Many-instruments Asymptotic Approximations Under Nonnormal Error Distributions

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Martijn Van Hasselt, Associate Professor (Creator)
The University of North Carolina at Greensboro (UNCG )
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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.

Additional Information

Econometric Theory, 26(2), 633–645
Language: English
Date: 2010
Econometrics, Asymptotic distribution, Nonnormal error distributions , Asymptotic methods, Maximum likelihood method

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