E-Stability vis-a-vis Determinacy Results for a Broad Class of Linear Rational Expectations Models

It is argued that learnability/E-stability is a necessary condition for a RE solution to be plausible. A class of linear models considered by Evans, G.W. and Honkapohja, S. [2001. Learning and Expectations in Macroeconomics, Princeton University Press.] is shown to include all models of the form used by King, R.G. and Watson, M.W. [1998. The solution of singular linear difference systems under rational expectations. International Economic Review 39, 1015–1026] and Klein, P. [2000. Using the generalized Schur form to solve a multivariate linear rational expectations model. Journal of Economic Dynamics and Control 24, 1405–1423], which permits any number of lags, leads, and lags of leads. For this broad class it is shown that, if current-period information is available in the learning process, determinacy is a sufficient condition for E-stability. It is not a necessary condition, however; there exist cases with more than one stable solution in which the solution based on the decreasing-modulus ordering of the system's eigenvalues is E-stable. If in such a case the other stable solutions are not E-stable, then the condition of indeterminacy may not be crucial for practical issues.