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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.e.u-tokyo.ac.jp/cirje/research/dp/2008/2008cf542.pdf
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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
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Handle: RePEc:tky:fseres:2008cf542

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  1. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, vol. 69(5), pages 1161-91, September.
  2. Hahn, Jinyong, 2002. "Optimal Inference With Many Instruments," Econometric Theory, Cambridge University Press, vol. 18(01), pages 140-168, February. [Downloadable!]
  3. 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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  4. 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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  5. 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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