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MANY INSTRUMENTS ASYMPTOTIC APPROXIMATIONSUNDER 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 asymptoticapproximation to the sampling distribution of thelimited information maximum likelihood estimator anda bias-corrected version of the two-stage leastsquares estimator. The approximation is obtained byallowing the number of instruments and theconcentration parameter to grow at the same rate asthe sample size. More specifically, we allow forpotentially nonnormal error distributions and obtainthe conventional asymptotic distribution and theresults of Bekker (1994,Econometrica 62, 657–681) andBekker and Van der Ploeg (2005, StatisticaNeerlandica 59, 139–267) as specialcases. The results show that when the errordistribution is not normal, in general both theproperties of the instruments and the third andfourth moments of the errors affect the asymptoticvariance. We compare our findings with those in therecent literature on many and weak instruments.

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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, FrankKleibergen, and Tony Lancaster for their supportand suggestions. The co-editor and two anonymousreferees provided valuable comments that greatlyimproved the presentation in this paper. I amresponsible for any remaining errors.

References

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