COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 739 "The Distribution of FIML in the Leading Case" Peter C.B. Phillips April 1985 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. |
