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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.

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File URL: http://www.ihs.ac.at/publications/eco/es-211.pdf
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Bibliographic Info

Paper provided by Institute for Advanced Studies in its series Economics Series with number 211.

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Length: 32 pages
Date of creation: May 2007
Date of revision:
Handle: RePEc:ihs:ihsesp:211

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Related research

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

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  1. Frank W. Agbola & Yvonne K. Saini & Maylene Y. Damoense,, 2004. "South Africa: Impact of HIV/AIDS on food demand," International Journal of Social Economics, Emerald Group Publishing, vol. 31(7), pages 721-731, July.
  2. Bell, Clive & Gersbach, Hans, 2009. "The macroeconomics of targeting: the case of an enduring epidemic," Journal of Health Economics, Elsevier, vol. 28(1), pages 54-72, January.
  3. 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.
  4. 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, Food and Agriculture Organization of the United Nations, vol. 2(2), pages 158-181.
  5. Brito, Paulo & Dilao, Rui, 2006. "Equilibrium price dynamics in an overlapping-generations exchange economy," MPRA Paper 699, University Library of Munich, Germany.
  6. David Canning, 2006. "The Economics of HIV/AIDS in Low-Income Countries: The Case for Prevention," Journal of Economic Perspectives, American Economic Association, vol. 20(3), pages 121-142, Summer.
  7. 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.
  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, 09.
  9. 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, 09.
  10. Jeff DeSimone & Edward J. Schumacher, 2004. "Compensating Wage Differentials and AIDS Risk," NBER Working Papers 10861, National Bureau of Economic Research, Inc.
  11. Robalino, David A. & Jenkins, Carol & El Maroufi, Karim, 2002. "Risks and macroeconomic impacts of HIV/AIDS in the Middle East and North Africa : why waiting to intervene can be costly," Policy Research Working Paper Series 2874, The World Bank.
  12. Lloyd, P J, 1991. "Aids: An Economic Approach to the Choice of Policies," The Economic Record, The Economic Society of Australia, vol. 67(197), pages 126-38, June.
  13. Simon Dixon & Scott McDonald & Jennifer Roberts, 2001. "HIV|AIDS and development in Africa," Journal of International Development, John Wiley & Sons, Ltd., vol. 13(4), pages 381-389.
  14. C Arndt & J D Lewis, 2000. "The Macro Implications of HIV/AIDS in South Africa: A Preliminary Assessment," South African Journal of Economics, Economic Society of South Africa, vol. 68(5), pages 380-392, December.
  15. 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.
  16. R Bonnel, 2000. "HIV/AIDS and Economic Growth: A Global Perspective," South African Journal of Economics, Economic Society of South Africa, vol. 68(5), pages 360-379, December.
  17. Emily Oster, 2005. "Sexually Transmitted Infections, Sexual Behavior, and the HIV/AIDS Epidemic," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 120(2), pages 467-515, May.
  18. Klaus Deininger & Anja Crommelynck & Gloria Kempaka, 2005. "Impact of AIDS on Family Composition, Welfare, and Investment: Evidence from Uganda ," Review of Development Economics, Wiley Blackwell, Wiley Blackwell, vol. 9(3), pages 303-324, 08.
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