Sensitivity of life disparity with respect to changes in mortality rates

This article is concerned with sensitivity analysis of life disparity with respect to changes in mortality rates. A relationship is derived that describes the effect on life disparity caused by a perturbation of the force of mortality. Recently Zhang and Vaupel introduced a “threshold age”, before which averting deaths reduces disparity, while averting deaths after that age increases disparity. I provide a refinement to this result by characterizing the ages at which averting deaths has an extremal impact on life disparity. The results are illustrated using data for the female populations of Denmark in 1835, and for the United States in 2005. 1 Max Planck Institute for Demographic Research, Konrad-Zuse-Straße 1, 18057 Rostock, Germany. E-mail: [email protected]. 2 The author thanks Carl Schmertmann for thoughtful recommendations, including the interpretation of the three summands in equation (5), that helped to improve and shorten the article, Joshua Goldstein for valuable suggestions concerning its structure and presentation and Thomas Cassidy for proofreading and further help with its shortening. Useful comments by James Vaupel and also Trifon Missov and Zhen Zhang are gratefully acknowledged. http://www.demographic-research.org 63 Wagner: Sensitivity of life disparity with respect to changes in mortality rates