Advertisement

Journal of Population Economics

, Volume 26, Issue 4, pp 1485–1522 | Cite as

The cost of uncertain life span

  • Ryan D. Edwards
Original Paper

Abstract

Much uncertainty surrounds the length of human life. The standard deviation in adult life span is about 15 years in the USA, and theory and evidence suggest that it is costly. I calibrate a utility-theoretic model that shows that 1 year in standard deviation is worth about half a life year. Differences in variance exacerbate health inequalities between and among rich and poor countries. Accounting for the cost of life-span variance appears to amplify recently discovered patterns of convergence in world average human well-being because the component of variance due to infant mortality has exhibited even more convergence than life expectancy.

Keywords

Health inequality Population health Convergence 

JEL Classification

I10 J17 O11 

Notes

Acknowledgements

I thank Deborah Balk, Neil Bennett, David Canning, Victor Fuchs, Ronald Lee, Shripad Tuljapurkar, David Weil, seminar participants at Queens College, CUNY, and at the Harvard Initiative for Global Health, and several anonymous referees for helpful comments.

References

  1. Aldy JE, Viscusi WK (2003) Age variations in workers’ value of statistical life. NBER Work Pap 10199Google Scholar
  2. Aldy JE, Viscusi WK (2008) Adjusting the value of a statistical life for age and cohort effects. Rev Econ Stat 90(3):573–581CrossRefGoogle Scholar
  3. Atkinson AB (1970) On the measurement of inequality. J Econ Theory 2(3):244–263CrossRefGoogle Scholar
  4. Banks J, Blundell R, Tanner S (1998) Is there a retirement savings puzzle? Am Econ Rev 88:769–788Google Scholar
  5. Barsky RB, Juster FT, Kimball MS, Shapiro MD (1997) Preference parameters and behavioral heterogeneity: an experimental approach in the health and retirement study. Q J Econ 112:537–579CrossRefGoogle Scholar
  6. Becker GS, Mulligan CB (1997) The endogenous determination of time preference. Q J Econ 112(3):729–758CrossRefGoogle Scholar
  7. Becker GS, Philipson TJ, Soares RR (2003) The quantity and quality of life and the evolution of world inequality. NBER Work Pap 9765Google Scholar
  8. Becker GS, Philipson TJ, Soares RR (2005) The quantity and quality of life and the evolution of world inequality. Am Econ Rev 95(1):277–291CrossRefGoogle Scholar
  9. Bell FC, Miller ML (2005) Life tables for the United States Social Security Area, 1900–2100, actuarial study no. 120, Office of the Chief Actuary, Social Security AdministrationGoogle Scholar
  10. Bernheim BD, Shleifer A, Summers LH (1985) The strategic bequest motive. J Polit Econ 93(6):1045–1076CrossRefGoogle Scholar
  11. Bishai DM (2004) Does time preference change with age? J Popul Econ 17(4):583–602CrossRefGoogle Scholar
  12. Bleichrodt H, Johannesson M (1997) The validity of QALYs: an experimental test of constant proportional tradeoff and utility independence. Med Decis Mak 17(1):21–32CrossRefGoogle Scholar
  13. Bleichrodt H, Quiggin J (1999) Life-cycle preferences over consumption and health: when is cost-effectiveness analysis equivalent to cost–benefit analysis? J Health Econ 18(6):681–708CrossRefGoogle Scholar
  14. Bommier A (2006) Uncertain lifetime and intertemporal choice: risk aversion as a rationale for time discounting. Int Econ Rev 47(4):1223–1246CrossRefGoogle Scholar
  15. Bommier A (2008) Rational impatience? Working paper, http://hal.archives-ouvertes.fr/hal-00441880/en/
  16. Bommier A, Villeneuve B (2011) Risk aversion and the value of risk to life. J Risk Insur. http://onlinelibrary.wiley.com/doi/10.1111/j.1539-6975.2010.01390.x/abstract
  17. Campbell JY, Viceira LM (2002) Strategic asset allocation: portfolio choice for long-term investors. Oxford University Press, OxfordCrossRefGoogle Scholar
  18. Chang FR (1991) Uncertain lifetimes, retirement and economic welfare. Economica 58(230):215–232CrossRefGoogle Scholar
  19. Costa DL (1998) The evolution of retirement: an American economic history. University of Chicago Press, Chicago, pp 1880–1990CrossRefGoogle Scholar
  20. Costa DL, Kahn ME (2004) Changes in the value of life, 1940–1980. J Risk Uncertain 29(2):159–180CrossRefGoogle Scholar
  21. Cutler D, Deaton A, Lleras-Muney A (2006) The determinants of mortality. J Econ Perspect 20(3):97–120CrossRefGoogle Scholar
  22. Cutler DM, Richardson E (1997) Measuring the health of the U.S. population. Brookings papers on economic activity. Microeconomics 97:217–271Google Scholar
  23. Deaton A (2004) Health in an age of globalization. In: Collins SM (ed) Brookings trade forum 2004: globalization, poverty, and inequality. University of Chicago Press, Chicago, pp 83–110Google Scholar
  24. Dynan KE, Skinner J, Zeldes SP (2004) Do the rich save more?. J Polit Econ 112(2):397–444CrossRefGoogle Scholar
  25. Edwards RD (2009) The cost of cyclical mortality. BE J Macroecon 9(1):Contributions, Article 7Google Scholar
  26. Edwards RD (2011) Changes in world inequality in length of life: 1970–2000. Popul Dev Rev 37(3):499–528CrossRefGoogle Scholar
  27. Edwards RD, Tuljapurkar S (2005) Inequality in life spans and a new perspective on mortality convergence across industrialized countries. Popul Dev Rev 31(4):645–675CrossRefGoogle Scholar
  28. Ehrlich I (2000) Uncertain lifetime, life protection, and the value of life saving. J Health Econ 19:341–367CrossRefGoogle Scholar
  29. Epstein LG, Zin SE (1989) Substitution, risk aversion, and the temporal behavior of consumption growth and asset returns I: a theoretical framework. Econometrica 57(4):937–969CrossRefGoogle Scholar
  30. Epstein LG, Zin SE (1991) Substitution, risk aversion, and the temporal behavior of consumption and asset returns: an empirical analysis. J Polit Econ 99(2):263–286CrossRefGoogle Scholar
  31. Finch CE, Crimmins EM (2004) Inflammatory exposure and historical changes in human life-spans. Science 305(5691):1736–1739CrossRefGoogle Scholar
  32. Fuchs VR (1982) Time preference and health: An exploratory study. In: Fuchs VR (ed) Economic aspects of health. University of Chicago Press, Chicago, chapter 3Google Scholar
  33. Fuchs VR, Ersner-Hershfield H (2008) Inequality in length of life. SIEPR Policy Brief October 1Google Scholar
  34. Hall RE, Jones CI (2004) The value of life and the rise in health spending. NBER Work Pap 10737Google Scholar
  35. Hall RE, Jones CI (2007) The value of life and the rise in health spending. Q J Econ 122(1):39–72CrossRefGoogle Scholar
  36. Hubbard RG, Judd KL (1987) Social security and individual welfare: precautionary saving, borrowing constraints, and the payroll tax. Am Econ Rev 77(4):630–646Google Scholar
  37. Hubbard RG, Skinner J, Zeldes SP (1994) The importance of precautionary motives in explaining individual and aggregate saving. Carnegie-Rochester Conf Ser Public Policy 40:59–125CrossRefGoogle Scholar
  38. Human Mortality Database (2009) University of California, Berkeley (USA) and Max Planck Institute for Demographic Research (Germany). Available at www.mortality.org.
  39. Hurd MD (1987) Savings of the elderly and desired bequests. Am Econ Rev 77(3):298–312Google Scholar
  40. Hurd MD (1989) Mortality risks and bequests. Econometrica 57(4):779–813CrossRefGoogle Scholar
  41. Hurd MD, Smith JP, Zissimopoulos J (2004) The effects of subjective survival on retirement and social security claiming. J Appl Econ 19(6):761–775CrossRefGoogle Scholar
  42. Ibbotson Associates (2002) Stocks, bonds, bills, and inflation yearbook. Ibbotson Associates, ChicagoGoogle Scholar
  43. Johansson PO (2002) On the definition and age-dependency of the value of a statistical life. J Risk Uncertain 25(3):251–263CrossRefGoogle Scholar
  44. Jones CI, Klenow PJ (2010) Beyond GDP? Welfare across countries and time. NBER Work Pap 16352Google Scholar
  45. Judge K, Mulligan J, Benzeval M (1998) Income inequality and population health. Soc Sci Med 46(4–5):567–579CrossRefGoogle Scholar
  46. Kalemli-Ozcan S, Weil DN (2010) Mortality change, the uncertainty effect, and retirement. J Econ Growth 15(1):65–91CrossRefGoogle Scholar
  47. Kalemli-Ozcan S, Ryder HE, Weil DN (2000) Mortality decline, human capital investment, and economic growth. J Dev Econ 62(1):1–23CrossRefGoogle Scholar
  48. Kelley AS (2011) Treatment intensity at end of life—time to act on the evidence. Lancet 378(9800):1364–1365CrossRefGoogle Scholar
  49. Kitagawa EM, Hauser PM (1973) Differential mortality in the united states: a study in socioeconomic epidemiology. Harvard University Press, CambridgeGoogle Scholar
  50. Kopczuk W, Lupton JP (2007) To leave or not to leave: the distribution of bequest motives. Rev Econ Stud 74(1):207–235CrossRefGoogle Scholar
  51. Kreps DM, Porteus EL (1978) Temporal resolution of uncertainty and dynamic choice theory. Econometrica 46(1):185–200CrossRefGoogle Scholar
  52. Kwok AC, Semel ME, Lipsitz SR, Bader AM, Barnato AE, Gawande AA, Jha AK (2011) The intensity and variation of surgical care at the end of life: a retrospective cohort study. Lancet 378(9800):1408–1413CrossRefGoogle Scholar
  53. Lee RD (2003) The demographic transition: three centuries of fundamental change. J Econ Perspect 17(4):167–190CrossRefGoogle Scholar
  54. Lee RD, Carter LR (1992) Modeling and forecasting U.S. mortality. J Am Stat Assoc 87(419):659–671Google Scholar
  55. Li Q, Tuljapurkar S (2004) Life, death, and the economy: mortality change in overlapping-generations models. Michigan Retirement Research Center Working Paper WP 2004-072Google Scholar
  56. Lichtenberg FR (2007) The impact of new drugs on us longevity and medical expenditure, 1990–2003: evidence from longitudinal, disease-level data. Am Econ Rev 97(2):438–443CrossRefGoogle Scholar
  57. Lopez AD, Ahmad OB, Guillot M, Inoue M, Ferguson BD, Salomon JA, Murray CJ, Hill KH (2002) World mortality in 2000: life tables for 191 countries. World Health Organization, GenevaGoogle Scholar
  58. Lucas RE (1987) Models of business cycles. Blackwell, New YorkGoogle Scholar
  59. Maas A, Wakker PP (1994) Additive conjoint measurement for multiattribute utility. J Math Psychol 38(1):86–101CrossRefGoogle Scholar
  60. Maddison A (2003) The world economy: historical statistics. OECD Development Cenre, ParisCrossRefGoogle Scholar
  61. McNeil BJ, Weichselbaum R, Pauker SG (1978) Fallacy of the five-year survival in lung cancer. N Engl J Med 299(25):1397–1401CrossRefGoogle Scholar
  62. Meara ER, Richards S, Cutler DM (2008) The gap gets bigger: changes in mortality and life expectancy, by education, 1981–2000. Health Aff 27(2):350–360CrossRefGoogle Scholar
  63. Miyamoto JM, Eraker SA (1985) Parameter estimates for a QALY utility model. Med Decis Mak 5(2):191–213CrossRefGoogle Scholar
  64. Moser K, Shkolnikov V, Leon DA (2005) World mortality 1950–2000: divergence replaces convergence from the late 1980s. Bull W H O 83(3):202–209Google Scholar
  65. Murphy KM, Topel RH (2006) The value of health and longevity. J Polit Econ 114(5):871–904CrossRefGoogle Scholar
  66. Nordhaus WD (2003) The health of nations: the contribution of improved health to living standards. In: Murphy KM, Topel RH (eds) Measuring the gains from medical research: an economic approach. University of Chicago Press, ChicagoGoogle Scholar
  67. Oeppen J, Vaupel JW (2002) Broken limits to life expectancy. Science 296:1029–1031CrossRefGoogle Scholar
  68. Picone G, Sloan F, Taylor Jr D (2004) Effects of risk and time preference and expected longevity on demand for medical tests. J Risk Uncertain 28(1):39–53CrossRefGoogle Scholar
  69. Pliskin JS, Shepard DS, Weinstein MC (1980) Utility functions for life years and health status. Oper Res 28(1):206–224CrossRefGoogle Scholar
  70. Ried W (1998) QALYs versus HYEs—what’s right and what’s wrong. a review of the controversy. J Health Econ 17(5):607–625CrossRefGoogle Scholar
  71. Rogers AR (1994) Evolution of time preference by natural selection. Am Econ Rev 84(3):460–481Google Scholar
  72. Rosen S (1988) The value of changes in life expectancy. J Risk Uncertain 1(3):285–304CrossRefGoogle Scholar
  73. Satchell S, Thorp S (2011) Uncertain survival and time discounting: intertemporal consumption plans for family trusts. J Popul Econ 24(1):239–266CrossRefGoogle Scholar
  74. Shkolnikov VM, Andreev EE, Begun AZ (2003) Gini coefficient as a life table function: computation from discrete data, decomposition of differences and empirical examples. Demogr Res 8(11):305–358CrossRefGoogle Scholar
  75. Slemrod J (2003) Thanatology and economics: the behavioral economics of death. Am Econ Rev 93(2):371–375CrossRefGoogle Scholar
  76. Smits J, Monden C (2009) Length of life inequality around the globe. Soc Sci Med 68(6):1114–1123. doi: 10.1016/j.socscimed.2008.12.034 CrossRefGoogle Scholar
  77. Stiggelbout AM, Kiebert GM, Kievit J, Leer JWH, Stoter G, de Haes JCJM (1994) Utility assessment in cancer patients: adjustment of time tradeoff scores for the utility of life years and comparison with standard gamble scores. Med Decis Mak 14(1):82–87CrossRefGoogle Scholar
  78. Strotz RH (1956) Myopia and inconsistency in dynamic utility maximization. Rev Econ Stud 23(3):165–180Google Scholar
  79. Tolley GS, Kenkel DS, Fabian RG (eds) (1994) Valuing health for policy: an economic approach. University of Chicago Press, ChicagoGoogle Scholar
  80. Verhoef LCG, Haan AFJD, van Daal WAJ (1994) Risk attitude in gambles with years of life: empirical support for prospect theory. Med Decis Mak 14(2):194–200CrossRefGoogle Scholar
  81. Viscusi WK (1993) The value of risks to life and health. J Econ Lit 31(4):1912–1946Google Scholar
  82. Viscusi WK, Aldy JE (2003) The value of a statistical life: a critical review of market estimates throughout the world. J Risk Uncertain 27(1):5–76CrossRefGoogle Scholar
  83. White KM (2002) Longevity advances in high-income countries. Popul Dev Rev 28(1):59–76CrossRefGoogle Scholar
  84. Wilmoth JR (2003) Human longevity in historical perspective. In: Timiras PS (ed) Physiological basis of aging and geriatrics. CRC, New York, pp 11–24Google Scholar
  85. Wilmoth JR, Horiuchi S (1999) Rectangularization revisited: variability of age at death within human populations. Demography 36(4):475–495CrossRefGoogle Scholar
  86. Wilson C (2001) On the scale of global demographic convergence 1950–2000. Popul Dev Rev 27(1):155–171CrossRefGoogle Scholar
  87. Yaari ME (1965) Uncertain lifetime, life insurance, and the theory of the consumer. Rev Econ Stud 32(2):137–150CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Queens CollegeCity University of New YorkFlushingUSA

Personalised recommendations