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Indeterminacy in dynamic models: When Diamond meets Ramsey

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  • Lloyd-Braga, Teresa
  • Nourry, Carine
  • Venditti, Alain

Abstract

In this paper, we consider an aggregate overlapping generations model with endogenous labour, consumption in both periods of life, homothetic preferences and productive external effects coming from the average capital and labour. We show that under realistic calibrations of the parameters, in particular a large enough share of first period consumption over the wage income, local indeterminacy of equilibria cannot occur with capital externalities alone but that it can occur when there are only, however small, labour externalities. More precisely, under gross substitutability, the existence of multiple equilibria requires a large enough elasticity of capital-labour substitution and a large enough elasticity of the labour supply. We also show that if labour externalities are slightly stronger and the elasticity of labour supply is larger, local indeterminacy occurs in a Cobb-Douglas economy. Finally, we show that, as a consequence of our restriction on first period consumption, a locally indeterminate steady state is generically characterized by an under-accumulation of capital. It follows therefore that while agents live over a finite number of periods, the conditions for the existence of locally indeterminate equilibria are very similar to those obtained within infinite horizon models and that from this point of view, Diamond meets Ramsey.
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  • Lloyd-Braga, Teresa & Nourry, Carine & Venditti, Alain, 2007. "Indeterminacy in dynamic models: When Diamond meets Ramsey," Journal of Economic Theory, Elsevier, vol. 134(1), pages 513-536, May.
  • Handle: RePEc:eee:jetheo:v:134:y:2007:i:1:p:513-536
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    Cited by:

    1. Bosi, Stefano & Seegmuller, Thomas, 2008. "Can heterogeneous preferences stabilize endogenous fluctuations," Journal of Economic Dynamics and Control, Elsevier, vol. 32(2), pages 624-647, February.
    2. Orlando Gomes, 2010. "Deterministic randomness in a model of finance and growth," Journal of Evolutionary Economics, Springer, vol. 20(1), pages 95-114, January.
    3. Zhang, Yan & Chen, Yan, 2009. "Endogenous income taxes in OLG economies," MPRA Paper 16412, University Library of Munich, Germany.
    4. Marta Aloi & Teresa Lloyd-Braga, 2010. "National labor markets, international factor mobility and macroeconomic instability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(3), pages 431-456, June.
    5. Thomas Seegmuller, 2009. "Capital-Labour Substitution And Endogenous Fluctuations: A Monopolistic Competition Approach With Variable Markup," The Japanese Economic Review, Japanese Economic Association, vol. 60(3), pages 301-319.
    6. Drugeon, Jean-Pierre & Nourry, Carine & Venditti, Alain, 2010. "On efficiency and local uniqueness in two-sector OLG economies," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 120-144, January.
    7. Seegmuller, Thomas, 2008. "Taste For Variety And Endogenous Fluctuations In A Monopolistic Competition Model," Macroeconomic Dynamics, Cambridge University Press, vol. 12(04), pages 561-577, September.
    8. Orlando Gomes, 2008. "Decentralized Allocation of Human Capital and Nonlinear Growth," Computational Economics, Springer;Society for Computational Economics, vol. 31(1), pages 45-75, February.
    9. Been-Lon Chen & Angus Chu, 2010. "On R&D spillovers, multiple equilibria and indeterminacy," Journal of Economics, Springer, vol. 100(3), pages 247-263, July.
    10. Jean-Pierre Drugeon & Carine Nourry & Alain Venditti, 2006. "Does dynamic efficiency rule out sunspot fluctuations ?," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00410787, HAL.
    11. Hippolyte d'Albis & Emmanuelle Augeraud-Véron & Hermen Jan Hupkes, 2012. "Discontinuous Initial Value Problems for Functional Differential-Algebraic Equations of Mixed Type," Documents de travail du Centre d'Economie de la Sorbonne 12043, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    12. Gomes, Orlando, 2009. "A two-dimensional non-equilibrium dynamic model," Structural Change and Economic Dynamics, Elsevier, vol. 20(3), pages 221-238, September.
    13. Chen, Yan & Zhang, Yan, 2010. "Externalities, income taxes and indeterminacy in OLG models," MPRA Paper 22370, University Library of Munich, Germany.
    14. Orlando Gomes, 2010. "Consumer confidence, endogenous growth and endogenous cycles," Journal of Economic Studies, Emerald Group Publishing, vol. 37(4), pages 377-404, September.
    15. Jaime McGovern & Olivier Morand & Kevin Reffett, 2013. "Computing minimal state space recursive equilibrium in OLG models with stochastic production," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 623-674, November.
    16. repec:hal:journl:halshs-00717412 is not listed on IDEAS
    17. Farmer Karl & Bednar-Friedl Birgit, 2017. "Existence and Efficiency of Stationary States in a Renewable Resource Based OLG Model with Different Harvest Costs," Studia Universitatis Babeș-Bolyai Oeconomica, Sciendo, vol. 62(3), pages 3-32, December.
    18. Guido Cazzavillan & Patrick A. Pintus, 2006. "Endogenous business cycles and dynamic inefficiency," International Journal of Economic Theory, The International Society for Economic Theory, vol. 2(3-4), pages 279-294.
    19. Stan Metcalfe, 2014. "George Shackle and The Schumpeterian Legacy," Graz Economics Papers 2014-08, University of Graz, Department of Economics.
    20. repec:hal:journl:halshs-00194292 is not listed on IDEAS

    More about this item

    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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