Life expectancy decomposition for non-stable populations

Life expectancy is one of the most widely used summary measures of population health, yet its interpretation relies heavily on the assumption of a stable population in which the denominators of death rates remain constant over time. Most established decomposition methods attribute changes in life expectancy to age-specific mortality, causes of death, or subgroup differences, implicitly assuming that population structures do not shift through migration or other compositional changes. In many real-world settings, however, this assumption is violated. Migration alters the size and age structure of the population at risk, and selective patterns of in- and out-migration can produce “lagged selection bias,” in which observed deaths no longer correspond accurately to the intended study population. These distortions undermine temporal comparisons of life expectancy and can obscure true changes in mortality. To address this methodological gap, we introduce a novel decomposition framework that explicitly incorporates migration and population dynamics, extending decomposition techniques to non-stable populations.

Our approach builds on iterative life table (ilt) methods, which estimate life expectancy using projected population counts that exclude net migrants. By contrasting ilt-based life expectancies with those derived from observed, migration-affected populations, we separate changes attributable to mortality improvements from those driven by compositional shifts and migration. The resulting framework decomposes total life expectancy change into three fundamental components: (1) mortality-driven gains; (2) population change; and 3) a residual component resulting from embedded migration — allowing researchers to quantify the contribution of each component to observed changes in life expectancy. Additionally, we extend age-specific decomposition techniques to non-stable populations by replacing age-specific deaths and growth rates sequentially in an order-independent manner. This provides detailed insight into how each age group contributes to overall change across the three components.

To illustrate the utility of the method, we analyze population and mortality data for Estonia, United States, and Sweden using Human Mortality Database data for 1999, 2009, and 2019. Our preliminary findings show substantial variation across countries in the drivers of life expectancy change. In Estonia, the 3.44-year increase in life expectancy at birth between 2004 and 2014 is driven predominantly by reductions in mortality, especially at younger ages. In contrast, United States’s 1.31-year increase during the same period is largely attributable to migration rather than improvements in survival. Age-specific decomposition further reveals that the gains in life expectancy at birth are concentrated at ages 65 and above due to population dynamics, while Estonia’s improvements stem primarily from reductions in deaths.

This method provides a new analytical lens for studying life expectancy in populations undergoing demographic change. By distinguishing mortality-driven trends from those produced by migration, reclassification, or data inconsistencies, it offers a more accurate foundation for interpreting life expectancy patterns in dynamic, non-stable populations.