Appendix: A

As discussed in the text, the U.N. projected number of oldest old persons (age 80+) in 2050 (99.6 million) is considerably smaller than our projected (114.4 million), and the projected age distributions among elderly population notably differ from each other (see Table 2). This discrepancy is partly due to differences in model specification and slightly different assumptions about future life expectancy. We classify the population into rural and urban sectors, but the U.N. did not. Starting years of our and the U.N.'s projections differ from each other. The U.N. used a constant 0.1 per thousand net international migration rate, but we did not. In our current research for preparing this paper, we performed a new exercise in which we combine rural and urban sectors, start our projection from 1995, and use the same life expectancy assumption and constant net international migration rate as the one used by the U.N.. In this new exercise, the only difference is the ways for interpolating agespecific death rates. The U.N. Population Division used model life tables to interpolate the 5year agespecific death rates in the future years. We followed an iterative procedure to alter the death rates proportionally at the same rate at all ages of singleyear specific, and the iterative procedure stops when the projected life expectancy at birth in the particular year is achieved ([1], [44]). The discrepancy between results from our new exercise and the U.N. projection even becomes larger: our new exercise projected 125 million oldest old persons in 2050, in contrast to the 99.6 million projected by U.N. Population projection. Therefore, we concluded that the discrepancy is mainly due to the different approaches for interpolating agespecific death rates in the future years. The U.N. model life table approach assumes that the age pattern of changes in death rates in the future is the same as what was observed in the past, namely, death rates decline faster at younger ages than at older ages. This approach has led to implausible values (almost zero) of projected death rates at some young ages when mortality level is very low ([3, p8], [27, p78], [16, p666]). The approach we employed assumes that changes in death rates at each age are proportional to the agespecific death rates, which implies faster decline of mortality at advanced ages than young ages when mortality level is low, and does not produce too low death rates at young ages. We compare the projected life tables with the same assumptions of life expectancies at birth but following the U.N. model life table approach and the approach of proportionally reducing death rates by us, respectively. The shapes of the curves of the two sets of life table survival probabilities look plausible, but the U.N. model life table survival probabilities are slightly higher before age 75, but significantly lower after age 80. Since the early 1970s, female death rates in Japan have declined at annual rates of about 3% for elders age 8089 and 2% for elders age 9099 [43, p856], which is substantially higher than the rate of decline at younger ages. Rates of progress in reducing mortality rates among the elderly age 60 and above in Sweden have accelerated over the course of the century, and from the 1960s to the 1980s ran at an average rate of 1 to 2 percent for females and half a percent for males [42, p303 Table12]. In most developed countries, the rate of reduction of death rates at older ages has been accelerated, especially since 1970 ([12], [43, p855]). If the recent trend of accelerated reduction mortality rates at advanced ages observed in several European countries persist in the future, our projected larger numbers and the higher proportion of oldest old persons may be closer to the reality. We also realize that the proportionally reducing death rates at all ages is not ideal either, and further research on how to forecast agespecific rates of changes in mortality is imperatively needed. Such research will be very useful to improve the accuracy of population projection, which may have major implications in aging studies and socioeconomic policymaking.


Family Dynamics of 63 Million (in 1990) to more than 330 Million (in 2050) Elders in China Zeng Yi, Linda George © 2000 MaxPlanckGesellschaft ISSN 14359871 http://www.demographicresearch.org/Volumes/Vol2/5 