۱- Introduction

۲- The mortality model

۳- The analytic expression for the old age threshold

۴- The analytic relationship between the OADR and the POADR under general mortality change

۵- Empirical assessment

۶- Conclusion

References

Abstract

Unlike other biological populations, the human population is experiencing long-run increases in life expectancy. Those lead to changes in age compositions not typical for other biological populations. Sanderson and Scherbov (2015a) demonstrated that, in many countries in Europe, faster increases in life expectancy lead to faster population aging when measured using the old-age dependency ratio and to slower population aging when measured using the prospective old-age dependency ratio that employs a dynamic old-age threshold. We examine this finding analytically and with simulations. We use an analytic decomposition of changes in mortality schedules into shift and compression processes. We show that shifts and compressions of mortality schedules push the two old-age dependency ratios in opposite directions. Our formal results are supported by simulations that show a positive effect of a mortality shift on the old-age dependency ratio and a negative effect of it on the prospective old-age dependency ratio. The effects are of opposite sign for a mortality compression. Our formal and simulation results generalize observed European trends and suggest that the inverse relationship between life expectancy and prospective old-age dependency would be observed more generally.

Conclusion

The OADR assumes that the old age starts at some fixed age regardless of time or place. Nevertheless, in a world where life expectancy is increasing, where people are often healthier at given ages than they were in the past, where age-specific cognitive functioning is improving, where older people are now more educated than they were in the past, and where people in OECD countries will generally be facing higher normal pension ages, another measure of aging, consistent with these changes, seems appropriate. The POADR is such a measure. Population aging, viewed from the perspective of the POADR looks very different from the picture provided by the OADR. Sanderson and Scherbov (2015a) showed that faster increases in life expectancy lead to slower rates of population aging when measured by the percentage increase in the POADR, in contrast to the faster rates of population aging when measured by the percentage increase in the OADR. We show why those differences were observed and, indeed, that they were predictable given the sorts of shifts and compressions that have been observed. Here, we have shown that, in a wide variety of life table populations, annual changes in OADRs and POADRs move in opposite directions. Ediev’s 2013a shiftcompression model provides an analytic two-parameter specification of the age distribution of adult deaths. We used that model to provide analytic expressions for both the OADR and the POADR in terms of shift and compression parameters. The theoretical expressions that we obtained predicted that the observed negative relationship between annual changes in OADRs and POADRs is exactly what we should expect to see. We estimated the shift and compression parameters using data from the countries in the Human Morality Database. The data showed that the change in the POADR was around −۰٫۳۸ times the change in the OADR. Our theoretical approximation predicted that it would be around −۰٫۳ times the change in the OADR.