Solving Nonlinear Rational Expectations Models by Eigenvalue–Eigenvector Decompositions
Solving Nonlinear Rational Expectations Models by Eigenvalue–Eigenvector Decompositions
Discusses the main issues involved in practical applications of solution methods that have been proposed for rational expectations models, based on eigenvalue–eigenvector decompositions. It starts by reviewing how a numerical solution can be derived for the standard deterministic Cass–Koopmans–Brock–Mirman economy, pointing out the relevance of stability conditions. Next the general structure used to solve linear rational expectations models, and its extension to nonlinear models, is summarized. The solution method is then applied to Hansen's (1985) model of indivisible labour, and comparisons with other solution approaches are discussed. It is then shown how the eigenvalue–eigenvector decomposition can help to separately identify variables of a similar nature (as is the case when physical capital and inventories are inputs in an aggregate production technology), and how the solution method can be adapted to deal with endogenous growth models.
Keywords: Cass–Koopmans–Brock–Mirman economy, dynamic economics models, eigenvalue–eigenvector decomposition, endogenous growth models, Hansen's model of indivisible labour, linear rational expectations models, macroeconomics, nonlinear rational expectations models, rational expectations models, solution methods, stability
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