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Imbalance effects in the Lucas model : An analytical exploration

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  • Raouf, BOUCEKKINE

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES) and UNIVERSITE CATHOLIQUE DE LOUVAIN, Center for Operations Research and Econometrics (CORE))

  • Ramon, RUIZ-TAMARIT

    (University of Valencia, Spain)

Abstract

In this note, we use a technique analogous to Xie’s method (1994) to solve analytically the Lucas model with externality in a specific parametric case. In particular, we characterize the shape of imbalance effects in this model. Our results are entirely consistent with the findings of the related computational literature. Moreover, our analytical investigation tends to show that these findings are robust to the presence of the Lucas externality as long as a unique equilibrium path exists.

Suggested Citation

  • Raouf, BOUCEKKINE & Ramon, RUIZ-TAMARIT, 2004. "Imbalance effects in the Lucas model : An analytical exploration," LIDAM Discussion Papers IRES 2004005, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  • Handle: RePEc:ctl:louvir:2004005
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    File URL: http://sites.uclouvain.be/econ/DP/IRES/2004-5.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Xie Danyang, 1994. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," Journal of Economic Theory, Elsevier, vol. 63(1), pages 97-112, June.
    3. Casey B. Mulligan & Xavier Sala-i-Martin, 1993. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 108(3), pages 739-773.
    4. 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.
    5. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
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    Cited by:

    1. Constantin Chilarescu, 2018. "The effect of externality on the transitional dynamics: the case of Lucas model," Economics Bulletin, AccessEcon, vol. 32767(3).
    2. Bofota, Youyou Baende & Boucekkine, Raouf & Bala, Alain Pholo, 2016. "Social Capital As An Engine Of Growth: Multisectoral Modeling And Implications," Macroeconomic Dynamics, Cambridge University Press, vol. 20(8), pages 2093-2122, December.
    3. Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
    4. 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.
    5. José Ramón Ruiz Tamarit & Manuel Sánchez Moreno, 2006. "Optimal Regulation And Growth In A Natural-Resource-Based Economy," Working Papers. Serie AD 2006-21, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    6. Christian Groth & Ronald Wendner, 2011. "Learning by Investing, Embodiment, and Speed of Convergence," EPRU Working Paper Series 2011-01, Economic Policy Research Unit (EPRU), University of Copenhagen. Department of Economics.
    7. C. Chilarescu & I. Viasu, 2019. "Uniqueness and Multiple Trajectories for the Case of Lucas Model," Computational Economics, Springer;Society for Computational Economics, vol. 54(3), pages 1157-1177, October.
    8. Robert Feicht & Wolfgang Stummer, 2010. "Complete Closed-form Solution to a Stochastic Growth Model and Corresponding Speed of Economic Recovery preliminary," DEGIT Conference Papers c015_041, DEGIT, Dynamics, Economic Growth, and International Trade.
    9. Groth, Christian & Wendner, Ronald, 2014. "Embodied learning by investing and speed of convergence," Journal of Macroeconomics, Elsevier, vol. 40(C), pages 245-269.
    10. Raouf Boucekkine & Blanca Martínez & J. Ramon Ruiz-Tamarit, 2018. "Optimal Population Growth as an Endogenous Discounting Problem: The Ramsey Case," Lecture Notes in Economics and Mathematical Systems, in: Gustav Feichtinger & Raimund M. Kovacevic & Gernot Tragler (ed.), Control Systems and Mathematical Methods in Economics, pages 321-347, Springer.
    11. Ryoji Hiraguchi, 2013. "On a closed-form solution to the stochastic Lucas–Uzawa model," Journal of Economics, Springer, vol. 108(2), pages 131-144, March.
    12. Mark Vancauteren & Daniel Weiserbs, 2011. "Intra-European Trade of Manufacturing Goods: An Extension of the Gravity Model," International Econometric Review (IER), Econometric Research Association, vol. 3(1), pages 1-24, April.
    13. Guerrini, Luca, 2010. "The Ramsey model with a bounded population growth rate," Journal of Macroeconomics, Elsevier, vol. 32(3), pages 872-878, September.
    14. Posch, Olaf, 2011. "Explaining output volatility: The case of taxation," Journal of Public Economics, Elsevier, vol. 95(11), pages 1589-1606.
    15. Hiraguchi, Ryoji, 2009. "A solution to the Lucas-Uzawa model with increasing returns to scale: Note," Economic Modelling, Elsevier, vol. 26(5), pages 831-834, September.
    16. Badibanga, Thaddee Mutumba, 2008. "Analyzing Growth and Welfare Effects of Public Policies in Models of Endogenous Growth with Human Capital: Evidence from South Africa," 2008 Annual Meeting, July 27-29, 2008, Orlando, Florida 6431, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    17. Ruiz-Tamarit, José Ramón, 2008. "The closed-form solution for a family of four-dimension nonlinear MHDS," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 1000-1014, March.
    18. Torre, Davide La & Marsiglio, Simone & Mendivil, Franklin & Privileggi, Fabio, 2019. "A stochastic economic growth model with health capital and state-dependent probabilities," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 81-93.
    19. Chilarescu, Constantin, 2008. "An analytical solutions for a model of endogenous growth," Economic Modelling, Elsevier, vol. 25(6), pages 1175-1182, November.
    20. Olaf Posch & Klaus Wälde, 2011. "On the link between volatility and growth," Journal of Economic Growth, Springer, vol. 16(4), pages 285-308, December.
    21. Raouf, BOUCEKKINE & Bity, DIENE & Theophile, AZOMAHOU, 2006. "The Growth economics of epidemics," Discussion Papers (ECON - Département des Sciences Economiques) 2006021, Université catholique de Louvain, Département des Sciences Economiques.
    22. Chilarescu, Constantin, 2009. "A closed-form solution to the transitional dynamics of the Lucas-Uzawa model," Economic Modelling, Elsevier, vol. 26(1), pages 135-138, January.
    23. Guerrini, Luca, 2010. "A closed-form solution to the Ramsey model with logistic population growth," Economic Modelling, Elsevier, vol. 27(5), pages 1178-1182, September.
    24. Raouf Boucekkine & Bity Diene & Theophile Azomahou, 2008. "Growth Economics of Epidemics: A Review of the Theory," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(1), pages 1-26.

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    More about this item

    Keywords

    Imbalance effects; Lucas model; Externality; Analytical solution;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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