The Correspondence Principle and Structural Stability in Non-Maximum Systems

The correspondence principle suggests a link between asymptotic stability properties of equilibria of economic models and the equilibrium response to data that describe the model or the model environment. However, this link has been impaired by a logical-mathematical deficiency. This paper, by introducing a conceptual requirement of (local) structural stability as part of the principle hypotheses, rectifies the relation between qualitative properties of equilibria and the analysis of variations. Two related examples are given. The first completes Dierkers’ proof of a unique equilibrium in regular Arrow–Debreu economies, where all price systems are locally stable relative to a tâtonnement process. The second validates linear approximation analysis of deterministic continuous time rational expectation models. The paper’s focus on local analysis makes it possible to handle potentially difficult problems in a straightforward manner. JEL Classification: C60, C62