The inverse relationship between life expectancy-induced changes in the old-age dependency ratio and the prospective old-age dependency ratio

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. (C) 2018 The Authors. Published by Elsevier Inc.