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Quantifying Lifespan Disparities: Which Measure to Use?

This presentation examines different measures of lifespan inequality and compares their effectiveness in quantifying disparities. Results show variations in rankings and sensitivity across countries and age distributions. The choice of measure matters in accurately assessing inequality.

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Quantifying Lifespan Disparities: Which Measure to Use?

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  1. Quantifying lifespan disparities: Which measure to use? Alyson van Raalte BSPS Conference, Manchester 12 September 2008

  2. Outline • Why measure lifespan inequality • Objectives • Considerations in choosing measures • Methods • Description of measures examined • Data • Decomposition technique used • Results • Lifespan inequality over time, across countries • Statistics of disagreement, testing for Lorenz dominance • Decomposition example, Japan in 1990s

  3. Why measure lifespan inequality

  4. Objectives • How different are the examined inequality measures? • In which parts of the age distribution are the different measures more sensitive? • What are the advantages and drawbacks to using the different measures?

  5. Considerations in choosing a measure • Criteria: • Lorenz Dominance • Pigou-Dalton Principle of Transfers • Scale and translation invariance • Population size independence • Considerations: • Aversion to inequality • Age spectrum examined • Pooled-sex data or separate male/female data • Sensitivity to data errors or period fluctuations • Compositional change in the population

  6. Lorenz curve

  7. Lorenz dominance

  8. Measures under examination • Comparing individuals to central value • Standard deviation / Coefficient of Variation • Interquartile range / IQRM • Comparing each individual to each other individual • Absolute inter-individual difference / Gini • Entropy of survival curve • Years of life lost due to death (e†) / Keyfitz’ Η

  9. Data • Countries used: Canada, Denmark, Japan, Russia, USA • All data from Human Mortality Database, 1960-2006 (2004 for USA and Canada) • Life table male death distributions • Full age range examined

  10. Methods • Statistics of disagreement • Over time: differences in the direction of inequality change • Across countries: differences in ranking • Testing for Lorenz dominance • Age decompositions (stepwise replacement) to determine why measures disagreed • Direction of inequality change unclear (Japan in 1990s)

  11. Results: Relative Measures

  12. Results: Absolute Measures

  13. Statistics of disagreement: Country Rankings • Absolute inequality: • Country rankings differed 25/45 years • SD alone ranked countries differently 9 times • IQR alone ranked countries differently 8 times • Relative inequality: • Country rankings differed 18/45 years • CV alone ranked countries differently 8 times • IQRM alone ranked countries differently 6 times • Lorenz dominance criterion broken: • 4 times by standard deviation • twice by interquartile range • never by relative measures

  14. Direction of inequality change • Absolute measures • 77/225 cases where absolute measures disagreed • AID disagreed with all other measures zero times • e† disagreed with all other measures six times • SD disagreed with all other measures seventeen times • IQR disagreed with all other measures thirty-seven times • Relative measures • 52/225 cases where absolute measures disagreed • Gini coefficient disagreed with all other measures zero times • Keyfitz’ H disagreed with all other measures four times • CV disagreed with all other measures seven times • IQRM disagreed with all other measures thirty times

  15. Example: Japan in the 1990s • Absolute inequality: • increased according to e†, AID and IQR • decreased according to SD • Relative inequality: • increased according to IQRM • decreased according to H, G, and CV

  16. Decomposing life expectancy increases

  17. Age decompositions: Absolute measures

  18. Age decompositions: Relative measures

  19. Summary of results • Differences in aversion to inequality: • SD/CV very sensitive to changes in infant mortality • Ages 50-85 most impacting IQR/IQRM (modern distributions) • e†/H and AID/G both sensitive to transfers around mean, but e†/H more sensitive to upper ages • Most cases of different rankings owed to different age profiles of mortality • Standard deviation and Interquartile Range both found to violate Lorenz dominance • IQR/IQRM and SD/CV disagreed most often with other measures in ranking distributions

  20. Conclusion The choice of inequality measure matters AID and e† are safe absolute inequality measures (of those studied) Gini and H are safe relative inequality measures

  21. Comments or Questions?

  22. Step-wise replacement decomposition • In theory any aggregate demographic measure can be decomposed • For differences between lifespan inequality measures, need only to replace mx values

  23. Step-wise decomposition example: SD

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