1. Session: Mortality Compression
Discussant: Dr. Leonid A. Gavrilov, Ph.D.
Center on Aging
NORC and The University of Chicago
Chicago, Illinois, USA

2. Debon, F. Martinez-Ruiz, F. Montes
Temporal evolution of some mortality indicators. Application to Spanish data
Debon, F. Martinez-Ruiz, F. Montes

3. Strengths
Compact presentation of mortality data and opportunity to reconstruct age-specific mortality.
Clear dynamics of kt coefficient gives an opportunity for mortality forecasts.

4. Historical changes of k parameters

5. Assumed only one factor of mortality change
Weaknesses
Assumed only one factor of mortality change
Younger age groups may have different factors compared to older groups

6. Changes in Mortality,
Swedish Females. Data source: Human Mortality Database

7. μ(x) = A + R e αx Gompertz-Makeham law
Until the 1950s, mortality changes were determined predominantly by the Makeham component
μ(x) = A + R e αx
Gompertz component
(senescent mortality)
Makeham component
(background mortality)

8. Mortality force (age, time) =
Extension of the Gompertz-Makeham Model Through the Factor Analysis of Mortality Trends
Mortality force (age, time) =
= a0(age) + a1(age) x F1(time) + a2(age) x F2(time)

9. Factor Analysis of Mortality Swedish Females
Data source: Human Mortality Database

10. Age dependence of parameter bx (multiplier to kt)

11. Opportunities
Interesting finding related to the age-time changes of residuals in the Lee-Carter model. Cohort effects.

12. Age-period changes in Lee-Carter model residuals

14. Threats
These models and forecasts are based on the past experience. Economic crisis and challenges of population aging may change mortality trends

15. Mortality Compression and Longevity Risk
Jack C. Yue

16. Strengths
Rectangularization issue was elegantly addressed using two simple indicators
Showed that compression of mortality is not so obvious – some indicators (SD, survival probability after mode) do not show compression of mortality

17. Weaknesses
The author argues that he used “raw” data from the Human Mortality Database. It is not clear which particular data were used. If the author used death rates from HMD life tables then the data are not entirely raw.
The author uses standard deviation supposedly in the whole age interval. It may be reasonable to use SD10

18. Human Mortality Database
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19. Opportunities It may be reasonable to use SD20.
Why not to use coefficient of variation?

20. Threats
Again it is possible that past experience may be irrelevant to future changes in economic situation and age structure
Recommendation to stop annuity payments at age 100 may be not a solution if more people survive to age 90 or 95