On the Asymptotic Optimality of the LIML Estimator with Possibly Many Instruments

T. W. Anderson, Naoto Kunitomo and Yukitoshi Matsushita
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T. W. Anderson: Department of Statistics and Department of Economics, Stanford University
Naoto Kunitomo: Faculty of Economics, University of Tokyo

No CIRJE-F-542, CIRJE F-Series from CIRJE, Faculty of Economics, 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.

Pages: 46 pages
Date: 2008-01
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (26)

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