Existence and stability of equilibria in OLG models under adaptive expectations
AbstractIn this paper we deal with an Overlapping Generations Model with production under three diverse assumptions about agents rationality; rational, adaptive and myopic expectations. We determine a uniqueness condition for stationary steady states in the model with perfect foresight which rests on the second derivatives of the production and utility functions. Such condition results to be more restrictive than the one developed for the model with myopic expectations which, due to the correspondence among steady states of the three models, could be considered as an alternative. Further, we completely develop the analysis of the model under adaptive expectations. We derive stability conditions and determine the bifurcation diagram in all the three cases. From the comparison it results that stability conditions for the case with rational expectations are less restrictive than for both adap- tive and myopic ones. We notice that, differently from what happens in the OLG model of pure exchange, the adaptive expectations do not improve local stability performances of the model with respect to myopic expectations; this is due to the fact that in our two-dimensional model a Neimark-Hopf bifurcation could arise, cutting off part of the parameter space which results to be stable in the myopic case.
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Bibliographic InfoPaper provided by Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze in its series DiMaD Working Papers with number 2001-01.
Length: 35 pages
Date of creation: May 2001
Date of revision:
Existence; Uniqueness; Stability; Overlapping Generations; Perfect Foresight; Myopic Expectations; Adaptive Expectations;
Find related papers by JEL classification:
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
- O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
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