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Katja Hanewald - Lee-Carter and the Macroeconomy
HUMBOLDT–UNIVERSITÄT ZU BERLIN
Mortality Modeling:
Lee-Carter and the Macroeconomy
Katja Hanewald
Humboldt-Universität zu Berlin
Collaborative Research Center 649: Economic Risk
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HUMBOLDT–UNIVERSITÄT ZU BERLIN
Katja Hanewald - Lee-Carter and the Macroeconomy
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
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HUMBOLDT–UNIVERSITÄT ZU BERLIN
Katja Hanewald - Lee-Carter and the Macroeconomy
Outline
 Literature Review
 Data
 Analysis
 Correlation Analysis
 Regression Analysis
 Conclusion
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HUMBOLDT–UNIVERSITÄT ZU BERLIN
Katja Hanewald - Lee-Carter and the Macroeconomy
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
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HUMBOLDT–UNIVERSITÄT ZU BERLIN
Katja Hanewald - Lee-Carter and the Macroeconomy
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?
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HUMBOLDT–UNIVERSITÄT ZU BERLIN
Katja Hanewald - Lee-Carter and the Macroeconomy
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:
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USA, Spain, and Japan (Tapia Granados, 2005a/b, 2008)
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Germany (Neumayer, 2004, Hanewald, 2008)
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Sweden (Tapia Granados and Ionides, 2008)
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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
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HUMBOLDT–UNIVERSITÄT ZU BERLIN
Katja Hanewald - Lee-Carter and the Macroeconomy
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
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HUMBOLDT–UNIVERSITÄT ZU BERLIN
Katja Hanewald - Lee-Carter and the Macroeconomy
Data
 Annual data for six OECD countries,1950-2005
 Australia, Canada, France, Japan, Spain, USA
 Lee-Carter mortality index kt
 Lee-Miller (2001) variant
60
Japan
40
 Treat males and females separately
 Age range: 30-85 (0-99)
20
0
-20
 Real GDP growth rates
-40
Males
-60
1950
1960
Females
1970
1980
1990
2000
 Unemployment rate changes
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HUMBOLDT–UNIVERSITÄT ZU BERLIN
Katja Hanewald - Lee-Carter and the Macroeconomy
Correlation Analysis
 Correlations between
 Macroeconomic fluctuations (DEconomic Indicatort)
 Changes in the mortality index (Dkt)
 Different time horizons
 Entire sample period (1951-2005)
 Subperiods
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HUMBOLDT–UNIVERSITÄT ZU BERLIN
Katja Hanewald - Lee-Carter and the Macroeconomy
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 agespecific mortality rates
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HUMBOLDT–UNIVERSITÄT ZU BERLIN
Katja Hanewald - Lee-Carter and the Macroeconomy
Correlation Analysis
Correlations between Dkt and real GDP growth rates:
Measure Australia Canada
1951–2005
Males
0.326*
0.384**
Females
0.269*
0.061
1951–1970
Males
0.326
0.520*
Females
0.295
0.409+
1971–1990
Males
0.235
0.369
Females
0.217
–0.150
1991–2005
Males
–0.081
–0.217
Females
–0.092
0.046
France Japan
Spain
USA
0.109
0.000
–0.076
0.051
0.000
0.036
0.285*
0.286*
0.229
0.166
–0.028
0.095
0.013
0.004
0.400†
0.406†
–0.176
–0.175
0.017
0.036
0.073
0.102
0.367
0.321
–0.271 –0.357 –0.161 –0.400
–0.171 –0.222 0.031 –0.113
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HUMBOLDT–UNIVERSITÄT ZU BERLIN
Katja Hanewald - Lee-Carter and the Macroeconomy
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
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HUMBOLDT–UNIVERSITÄT ZU BERLIN
 Moving correlations between Dkt and real GDP growth rates
0.6
Japan
Correlation
Coeff.
0.4
Males
Females
0.2
0
1950
1955
1960
1965
1970
1975
1980
1985
1990
-0.2
-0.4
Year
0.6
United States
Males Females
0.4
Correlation
Coeff.
Katja Hanewald - Lee-Carter and the Macroeconomy
Correlation Analysis
0.2
0
-0.2
1950
1955
1960
1965
1970
1975
1980
1985
1990
-0.4
Year
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HUMBOLDT–UNIVERSITÄT ZU BERLIN
Katja Hanewald - Lee-Carter and the Macroeconomy
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
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HUMBOLDT–UNIVERSITÄT ZU BERLIN
Katja Hanewald - Lee-Carter and the Macroeconomy
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
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HUMBOLDT–UNIVERSITÄT ZU BERLIN
Katja Hanewald - Lee-Carter and the Macroeconomy
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)
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HUMBOLDT–UNIVERSITÄT ZU BERLIN
Katja Hanewald - Lee-Carter and the Macroeconomy
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
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 Stability of the coefficient on real GDP growth: Chow test
sequence
25
Canada
United States
F(1, 52)
Andrew s Critical Value
20
Chow Test Sequence
Katja Hanewald - Lee-Carter and the Macroeconomy
Regression Analysis
15
10
5
0
1960
1965
1970
1975
1980
1985
1990
1995
Break Year
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HUMBOLDT–UNIVERSITÄT ZU BERLIN
Katja Hanewald - Lee-Carter and the Macroeconomy
Regression Analysis
 Model the structural change using dummy variables
0, t  1951, , x  1
Dx  
1, t  x, , 2005
 Example: Canadian males (1951-2005, adj. R² = 0.416)
Dkt   1.119***  18.187 *** 15.088*** D1976  18.997 **  D1996   D ln( real GDPt )
1.119  18.187  D ln(real GDPt ), t  1951, ,1975

 1.119  3.099  D ln(real GDPt ) , t  1976, ,1995
1.119  15.898  D ln(real GDP ), t  1996, , 2005
t

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HUMBOLDT–UNIVERSITÄT ZU BERLIN
Katja Hanewald - Lee-Carter and the Macroeconomy
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
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