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MANY INSTRUMENTS ASYMPTOTIC APPROXIMATIONS UNDER NONNORMAL ERROR DISTRIBUTIONS

Published online by Cambridge University Press:  18 August 2009

Martijn van Hasselt
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Abstract

In this paper we derive an alternative asymptotic approximation to the sampling distribution of the limited information maximum likelihood estimator and a bias-corrected version of the two-stage least squares estimator. The approximation is obtained by allowing the number of instruments and the concentration parameter to grow at the same rate as the sample size. More specifically, we allow for potentially nonnormal error distributions and obtain the conventional asymptotic distribution and the results of Bekker (1994, Econometrica 62, 657–681) and Bekker and Van der Ploeg (2005, Statistica Neerlandica 59, 139–267) as special cases. The results show that when the error distribution is not normal, in general both the properties of the instruments and the third and fourth moments of the errors affect the asymptotic variance. We compare our findings with those in the recent literature on many and weak instruments.

Type
Brief Report
Information
Econometric Theory , Volume 26 , Issue 2 , April 2010 , pp. 633 - 645
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

I thank Paul Bekker, John Knight, Frank Kleibergen, and Tony Lancaster for their support and suggestions. The co-editor and two anonymous referees provided valuable comments that greatly improved the presentation in this paper. I am responsible for any remaining errors.

References

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