02345cam a22002537 4500001000600000003000500006005001700011008004100028100002500069245014600094260006600240490004100306500002000347520116800367530006101535538007201596538003601668690005701704690013901761710004201900830007601942856003702018856003602055w9960NBER20170919155005.0170919s2003 mau||||fs|||| 000 0 eng d1 aMcCallum, Bennett T.14aThe Unique Minimum State Variable RE Solution is E-Stable in All Well Formulated Linear Modelsh[electronic resource] /cBennett T. McCallum. aCambridge, Mass.bNational Bureau of Economic Researchc2003.1 aNBER working paper seriesvno. w9960 aSeptember 2003.3 aThis 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. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web. 7aE00 - General2Journal of Economic Literature class. 7aC6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling2Journal of Economic Literature class.2 aNational Bureau of Economic Research. 0aWorking Paper Series (National Bureau of Economic Research)vno. w9960.4 uhttp://www.nber.org/papers/w996041uhttp://dx.doi.org/10.3386/w9960