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Parameter identification, population and economic growth in an extended Lucas and Uzawa-type two sector model

Author

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  • Alberto BUCCI

    ()

  • Herb E. KUNZE

    ()

  • Davide LA TORRE

    ()

Abstract

The aim of this paper is twofold. First of all we re-examine the long-run relationship between population and economic growth. To do this we extend the Lucas-Uzawa model along two different directions: we introduce the growth of the physical capital stock into the human capital supply equation and include in the intertemporal maximization problem of the representative household a preference parameter controlling for the degree of agents’ altruism towards future generations. These two extensions allow us to capture eventual complementarity/substitutability links between physical and human capital in the production of new human capital and to study how such links, along with agents’ altruism, may impact on the interplay between economic and demographic growth along the balanced growth path equilibrium. In the second part of this paper we develop the inverse problem for this extended Lucas-Uzawa model. The method we are going to use is based on fractals and has been developed by two of the authors in recent papers. Through the solution of the inverse problem one can get the estimation of some key-parameters such as the total factor productivity, the productivity of human capital in the production of new skills, the physical capital share in total income, the inverse of the intertemporal elasticity of substitution in consumption, the depreciation rate of (physical and human) capital and the parameter controlling for the degree of altruism towards future generations.

Suggested Citation

  • Alberto BUCCI & Herb E. KUNZE & Davide LA TORRE, 2008. "Parameter identification, population and economic growth in an extended Lucas and Uzawa-type two sector model," Departmental Working Papers 2008-34, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
  • Handle: RePEc:mil:wpdepa:2008-34
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    File URL: http://wp.demm.unimi.it/files/wp/2008/DEMM-2008_034wp.pdf
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    References listed on IDEAS

    as
    1. Oded Galor & Omer Moav, 2002. "Natural Selection and the Origin of Economic Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 117(4), pages 1133-1191.
    2. Alberto Bucci & Davide Torre, 2009. "Population and economic growth with human and physical capital investments," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 56(1), pages 17-27, March.
    3. Laitner, John & Ohlsson, Henry, 2001. "Bequest motives: a comparison of Sweden and the United States," Journal of Public Economics, Elsevier, vol. 79(1), pages 205-236, January.
    4. 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.
    5. Miguel-Angel Martín & Agustín Herranz, 2004. "Human capital and economic growth in Spanish regions," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 10(4), pages 257-264, November.
    6. Herb E. KUNZE & Davide LA TORRE & Edward R. VRSCAY, 2008. "From iterated function systems to iterated multifunction systems," Departmental Working Papers 2008-39, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    7. 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.
    8. Christopher Laincz & Pietro Peretto, 2006. "Scale effects in endogenous growth theory: an error of aggregation not specification," Journal of Economic Growth, Springer, vol. 11(3), pages 263-288, September.
    9. Davide La Torre & Herb Kunze & Ed Vrscay, 2006. "Inverse problems for random differential equations using the collage method for random contraction mappings," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1036, Universitá degli Studi di Milano.
    10. repec:kap:iaecre:v:10:y:2004:i:4:p:257-264 is not listed on IDEAS
    11. Mino, Kazuo, 1996. "Analysis of a Two-Sector Model of Endogenous Growth with Capital Income Taxation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(1), pages 227-251, February.
    12. Herb E. KUNZE & Davide LA TORRE & Edward R. VRSCAY, 2007. "Solving inverse problems for random equations and applications," Departmental Working Papers 2007-44, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    13. Davide La Torre & Herb Kunze & Edward Vrscay, 2006. "Random fixed point equations and inverse problems by collage theorem," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1030, Universitá degli Studi di Milano.
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    More about this item

    Keywords

    Population Growth; Two-Sector Endogenous Growth Models; Human Capital Investment; Physical Capital Accumulation; Fractal-based Methods; Inverse Problems; Collage Theorem;

    JEL classification:

    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • J24 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Human Capital; Skills; Occupational Choice; Labor Productivity
    • J10 - Labor and Demographic Economics - - Demographic Economics - - - General

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