BACKGROUND
Sanderson and Scherbov (2015) demonstrated that there was an inverse relation between the speeds of aging as measured by the conventional and the prospective old-age dependency ratios.

OBJECTIVE and METHODS
Here, we examine this counterintuitive finding analytically and with simulations. To this end, we decompose changes in mortality schedules into shift and compression processes. After studying the effects of these two processes on the dependency ratios analytically, we examine the effects empirically, using the HMD data.

RESULTS
Theory shows that the two mortality processes (of shift and compression) 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 conventional old-age dependency ratio and a negative effect of it on the prospective old-age dependency ratio. The effects are of opposite sign for the mortality compression. The analytical and empirical results also suggest the effect of the shift is stronger than the effect of compression. Hence, mortality declines, typically, imply increasing conventional but decreasing prospective old-age dependency ratios.

CONCLUSIONS
Our formal and empirical results taken together they suggest that the inverse relation between the conventional and prospective old-age dependency ratios is a universal feature of human mortality change.

CONTRIBUTION
This paper contributes to the literature on formal demographic analysis, particularly on the effects of mortality shifts and compression on dependency ratios. It demonstrates that the counter-intuitive finding in Sanderson and Scherbov (2015) is a fundamental feature of human mortality change. We also contribute in showing usefulness of the shift-compression decomposition model of mortality change developed in (Dalkhat M. Ediev 2013).