Extension, Compression, and Beyond: A Unique Classification System for Mortality Evolution Patterns

Matthias Börger, Martin Genz, Jochen Ruß

A variety of literature addresses the question of how the age distribution of deaths changes over time as life expectancy increases. However, corresponding terms such as extension, compression, or rectangularization are sometimes defined only vaguely, and statistics used to detect certain scenarios can be misleading. The matter is further complicated because mixed scenarios can prevail, and the considered age range can have an impact on observed mortality patterns. In this article, we establish a unique classification framework for realized mortality scenarios that allows for the detection of both pure and mixed scenarios. Our framework determines whether changes of the deaths curve over time show elements of extension or contraction; compression or decompression; left- or right-shifting mortality; and concentration or diffusion. The framework not only can test the presence of a particular scenario but also can assign a unique scenario to any observed mortality evolution. Furthermore, it can detect different mortality scenarios for different age ranges in the same population. We also present a methodology for the implementation of our classification framework and apply it to mortality data for U.S. females.