Identifying restrictions of linear equations with applications to simultaneous equations and cointegration

Abstract

The identification problem for simultaneous equations is solved by the well-known rank condition which gives a necessary and sufficient condition for the parameters to be uniquely or statistically identified by linear restrictions. This paper formulates and solves another problem: Given a set of linear restrictions, which conditions should they satisfy for most parameter values to be identified? The main result of the paper is a simple algebraic condition on a set of linear restrictions that guarantees that most parameters satisfying the restrictions are uniquely identified.