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A characterization of Markov equilibrium in stochastic overlapping generations models

Author

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  • Kim, Eungsik
  • Spear, Stephen

Abstract

This paper characterizes the Markov equilibrium in stochastic overlapping generations models with both pure exchange and production using the theory of linear iterated function systems. We provide conditions for the linearized Markov equilibrium to have an absolutely continuous invariant measure or a singular invariant measure. We also examine relationships between the linear equilibrium system and the model parameters. This analysis identifies the set of economies for each type of invariant measure. We show that the attractor of the singular invariant measure exhibits fractal patterns, which supports the proposition that self-affinity patterns in financial data can be explained via rational expectations equilibrium as an economic mechanism.

Suggested Citation

  • Kim, Eungsik & Spear, Stephen, 2021. "A characterization of Markov equilibrium in stochastic overlapping generations models," Journal of Economic Dynamics and Control, Elsevier, vol. 124(C).
    • Handle: RePEc:eee:dyncon:v:124:y:2021:i:c:s0165188920301913
    DOI: 10.1016/j.jedc.2020.104023
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    More about this item

    Keywords

    Markov equilibrium; Linear iterated function system; Invariant measure; Exchange and production economy; Fractal self-affine attractor;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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