Mortality Modeling: Lee-Carter and the Macroeconomy Katja Hanewald

1. Mortality Modeling: Lee-Carter and the Macroeconomy Katja Hanewald Humboldt-Universität zu Berlin Collaborative Research Center 649: Economic Risk

2. Summary • Mortality reacts to macroeconomic changes • Effect is introduced into the Lee-Carter framework • Important result for the regulation and risk management of life insurance companies

3. Outline • Literature Review • Data • Analysis • Correlation Analysis • Regression Analysis • Conclusion

4. Literature Review • Combine two domains of the demographic literature (1) Stochastic Mortality Modeling • Lee-Carter (1992): “The earliest model and still the most popular” • Universal method, has been applied to various countries • Standard variant: Lee-Miller (2001) • Two stages: ln(mx,t) = ax + bx ∙ kt+ ex,t • kt usually modeled as random walk with drift

5. Literature Review • Mortality index kt: • Key driver of mortality dynamics in the LC model • “Index of the level of mortality” (Lee and Carter, 1992) • “Dominant temporal pattern in the decline of mortality” (Tuljapurkar et al., 2000) • “Random period effect” (Cairns et al., 2008) • kt– Just an unobserved latent variable?

6. Literature Review (2) Mortality and Macroeconomic Fluctuations • Ruhm (2000): Mortality rates in the USA fluctuate procyclically over the period 1972–1991 • Similar patterns observed for: • USA, Spain, and Japan (Tapia Granados, 2005a/b, 2008) • Germany (Neumayer, 2004, Hanewald, 2008) • Sweden (Tapia Granados and Ionides, 2008) • 23 OECD countries, 1960–1997 (Gerdtham and Ruhm, 2006) • Procyclical deaths: motor vehicle crashes, CVD, liver ailments, influenza/pneumonia • Acyclical/countercyclical: cancer, suicide, diabetes mellitus

7. Popular mortality forecasting framework: Lee-Carter model Central Idea Reaction of age-specific mortality rates to economic fluctuations Introduce the link between mortality and the macroeconomy into the LC model via the mortality index kt  Direct translation into age-specific death rates

8. Data • Annual data for six OECD countries,1950-2005 • Australia, Canada, France, Japan, Spain, USA • Lee-Carter mortality index kt • Lee-Miller (2001) variant • Treat males and females separately • Age range: 30-85 (0-99) • Real GDP growth rates • Unemployment rate changes

9. Correlation Analysis • Correlations between • Macroeconomic fluctuations (DEconomicIndicatort) • Changes in the mortality index (Dkt) • Different time horizons • Entire sample period (1951-2005) • Subperiods

10. Correlation Analysis • Entire sample period (1951-2005): • Significant procyclical correlations in Aus, Can, Jap, USA • Corr. range between 27% (females, Aus) and 38% (males, Can) • Cross-correlations: no lag • Interpretation: Reductions in mortality tend to be smaller when the economy strengthens • Findings agree with results of Ruhm (2000) and others for age-specific mortality rates

11. Correlation Analysis Correlations between Dkt and real GDP growth rates:

12. Correlation Analysis • Three subperiods • Structural change observed in all six countries • Relation reverses in most cases • Results for unemployment rates support findings • Study moving correlations: • Correlations over 20-year subperiods • Moving starting points

13. Correlation Analysis • Moving correlations between Dkt and real GDP growth rates

14. Discussion • Age-specific death rates of U.S. males • 1951–1970 vs. 1991–2005: Correlations for 40 of 56 age groups reverse from positive to negative • Tapia Granados (2008): similar tendency for age-specific mortality rates in Japan • Explanation: Changes in the causes of death

15. Discussion • Changes in the causes of death • Early 1970s: Dramatic decline in CVD mortality • 1990s: Reduced mortality from tobacco and alcohol consumption, motor vehicle crashes, influenza/pneumonia • Ongoing: Substantial increase in deaths attributable to poor diet and lack of physical activity

16. Regression Analysis • Standard RW model Dkt = q + et ,with et~ N(0,s) iid • Extended RW model: Dkt = q +b ∙DEconomic Indicatort + et , withet~ N(0,s ) iid • Separate models for males/females for all countries • Example: Mortality index of Canadian males Dkt = –1.359***+ 15.173**∙ Dln(real GDPt)+ et (0.218) (5.004)

17. Regression Analysis • Check all models’ error properties • Test for parameter stability (Quandt-Andrews Test) • Generalization of Chow’s break-point test • Treats the date of a potential structural break as unknown • Significant break years identified for males at the beginning of the 1970s (Aus: 1971, Jap & USA: 1973, Can: 1976) • Further candidate years

18. Regression Analysis • Stability of the coefficient on real GDP growth: Chow test sequence

19. Regression Analysis • Model the structural change using dummy variables • Example: Canadian males (1951-2005, adj. R² = 0.416)

20. Conclusion • LC mortality index kt correlates significantly with macroeconomic fluctuations • Common understandingof kt • Link between economic conditions and aggregate mortality is subject to a structural change • Established relationship • Important implications for life insurers: Hanewald, Post, and Gründl (2009, SSRN