Abstract
There is considerable interest in demography in comparing mortality by race and by sex to determine the magnitude of the differentials, to understand why they exist and to detect if they are changing over time. The question is if they will converge, and if so, how soon. For race, nowhere is that interest so evident as in the controversy over the well-researched black/white mortality crossover. A persistent decline in the age of crossover signals convergence, while advancing age of crossover indicates mortality divergence. Even so, white and nonwhite life expectancies have been converging generally over time. A similar concern is shown with sex differences since they have displayed a marked increase in the later twentieth century. The confounding of race and sex in mortality analyses invites the desegregation of the U.S. population into four race-sex specific groups, and an investigation of their pairings to understand their possible relationships well into the future. This paper does so by extending the mortality analysis by Lee and Carter (1992) for the total U.S. population and Carter and Lee (1992) for U.S. sex differentials. The basic approach is to examine some life table functions derived from forecasts of mortality for white males, white females, nonwhite males and nonwhite females using the Lee-Carter method (Lee and Carter 1992). We focus on puzzling patterns of life expectancy forecasts that show white and nonwhite life expectancies at birth initially continuing their historic decline, but then reversing themselves and increasing in the latter part of the forecast period.
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Notes
- 1.
Manton and Stallard (1984) express the death process for chronic degenerative diseases as a sequence of age and time dependent transitions from a state of well being to a chronic disease state to a death state. The distributional pattern of deaths for a cohort is best captured in a generation life table. For practical reasons, period life tables are substituted, resulting in the analysis of approximate or synthetic cohorts. Generation tables are a record of the temporal mortality experience of a single cohort at a single point in time. Therefore, period tables cannot mirror exactly the temporality of cohort experience. Still, there are compelling reasons why a period approach may be more profitable for this analysis. Gomez (1990), in his analysis of Norwegian mortality data, considers a model like that used in this study, but enriched by cohort effects, which turn out to be significant and interesting. However, for purposes of forecasting, he finds the period model to be preferable. Wilmoth (1990) and Wilmoth et al. (1989) fit more elaborate models with a cohort basis rather than a period basis. Then each cohort would receive some value of k. There are various reasons why we did not proceed this way: (1) we do not believe it is empirically correct that a cohort’s mortality experience is dominantly shaped in its early years (if we have to choose between period and cohort, the period approach comes closer to the truth); (2) lacking genuine and reliable mortality rates by single years of age, implementation of the cohort approach with U.S. data would be at best very rough; (3) age truncation for cohorts at both ends of the data matrix would pose serious difficulties; and (4) the error-covariance structure for the forecasts of rates in any given year would be vastly more complicated with a cohort approach.
- 2.
Vector ARMA models of WM, NM, WF, and NF were estimated by sex and to no avail. The stationarity-invertibility principle was nearly violated in parameter estimation, resulting in some values close to 1. These model are deemed too unstable to be considered seriously in the study and, so, are not included.
- 3.
These confidence intervals are not adjusted for uncertainty inherent in the drift term. Taking into account the increase in forecast standard error due to the drift parameter expands the confidence intervals by the year 2065 to 11.67 (versus 8.4), 9.00 (versus 6.5), 11.79 (versus 8.3), and 6.35 (versus 4.5) for white males, white females, nonwhite males and nonwhite females, respectively. Details of this estimation problem for the total population are found in Lee and Carter (1992, see especially Appendix 2) and for sexes in Carter and Lee (1992).
- 4.
Perhaps a most revealing example of the impact of environment is the historic prevalence of malaria in a geographic belt around the world from the Mediterranean region to a band from West Africa to Madagascar to Asia. In these regions, a high prevalence of malaria correlates with a high frequency of a certain race-specific genetic disease: sickle cell anemia from West Africa to Madagascar and thalassemia in the Mediterranean, Asia Minor, India and some parts of Indonesia. Both diseases result from an abnormal form of the protein haemoglobin resulting from a defective pair of genes. In both instances, inheriting the disease results (under a deficit of oxygen) in mortality, inheriting a healthy pair of genes results in immunity to the disease, inheriting one defective gene results in very mild susceptibility to the disease with an advantage of some immunity to malaria. None of these diseases are exclusive to the specific races so designated as their carriers; these races simply have extremely higher frequencies of genetic susceptibility.
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Carter, L.R. (2010). Long-Run Relationships in Differential U.S. Mortality Forecasts by Race and Sex: Tests for Co-integration . In: Tuljapurkar, S., Ogawa, N., Gauthier, A. (eds) Ageing in Advanced Industrial States. International Studies in Population, vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3553-0_3
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