The Distribution of FIML in the Leading Case

No 739, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: In a recent article (1984a) Phillips showed 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. The purpose of the present note is to show that the same result holds for the full information maximum likelihood (FIML) estimator. Our proof relies on the theory of invariant measures on a Stiefel manifold. This approach provides a major simplification of the derivation of the LIML result given in the earlier article and extends to the FIML case without difficulty. We start by illustrating its use for LIML.

Keywords: Distribution theory; Stiefel manifold; invariant measure; FIML; LIML (search for similar items in EconPapers)
Pages: 8 pages
Date: 1985-04
Note: CFP 638.
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Published in International Economic Review (February 1986), 27(1): 239-243

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