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On human capital and economic growth with random technology shocks

Author

Listed:
  • Alberto BUCCI
  • Cinzia COLAPINTO
  • Martin FORSTER
  • Davide LA TORRE

Abstract

We embed the Uzawa-Lucas human capital accumulation technology into the Mankiw-Romer-Weil exogenous growth model. The paper is divided into two parts. In the first part we assume that the rate of technological progress is exogenous and deterministic and study the local dynamics of the model around its steady-state equilibrium. The first order conditions lead to a system of four nonlinear differential equations. By reducing the dimension of the system to three, we find that the equilibrium is a saddle point. If the equations system is attacked in its original dimension, and by making use of an arbitrage condition, we prove that the equilibrium is unstable. In the second part of the paper technology is assumed to be subject to random shocks driven by a geometric Brownian motion. Using the Hamilton-Jacobi-Bellman equation, and through numerical simulations, we discuss the effects of technology shocks on the optimal policies of consumption and the allocation of human capital across sectors.

Suggested Citation

  • Alberto BUCCI & Cinzia COLAPINTO & Martin FORSTER & Davide LA TORRE, 2008. "On human capital and economic growth with random technology shocks," Departmental Working Papers 2008-36, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    • Handle: RePEc:mil:wpdepa:2008-36
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    File URL: http://wp.demm.unimi.it/files/wp/2008/DEMM-2008_036wp.pdf
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    References listed on IDEAS

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    5. Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), 2006. "Handbook on Optimal Growth 1," Springer Books, Springer, number 978-3-540-32310-5, April.
    6. Holger Strulik, 2005. "The Role of Human Capital and Population Growth in R&D‐based Models of Economic Growth," Review of International Economics, Wiley Blackwell, vol. 13(1), pages 129-145, February.
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    8. 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.
    9. Lars J. Olson & Santanu Roy, 2006. "Theory of Stochastic Optimal Economic Growth," Springer Books, in: Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), Handbook on Optimal Growth 1, chapter 11, pages 297-335, Springer.
    10. Arnold, Lutz G., 1998. "Growth, Welfare, and Trade in an Integrated Model of Human-Capital Accumulation and Research," Journal of Macroeconomics, Elsevier, vol. 20(1), pages 81-105, January.
    11. 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:

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    2. 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.
    3. Md. Azizul Baten & Anton Abdulbasah Kamil, 2013. "Optimal Consumption in a Stochastic Ramsey Model with Cobb-Douglas Production Function," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-8, March.

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    More about this item

    Keywords

    Economic Growth; Physical and Human Capital Accumulation; Technology Shocks;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • J24 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Human Capital; Skills; Occupational Choice; Labor Productivity
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • O33 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes

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