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Global analysis and indeterminacy in a two-sector growth model with human capital

Author

Listed:
  • Angelo Antoci
  • Marcello Galeotti
  • Paolo Russu

Abstract

type="main" xml:lang="en"> The purpose of the present paper is to highlight some features of global dynamics of the two-sector growth model with accumulation of human and physical capital analyzed by Brito and Venditti, which is a specialization of the model proposed by Mulligan and Sala-i-Martín. In particular, our analysis focuses on the context in which the Brito–Venditti system admits two balanced growth paths, each corresponding, after a change of variables, to an equilibrium point of a three-dimensional system, and proves the possible existence of points P ‾ such that in any neighborhood of P ‾ lying on the plane corresponding to fixed values of the state variables there exist points Q ‾ whose positive trajectories tend to either equilibrium point. This implies that equilibrium selection in the Brito–Venditti system may depend on the expectations of economic agents rather than on the history of the economy. That is, economies with identical technologies and preferences, starting from the same initial values of the state variables (history), may follow rather different equilibrium trajectories according to the economic agents’ choices of the initial values of the jumping variables (expectations). Moreover, we prove that the basins of attraction (two or three-dimensional) of locally indeterminate equilibrium points may be very large, as they can extend up to the boundary of the system phase space.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:ijethy:v:10:y:2014:i:4:p:313-338
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    References listed on IDEAS

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    1. 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.
    2. Benhabib Jess & Farmer Roger E. A., 1994. "Indeterminacy and Increasing Returns," Journal of Economic Theory, Elsevier, vol. 63(1), pages 19-41, June.
    3. Antoci, Angelo & Galeotti, Marcello & Russu, Paolo, 2011. "Poverty trap and global indeterminacy in a growth model with open-access natural resources," Journal of Economic Theory, Elsevier, vol. 146(2), pages 569-591, March.
    4. Tarek Coury & Yi Wen, 2009. "Global indeterminacy in locally determinate real business cycle models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(1), pages 49-60, March.
    5. 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.
    6. Paolo Mattana & Kazuo Nishimura & Tadashi Shigoka, 2009. "Homoclinic bifurcation and global indeterminacy of equilibrium in a two‐sector endogenous growth model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(1), pages 25-47, March.
    7. Slobodyan, Sergey, 2007. "Indeterminacy and stability in a modified Romer model," Journal of Macroeconomics, Elsevier, vol. 29(1), pages 169-177, March.
    8. Brito, Paulo & Venditti, Alain, 2010. "Local and global indeterminacy in two-sector models of endogenous growth," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 893-911, September.
    9. Kazuo Mino & Kazuo Nishimura & Koji Shimomura & Ping Wang, 2008. "Equilibrium dynamics in discrete-time endogenous growth models with social constant returns," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(1), pages 1-23, January.
    10. Mino, Kazuo, 2003. "Human Capital Formation and Patterns of Growth with Multiple Equilibria," MPRA Paper 58146, University Library of Munich, Germany.
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    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. repec:eee:jetheo:v:172:y:2017:i:c:p:451-477 is not listed on IDEAS
    3. 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.
    4. OA Carboni & P. Russu, 2012. "Global Indeterminacy in a Tourism Sector Model," Working Paper CRENoS 201230, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.

    More about this item

    JEL classification:

    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • O10 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - General
    • E24 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Employment; Unemployment; Wages; Intergenerational Income Distribution; Aggregate Human Capital; Aggregate Labor Productivity
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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