CFDP 739

The Distribution of FIML in the Leading Case


Publication Date: April 1985

Pages: 8


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.


Distribution theory, Stiefel manifold, Invariant measure, FIML, LIML

JEL Classification Codes:  211

See CFP: 638