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Quantifying lifespan disparities: Which measure to use? Alyson van Raalte

Quantifying lifespan disparities: Which measure to use? Alyson van Raalte BSPS Conference, Manchester 12 September 2008. Outline. Why measure lifespan inequality Objectives Considerations in choosing measures Methods Description of measures examined Data

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Quantifying lifespan disparities: Which measure to use? Alyson van Raalte

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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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