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A CLOSED-FORM SOLUTION FOR THE HEALTH CAPITAL MODEL*

Published online by Cambridge University Press:  09 September 2015

Holger Strulik
Holger Strulik*
Affiliation:
University of Goettingen, Goettingen, Germany
*
Email: [email protected]
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Abstract:

This paper provides a closed-form solution for the health capital model of health demand. The results are exploited in order to prove analytically the comparative dynamics of the model. Results are derived for the so-called pure investment model, the pure consumption model and a combination of both types of models. Given the plausible assumptions that (i) health declines with age and that (ii) the health capital stock at death is lower than the health capital stock needed for eternal life, it is shown that the optimal solution implies eternal life.

Keywords

LongevityAgingHealthHealth Care DemandD10D90I20
Type
Short Papers
Information
Journal of Demographic Economics , Volume 81 , Issue 3 , September 2015 , pp. 301 - 316
Copyright
Copyright © Université catholique de Louvain 2015 

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Footnotes

*

I would like to thank Carl-Johan Dalgaard, Gustav Feichtinger, Volker Grossmann, Ben Heijdra, Volker Meier, Johannes Schuenemann, Timo Trimborn, and four anonymous referees for helpful comments.

References

REFERENCES

Acemoglu, Daron (2009) Introduction to Modern Economic Growth. Princeton, NJ: Princeton University Press.Google Scholar
Arking, Robert (2006) The Biology of Aging: Observations and Principles. Oxford: Oxford University Press.Google Scholar
Case, Anne and Deaton, Angus S. (2005) Broken down by work and sex: how our health declines. In Wise, D. A. (ed.), Analyses in the Economics of Aging, pp. 185–212. Chicago: University of Chicago Press.Google Scholar
Cropper, Maureen L. (1977) Health, investment in health, and occupational choice. Journal of Political Economy 85, 1273–1294.Google Scholar
Dalgaard, Carl-Johan and Strulik, Holger (2014) Optimal aging and death: understanding the Preston curve. Journal of the European Economic Association 12, 672–701.CrossRefGoogle Scholar
Dalgaard, Carl-Johan and Strulik, Holger (2015) The economics of health demand and human aging: health capital vs. health deficits. Discussion Paper, University of Goettingen.Google Scholar
Ehrlich, Isaac and Chuma, Hiroyuki (1990) A model of the demand for longevity and the value of life extension. Journal of Political Economy 98, 761–82.Google Scholar
Eisenring, Christoph (1999) Comparative dynamics in a health investment model. Journal of Health Economics 18, 655–660.Google Scholar
Forster, Martin (2001) The meaning of death: some simulations of a model of healthy and unhealthy consumption. Journal of Health Economics 20, 613–638.Google Scholar
Friedman, Milton (1953) Essays in Positive Economics. University of Chicago Press, Chicago.Google Scholar
Galama, Titus and Kapteyn, Arie (2011) Grossman’s missing health threshold. Journal of Health Economics 30, 1044–1056.CrossRefGoogle ScholarPubMed
Galama, Titus, Hullegie, Patrick, Meijer, Eric and Outcault, Sarah (2012) Is there empirical evidence for decreasing returns to scale in a health capital model? Health Economics 21, 1080–1100.Google Scholar
Gavrilov, Leonid A. and Gavrilova, Natalia S. (1991) The Biology of Human Life Span: A Quantitative Approach. London: Harwood Academic Publishers.Google Scholar
Grossman, Michael (1972) On the concept of health capital and the demand for health. Journal of Political Economy 80, 223–255.Google Scholar
Grossman, Michael (1998) On optimal length of life. Journal of Health Economics 17, 499–509.Google Scholar
Grossman, Michael (2000) The human capital model. In Culyer, Anthony J. and Newhouse, Joseph P. (eds.) Handbook of Health Economics, vol. 1, pp. 347–408. Amsterdam: Elsevier.Google Scholar
Hall, Robert E. and Jones, Charles I. (2007) The value of life and the rise in health spending. Quarterly Journal of Economics 122, 39–72.Google Scholar
Havranek, Tomas, Horvath, Roman, Irsova, Zuzana and Rusnak, Marek (2013) Cross-country heterogeneity in intertemporal substitution. IES Working Paper No. 11/2013, Institute of Economic Studies, Charles University in Prague.Google Scholar
Jacobson, Lena (2000) The family as producer of health – an extended Grossman model. Journal of Health Economics 19, 611–637.Google Scholar
Jacquard, Albert (1982) Heritability of human longevity. In: Preston, Samuel H. (ed.) Biological and Social Aspects of Mortality and the Length of Life, pp. 303–313. Liege: Ordina Editions.Google Scholar
Kuhn, Michael, Wrzaczek, Stefan, Prskawetz, Alexia and Feichtinger, Gustav (2012) Optimal choice of health and retirement in a life-cycle model. Working Papers in Economic Theory and Policy No. 01/2012, Vienna University of Technology.Google Scholar
Laporte, Audrey and Ferguson, Brian S. (2007) Investment in health when health is stochastic. Journal of Population Economics 20, 423–444.Google Scholar
McFadden, Daniel (2008) Human capital accumulation and depreciation. Applied Economic Perspectives and Policy 30, 379–385.Google Scholar
Meier, Volker (2000) On the demand for preventive care. OR-Spektrum 22, 381–402.Google Scholar
Mitnitski, Arnold B., Bao, Le and Rockwood, Kenneth (2006) Going from bad to worse: a stochastic model of transitions in deficit accumulation, in relation to mortality. Mechanisms of Ageing and Development 127, 490–493.Google Scholar
Mitnitski, Arnold B., Mogilner, Alexander J., MacKnight, Chris and Rockwood, Kenneth (2002a) The accumulation of deficits with age and possible invariants of aging. Scientific World 2, 1816–1822.Google Scholar
Mitnitski, Arnold B., Mogilner, Alexander J., MacKnight, Chris and Rockwood, Kenneth (2002b) The mortality rate as a function of accumulated deficits in a frailty index. Mechanisms of Ageing and Development 123, 1457–1460.Google Scholar
Mitnitski, Arnold, Song, Xiaowei, Skoog, Ingmar, Broe, G. A., Cox, Jafna L., Grunfeld, Eva and Rockwood, Kenneth (2005) Relative fitness and frailty of elderly men and women in developed countries and their relationship with mortality. Journal of the American Geriatrics Society 53, 2184–2189.Google Scholar
Muurinen, Jaana-Marja (1982) Demand for health: a generalised Grossman model. Journal of Health Economics 1, 5–28.Google Scholar
Oniki, Hajime (1973) Comparative dynamics (sensitivity analysis) in optimal control theory. Journal of Economic Theory 6, 265–283.Google Scholar
Ried, Walter (1998) Comparative dynamic analysis of the Grossman model. Journal of Health Economics 17, 383–425.Google Scholar
Strulik, Holger (2014) A closed-form Solution for the Health Capital Model. Cege Discussion Paper 222, University of Goettingen.Google Scholar
van Kippersluis, Hans and Galama, Titus J. (2014) Wealth and health behavior: Testing the concept of a health cost. European Economic Review 72, 197–220.Google Scholar
Wagstaff, Adam (1986) The demand for health: some new empirical evidence. Journal of Health Economics 5, 195–233.Google Scholar