Identifiability of a simultaneous equations model of economy: a structural view

Abstract

The simultaneous equations model is standard in econometric analysis. In such a framework, however, some equations can be unidentifiable; meaning that such an equation cannot be determined uniquely from statistical data. A necessary and sufficient condition for identifiability is widely known under the name of the rank condition. However, to verify this condition, we need to know all equations of the model in advance. This is impossible, since these equations are to be estimated from data, and estimation is meaningful only if the equations are known to be identifiable. We develop a necessary and sufficient condition for identifiability that is completely free from statistical data but only dependent on the structure of the model. That is, in this characterization of identifiability we only need to know which variables are included in each equation. Graph theory is used to describe the result, and a network flow algorithm is given to test for this condition. A few illustrative examples are also given.