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Indeterminacy and nonlinear dynamics in an OLG growth model with endogenous labour supply and inherited tastes

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  • Gori, Luca
  • Sodini, Mauro

Abstract

This study analyses the dynamics of a two-dimensional overlapping generations economy with endogenous labour supply à la Reichlin (1986) and aspirations, i.e. effective consumption by individuals of the current generation depends on the standard of living (based on consumption experience) of those that belong to the previous generation. We show that the relative importance of aspirations in utility is responsible for the existence of either one (normalised) steady state or two steady states. In particular, when the relative degree of aspiration is fairly high, the supply of labour becomes higher than those corresponding to the normalised steady state because individuals want to increase the amount of time spent at work when they are young in order to increase consumption possibilities when they are old, since the relative importance of past consumption is high in such a case. As regards local stability, the normalised steady state can be determinate or indeterminate and can undergo either a transcritical bifurcation or supercritical flip bifurcation depending on the intensity of the taste externality. Moreover, some interesting global dynamic properties emerge: indeed, when the relative importance of aspirations is strong enough, cyclical or quasi-cyclical behaviour and/or coexistence of attractors may occur. In particular, this last phenomena may cause global indeterminacy even if the stationary equilibria are locally determinate.

Suggested Citation

  • Gori, Luca & Sodini, Mauro, 2012. "Indeterminacy and nonlinear dynamics in an OLG growth model with endogenous labour supply and inherited tastes," MPRA Paper 35942, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:35942
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    1. Pintus, Patrick & Sands, Duncan & de Vilder, Robin, 2000. "On the transition from local regular to global irregular fluctuations," Journal of Economic Dynamics and Control, Elsevier, vol. 24(2), pages 247-272, February.
    2. Jaime Alonso-Carrera & Jordi Caballé & Xavier Raurich, 2007. "Aspirations, Habit Formation, and Bequest Motive," Economic Journal, Royal Economic Society, vol. 117(520), pages 813-836, April.
    3. Chen, Been-Lon & Hsu, Mei, 2007. "Admiration is a source of indeterminacy," Economics Letters, Elsevier, vol. 95(1), pages 96-103, April.
    4. William G. Gale & John Karl Scholz, 1994. "Intergenerational Transfers and the Accumulation of Wealth," Journal of Economic Perspectives, American Economic Association, vol. 8(4), pages 145-160, Fall.
    5. de la Croix, David, 2001. "Growth dynamics and education spending: The role of inherited tastes and abilities," European Economic Review, Elsevier, vol. 45(8), pages 1415-1438, August.
    6. Anna Agliari & George Vachadze, 2011. "Homoclinic and Heteroclinic Bifurcations in an Overlapping Generations Model with Credit Market Imperfection," Computational Economics, Springer;Society for Computational Economics, vol. 38(3), pages 241-260, October.
    7. Gardini, Laura & Hommes, Cars & Tramontana, Fabio & de Vilder, Robin, 2009. "Forward and backward dynamics in implicitly defined overlapping generations models," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 110-129, August.
    8. Alonso-Carrera, Jaime & Caballe, Jordi & Raurich, Xavier, 2005. "Growth, habit formation, and catching-up with the Joneses," European Economic Review, Elsevier, vol. 49(6), pages 1665-1691, August.
    9. Benhabib Jess & Farmer Roger E. A., 1994. "Indeterminacy and Increasing Returns," Journal of Economic Theory, Elsevier, vol. 63(1), pages 19-41, June.
    10. Masako Ikefuji & Kazuo Mino, 2009. "Internal vs. External Habit Formation in a Growing Economy with Overlapping Generations," ISER Discussion Paper 0750, Institute of Social and Economic Research, Osaka University.
    11. Hiraguchi, Ryoji, 2011. "A two sector endogenous growth model with habit formation," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 430-441, April.
    12. Been-Lon Chen, 2007. "Multiple BGPs in a Growth Model with Habit Persistence," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(1), pages 25-48, February.
    13. Stutzer, Alois, 2004. "The role of income aspirations in individual happiness," Journal of Economic Behavior & Organization, Elsevier, vol. 54(1), pages 89-109, May.
    14. Croix, David de la & Michel, Philippe, 1999. "Optimal growth when tastes are inherited," Journal of Economic Dynamics and Control, Elsevier, vol. 23(4), pages 519-537, February.
    15. Nourry, Carine, 2001. "Stability of equilibria in the overlapping generations model with endogenous labor supply," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1647-1663, October.
    16. de Vilder, Robin, 1996. "Complicated Endogenous Business Cycles under Gross Substitutability," Journal of Economic Theory, Elsevier, vol. 71(2), pages 416-442, November.
    17. Alonso-Carrera, Jaime & Caballé, Jordi & Raurich, Xavier, 2008. "Can consumption spillovers be a source of equilibrium indeterminacy?," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2883-2902, September.
    18. Jaime Alonso-Carrera & Jordi Caballé & Xavier Raurich, 2004. "Consumption Externalities, Habit Formation and Equilibrium Efficiency," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(2), pages 231-251, June.
    19. Cazzavillan, Guido & Lloyd-Braga, Teresa & Pintus, Patrick A., 1998. "Multiple Steady States and Endogenous Fluctuations with Increasing Returns to Scale in Production," Journal of Economic Theory, Elsevier, vol. 80(1), pages 60-107, May.
    20. Mark Weder, 2000. "Consumption Externalities, Production Externalities and Indeterminacy," Metroeconomica, Wiley Blackwell, vol. 51(4), pages 435-453, November.
    21. Lionel Artige & Carmen Camacho & David De La Croix, 2004. "Wealth Breeds Decline: Reversals of Leadership and Consumption Habits," Journal of Economic Growth, Springer, vol. 9(4), pages 423-449, December.
    22. Boldrin, Michele & Rustichini, Aldo, 1994. "Growth and Indeterminacy in Dynamic Models with Externalities," Econometrica, Econometric Society, vol. 62(2), pages 323-342, March.
    23. Kazuo Mino, 2008. "Growth And Bubbles With Consumption Externalities," The Japanese Economic Review, Japanese Economic Association, vol. 59(1), pages 33-53, March.
    24. Shankha Chakraborty & Mausumi Das, 2005. "Mortality, Human Capital and Persistent Inequality," Journal of Economic Growth, Springer, vol. 10(2), pages 159-192, June.
    25. Reichlin, Pietro, 1986. "Equilibrium cycles in an overlapping generations economy with production," Journal of Economic Theory, Elsevier, vol. 40(1), pages 89-102, October.
    26. de la Croix, David, 1996. "The dynamics of bequeathed tastes," Economics Letters, Elsevier, vol. 53(1), pages 89-96, October.
    27. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    28. Raquel Carrasco & José M. Labeaga & J. David López-Salido, 2005. "Consumption and Habits: Evidence from Panel Data," Economic Journal, Royal Economic Society, vol. 115(500), pages 144-165, January.
    29. Lahiri, Amartya & Puhakka, Mikko, 1998. "Habit Persistence in Overlapping Generations Economies under Pure Exchange," Journal of Economic Theory, Elsevier, vol. 78(1), pages 176-186, January.
    30. Cazzavillan, Guido, 2001. "Indeterminacy and Endogenous Fluctuations with Arbitrarily Small Externalities," Journal of Economic Theory, Elsevier, vol. 101(1), pages 133-157, November.
    31. David De La Croix & Jean-Pierre Urbain, 1998. "Intertemporal substitution in import demand and habit formation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(6), pages 589-612.
    32. McBride, Michael, 2001. "Relative-income effects on subjective well-being in the cross-section," Journal of Economic Behavior & Organization, Elsevier, vol. 45(3), pages 251-278, July.
    33. Grandmont, Jean-Michel & Pintus, Patrick & de Vilder, Robin, 1998. "Capital-Labor Substitution and Competitive Nonlinear Endogenous Business Cycles," Journal of Economic Theory, Elsevier, vol. 80(1), pages 14-59, May.
    34. Luca Gori & Mauro Sodini, 2011. "Nonlinear Dynamics in an OLG Growth Model with Young and Old Age Labour Supply: The Role of Public Health Expenditure," Computational Economics, Springer;Society for Computational Economics, vol. 38(3), pages 261-275, October.
    35. Hurd, Michael D, 1987. "Savings of the Elderly and Desired Bequests," American Economic Review, American Economic Association, vol. 77(3), pages 298-312, June.
    36. Ferson, Wayne E. & Constantinides, George M., 1991. "Habit persistence and durability in aggregate consumption: Empirical tests," Journal of Financial Economics, Elsevier, vol. 29(2), pages 199-240, October.
    37. Galor, Oded & Weil, David N, 1996. "The Gender Gap, Fertility, and Growth," American Economic Review, American Economic Association, vol. 86(3), pages 374-387, June.
    38. Wendner, Ronald, 2003. "Do habits raise consumption growth?," Research in Economics, Elsevier, vol. 57(2), pages 151-163, June.
    39. Douglas Gollin, 2002. "Getting Income Shares Right," Journal of Political Economy, University of Chicago Press, vol. 110(2), pages 458-474, April.
    40. Lawrence J. Christiano & Michele Boldrin & Jonas D. M. Fisher, 2001. "Habit Persistence, Asset Returns, and the Business Cycle," American Economic Review, American Economic Association, vol. 91(1), pages 149-166, March.
    41. Gali, Jordi, 1994. "Keeping Up with the Joneses: Consumption Externalities, Portfolio Choice, and Asset Prices," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 26(1), pages 1-8, February.
    42. Boldrin, Michele & Christiano, Lawrence J. & Fisher, Jonas D.M., 1997. "Habit Persistence And Asset Returns In An Exchange Economy," Macroeconomic Dynamics, Cambridge University Press, vol. 1(02), pages 312-332, June.
    43. Bunzel, Helle, 2006. "Habit persistence, money, and overlapping generations," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2425-2445, December.
    44. Carroll, Christopher D., 2000. "Solving consumption models with multiplicative habits," Economics Letters, Elsevier, vol. 68(1), pages 67-77, July.
    45. David De La Croix & Philippe Michel, 2001. "Altruism and Self-Restraint," Annals of Economics and Statistics, GENES, issue 63-64, pages 233-259.
    46. Geoffrey Hodgson, 2010. "Choice, habit and evolution," Journal of Evolutionary Economics, Springer, vol. 20(1), pages 1-18, January.
    47. repec:ebl:ecbull:v:4:y:2002:i:7:p:1-10 is not listed on IDEAS
    48. Farmer, Roger E. A., 1986. "Deficits and cycles," Journal of Economic Theory, Elsevier, vol. 40(1), pages 77-88, October.
    49. Ronald Wendner, 2002. "Capital Accumulation and Habit Formation," Economics Bulletin, AccessEcon, vol. 4(7), pages 1-10.
    50. repec:adr:anecst:y:2001:i:63-64:p:12 is not listed on IDEAS
    51. Antoci, Angelo & Sodini, Mauro, 2009. "Indeterminacy, bifurcations and chaos in an overlapping generations model with negative environmental externalities," MPRA Paper 13750, University Library of Munich, Germany.
    52. Yokoo, Masanori, 2000. "Chaotic dynamics in a two-dimensional overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 909-934, June.
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    More about this item

    Keywords

    Aspirations; Indeterminacy; Labour supply; OLG model; Nonlinear dynamics;

    JEL classification:

    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • J22 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Time Allocation and Labor Supply
    • 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

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