On human capital and economic growth with random technology shocks
AbstractWe 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.
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Bibliographic InfoPaper provided by Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano in its series Departmental Working Papers with number 2008-36.
Date of creation: 05 Nov 2008
Date of revision:
Economic Growth; Physical and Human Capital Accumulation; Technology Shocks;
Find related papers by 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, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
- O33 - Economic Development, Technological Change, and Growth - - Technological Change; Research and Development; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-06-17 (All new papers)
- NEP-DEV-2009-06-17 (Development)
- NEP-DGE-2009-06-17 (Dynamic General Equilibrium)
- NEP-HRM-2009-06-17 (Human Capital & Human Resource Management)
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- 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.
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