The Unique Minimum State Variable RE Soluiton is E-Stable in All Well Formulated Linear Models

This paper explores the relationship between the closely linked concepts of E-stability and least-squares learnability, featured in important recent work by Evans and Honkapohja (1999, 2001), and the minimum-state-variable (MSV) solution concept introduced by McCallum (1983) and used by many researchers for rational expectations (RE) analysis. It is shown that the MSV solution, which is unique by construction, is E-stable—and therefore LS learnable if nonexplosive—in all linear RE models that satisfy conditions for being “well formulated.” The latter property, introduced in the paper, consists of two requirements. The first is that a model’s structural parameters are restricted so as to avoid any infinite discontinuity, of the steady state values of endogenous variables, in response to small changes in these parameters. (It can be expressed cleanly in terms of the eigenvalues of a matrix that is the sum of those attached to the one period ahead and one period lagged values of the endogenous variables in a first-order vector formulation of the model.) The second, which is needed infrequently, is that the parameters are restricted to prevent any infinite discontinuities in the MSV solution response coefficients.