Mortality comparisons and age: a new mortality curve

Abstract

This paper introduces a new mortality curve to illustrate and measure mortality and its relation to age. The curve is a form of ‘concentration curve’, and plots the proportion of total deaths against the corresponding proportion of people, where individuals are arranged from youngest to oldest. A mortality index is based on the normalised area measure of the distance of the concentration curve from a ‘best case’ scenario. Results analogous to Lorenz orderings (in the context of income distribution) are derived. The measure is illustrated using mortality data for several countries. The aim is to supplement the standard Crude Death Rate with a ‘mortality-inefficiency’ measure in a composite index of mortality which attends to both the mean and the dispersion of an age-distribution of deaths.

KEYWORDS:

• Mortality curve
• mortality-inefficiency measure
• crude death rate
• optimally distributed equivalent death rate
• Lorenz curve
• Gini coefficient
• mean income
• equally distributed equivalent income

Acknowledgement

Subramanian would like to thank, without implicating, Debraj Ray for many valuable discussions on the subject of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Thus, in exercises involving comparisons, the cardinal significance of any particular comparison is compromised by the fact that it is a variable function of the precise standard population employed. However, an alternative approach involves the use of decomposition methods: see Philip, Ray, and Subramanian (2021).

2 On poverty, see the TIP (‘three “I”s of poverty’) curves of Jenkins and Lambert (1997), and on mobility, see the TIM (‘three "I"s of mobility’) curves of Creedy and Gemmell (2019). On concentration curves in the measurement of tax progressivity, see Lambert (1993).

3 It is a weighted sum of individuals’ incomes, with weights equal to the ‘inverse rank’ of the individuals (with incomes arranged in ascending rank order). For further discussion, see, for example, Sen (1970).

4 The famous Atkinson measure also belongs to this class, but has a different social welfare function than that giving rise to the Gini measure; see Atkinson (1970).

5 This draws on Subramanian (2021).

6 In the New Zealand case, with high and variable migration, it is acknowledged that there may be inaccuracies regarding information about the ages of individuals.