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Age-Specific Variation in Adult Mortality Rates in Developed Countries

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Abstract

This paper investigates historical changes in both single-year-of-age adult mortality rates and variation of the single-year mortality rates around expected values within age intervals over the past two centuries in 15 developed countries. We apply an integrated hierarchical age-period-cohort—variance function regression model to data from the human mortality database. We find increasing variation of the single-year rates within broader age intervals over the life course for all countries, but the increasing variation slows down at age 90 and then increases again after age 100 for some countries; the variation significantly declined across cohorts born after the early 20th century; and the variation continuously declined over much of the last two centuries but has substantially increased since 1980. Our further analysis finds the recent increases in mortality variation are not due to increasing proportions of older adults in the population, trends in mortality rates, or disproportionate delays in deaths from degenerative and man-made diseases, but rather due to increasing variations in young and middle-age adults.

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Notes

  1. Snijders and Bosker (1999, pp. 43–44) provide summaries of conventional statistical wisdom and methodological guidelines for choosing between the fixed or random specifications. They point out that if the categories are regarded as unique entities and the objective of the analysis is primarily to draw conclusions pertaining to each of the categories, then it is appropriate to treat the effects as fixed. On the other hand, if the categories are regarded as a sample from a (real or hypothetical) population and the objective of the analysis is to make inferences about this population, then the random coefficients model is appropriate. In the present analysis, the age range of the human populations analyzed is a complete listing of all possible ages, while the time periods and cohorts analyzed are only a sample of all possible periods and cohorts. Accordingly, the specification of the age effects as fixed and those of the periods and cohorts as random is consistent with conventional statistical practice.

  2. Age-specific mortality rates are cross-classified by both the time periods and the birth cohorts. Each cell is an intersection of a cohort and a period.

  3. At Step 1 of the two-step HAPC-VFR estimation algorithm, it is assumed that the errors—the distributions of the observed single-year-of-age mortality rates from their within-10-year-age-interval-expected values – in the regression are normally distributed. An examination of the empirically estimated residual distributions from application of Step 1 to the single-year-of-age mortality rates grouped into the 10-year age interval found them to be bell-shaped and well approximated by the normal errors specification. At Step 2 of the estimation algorithm, the regression models are specified in terms of deviations of the observed mortality rates from those expected on the basis of the estimated Step 1 models. Since the estimated residuals at Step 1 are well approximated by the normal errors assumption, and since the squares of the normally distributed errors have a known (gamma) statistical distribution, the distributional assumptions of Step 2 are similarly well suited to this application.

  4. For brevity, the results of estimation of the HAPC-VFR model for each of the 15 countries are presented graphically. The numerical estimates are available from the authors on request.

  5. Most of the countries do not have data until the late-1800s. While we used all of the data to estimate the models, we do not substantively interpret any of the period effects estimates until at least 1900.

  6. The estimated residual mortality variations continuously declined from the mid-18th century in Sweden and from the mid-19th century in the countries for which the data series date sufficiently far back in time. The numerical estimates and figure are available upon request from the authors.

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Acknowledgments

An earlier version of this paper was presented at the demography workshop at the Population Research Center at the University of Chicago, the 2012 annual meeting of the Population Association of America, May 3–5, San Francisco, CA, and the 2013 Keyfitz symposium on mathematical demography at the Ohio State University. We thank Kathleen Cagney, Michal Engelman, Shiro Horiuchi, Diane Lauderdale, Linda Waite, and Kazuo Yamaguchi for useful comments.

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Authors and Affiliations

  1. Department of Sociology, Institute for Population Research, The Ohio State University, 106 Townsend Hall, 1885 Neil Avenue Mall, Columbus, OH, 43210, USA

    Hui Zheng

  2. Department of Sociology, Lineberger Comprehensive Cancer Center, Carolina Population Center, University of North Carolina at Chapel Hill, Chapel Hill, USA

    Y. Claire Yang

  3. Department of Sociology, Duke University, Durham, USA

    Kenneth C. Land

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  1. Hui Zheng
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Correspondence to Hui Zheng.

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Zheng, H., Yang, Y.C. & Land, K.C. Age-Specific Variation in Adult Mortality Rates in Developed Countries. Popul Res Policy Rev 35, 49–71 (2016). https://doi.org/10.1007/s11113-015-9379-4

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