The Stationary Population Model and Its Identity: A Unifying Framework for Global Aging

James R. Carey, University of California at Davis
Arni Rao, Medical College of Georgia

This paper introduces a novel approach to understanding population aging inspired by the stationary population identity—an indisputable truth in mathematical demography that equates the distributions of life lived and life left in replacement populations. Building on this concept, the paper develops the Paired Population Analysis model, which compares a stationary, zero-growth population to real-world populations. This comparison yields new metrics, such as the Dual Average Age, Dissimilarity Indices, and Dynamic Age Index, which help to better understand population aging by revealing the alignment or divergence between theoretical and actual demographic patterns. A global analysis of 200 countries uncovers key trends, including a projected convergence by 2100 where many populations will achieve a ratio of average age to average years remaining of roughly one, marking a demographic equilibrium. Europe and Northern America are expected to reach this point earlier, while regions like Africa, due to different fertility and mortality patterns, will achieve this balance later. By integrating life lived and life left distributions, the framework offers refined insights into global demographic transitions and highlights population aging as a significant challenge in the 21st century. These findings hold critical implications for demographic research and policy planning worldwide.

Keywords: Population Ageing, Mathematical demography , Data visualisation , Population projections, forecasts, and estimations

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