The Unique Minimum State Variable Re Solution is E-Stable in All Well Formulated Linear Models
35 Pages Posted: 8 Nov 2010
Date Written: September 2003
This paper explores the relationship between the closely linked concepts of E-stability and least-squares learnability, featured in recent work by Evans and Honkapohja (1999, 2001), and the minimum-state-variable (MSV) solution defined 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 when nonexplosive--in all linear RE models that satisfy conditions for being well formulated.' The latter property involves two requirements. The first is that values of the model's 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 is expressed 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 response coefficients.
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