Am I Halfway? Life Lived = Expected Life

  • Vladimir Canudas-RomoEmail author
  • Virginia Zarulli
Part of the The Springer Series on Demographic Methods and Population Analysis book series (PSDE, volume 39)


We have reached halfway in life when our age equals our remaining life expectancy at that age. This relationship in stable population models between life lived and life left has captured the attention of mathematical demographers since Lotka. Our paper aims to contribute to the halfway-age debate by showing its time trends under mortality models and with current data from high longevity countries. We further contrast the halfway-age results by sex, and between period and cohort perspectives. We find that in 1850 life expectancy at birth was higher than halfway-age by around 10 years (HMD-mean halfway-age of 33.3 and 32.2 against HMD-mean life expectancy of 44.3 and 41.4 for women and men respectively). Nevertheless, declines in mortality at young ages radically changed life expectancy and it is found today at the same level as the double of halfway-age. While the period perspective puts halfway-age for females and males at 41.8 and 39.5 in 2010, for cohorts born in 2010 this might be as high as 10 years more. The stage of midlife has always been considered an important step in the life of human beings. However, there is no agreement on which is the age or age-range that represents the middle phase. Here we have further added the notion that halfway-age is not a static index but a moving age. Current and future progress in reducing mortality at older ages will require redefining our notion of midlife.


Life expectancy Midlife Halfway-age Lotka Mortality models Mortality measures 



We would like to thank Robert Schoen, Michel Guillot, Carlo Giovanni Camarda and the Max Planck Odense Center group for their comments and suggestion on how to improve our study.


  1. Bongaarts, J., & Feeney, G. (2008). How long do we live? In E. Barbi, J. W. Vaupel, & J. Bongaarts (Eds.), The quantum and tempo of life-cycle events (pp. 29–65). Berlin/Heidelberg: Springer.Google Scholar
  2. Brown, S. (1995). Life begins at 40? Further thoughts on marketing’s “mid-life crisis”. Marketing Intelligence & Planning, 13(1), 4–17.CrossRefGoogle Scholar
  3. Canudas-Romo, V. (2008). The modal age at death and the shifting mortality hypothesis. Demographic Research, 19(30), 1179–1204.CrossRefGoogle Scholar
  4. Canudas-Romo, V. (2010). Three measures of longevity: Time trends and record values. Demography, 47(2), 299–312.CrossRefGoogle Scholar
  5. Canudas-Romo, V., & Schoen, R. (2005). Age-specific contributions to changes in the period and cohort life expectancy. Demographic Research, 13(3), 63–82.CrossRefGoogle Scholar
  6. Cohen, P. (2012). In our prime: The invention of middle age. New York: Simon and Schuster.Google Scholar
  7. Dannefer, D. (1984). Adult development and social theory: A paradigmatic reappraisal. American Sociological Review, 49(1), 100–116.CrossRefGoogle Scholar
  8. Durling, R. M. (1996). The divine comedy of Dante Alighieri. Oxford: Oxford University Press.Google Scholar
  9. Engelman, M., Caswell, H., & Agree, E. (2014). Why do lifespan variability trends for the young and old diverge? A perturbation analysis. Demographic Research, 30(48), 1367–1396.CrossRefGoogle Scholar
  10. Gavrilov, L. A., & Gavrilova, N. S. (1991). The biology of life span: A quantitative approach. Chur: Harwood Academic Publications.Google Scholar
  11. Goldstein, J. R. (2009). Life lived equals life left in stationary populations. Demographic Research, 20(2), 3–6.CrossRefGoogle Scholar
  12. Goldstein, J. R. (2012). Historical addendum to life lived equals life left in stationary populations. Demographic Research, 26(7), 167–172.CrossRefGoogle Scholar
  13. Goldstein, J. R., & Wachter, K. W. (2006). Relationships between period and cohort life expectancy: Gaps and lags. Population Studies, 60(3), 257–269.CrossRefGoogle Scholar
  14. Golembiewski, R. T. (1978). Mid-life transition and mid-career crisis: A special case for individual development. Public Administration Review, 38(3), 215–222.CrossRefGoogle Scholar
  15. Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London, 115, 513–583.CrossRefGoogle Scholar
  16. Horiuchi, S., Ouellette, N., Cheung, S. L. K., & Robine, J.-M. (2013). Modal age at death: lifespan indicator in the era of longevity extension. Vienna Yearbook of Population Research, 11, 37–69.Google Scholar
  17. Human Mortality Database. (2015). University of California, Berkeley (USA), and Max Planck Institute for Demographic Research Germany. Available at
  18. Lee, R., & Carter, L. R. (1992). Modeling and forecasting US mortality. Journal of the American Statistical Association, 87(419), 659–671.Google Scholar
  19. Lee, R. et al. (2011). NTA country report, US, 2003.N.T.A. (
  20. Li, N., & Lee, R. (2005). Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method. Demography, 42(3), 575–594.CrossRefGoogle Scholar
  21. Lotka, A. J. (1939). ThéorieAnalytique des Associations Biologiques, II. Paris, Hermann et Cie.Google Scholar
  22. Lotka, A. J. (1998). Analytical theory of biological populations. London: Plenum Press.CrossRefGoogle Scholar
  23. Makeham, W. M. (1860). On the law of mortality and the construction of annuity tables. The Assurance Magazine, and Journal of the Institute of Actuaries, 8(6), 301–310.Google Scholar
  24. Midlife in the United States. (2013). MIDUS. University of Wisconsin – Madison, Institute on Aging.Google Scholar
  25. Missov, T. I., Lenart, A., Laszlo, N., Canudas-Romo, V., & Vaupel, J. W. (2015). The Gompertz force of mortality as a function of the mode. Demographic Research, 32(36), 1031–1048.CrossRefGoogle Scholar
  26. Overstreet, L. R. (2009). The Greek concept of the “seven stages of life” and its new testament significance. Bulletin for Biblical Research, 19(4), 537–563.Google Scholar
  27. Sanderson, W. C., & Scherbov, S. (2005). Average remaining lifetimes can increase as human populations age. Nature, 435(7043), 811–813.CrossRefGoogle Scholar
  28. Sanderson, W. C., & Scherbov, S. (2007). A new perspective on population aging. Demographic Research, 16(2), 27–58.CrossRefGoogle Scholar
  29. Sanderson, W. C., & Scherbov, S. (2010). Remeasuring aging. Science, 329(5997), 1287–1288.CrossRefGoogle Scholar
  30. Sanderson, W. C., & Scherbov, S. (2013). The characteristics approach to the measurement of population aging. Population and Development Review, 39(4), 673–685.CrossRefGoogle Scholar
  31. Schoen, R., Jonsson, S. H., & Tufis, P. (2004). A population with continually declining mortality (Working Paper 04–07), Population Research Institute, Pennsylvania State University, PA.Google Scholar
  32. Shakespeare, W. (1989). William Shakespeare: the complete works. New York: Barnes & Noble Publishing.Google Scholar
  33. Siler, W. (1979). A competing-risk model for animal mortality. Ecology, 60(4), 750–757.CrossRefGoogle Scholar
  34. Thatcher, A. R., Kannisto, V., & Vaupel, J. W. (1998). The force of mortality at ages 80 to 120. (Odense monographs on population aging, Vol. 5, 104p) Odense: Odense University Press.Google Scholar
  35. Vaupel, J. W. (2009). Life lived and left: Carey’s equality. Demographic Research, 20(3), 7–10.CrossRefGoogle Scholar
  36. Willis, S. L., & Reid, J. B. (1998). Life in the middle: Psychological and social development in middle age. San Diego: Academic.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Max-Planck Odense Center on the Biodemography of AgingUniversity of Southern DenmarkOdense CDenmark

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