On the Asymptotic Optimality of the LIML Estimator with Possibly Many Instruments
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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- Morimune, Kimio, 1983. "Approximate Distributions of k-Class Estimators When the Degree of Overidentifiability Is Large Compared with the Sample Size," Econometrica, Econometric Society, vol. 51(3), pages 821-41, May.
- 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.
- Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
- 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.
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