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Indeterminacy and sunspots in two-sector RBC models with generalized no-income-effect preferences

Author

Listed:
  • Frédéric Dufourt

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Kazuo Nishimura

    (Kyōto daigaku = Kyoto University, Kobe University)

  • Alain Venditti

    (Edhec Business School - Edhec - EDHEC - EDHEC Business School - UCL - Université catholique de Lille, GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

We analyze sunspot-driven fluctuations in the standard two-sector \RBC\ model with moderate increasing returns to scale and generalized no-income-effect preferences à la Greenwood, Hercovitz and Huffman [13]. 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. We show that local indeterminacy occurs through flip and Hopf bifurcations for a large set of values for the elasticity of intertemporal substitution in consumption, provided that the labor supply is sufficiently inelastic. 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 two-sector \RBC\ models.

Suggested Citation

  • Frédéric Dufourt & Kazuo Nishimura & Alain Venditti, 2015. "Indeterminacy and sunspots in two-sector RBC models with generalized no-income-effect preferences," Post-Print hal-01457296, HAL.
    • Handle: RePEc:hal:journl:hal-01457296
    DOI: 10.1016/j.jet.2015.03.005
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    Cited by:

    1. Stephen McKnight & Laura Povoledo, 2022. "Endogenous fluctuations and international business cycles," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 55(1), pages 312-348, February.
    2. Kazuo Nishimura & Florian Pelgrin & Alain Venditti, 2022. "Medium term endogenous fluctuations in three-sector optimal growth models," Working Papers hal-03923999, HAL.
    3. Been-Lon Chen & Mei Hsu & Yu-Shan Hsu, 2018. "Progressive taxation and macroeconomic stability in two-sector models with social constant returns," Journal of Economics, Springer, vol. 125(1), pages 51-68, September.
    4. Pelgrin, Florian & Venditti, Alain, 2022. "On the long-run fluctuations of inheritance in two-sector OLG models," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    5. Dufourt, Frédéric & Venditti, Alain & Vivès, Rémi, 2018. "On sunspot fluctuations in variable capacity utilization models," Journal of Mathematical Economics, Elsevier, vol. 76(C), pages 80-94.
    6. Takashi Kamihigashi, 2017. "Regime-Switching Sunspot Equilibria in a One-Sector Growth Model with Aggregate Decreasing Returns and Small Externalities," Studies in Economic Theory, in: Kazuo Nishimura & Alain Venditti & Nicholas C. Yannelis (ed.), Sunspots and Non-Linear Dynamics, chapter 0, pages 125-146, Springer.
    7. Yoichi Gokan, 2017. "Do Consumption Externalities Correspond to the Indivisible Tax Rates on Consumpiton?," CIRJE F-Series CIRJE-F-1041, CIRJE, Faculty of Economics, University of Tokyo.
    8. Kevin X.D. Huang & Qinglai Meng & Jianpo Xue, 2019. "Capital Income Taxation and Aggregate Instability," Vanderbilt University Department of Economics Working Papers 19-00007, Vanderbilt University Department of Economics.
    9. Boucekkine, Raouf & Seegmuller, Thomas & Venditti, Alain, 2021. "Advances in growth and macroeconomic dynamics: In memory of Carine Nourry," Mathematical Social Sciences, Elsevier, vol. 112(C), pages 1-6.
    10. Been‐Lon Chen & Shun‐Fa Lee & Xavier Raurich, 2020. "Non‐separable utilities and aggregate instability," International Journal of Economic Theory, The International Society for Economic Theory, vol. 16(2), pages 222-237, June.
    11. Yoichi Gokan, 2017. "Do Consumption Externalities Correspond to the Indivisible Tax Rates on Consumpiton?," CIRJE F-Series CIRJE-F-1040, CIRJE, Faculty of Economics, University of Tokyo.
    12. Guerrazzi, Marco, 2025. "A two-sector model of optimal growth in which labour is employed only in the industry of consumption goods: A complete characterization of equilibrium paths," MPRA Paper 126101, University Library of Munich, Germany.
    13. Frédéric Dufourt & Kazuo Nishimura & Alain Venditti, 2022. "Expectations, self-fulfilling prophecies and the business cycle," Working Papers hal-03923946, HAL.
    14. Frédéric Dufourt & Kazuo Nishimura & Alain Venditti, 2016. "Sunspot fluctuations in two-sector models: New results with additively separable preferences," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(1), pages 67-83, March.
    15. Guerrazzi, Marco, 2025. "A two-sector model of optimal growth in which labour is employed only in the industry of investment goods: A complete characterization of equilibrium paths," MPRA Paper 126299, University Library of Munich, Germany.
    16. Frédéric Dufourt & Kazuo Nishimura & Carine Nourry & Alain Venditti, 2017. "Sunspot Fluctuations in Two-Sector Models with Variable Income Effects," Studies in Economic Theory, in: Kazuo Nishimura & Alain Venditti & Nicholas C. Yannelis (ed.), Sunspots and Non-Linear Dynamics, chapter 0, pages 71-96, Springer.
    17. Nishimura, Kazuo & Pelgrin, Florian & Venditti, Alain, 2025. "Business cycles fluctuations in three-sector intertemporal equilibrium models," Journal of Economic Theory, Elsevier, vol. 226(C).
    18. Abad, Nicolas & Venditti, Alain, 2021. "A Note On Balanced-Budget Income Taxes And Aggregate (In)Stability In Multi-Sector Economies," Macroeconomic Dynamics, Cambridge University Press, vol. 25(3), pages 824-843, April.
    19. Kevin x.d. Huang & Qinglai Meng & Jianpo Xue, 2019. "Capital Income Taxation and Aggregate Instability," Vanderbilt University Department of Economics Working Papers 19-00007, Vanderbilt University Department of Economics.
    20. Takuma Kunieda & Kazuo Nishimura, 2020. "Does Financial Development Amplify Sunspot Fluctuations?," Discussion Paper Series 204, School of Economics, Kwansei Gakuin University.
    21. Frédéric Dufourt & Kazuo Nishimura & Alain Venditti, 2025. "Expectations, beliefs and the business cycle: tracing back to the deep economic drivers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 79(1), pages 89-149, February.

    More about this item

    Keywords

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    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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