Improvements in Life expectancy and sustainability of social

Improvements in Life expectancy and sustainability of social security schemes – A Danish perspective Chresten Dengsoe

Agenda • Part I – Evolution of Danish mortality – Decomposition of life expectancy gains • Part II – Small population modelling (SAINT framework) – Old-age mortality (frailty theory) – A model for Danish mortality 2 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. – 27 -28 April 2010

Evolution of Danish male mortality Life expectancy 36 yrs (1835) Life expectancy 76 yrs (2006) Cholera epidemic (1853) Spanish Flu (1918) World War II (1945) 3 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. – 27 -28 April 2010

Evolution of Danish female mortality Life expectancy 40 yrs (1835) Δlife expectancy = 13 yrs Δlife expectancy = 21 yrs Life expectancy 80 yrs (2006) Δlife expectancy = 6 yrs 4 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. – 27 -28 April 2010

Expected total life times of Danish females 90 80 70 60 40 20 90 80 70 0 0 5 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. – 27 -28 April 2010

Age and period decomposition of female life expectancy gains Period Δe 6 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. – 27 -28 April 2010

Conclusions • Methodology for decomposing life expectancy gains • Life expectancy gain of 40 years from 1835 to 2006 – about half due to reductions in infant and child mortality – since 1950 gains mainly due to improving old-age mortality 7 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. – 27 -28 April 2010

Part II: Small population mortality modelling • Characteristics of small population mortality – data highly volatile, but with underlying structure • The SAINT framework – short-term deviations from long-term trend • Frailty and old-age mortality • A model for Danish mortality 8 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. – 27 -28 April 2010

Development in Danish mortality Danish female mortality Very little improvement at the highest ages Age 100 90 High annual rates of improvement 80 70 60 50 40 Sharp decline in young age mortality 30 20 Stagnation/increase from 1980 to 1995 9 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. – 27 -28 April 2010

Simple projections – unstable and implausible Danish female mortality Reasonable short-term projections Age 100 90 80 70 60 50 40 30 20 1990 Implausible long-term projections lacking (biological) structure 10 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. – 27 -28 April 2010

Characteristics of small population mortality • Challenge: Produce plausible, long-term forecasts reflecting both the underlying trend and the ”wildness” seen in data • Idea: Estimate the underlying trend from more regular reference data 11 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. – 27 -28 April 2010

Steady decline in international mortality levels International female mortality Age 100 90 Small improvements at the highest ages 80 70 60 Regular pattern of improvements 50 40 30 20 12 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. – 27 -28 April 2010

Danish fluctuations around stable international trend Danish and international female mortality Danish life expectancy among the highest in the world Age 100 90 80 70 60 50 40 Denmark falling behind the international trend Is this the beginning of a catch up period? 30 20 13 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. – 27 -28 April 2010

Danish mortality – fit and forecast Danish female mortality and international trend Similar development in old age mortality Age 100 90 80 70 Denmark falling behind … and catching up again 60 50 40 30 20 14 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. – 27 -28 April 2010

Summary • SAINT framework – small population regarded as subpopulation of reference population (for example country vs international, region vs country, etc. ) • Trend – estimated from larger reference population – parametric surface derived from frailty theory – guarantees robust, coherent forecasts • Spread – VAR-model for deviations of small population mortality from trend – forecasts and confidence intervals easily obtained 15 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. – 27 -28 April 2010

Appendices References: • Jarner, Kryger and Dengsøe (2008) The evolution of death rates and life expectancy in Denmark. Scandinavian Actuarial Journal 108, 147 -173. • Jarner and Kryger (2008). Modelling adult mortality in small populations: The SAINT model. Preprint. 16 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. – 27 -28 April 2010

Homogeneous cohort – no selection Intensity (μ) Gompertz-Makeham intensity: (x) 17 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. – 27 -28 April 2010

Selection effects within a cohort Cohort: Intensity (μ) Individual: (x) 18 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. – 27 -28 April 2010

Cohort lifetimes Expected lifetimes of Danish females SAINT projection Age 0 20 40 60 No future improvements 60 40 20 0 19 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. – 27 -28 April 2010