IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/halshs-00408018.html
   My bibliography  Save this paper

Local and global indeterminacy in two-sector models of endogenous growth

Author

Listed:
  • Paulo Brito

    (ISEG - Technical University of Lisbon, UECE - UECE)

  • Alain Venditti

    (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

In this paper we consider a two-sector endogenous growth model where the productions of the final good and human capital require economy-wide external effects. Assuming constant returns to scale at the private and social levels, we show that local and global indeterminacy of equilibrium paths are compatible with any values for the elasticity of intertemporal substitution in consumption and any sign for the capital intensity difference across the two sectors.

Suggested Citation

  • Paulo Brito & Alain Venditti, 2009. "Local and global indeterminacy in two-sector models of endogenous growth," Working Papers halshs-00408018, HAL.
    • Handle: RePEc:hal:wpaper:halshs-00408018
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00408018
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-00408018/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-1037, October.
    2. Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 63(1), pages 113-142, June.
    3. Tapan Mitra, 1998. "On Equilibrium Dynamics Under Externalities in a Model of Economic Development," The Japanese Economic Review, Japanese Economic Association, vol. 49(2), pages 85-107, June.
    4. Bloise, Gaetano, 2001. "A Geometric Approach to Sunspot Equilibria," Journal of Economic Theory, Elsevier, vol. 101(2), pages 519-539, December.
    5. Jess Benhabib & Qinglai Meng & Kazuo Nishimura, 2012. "Indeterminacy Under Constant Returns to Scale in Multisector Economies," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 403-412, Springer.
    6. Azariadis, Costas & Stachurski, John, 2005. "Poverty Traps," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 1, chapter 5, Elsevier.
    7. Santos, Manuel S., 2002. "On Non-existence of Markov Equilibria in Competitive-Market Economies," Journal of Economic Theory, Elsevier, vol. 105(1), pages 73-98, July.
    8. Rebelo, Sergio, 1991. "Long-Run Policy Analysis and Long-Run Growth," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 500-521, June.
    9. Bond, Eric W. & Wang, Ping & Yip, Chong K., 1996. "A General Two-Sector Model of Endogenous Growth with Human and Physical Capital: Balanced Growth and Transitional Dynamics," Journal of Economic Theory, Elsevier, vol. 68(1), pages 149-173, January.
    10. Xie Danyang, 1994. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," Journal of Economic Theory, Elsevier, vol. 63(1), pages 97-112, June.
    11. Raouf Boucekkine & Blanca Martínez & José Ramón Ruiz‐Tamarit, 2008. "Note on global dynamics and imbalance effects in the Lucas–Uzawa model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(4), pages 503-518, December.
    12. Casey B. Mulligan & Xavier Sala-i-Martin, 1993. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(3), pages 739-773.
    13. Antonio Ladrón-de-Guevara & Salvador Ortigueira & Manuel S. Santos, 1999. "A Two-Sector Model of Endogenous Growth with Leisure," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 609-631.
    14. Caballe, Jordi & Santos, Manuel S, 1993. "On Endogenous Growth with Physical and Human Capital," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 1042-1067, December.
    15. Paolo Mattana & Kazuo Nishimura & Tadashi Shigoka, 2012. "Homoclinic Bifurcation and Global Indeterminacy of Equilibrium in a Two-Sector Endogenous Growth Model," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 427-451, Springer.
    16. Chamley, Christophe, 1993. "Externalities and Dynamics in Models of "Learning or Doing."," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(3), pages 583-609, August.
    17. Basu, Susanto & Fernald, John G, 1997. "Returns to Scale in U.S. Production: Estimates and Implications," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 249-283, April.
    18. Boucekkine, R. & Ruiz-Tamarit, J.R., 2008. "Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 33-54, January.
    19. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
    20. Kazuo Nishimura & Harutaka Takahashi & Alain Venditti, 2012. "Global Externalities, Endogenous Growth and Sunspot Fluctuations," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 413-425, Springer.
    21. Drugeon, Jean-Pierre, 2008. "On intersectoral asymmetries in factors substitutability, "Equilibrium Production Possibility Frontiers" and the emergence of indeterminacies," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 277-315, February.
    22. Ladron-de-Guevara, Antonio & Ortigueira, Salvador & Santos, Manuel S., 1997. "Equilibrium dynamics in two-sector models of endogenous growth," Journal of Economic Dynamics and Control, Elsevier, vol. 21(1), pages 115-143, January.
    23. Manuel Santos, "undated". "On Non-Existence of Markov Equilibria in Competitive-Market Economies," Working Papers 2133305, Department of Economics, W. P. Carey School of Business, Arizona State University.
    24. Mino, Kazuo, 2001. "Indeterminacy and Endogenous Growth with Social Constant Returns," Journal of Economic Theory, Elsevier, vol. 97(1), pages 203-222, March.
    25. Jean-Pierre Drugeon, 2008. "On Intersectoral Asymmetries in Factors Substitutability “Equilibrium Production Possibility Frontiers” and the emergence of indeterminacies," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00182205, HAL.
    26. Jean-Pierre Drugeon, 2008. "On Intersectoral Asymmetries in Factors Substitutability “Equilibrium Production Possibility Frontiers” and the emergence of indeterminacies," Post-Print hal-00182205, HAL.
    27. Ben-Gad, Michael, 2003. "Fiscal policy and indeterminacy in models of endogenous growth," Journal of Economic Theory, Elsevier, vol. 108(2), pages 322-344, February.
    28. Nishimura, Kazuo & Venditti, Alain, 2004. "Indeterminacy And The Role Of Factor Substitutability," Macroeconomic Dynamics, Cambridge University Press, vol. 8(4), pages 436-465, September.
    29. Jean-Pierre Drugeon & Odile Poulsen & Alain Venditti, 2003. "On Intersectoral allocations, factors substitutability and multiple long-run growth paths," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(1), pages 175-183, January.
    30. Xavier Raurich, 2001. "Indeterminancy and Government Spending in a Two-Sector Model of Endogenous Growth," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(1), pages 210-229, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bella, Giovanni & Mattana, Paolo, 2014. "Global indeterminacy of the equilibrium in the Chamley model of endogenous growth in the vicinity of a Bogdanov–Takens bifurcation," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 69-79.
    2. Maxime Menuet & Alexandru Minea & Patrick Villieu, 2019. "Increasing Returns, Balanced-Budget Rules, and Aggregate Fluctuations," Post-Print hal-02315041, HAL.
    3. Maxime Menuet & Alexandru Minea & Patrick Villieu, 2019. "Endogenous fluctuations and the balanced-budget rule: taxes versus spending-based adjustment," Post-Print halshs-02315727, HAL.
    4. Bella, Giovanni, 2017. "Homoclinic bifurcation and the Belyakov degeneracy in a variant of the Romer model of endogenous growth," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 452-460.
    5. Angelo Antoci & Marcello Galeotti & Paolo Russu, 2014. "Global analysis and indeterminacy in a two-sector growth model with human capital," International Journal of Economic Theory, The International Society for Economic Theory, vol. 10(4), pages 313-338, December.
    6. Daria ONORI & Francesco MAGRIS & Antoine LE RICHE, 2017. "Monetary Rules in a Two-Sector Endogenous Growth Model with Cash-in-Advance Constraint," LEO Working Papers / DR LEO 2504, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    7. Nastasia Henry & Alain Venditti, 2023. "On the (de)stabilization role of protectionism: Theory and evidence," Working Papers hal-04311555, HAL.
    8. Maxime MENUET & Alexandru MINEA & Patrick VILLIEU, 2017. "Public Debt, Endogenous Growth Cycles and Indeterminacy," LEO Working Papers / DR LEO 2467, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    9. Antoine Riche & Francesco Magris & Daria Onori, 2020. "Monetary rules in a two-sector endogenous growth model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(4), pages 1049-1100, June.
    10. Nishimura Kazuo & Shigoka Tadashi, 2019. "Hopf bifurcation and the existence and stability of closed orbits in three-sector models of optimal endogenous growth," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(4), pages 1-21, September.
    11. Antoci, Angelo & Borghesi, Simone & Galeotti, Marcello & Russu, Paolo, 2022. "Maladaptation to environmental degradation and the interplay between negative and positive externalities," European Economic Review, Elsevier, vol. 143(C).
    12. Yoichiro Tamanyu, 2020. "The Role of Nonlinearity in Indeterminate Models: An Application to Expectations-Driven Liquidity Traps," Keio-IES Discussion Paper Series 2020-023, Institute for Economics Studies, Keio University.
    13. Fu, Wentao & Le Riche, Antoine, 2021. "Endogenous growth model with Bayesian learning and technology selection," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 58-71.
    14. Bella, Giovanni & Mattana, Paolo & Venturi, Beatrice, 2017. "Shilnikov chaos in the Lucas model of endogenous growth," Journal of Economic Theory, Elsevier, vol. 172(C), pages 451-477.
    15. Carboni, Oliviero A. & Russu, Paolo, 2013. "Linear production function, externalities and indeterminacy in a capital-resource growth model," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 422-428.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Garcia-Belenguer, Fernando, 2007. "Stability, global dynamics and Markov equilibrium in models of endogenous economic growth," Journal of Economic Theory, Elsevier, vol. 136(1), pages 392-416, September.
    2. García-Belenguer, Fernando, 2006. "Stability, Global Dynamics and Markov Equilibrium in Models of Economic Growth," Working Papers in Economic Theory 2006/05, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
    3. Bella, Giovanni & Mattana, Paolo & Venturi, Beatrice, 2017. "Shilnikov chaos in the Lucas model of endogenous growth," Journal of Economic Theory, Elsevier, vol. 172(C), pages 451-477.
    4. Ghiglino, Christian, 2002. "Introduction to a General Equilibrium Approach to Economic Growth," Journal of Economic Theory, Elsevier, vol. 105(1), pages 1-17, July.
    5. Chen, Been-Lon & Lee, Shun-Fa, 2008. "Corrigendum to "Congestible public goods and local indeterminacy: A two-sector endogenous growth model": [Journal of Economic Dynamics & Control 31 (7) (2007) 2486-2518]," Journal of Economic Dynamics and Control, Elsevier, vol. 32(4), pages 1356-1356, April.
    6. Ladron-de-Guevara, Antonio & Ortigueira, Salvador & Santos, Manuel S., 1997. "Equilibrium dynamics in two-sector models of endogenous growth," Journal of Economic Dynamics and Control, Elsevier, vol. 21(1), pages 115-143, January.
    7. Gomez Suarez, Manuel A., 2008. "Utility and production externalities, equilibrium efficiency and leisure specification," Journal of Macroeconomics, Elsevier, vol. 30(4), pages 1496-1519, December.
    8. Nishimura, Kazuo & Venditti, Alain, 2004. "Indeterminacy And The Role Of Factor Substitutability," Macroeconomic Dynamics, Cambridge University Press, vol. 8(4), pages 436-465, September.
    9. Arantza Gorostiaga & Jana Hromcová & Miguel-Ángel López-García, 2013. "Optimal taxation in the Uzawa–Lucas model with externality in human capital," Journal of Economics, Springer, vol. 108(2), pages 111-129, March.
    10. Been‐Lon Chen & Shun‐Fa Lee, 2012. "Intersectoral Spillovers, Relative Prices and Development Traps," Review of Development Economics, Wiley Blackwell, vol. 16(2), pages 243-261, May.
    11. Been-Lon Chen & Shun-Fa Lee, 2005. "Congestible Public Goods and Indeterminacy in a Two-sector Endogenous Growth Model," IEAS Working Paper : academic research 05-A003, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    12. De, Supriyo, 2014. "Intangible capital and growth in the ‘new economy’: Implications of a multi-sector endogenous growth model," Structural Change and Economic Dynamics, Elsevier, vol. 28(C), pages 25-42.
    13. Benhabib, Jess & Gali, Jordi, 1995. "On growth and indeterminacy: some theory and evidence," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 43(1), pages 163-211, December.
    14. Been-Lon Chen & Shun-Fa Lee, 2009. "General Fund Financing, Earmarking, Economic Stabilization, and Welfare," Public Finance Review, , vol. 37(5), pages 507-538, September.
    15. Pedro Garcia-Castrillo & Marcos Sanso, 2000. "Human Capital and Optimal Policy in a Lucas-type Model," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(4), pages 757-770, October.
    16. Dirk Bethmann & Markus Reiß, 2012. "Simplifying numerical analyses of Hamilton–Jacobi–Bellman equations," Journal of Economics, Springer, vol. 107(2), pages 101-128, October.
    17. Barañano Mentxaka, Ilaski & San Martín Lizarralde, Marta, 2015. "Optimal Taxation and Indeterminacy in the Uzawa-Lucas Model with Sector-specific Externalities," IKERLANAK 16781, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    18. Kejak, Michal, 2003. "Stages of growth in economic development," Journal of Economic Dynamics and Control, Elsevier, vol. 27(5), pages 771-800, March.
    19. Stephen J. Turnovsky, 2000. "Growth in an open economy: some recent developments," Working Paper Research 05, National Bank of Belgium.
    20. Alonso-Carrera, Jaime & Freire-Seren, Maria Jesus, 2004. "Multiple equilibria, fiscal policy, and human capital accumulation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 841-856, January.

    More about this item

    Keywords

    Two-sector model; endogenous growth; economy-wide externalities; local and global indeterminacy;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:halshs-00408018. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.