The Distribution of FIML in the Leading Case

Phillips (1984) has shown that the distribution of the limited information maximum likelihood (LIML) estimator of the coefficients of the endogenous variables in a single structural equation is multivariate Cauchy in the leading (totally unidentified) case. An attempt is made to show that the same r...

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Bibliographic Details
Published in:International economic review (Philadelphia) 1986-02, Vol.27 (1), p.239-243
Main Author: Phillips, P. C. B.
Format: Article
Language:English
Subjects:
Coefficients
Covariance matrices
Economic theory
Estimates
Estimators
International economics
Mathematical models
Matrices
Maximum likelihood estimation
Variable coefficients
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Summary:Phillips (1984) has shown that the distribution of the limited information maximum likelihood (LIML) estimator of the coefficients of the endogenous variables in a single structural equation is multivariate Cauchy in the leading (totally unidentified) case. An attempt is made to show that the same result holds for the full information maximum likelihood (FIML) estimator. The proof relies on the theory of invariant measures on a Stiefel manifold. This approach offers a major simplification of the derivation of the LIML result in Phillips' earlier article and extends to the FIML case without difficulty.
ISSN:0020-6598
1468-2354
DOI:10.2307/2526618