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Welfare Analysis of HIV/AIDS: Formulating and Computing a Continuous Time Overlapping Generations Policy Model

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  • Shorish, Jamsheed

    (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria and Department of Economics, University of Illinois at Urbana-Champaign)

Abstract

We introduce a continuous time overlapping generations demographic model, in which a social planner seeks to generate an optimal policy for influencing the demographic change of the underlying population in a neoclassical growth model. The model has the notable feature that the underlying state space is a continuum, leading to a Hamilton-Jacobi-Bellman PDE system which is defined over a Hilbert space generated by the ages of the population cohorts. In this technical report the dynamic programming problem is presented and the numerical approximation using a finite difference approximation is derived. This analysis is part of a larger research program on welfare analysis and policy development for the HIV/AIDS global pandemic.

Suggested Citation

  • Shorish, Jamsheed, 2007. "Welfare Analysis of HIV/AIDS: Formulating and Computing a Continuous Time Overlapping Generations Policy Model," Economics Series 211, Institute for Advanced Studies.
  • Handle: RePEc:ihs:ihsesp:211
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    File URL: http://www.ihs.ac.at/publications/eco/es-211.pdf
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    References listed on IDEAS

    as
    1. McDonald, Scott & Roberts, Jennifer, 2006. "AIDS and economic growth: A human capital approach," Journal of Development Economics, Elsevier, vol. 80(1), pages 228-250, June.
    2. Silvia Faggian & Fausto Gozzi, 2004. "On The Dynamic Programming Approach For Optimal Control Problems Of Pde'S With Age Structure," Mathematical Population Studies, Taylor & Francis Journals, vol. 11(3-4), pages 233-270.
    3. T. S. Jayne & Marcela Villarreal & Prabhu Pingali & Günter Hemrich, 2005. "HIV/AIDS and the Agricultural Sector: Implications for Policy in Eastern and Southern Africa," The Electronic Journal of Agricultural and Development Economics, Food and Agriculture Organization of the United Nations, vol. 2(2), pages 158-181.
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    5. Stephen Dike, 2002. "Research on the Economic Impact of HIV/AIDS in South Africa:Review of Methodology and Lessons Learned," South African Journal of Economics, Economic Society of South Africa, vol. 70(7), pages 606-609, September.
    6. Lilani Kumaranayake & Charlotte Watts, 2001. "Resource allocation and priority setting of HIV|AIDS interventions: addressing the generalized epidemic in sub-Saharan Africa," Journal of International Development, John Wiley & Sons, Ltd., vol. 13(4), pages 451-466.
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    8. Céecile Ambert, 2002. "The Economic Impact of HIV/AIDS on the Construction Sector: Supply Side Implications for Housing Policy," South African Journal of Economics, Economic Society of South Africa, vol. 70(7), pages 584-596, September.
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    More about this item

    Keywords

    Optimal control; continuous time overlapping generations; Hamilton-Jacobi-Bellman PDE; finite difference approximation; HIV/AIDS; demographic modeling;

    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
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

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