Testing for structural change in a linear simultaneous equations model under limited information

Abstract

The testing of structural change in the linear simultaneous equations model is considered under limited information on a single structural equation. Four testing problems are formulated according to the state of structural change in other structural equations, and appropriate likelihood functions and large sample locally most powerful tests for each problem are presented. The Lagrange multiplier and likelihood ratio (or asymptotically equivalent) tests based on the concentrated likehood function with the well known limited information maximum likehood (or two-stage least-squares) estimator as the maximum likelihood (or its asymptotically equivalent) estimator under null hypotheses are shown invalid for testing structural change of a single structural equation. However, the Wald test is shown effective and convenient for testing structural change of a single structural equation.