The Exact Finite-Sample Distribution of the Limited-Information Maximum Likelihood Estimator in the Case of Two Included Endogenous Variables

Abstract

Abstract This article is concerned with the exact finite-sample distribution of the limited-information maximum likelihood estimator when the structural equation being estimated contains two endogenous variables and is identifiable in a complete system of linear stochastic equations. The density function derived, which is represented as a doubly infinite series of a complicated form, reveals the important fact that for arbitrary values of the parameters in the model, the LIML estimator does not possess moments of order greater than or equal to one