The measurement of structural ageing – an axiomatic approach

The structural ageing of the population is one of the key global trends of the 21st Century. In this paper, we outline four axioms that, along with easy interpretability, we believe should underpin a theoretically valid measure of structural ageing: (1) population size invariance; (2) strong dominance; (3) weak dominance; and (4) age sensitivity. We then present a class of structural ageing indices that satisfy the axioms and are easily interpretable, with root-mean-squared-age (RMSA) as our preferred measure within the class. Using historical and cross-national data from the World Population Prospects, state-level data from the US Census Bureau, and local-authority-level data from New Zealand, we demonstrate that our preferred measure is correlated with conventional measures of structural ageing. Nevertheless, in each case there are large disparities in ranking for some countries, states, or local authorities between the different measures. These ranking disparities could be highly consequential for the allocation of resources, particularly between states or local areas within countries. Our proposed class of measures may help to avoid these disparities due to their axiomatically-consistent nature. Finally, we present considerations for future extensions of this important work, including the development of equivalent measures based on prospective age.