Perturbation analysis of indices of lifespan variability
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.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ryan D. Edwards, 2011. "Changes in World Inequality in Length of Life: 1970–2000," Population and Development Review, The Population Council, Inc., vol. 37(3), pages 499-528, 09.
- Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469, Diciembre.
- Ryan D. Edwards & Shripad Tuljapurkar, 2005. "Inequality in Life Spans and a New Perspective on Mortality Convergence Across Industrialized Countries," Population and Development Review, The Population Council, Inc., vol. 31(4), pages 645-674.
- repec:cup:cbooks:9780521822893 is not listed on IDEAS
When requesting a correction, please mention this item's handle: RePEc:dem:wpaper:wp-2012-004. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Peter Wilhelm)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.