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On the Convergence Criterion in Three-Period-Lived Overlapping Generations Models

Author

Listed:
  • Jean-Paul Barinci

    (EPEE - Centre d'Etudes des Politiques Economiques - UEVE - Université d'Évry-Val-d'Essonne - Université Paris-Saclay)

  • Hye-Jin Cho

    (Durham University)

  • Jean-Pierre Drugeon

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CNRS - Centre National de la Recherche Scientifique)

Abstract

This article considers a three-period-lived pure exchange overlapping generations economy and clarifies the role of market complementarities in the scope for Kehoe & Levine's convergence criterion in order to reduce the size of continuation equilibria and establish uniqueness and determinacy. The argument is based upon the price-relatedness of dated goods and the way the law of demand, gross substitutability and the scope for asymmetric complementarities come into play when three periods lifespans are considered. The nature of these restriions is clarified in the context of stationary economies and the way it relates to equilibrium continuation and Kehoe & Levine's determinacy is made precise. A detailed articulation between complementarities and determinacy is finally provided in the context of Samuelson intermediate economies. The key role of dated goods spaced one period apart and entering in an additive way is emphasised in the determinacy result while the importance of asymetric complementarities between isolated goods spaced two periods apart is also pointed out.

Suggested Citation

  • Jean-Paul Barinci & Hye-Jin Cho & Jean-Pierre Drugeon, 2024. "On the Convergence Criterion in Three-Period-Lived Overlapping Generations Models," PSE Working Papers halshs-04850529, HAL.
  • Handle: RePEc:hal:psewpa:halshs-04850529
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-04850529v1
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    References listed on IDEAS

    as
    1. Gorokhovsky, Alexander & Rubinchik, Anna, 2022. "Necessary and sufficient conditions for determinacy of asymptotically stationary equilibria in OLG models," Journal of Economic Theory, Elsevier, vol. 204(C).
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    6. Lahiri, Amartya & Puhakka, Mikko, 1998. "Habit Persistence in Overlapping Generations Economies under Pure Exchange," Journal of Economic Theory, Elsevier, vol. 78(1), pages 176-186, January.
    7. Jonathan L. Burke, 2022. "Generic determinacy among stationary overlapping generations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 977-993, June.
    8. Kehoe, Timothy J. & Levine, David K. & Mas-Colell, Andreu & Woodford, Michael, 1991. "Gross substitutability in large-square economies," Journal of Economic Theory, Elsevier, vol. 54(1), pages 1-25, June.
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