COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 658

"The Exact Distribution of LIML: I"

Peter C.B. Phillips

December 1982

It is shown that the exact finite sample distribution of the limited information maximum likelihood (LIML) estimator in a general and leading single equation case is multivariate Cauchy. When the LIML estimator utilizes a known error covariance matrix (LIMLK) it is proved that the same Cauchy distribution still applies. The corresponding result for the instrumental variable (IV) estimator is a form of multivariate t density where the degrees of freedom depend on the number of instruments.

See CFP 589