IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/15288.html
   My bibliography  Save this paper

Variance in Death and Its Implications for Modeling and Forecasting Mortality

Author

Listed:
  • Shripad Tuljapurkar
  • Ryan D. Edwards

Abstract

Entropy, or the gradual decline through age in the survivorship function, reflects the considerable amount of variance in length of life found in any human population. Part is due to the well-known variation in life expectancy between groups: large differences according to race, sex, socioeconomic status, or other covariates. But within-group variance is very large even in narrowly defined groups, and it varies strongly and inversely with the group average length of life. We show that variance in length of life is inversely related to the Gompertz slope of log mortality through age, and we reveal its relationship to variance in a multiplicative frailty index. Our findings bear a variety of implications for modeling and forecasting mortality. In particular, we examine how the assumption of proportional hazards fails to account adequately for differences in subgroup variance, and we discuss how several common forecasting models treat the variance along the temporal dimension.

Suggested Citation

  • Shripad Tuljapurkar & Ryan D. Edwards, 2009. "Variance in Death and Its Implications for Modeling and Forecasting Mortality," NBER Working Papers 15288, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:15288
    Note: AG EH
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w15288.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. John Bongaarts, 2005. "Long-range trends in adult mortality: Models and projection methods," Demography, Springer;Population Association of America (PAA), vol. 42(1), pages 23-49, February.
    2. Ryan D. Edwards, 2010. "Trends in World Inequality in Life Span Since 1970," NBER Working Papers 16088, National Bureau of Economic Research, Inc.
    3. John Wilmoth & Shiro Horiuchi, 1999. "Rectangularization revisited: Variability of age at death within human populations," Demography, Springer;Population Association of America (PAA), vol. 36(4), pages 475-495, November.
    4. Ryan Edwards, 2013. "The cost of uncertain life span," Journal of Population Economics, Springer;European Society for Population Economics, vol. 26(4), pages 1485-1522, October.
    5. Shripad Tuljapurkar & Carl Boe, 1998. "Mortality Change and Forecasting," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(4), pages 13-47.
    6. John Bongaarts & Griffith Feeney, 2002. "How Long Do We Live?," Population and Development Review, The Population Council, Inc., vol. 28(1), pages 13-29, March.
    7. Edwards Ryan D, 2009. "The Cost of Cyclical Mortality," The B.E. Journal of Macroeconomics, De Gruyter, vol. 9(1), pages 1-19, March.
    8. Shripad Tuljapurkar, 1998. "Forecasting Mortality Change," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(4), pages 127-134.
    9. Ryan D. Edwards & Shripad Tuljapurkar, 2005. "Inequality in Life Spans and a New Perspective on Mortality Convergence Across Industrialized Countries," Population and Development Review, The Population Council, Inc., vol. 31(4), pages 645-674, December.
    10. Shripad Tuljapurkar & Nan Li & Carl Boe, 2000. "A universal pattern of mortality decline in the G7 countries," Nature, Nature, vol. 405(6788), pages 789-792, June.
    11. Siu Cheung & Jean-Marie Robine & Edward Tu & Graziella Caselli, 2005. "Three dimensions of the survival curve: horizontalization, verticalization, and longevity extension," Demography, Springer;Population Association of America (PAA), vol. 42(2), pages 243-258, May.
    12. Shripad Tuljapurkar & Carl Boe, "undated". "Mortality Change and Forecasting: How Much and How Little Do We Know?," Pension Research Council Working Papers 98-2, Wharton School Pension Research Council, University of Pennsylvania.
    13. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Duncan Gillespie & Meredith Trotter & Shripad Tuljapurkar, 2014. "Divergence in Age Patterns of Mortality Change Drives International Divergence in Lifespan Inequality," Demography, Springer;Population Association of America (PAA), vol. 51(3), pages 1003-1017, June.
    2. Claudia Nau & Glenn Firebaugh, 2012. "A New Method for Determining Why Length of Life is More Unequal in Some Populations Than in Others," Demography, Springer;Population Association of America (PAA), vol. 49(4), pages 1207-1230, November.
    3. Ryan D. Edwards, 2010. "Trends in World Inequality in Life Span Since 1970," NBER Working Papers 16088, National Bureau of Economic Research, Inc.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shripad Tuljapurkar & Ryan Edwards, 2011. "Variance in death and its implications for modeling and forecasting mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 24(21), pages 497-526.
    2. Booth, Heather, 2006. "Demographic forecasting: 1980 to 2005 in review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 547-581.
    3. Duncan Gillespie & Meredith Trotter & Shripad Tuljapurkar, 2014. "Divergence in Age Patterns of Mortality Change Drives International Divergence in Lifespan Inequality," Demography, Springer;Population Association of America (PAA), vol. 51(3), pages 1003-1017, June.
    4. Pitacco, Ermanno, 2004. "Survival models in a dynamic context: a survey," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 279-298, October.
    5. Marie-Pier Bergeron-Boucher & Marcus Ebeling & Vladimir Canudas-Romo, 2015. "Decomposing changes in life expectancy: Compression versus shifting mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 33(14), pages 391-424.
    6. Gonzaga, Marcos Roberto & Queiroz, Bernardo L & Lima, Everton, 2017. "Compression of mortality: the evolution in the variability in the age of death in Latin America," OSF Preprints pdnfk, Center for Open Science.
    7. Ryan D. Edwards, 2010. "Trends in World Inequality in Life Span Since 1970," NBER Working Papers 16088, National Bureau of Economic Research, Inc.
    8. Iñaki Permanyer & Jeroen Spijker & Amand Blanes & Elisenda Renteria, 2018. "Longevity and Lifespan Variation by Educational Attainment in Spain: 1960–2015," Demography, Springer;Population Association of America (PAA), vol. 55(6), pages 2045-2070, December.
    9. Dustin Brown & Mark Hayward & Jennifer Montez & Robert Hummer & Chi-Tsun Chiu & Mira Hidajat, 2012. "The Significance of Education for Mortality Compression in the United States," Demography, Springer;Population Association of America (PAA), vol. 49(3), pages 819-840, August.
    10. Isaac Sasson, 2016. "Trends in Life Expectancy and Lifespan Variation by Educational Attainment: United States, 1990–2010," Demography, Springer;Population Association of America (PAA), vol. 53(2), pages 269-293, April.
    11. Patrick Meyer & Gregory Ponthiere, 2020. "Human lifetime entropy in a historical perspective (1750–2014)," Cliometrica, Journal of Historical Economics and Econometric History, Association Française de Cliométrie (AFC), vol. 14(1), pages 129-167, January.
    12. Alyson van Raalte & Pekka Martikainen & Mikko Myrskylä, 2014. "Lifespan Variation by Occupational Class: Compression or Stagnation Over Time?," Demography, Springer;Population Association of America (PAA), vol. 51(1), pages 73-95, February.
    13. Michal Engelman & Vladimir Canudas‐Romo & Emily M. Agree, 2010. "The Implications of Increased Survivorship for Mortality Variation in Aging Populations," Population and Development Review, The Population Council, Inc., vol. 36(3), pages 511-539, September.
    14. Lucia Zanotto & Vladimir Canudas-Romo & Stefano Mazzuco, 2021. "A Mixture-Function Mortality Model: Illustration of the Evolution of Premature Mortality," European Journal of Population, Springer;European Association for Population Studies, vol. 37(1), pages 1-27, March.
    15. Vladimir Canudas-Romo, 2008. "The modal age at death and the shifting mortality hypothesis," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 19(30), pages 1179-1204.
    16. Ugofilippo Basellini & Vladimir Canudas-Romo & Adam Lenart, 2019. "Location–Scale Models in Demography: A Useful Re-parameterization of Mortality Models," European Journal of Population, Springer;European Association for Population Studies, vol. 35(4), pages 645-673, October.
    17. Annamaria Olivieri & Ermanno Pitacco, 2012. "Life tables in actuarial models: from the deterministic setting to a Bayesian approach," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 127-153, June.
    18. A. Roger Thatcher & Siu Lan Karen Cheung & Shiro Horiuchi & Jean-Marie Robine, 2010. "The compression of deaths above the mode," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 22(17), pages 505-538.
    19. Hui Zheng & Y. Claire Yang & Kenneth C. Land, 2016. "Age-Specific Variation in Adult Mortality Rates in Developed Countries," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 35(1), pages 49-71, February.
    20. Nadine Ouellette & Robert Bourbeau, 2011. "Changes in the age-at-death distribution in four low mortality countries: A nonparametric approach," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 25(19), pages 595-628.

    More about this item

    JEL classification:

    • I1 - Health, Education, and Welfare - - Health
    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts
    • N3 - Economic History - - Labor and Consumers, Demography, Education, Health, Welfare, Income, Wealth, Religion, and Philanthropy

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nbr:nberwo:15288. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.