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Indeterminacy and Sunspot Fluctuations in Two-Sector RBC models: Theory and Calibration

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  • Frédéric Dufourt

    ()
    (AMSE - Aix-Marseille School of Economics - Aix-Marseille Univ. - Centre national de la recherche scientifique (CNRS) - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - Ecole Centrale Marseille (ECM), IUF - Institut Universitaire de France - Ministère de l'Enseignement Supérieur et de la Recherche Scientifique)

  • Kazuo Nishimura

    (Institute of Economic Research, Kyoto University - Kyoto University)

  • Alain Venditti

    ()
    (AMSE - Aix-Marseille School of Economics - Aix-Marseille Univ. - Centre national de la recherche scientifique (CNRS) - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - Ecole Centrale Marseille (ECM), EDHEC Business School - Département Comptabilité, Droit, Finance et Economie)

Abstract

We analyze sunspot-driven fluctuations in the standard 2-sector RBC model with moderate increasing returns to scale. We provide a detailed theoretical analysis enabling us to derive relevant bifurcation loci and to characterize the steady-state local stability properties as a function of various structural parameters. With GHH preferences, we show that local indeterminacy occurs through flip and Hopf bifurcations for a large set of values of the elasticity of intertemporal substitution in consumption if the labor supply is sufficiently inelastic. With additively-separable preferences, we prove that local indeterminacy occurs through flip and Hopf bifurcations for any value of the elasticity of the labor supply, and can even be compatible with an arbitrarily low elasticity of intertemporal substitution in consumption. Finally, we provide a detailed quantitative analysis of the model. Computing, on a quarterly basis, a new set of empirical moments related to two broadly defined consumption and investment sectors, we are able to identify, among the set of admissible calibrations consistent with sunspot equilibria, the ones that provide the best fit of the data. The model properly calibrated solves several empirical puzzles traditionally associated with 2-sector RBC models.

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Paper provided by HAL in its series Working Papers with number halshs-00796703.

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Date of creation: Feb 2013
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Handle: RePEc:hal:wpaper:halshs-00796703

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Related research

Keywords: indeterminacy; sunspots; two-sector model; sector-specific externalities; real business cycles;

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  1. Casey B. Mulligan, 2002. "Capital, Interest, and Aggregate Intertemporal Substitution," NBER Working Papers 9373, National Bureau of Economic Research, Inc.
  2. Baxter, Marianne, 1996. "Are Consumer Durables Important for Business Cycles?," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 147-55, February.
  3. Jean-Michel Grandmont & P, A, Pintus & R, De Vilder, 1997. "Capital-Labor Substitution and Competitive Nonlinear Endogenous Business Cycles," Working Papers 97-28, Centre de Recherche en Economie et Statistique.
  4. Patrick-Antoine Pintus, 2009. "Local Determinacy with Non-separable Utility," Working Papers halshs-00409585, HAL.
  5. Nishimura, Kazuo & Venditti, Alain, 2010. "Indeterminacy and expectation-driven fluctuations with non-separable preferences," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 46-56, July.
  6. Garnier, Jean-Philippe & Nishimura, Kazuo & Venditti, Alain, 2013. "Local Indeterminacy In Continuous-Time Models: The Role Of Returns To Scale," Macroeconomic Dynamics, Cambridge University Press, vol. 17(02), pages 326-355, March.
  7. Jean-Philippe Garnier & Kazuo Nishimura & Alain Venditti, 2007. "Intertemporal Substitution In Consumption, Labor Supply Elasticity And Sunspot Fluctuations In Continuous-Time Models," Working Papers halshs-00352367, HAL.
  8. Kazuo Nishimura & Carine Nourry & Alain Venditti, 2008. "Indeterminacy in aggregate models with small externalities: an interplay between preferences and technology," Working Papers halshs-00281428, HAL.
  9. Nishimura, Kazuo & Venditti, Alain, 2007. "Indeterminacy in discrete-time infinite-horizon models with non-linear utility and endogenous labor," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 446-476, April.
  10. Hintermaier, Thomas, 2003. "On the minimum degree of returns to scale in sunspot models of the business cycle," Journal of Economic Theory, Elsevier, vol. 110(2), pages 400-409, June.
  11. Jonathan Gruber, 2006. "A Tax-Based Estimate of the Elasticity of Intertemporal Substitution," NBER Working Papers 11945, National Bureau of Economic Research, Inc.
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