Arriaga Meets Kitagawa. Life Expectancy Decomposition With Population Subgroups

Abstract

An Arriaga decomposition partitions differences in life expectancy into contributions from mortality rate differences in each age. A Kitagawa decomposition partitions a difference between two weighted means into effects from differences in structure and from differences in each element of the weighted value. Life expectancy differences between like-defined subpopulations can be decomposed using the Arriaga method, or a different suitable decomposition method. If combined (or total) life expectancy is treated as a weighted average of the subpopulations, then the results of subgroup-specific decompositions can substitute the rate component from a Kitagawa decomposition of combined life expectancy. This is valid as long as the relative weight of each subpopulation is part of the initial conditions of the combined lifetable, and group prevalence in later ages is determined only by mortality. The composition component of the same Kitagawa decomposition gives the effect of differing subgroup composition on total life expectancy differences. Notable properties of the method include: (i) it accommodates any number of subpopulations, (ii) it easily incorporates cause-of-death information, and (iii) composition is considered only in the initial conditions. We apply the method to Spanish cause- and education-specific data. This method can further disentangle the effects of mortality and composition differences, helping to explain or clarify paradoxes and contemporary or forthcoming life expectancy changes as partly driven by shifts in cohort composition. We give both R code and spreadsheet implementations of the method.