MPIDR Working Paper
Perturbation analysis of indices of lifespan variability
MPIDR Working Paper WP-2012-004, 43 pages.
Rostock, Max Planck Institute for Demographic Research (January 2012)
Revised January 2013. This working paper has been published. See the link above for further information.
A number of indices have been used in recent years to calculate
lifespan variation, each with different underlying properties. Although
these indices are assumed to be interchangeable, little research has
been conducted to show under which conditions this assumption is
appropriate, or how to compare their responses to the underlying mortality schedule. We compare seven indices of lifespan variation: life
disparity, the Gini coefficient, the standard deviation, the variance,
Theil's index, the mean logarithmic deviation, and the inter-quartile
range. We derive the sensitivity and elasticity of each index by applying Markov chain theory and matrix calculus. Using empirical French
and Russian male data we compare the underlying sensitivities to mortality change under different mortality regimes in order to test under
which conditions the indices might differ in their conclusions about the
magnitude of lifespan variation. Finally we demonstrate how integrating these sensitivities can be used as a method of age decomposition.
The result is an easily computable method for calculating the properties of this important class of longevity indices.
Keywords: inequality, mathematical demography, mortality measurement