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Necessary and Sufficient Conditions for Determinacy of Asymptotically Stationary Equilibria in Olg Models

Author

Listed:
  • Alexander Gorokhovsky

    (Dept. of Mathematics University of Colorado at Boulder)

  • Anna Rubinchik

    (Dept. of Economics; University of Haifa)

Abstract

We propose a criterion for determining whether a local policy analysis can be made in a given equilibrium in an overlapping generations model. The criterion can be applied to models with infinite past and future as well as those with a truncated past. The equilibrium is not necessarily a steady state; for example, demographic and type composition of the population or individuals’ endowments can change over time. However, asymptotically, the equilibrium should be stationary. The two limiting stationary paths at either end of the timeline do not have to be the same. If they are, conditions for local uniqueness are far more stringent for an economy with a truncated past as compared to its counterpart with an infinite past. In addition, we illustrate our main result using a textbook model with a single physical good, a two-period life-cycle and a single type of consumer. In this model we show how to calculate a response to a policy change using the implicit function theorem.

Suggested Citation

  • Alexander Gorokhovsky & Anna Rubinchik, 2019. "Necessary and Sufficient Conditions for Determinacy of Asymptotically Stationary Equilibria in Olg Models," Cowles Foundation Discussion Papers 2179, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:2179
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d21/d2179.pdf
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    References listed on IDEAS

    as
    1. Chris Shannon & William R. Zame, 2002. "Quadratic Concavity and Determinacy of Equilibrium," Econometrica, Econometric Society, vol. 70(2), pages 631-662, March.
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    4. Kehoe, Timothy J. & Levine, David K., 1984. "Regularity in overlapping generations exchange economies," Journal of Mathematical Economics, Elsevier, vol. 13(1), pages 69-93, April.
    5. Kehoe, Timothy J & Levine, David K, 1985. "Comparative Statics and Perfect Foresight in Infinite Horizon Economies," Econometrica, Econometric Society, vol. 53(2), pages 433-453, March.
    6. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
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    9. Krueger, Dirk & Ludwig, Alexander, 2018. "Optimal taxes on capital in the OLG model with uninsurable idiosyncratic income risk," SAFE Working Paper Series 201, Research Center SAFE - Sustainable Architecture for Finance in Europe, Goethe University Frankfurt.
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    More about this item

    Keywords

    Overlapping generations; Implicit function theorem; Determinacy; Time-invariance; Comparative statics;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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