Title

The Exact Distribution of LIML: I

Document Type

Discussion Paper

Publication Date

12-1-1982

CFDP Number

658

CFDP Pages

23

Abstract

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.

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