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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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 134 (2007)
Issue (Month): 1 (May)
Pages: 513-536

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Handle: RePEc:eee:jetheo:v:134:y:2007:i:1:p:513-536

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Web page: http://www.elsevier.com/locate/inca/622869

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  1. Cazzavillan, Guido & Lloyd-Braga, Teresa & Pintus, Patrick A., 1998. "Multiple Steady States and Endogenous Fluctuations with Increasing Returns to Scale in Production," Journal of Economic Theory, Elsevier, vol. 80(1), pages 60-107, May.
  2. Reichlin, Pietro, 1986. "Equilibrium cycles in an overlapping generations economy with production," Journal of Economic Theory, Elsevier, vol. 40(1), pages 89-102, October.
  3. Nourry, C., 1998. "Stability of Equilibria in the Overlapping Generations Model with Endogenous Labor Supply," G.R.E.Q.A.M. 98a01, Universite Aix-Marseille III.
  4. Boldrin, Michele & Rustichini, Aldo, 1994. "Growth and Indeterminacy in Dynamic Models with Externalities," Econometrica, Econometric Society, vol. 62(2), pages 323-42, March.
  5. Cazzavillan, Guido & Pintus, Patrick A., 2006. "Capital externalities in OLG economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(7), pages 1215-1231, July.
  6. Benhabib Jess & Farmer Roger E. A., 1994. "Indeterminacy and Increasing Returns," Journal of Economic Theory, Elsevier, vol. 63(1), pages 19-41, June.
  7. Thomas Seegmuller & Leonor Modesto & Teresa Lloyd-Braga, 2008. "Market Imperfections and Endogenous Fluctuations," 2008 Meeting Papers 739, Society for Economic Dynamics.
  8. Grandmont, Jean-Michel & Pintus, Patrick & de Vilder, Robin, 1998. "Capital-Labor Substitution and Competitive Nonlinear Endogenous Business Cycles," Journal of Economic Theory, Elsevier, vol. 80(1), pages 14-59, May.
  9. Guido Cazzavillan & Patrick A. Pintus, 2004. "Robustness of Multiple Equilibria in OLG Economies," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 7(2), pages 456-475, April.
  10. Galor, Oded & Ryder, Harl E., 1991. "Dynamic efficiency of steady-state equilibria in an overlapping-generations model with productive capital," Economics Letters, Elsevier, vol. 35(4), pages 385-390, April.
  11. Cazzavillan, Guido, 2001. "Indeterminacy and Endogenous Fluctuations with Arbitrarily Small Externalities," Journal of Economic Theory, Elsevier, vol. 101(1), pages 133-157, November.
  12. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448 Elsevier.
  13. repec:fth:inseep:9728 is not listed on IDEAS
  14. Duffy, John & Papageorgiou, Chris, 2000. " A Cross-Country Empirical Investigation of the Aggregate Production Function Specification," Journal of Economic Growth, Springer, vol. 5(1), pages 87-120, March.
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