with Possibly 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

    (CIRJE, University of Tokyo)

Abstract

We 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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File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2008/2008cf542.pdf
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Bibliographic Info

Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-542.

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Length: 46 pages
Date of creation: Jan 2008
Date of revision:
Handle: RePEc:tky:fseres:2008cf542

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Cited by:
  1. 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.
  2. 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.

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