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Admissible utility functions for health, longevity, and wealth: integrating monetary and life-year measures

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Abstract

The value of reducing health and mortality risks is often measured using value per statistical life (VSL) or one of several life-year measures (e.g., life years, quality-adjusted life years, disability-adjusted life years). I derive the utility function that is admissible when preferences for health and longevity, conditional on wealth, are consistent with any life-year measure (LYM) and examine the implications for marginal willingness to pay (WTP) for increases in health, longevity, and current-period survival probability. I conclude that marginal WTP for any LYM is decreasing and that VSL is increasing in the LYM. These results imply that cost-effectiveness analysis using a fixed monetary value per LYM is not consistent with economic welfare theory and that the benefit of a health improvement cannot be calculated by multiplying the change in a LYM by a constant.

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Notes

  1. Constant exponential discounting is most common, but other discounting functions can be incorporated by replacing δ τ with δ τ (Harvey 1994).

  2. Murphy and Topel (2006) define V(·) as a function of both consumption and leisure.

  3. The Yaari model is obtained as a special case of equation (1.4) by setting \( \upsilon \left(\tau \right)=\frac{1-\delta }{\delta } \), which is the discount rate in model (1.2).

  4. For values of w sufficiently small, it is possible that utility is decreasing in t. Assumption (1.10a) may be interpreted as excluding values of w for which life is worse than death.

  5. That is, V(x) = x (1–r)/(1 – r), r ≠ 1; V(x) = ln(x), r = 1, where r is the measure of relative risk aversion (Pratt 1964).

  6. That is, V(x) = (1/r) (1 – e -rx) where r is the discount rate and also the Arrow-Pratt measure of absolute risk aversion (Pratt 1964).

  7. Using model (1.2) to estimate WTP per QALY, Bleichrodt and Quiggin (1999) assume that individuals allocate medical and other spending to obtain constant health and consumption over their lifetimes. The assumption that health can be made constant over the lifecycle through allocation of spending seems implausible given that health deteriorates with age and not all impairments can be eliminated by treatment.

  8. Empirically, risk aversion may decrease with health and life expectancy because these factors increase expected lifetime wealth (Hammitt et al. 2009). In contrast, equation (3.3) holds wealth fixed.

  9. One reason that VSL increases with age over younger ages is that income rises over these ages and individuals cannot borrow against future increases. Hence VSL and current consumption are correlated over the lifecycle (Kniesner et al. 2006). In contrast, equation (5.2) is conditioned on fixed wealth.

  10. The effect of financial risk aversion on VSL is also ambiguous (Eeckhoudt and Hammitt 2004).

References

  • Adler, M. (2006). QALYs and policy evaluation: A new perspective. Yale Journal of Health Policy, Law, and Ethics, 6, 1–92.

    Google Scholar 

  • Aldy, J. E., & Viscusi, W. K. (2007). Age differences in the value of statistical life: Revealed preference evidence. Review of Environmental Economics and Policy, 1, 241–260.

    Article  Google Scholar 

  • Aldy, J. E., & Viscusi, W. K. (2008). Adjusting the value of a statistical life for age and cohort effects. Review of Economics and Statistics, 90, 573–581.

    Article  Google Scholar 

  • Aumann, R. J., & Kurz, M. (1977). Power and taxes. Econometrica, 45, 1137–1161.

    Article  Google Scholar 

  • Barksy, R. B., Juster, F. T., Kimball, M. S., & Shapiro, M. D. (1997). Preference parameters and behavioral heterogeneity: An experimental approach in the Health and Retirement Study. Quarterly Journal of Economics, 112, 537–580.

    Article  Google Scholar 

  • Bleichrodt, H., & Quiggin, J. (1999). Life-cycle preferences over consumption and health: When is cost-effectiveness analysis equivalent to cost-benefit analysis? Journal of Health Economics, 18, 681–708.

    Article  Google Scholar 

  • Bleichrodt, H., Wakker, P., & Johannesson, M. (1997). Characterizing QALYs by risk neutrality. Journal of Risk and Uncertainty, 15, 107–114.

    Article  Google Scholar 

  • Bommier, A., & Villeneuve, B. (2012). Risk aversion and the value of risk to life. Journal of Risk and Insurance, 79, 77–103.

    Article  Google Scholar 

  • Cutler, D.M., & Richardson, E. (1997). Measuring the health of the U.S. population. Brookings Papers Microeconomics, 217–271.

  • Dolan, P., & Edlin, R. (2002). Is it really possible to build a bridge between cost-benefit analysis and cost-effectiveness analysis? Journal of Health Economics, 21, 827–843.

    Google Scholar 

  • Domeij, D., & Johannesson, M. (2006). Consumption and health. Contributions to Macroeconomics 6(1), Article 6.

    Google Scholar 

  • Drèze, J. (1962). L’utilité sociale d’une vie humaine. Revue Française de Recherche Opèrationelle, 6, 93–118.

    Google Scholar 

  • Eeckhoudt, L. R., & Hammitt, J. K. (2004). Does risk aversion increase the value of mortality risk? Journal of Environmental Economics and Management, 47, 13–29.

    Article  Google Scholar 

  • Eeckhoudt, L. R., Godfroid, P. H., & Marchand, M. (1998). Risque de santé, médicine préventive, et médicine curative. Revue d’Économie Politique, 108, 321–337.

    Google Scholar 

  • Evans, W. N., & Viscusi, W. K. (1991). Estimation of state-dependent utility functions using survey data. Review of Economics and Statistics, 73, 94–104.

    Article  Google Scholar 

  • Finkelstein, A., Luttmer, E. F. P., & Notowidigdo, M. J. (2013). What good is wealth without health? The effect of health on the marginal utility of consumption. Journal of the European Economic Association, 11(S1), 221–258.

    Article  Google Scholar 

  • Foncel, J., & Treich, N. (2005). Fear of ruin. Journal of Risk and Uncertainty, 31, 289–300.

    Article  Google Scholar 

  • French, M. T., & Mauskopf, J. A. (1992). A quality-of-life method for estimating the value of avoided morbidity. American Journal of Public Health, 82, 1533–1555.

    Article  Google Scholar 

  • Garber, A. M., & Phelps, C. E. (1997). Economic foundations of cost-effectiveness analysis. Journal of Health Economics, 16, 1–31.

    Article  Google Scholar 

  • Gold, M. R., Siegel, J. E., Russell, L. B., & Weinstein, M. C. (1996). Cost-effectiveness in health and medicine. Oxford: Oxford University Press.

    Google Scholar 

  • Grossman, M. (1972). On the concept of health capital and the demand for health. Journal of Political Economy, 80, 223–255.

    Article  Google Scholar 

  • Hammitt, J. K. (2002). QALYs versus WTP. Risk Analysis, 22, 985–1001.

    Article  Google Scholar 

  • Hammitt, J. K., Haninger, K., & Treich, N. (2009). Effects of health and longevity on financial risk tolerance. Geneva Risk and Insurance Review, 34, 117–139.

    Article  Google Scholar 

  • Haninger, K., & Hammitt, J. K. (2011). Diminishing willingness to pay per quality-adjusted life year: Valuing acute foodborne illness. Risk Analysis, 31, 1363–1380.

    Article  Google Scholar 

  • Harvey, C. M. (1994). The reasonableness of non-constant discounting. Journal of Public Economics, 53, 31–51.

    Article  Google Scholar 

  • Hirth, R. A., Chernew, M. E., Miller, E., Fendrick, A. M., & Weissert, W. G. (2000). Willingness to pay for a quality-adjusted life year: In search of a standard. Medical Decision Making, 20, 332–342.

    Article  Google Scholar 

  • Johannesson, M. (1995). The relationship between cost-effectiveness analysis and cost-benefit analysis. Social Science and Medicine, 41, 483–489.

    Article  Google Scholar 

  • Johnson, F. R., Fries, E. E., & Banzhaf, H. S. (1997). Valuing morbidity: An integration of the willingness-to-pay and health-status index literatures. Journal of Health Economics, 16, 641–665.

    Article  Google Scholar 

  • Jones-Lee, M. W. (1974). The value of changes in the probability of death or injury. Journal of Political Economy, 82, 835–849.

    Article  Google Scholar 

  • Keeney, R., & Raiffa, H. (1993). Decisions with multiple objectives: Preferences and value tradeoffs. Reprint, Cambridge: Cambridge University Press.

    Google Scholar 

  • Kniesner, T., Viscusi, W. K., & Ziliak, J. (2006). Life-cycle consumption and the age-adjusted value of life. Contributions to Economic Analysis & Policy, 5(1), 1–34. Article 4.

    Google Scholar 

  • Krupnick, A. (2007). Mortality-risk valuation and age: Stated-preference evidence. Review of Environmental Economics and Policy, 1, 261–282.

    Article  Google Scholar 

  • Krupnick, A., Alberini, A., Cropper, M., Simon, N., O’Brien, B., Goeree, R., & Heintzelman, M. (2002). Age, health, and the willingness to pay for mortality risk reductions: A contingent valuation survey of Ontario residents. Journal of Risk and Uncertainty, 24, 161–186.

    Article  Google Scholar 

  • Mehrez, A., & Gafni, A. (1989). Quality adjusted life years, utility theory, and healthy years equivalents. Medical Decision Making, 9, 142–149.

    Article  Google Scholar 

  • Meltzer, D. (1997). Accounting for future costs in medical cost-effectiveness analysis. Journal of Health Economics, 16, 33–64.

    Article  Google Scholar 

  • Miyamoto, J. M., & Eraker, S. A. (1985). Parameter estimates for a QALY utility model. Medical Decision Making, 5, 191–213.

    Article  Google Scholar 

  • Miyamoto, J. M., Wakker, P. P., Bleichrodt, H., & Peters, H. J. M. (1998). The zero-condition: A simplifying assumption in QALY measurement and multiattribute utility. Management Science, 44, 839–849.

    Article  Google Scholar 

  • Moore, M. J., & Viscusi, W. K. (1988). The quantity-adjusted value of life. Economic Inquiry, 26, 369–388.

    Article  Google Scholar 

  • Murphy, K. M., & Topel, R. H. (2006). The value of health and longevity. Journal of Political Economy, 114, 871–904.

    Article  Google Scholar 

  • Murray, C. J. L. (1994). Quantifying the burden of disease: The technical basis for disability-adjusted life years. Bulletin of the World Health Organization, 72, 429–445.

    Google Scholar 

  • Ng, Y.-K. (1992). The older the more valuable: Divergence between utility and dollar values of life as one ages. Journal of Economics, 55, 1–16.

    Article  Google Scholar 

  • Pinto-Prades, J. L., Loomes, G., & Brey, R. (2009). Trying to estimate a monetary value for the QALY. Journal of Health Economics, 28, 553–562.

    Article  Google Scholar 

  • Pliskin, J. S., Shepard, D. S., & Weinstein, M. C. (1980). Utility functions for life years and health status. Operations Research, 28, 206–224.

    Article  Google Scholar 

  • Pratt, J. W. (1964). Risk aversion in the small and in the large. Econometrica, 32, 122–136.

    Article  Google Scholar 

  • Rey, B., & Rochet, J.-C. (2004). Health and wealth: How do they affect individual preferences? Geneva Papers on Risk and Insurance Theory, 29, 43–54.

    Article  Google Scholar 

  • Robinson, L. A. (2007). How U.S. government agencies value mortality risk reductions. Review of Environmental Economics and Policy, 1, 283–299.

    Article  Google Scholar 

  • Rosen, S. (1988). The value of changes in life expectancy. Journal of Risk and Uncertainty, 1, 285–304.

    Article  Google Scholar 

  • Shepard, D. S., & Zeckhauser, R. J. (1984). Survival versus consumption. Management Science, 30, 423–439.

    Article  Google Scholar 

  • Sloan, F. A., Viscusi, W. K., Chesson, H. W., Conover, C. J., & Whetten-Goldstein, K. (1998). Alternative approaches to valuing intangible health losses: The evidence for multiple sclerosis. Journal of Health Economics, 17, 475–97.

    Article  Google Scholar 

  • Smith, V. K., Evans, M. F., Kim, H., & Taylor, Jr., D. H. (2004). Do the near-elderly value mortality risks differently? Review of Economics and Statistics, 86, 423–429.

    Google Scholar 

  • Tolley, G., Kenkel, D., & Fabian, R. (Eds.). (1994). Valuing health for policy: An economic approach. Chicago: University of Chicago Press.

    Google Scholar 

  • Van Houtven, G., Powers, J., Jessup, A., & Yang, J.-C. (2006). Valuing avoided morbidity using meta-regression analysis: What can health status measures and QALYs tell us about willingness-to-pay? Health Economics, 15, 775–795.

    Article  Google Scholar 

  • Viscusi, W. K., & Evans, W. N. (1990). Utility functions that depend on health status: Estimates and economic implications. American Economic Review, 80, 353–374.

    Google Scholar 

  • Weinstein, M. C., Shepard, D. S., & Pliskin, J. S. (1980). The economic value of changing mortality probabilities: A decision-theoretic approach. Quarterly Journal of Economics, 94, 373–396.

    Article  Google Scholar 

  • Yaari, M. E. (1965). Uncertain lifetime, life insurance, and the theory of the consumer. Review of Economic Studies, 32, 137–150.

    Article  Google Scholar 

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Acknowledgment

Financial support was provided by INRA (the French national institute for agricultural research) and the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013) grant agreement no. 230589. I thank the editor and two anonymous referees for helpful comments.

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  1. Harvard University (Center for Risk Analysis), 718 Huntington Ave., Boston, MA, 02115, USA

    James K. Hammitt

  2. Toulouse School of Economics (LERNA-INRA), 21 allée de Brienne, 31000, Toulouse, France

    James K. Hammitt

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Hammitt, J.K. Admissible utility functions for health, longevity, and wealth: integrating monetary and life-year measures. J Risk Uncertain 47, 311–325 (2013). https://doi.org/10.1007/s11166-013-9178-4

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