Abstract
Whereas period life expectancy constitutes an intuitive indicator of the survival conditions prevailing at a particular period, this paper argues that, given the existence of welfare interdependencies, that widespread indicator is nonetheless an incomplete measure of the longevity achievements relevant for human well-being. The central importance of coexistence for human-beings implies that usual life expectancy measures should be complemented by joint life expectancy indicators, which measure the average coexistence time under particular survival conditions. After a study of the theoretical foundations of ‘single’ and ‘joint’ life expectancy indicators, it is shown that joint life expectancy measures tend to enrich significantly the comparison of longevity achievements across countries and periods. Moreover, the introduction of joint life expectancy indicators—as a complement to conventional life expectancy measures—into multi-variable indexes such as the United Nations’ HDI is also shown to affect international rankings of standards of living to a non negligible extent.
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Notes
A (period) life-table shows the probabilities to survive up to different ages conditionally on the vector of age-specific probabilities of death prevailing at a particular period.
Throughout this paper, what I shall call ‘welfare’ can refer either to how well people feel (i.e. subjective well-being) or to how well people are (i.e. objective well-being): whether welfare is supposed to be subjective or objective has, in the present context, no importance for the precise way in which longevity achievements should be measured.
One should notice that, as emphasized by Vaupel (1986), probabilities of death at high ages have, compared to the ones at low ages, a stronger influence on life expectancy measures.
See Friedkin (1998).
See Needleman (1976) on the empirical estimation of altruism coefficients on the basis of kidney transplant data.
On a modified version of the HDI taking inequalities into account, see Hicks (1997).
On each dimension x, the index for a country A is equal to \({\frac{x(A)-{\rm Minimum}(x)}{{\rm Maximum}(x)-{\rm Minimum}(x)}}\) . For the adult literacy rates and enrolment rates, the minimum and maximum levels are fixed to 0% and 100% (see UN 2003).
In the rest of this section, single and joint life expectancy statistics are average for both sexes. Probabilities of survival up to different ages are extrapolated from the abridged life-tables of United Nations Population Division (2005), available online at http://www.un.org/popin/data.htm..
From now, our sample excludes micro-countries, such as Monaco, Andorra, and San Marino, which are not ranked by the United Nations (see UN 2003).
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Ponthiere, G. Measuring longevity achievements under welfare interdependencies: a case for joint life expectancy indicators. Soc Indic Res 84, 203–230 (2007). https://doi.org/10.1007/s11205-007-9099-1
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DOI: https://doi.org/10.1007/s11205-007-9099-1