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: 1.Lorenz Dominance 2.Pigou-Dalton Principle of Transfers 3.Scale and translation invariance 4.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 1.The choice of inequality measure matters 2.AID and e† are safe absolute inequality measures (of those studied) 3.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 m x values CanadaJapan Agemx 00.005700.00352 10.000320.00055 20.000180.00033 30.000220.00027 …… 110+0.72110.7008 SD15.3114.86

23. Step-wise decomposition example: SD 1st replacement2nd replacementFinal replacement CanadaJapanContr.CanadaJapanContr.CanadaJapanContr. Agemx 00.00570 0.420.00570 0.420.005700.003520.42 10.000320.00055 … 0.00032 -0.040.00032 -0.04 20.000180.00033 … 0.000180.00033…0.00018 0.03 30.000220.00027 … 0.000220.00027…0.00022 0.01 …… … … 110+0.72110.7008 … 0.72110.7008 … 0.7211 0 SD15.3115.28 15.3115.24 15.31 0.45 Original mx 00.005700.00352 10.000320.00055 …… 110+0.72110.7008 SD15.3114.86