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Existence and stability of equilibria in OLG models under adaptive expectations


  • Michele Longo

    () (Dipartimento di Discipline matematiche, Finanza Matematica ed Econometria - Universita' Cattolica del Sacro Cuore)

  • Vincenzo Valori

    () (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze)


In 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.

Suggested Citation

  • Michele Longo & Vincenzo Valori, 2001. "Existence and stability of equilibria in OLG models under adaptive expectations," Working Papers - Mathematical Economics 2001-01, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
  • Handle: RePEc:flo:wpaper:2001-01

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    Cited by:

    1. Chen, Hung-Ju & Li, Ming-Chia & Lin, Yung-Ju, 2008. "Chaotic dynamics in an overlapping generations model with myopic and adaptive expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 67(1), pages 48-56, July.
    2. Fanti, Luciano & Gori, Luca, 2011. "Public health spending, old-age productivity and economic growth: Chaotic cycles under perfect foresight," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 137-151, April.
    3. Chen, Hung-Ju & Li, Ming-Chia, 2008. "Productive public expenditures, expectation formations and nonlinear dynamics," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 109-126, July.

    More about this item


    Existence; Uniqueness; Stability; Overlapping Generations; Perfect Foresight; Myopic Expectations; Adaptive Expectations;

    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, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models


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