1. Katja Hanewald - Lee-Carter and the Macroeconomy H U M B O L D T – U N I V E R S I T Ä T Z U B E R L I N - 1 - Mortality Modeling: Lee-Carter and the Macroeconomy Katja Hanewald Humboldt-Universität zu Berlin Collaborative Research Center 649: Economic Risk

2. Katja Hanewald - Lee-Carter and the Macroeconomy H U M B O L D T – U N I V E R S I T Ä T Z U B E R L I N - 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. Katja Hanewald - Lee-Carter and the Macroeconomy H U M B O L D T – U N I V E R S I T Ä T Z U B E R L I N - 3 - Outline  Literature Review  Data  Analysis  Correlation Analysis  Regression Analysis  Conclusion

4. Katja Hanewald - Lee-Carter and the Macroeconomy H U M B O L D T – U N I V E R S I T Ä T Z U B E R L I N - 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(m x,t ) = a x + b x ∙ k t +  x,t  k t usually modeled as random walk with drift

5. Katja Hanewald - Lee-Carter and the Macroeconomy H U M B O L D T – U N I V E R S I T Ä T Z U B E R L I N - 5 - Literature Review  Mortality index k t :  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)  k t – Just an unobserved latent variable?

6. Katja Hanewald - Lee-Carter and the Macroeconomy H U M B O L D T – U N I V E R S I T Ä T Z U B E R L I N - 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. Katja Hanewald - Lee-Carter and the Macroeconomy H U M B O L D T – U N I V E R S I T Ä T Z U B E R L I N - 7 - Central Idea Popular mortality forecasting framework: Lee-Carter model Introduce the link between mortality and the macroeconomy into the LC model via the mortality index k t  Direct translation into age-specific death rates Reaction of age-specific mortality rates to economic fluctuations

8. Katja Hanewald - Lee-Carter and the Macroeconomy H U M B O L D T – U N I V E R S I T Ä T Z U B E R L I N - 8 - Data  Annual data for six OECD countries,1950-2005  Australia, Canada, France, Japan, Spain, USA  Lee-Carter mortality index k t  Lee-Miller (2001) variant  Treat males and females separately  Age range: 30-85 (0-99)  Real GDP growth rates  Unemployment rate changes

9. Katja Hanewald - Lee-Carter and the Macroeconomy H U M B O L D T – U N I V E R S I T Ä T Z U B E R L I N - 9 - Correlation Analysis  Correlations between  Macroeconomic fluctuations (  Economic Indicator t )  Changes in the mortality index (  k t )  Different time horizons  Entire sample period (1951-2005)  Subperiods

10. Katja Hanewald - Lee-Carter and the Macroeconomy H U M B O L D T – U N I V E R S I T Ä T Z U B E R L I N - 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. Katja Hanewald - Lee-Carter and the Macroeconomy H U M B O L D T – U N I V E R S I T Ä T Z U B E R L I N - 11 - Correlation Analysis Correlations between  k t and real GDP growth rates: Measure AustraliaCanadaFrance Japan SpainUSA 1951–2005 Males0.326*0.384**0.109–0.0760.0000.285* Females0.269*0.0610.0000.0510.0360.286* 1951–1970 Males0.3260.520*0.229–0.0280.0130.400 † Females0.2950.409 + 0.1660.0950.0040.406 † 1971–1990 Males0.2350.369–0.1760.0170.0730.367 Females0.217–0.150–0.1750.0360.1020.321 1991–2005 Males–0.081–0.217–0.271–0.357–0.161–0.400 Females–0.0920.046–0.171–0.2220.031–0.113

12. Katja Hanewald - Lee-Carter and the Macroeconomy H U M B O L D T – U N I V E R S I T Ä T Z U B E R L I N - 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. Katja Hanewald - Lee-Carter and the Macroeconomy H U M B O L D T – U N I V E R S I T Ä T Z U B E R L I N - 13 - Correlation Analysis  Moving correlations between  k t and real GDP growth rates

14. Katja Hanewald - Lee-Carter and the Macroeconomy H U M B O L D T – U N I V E R S I T Ä T Z U B E R L I N - 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. Katja Hanewald - Lee-Carter and the Macroeconomy H U M B O L D T – U N I V E R S I T Ä T Z U B E R L I N - 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. Katja Hanewald - Lee-Carter and the Macroeconomy H U M B O L D T – U N I V E R S I T Ä T Z U B E R L I N - 16 - Regression Analysis  Standard RW model  k t =  +  t, with  t ~ N(0,  ) iid  Extended RW model:  k t =  +  ∙  Economic Indicator t +  t, with  t ~ N(0,  ) iid  Separate models for males/females for all countries  Example: Mortality index of Canadian males  k t = –1.359*** + 15.173** ∙  ln(real GDP t ) +  t (0.218) (5.004)

17. Katja Hanewald - Lee-Carter and the Macroeconomy H U M B O L D T – U N I V E R S I T Ä T Z U B E R L I N - 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. Katja Hanewald - Lee-Carter and the Macroeconomy H U M B O L D T – U N I V E R S I T Ä T Z U B E R L I N - 18 - Regression Analysis  Stability of the coefficient on real GDP growth: Chow test sequence

19. Katja Hanewald - Lee-Carter and the Macroeconomy H U M B O L D T – U N I V E R S I T Ä T Z U B E R L I N - 19 - Regression Analysis  Model the structural change using dummy variables  Example: Canadian males (1951-2005, adj. R² = 0.416)

20. Katja Hanewald - Lee-Carter and the Macroeconomy H U M B O L D T – U N I V E R S I T Ä T Z U B E R L I N - 20 - Conclusion  LC mortality index k t correlates significantly with macroeconomic fluctuations  Common understanding of k t  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