Mortality Modeling:

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 19721991
• 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, 19601997 (Gerdtham and Ruhm,
  2006)
• Procyclical deaths motor vehicle crashes, CVD,
  liver ailments, influenza/pneumonia
• Acyclical/countercyclical cancer, suicide,
  diabetes mellitus

7
Central Idea

• Popular mortality forecasting framework
  Lee-Carter model

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 (DEconomic Indicatort)
  
• 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
• 19511970 vs. 19912005 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 , with et
  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 Chows 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 understanding of 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