Download - Mortality Trend–Model and Analysis
1
Mortality Trend–Model and Analysis
May 21, 2013Lina Xu
2
1. Methods to model Mortality Improvement
2. Lee Carter Model
3. Model fit/Analysis/Result
4. Industry Mortality Improvement Study
5. Conclusion
Overview
Methods Used for Mortality Improvement Factor
1. SOA2. CMIB3. Other Actuarial Method4. Lee-Carter
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
3
SOA Methods –Formula
This method will have a base rate q1994 and the reduction factor AAx for each age x.
SOA Group Annuity Valuation Table Task Force GAR94 TablesAAx was obtained: 1. Data Source
CSRS for age 25-65 for 1987-93add SSA for age 1-24 and 60-120 for 1977-93
2. Average TrendsLinear Regression of log(mx,t) 5-year age group for data CSRS and SSA for1987-
1993 and 1977-1993 respectively
Methods Used for Mortality Improvement Factor
nxx
nx AAqq )1(19941994
4Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
CMIB Methods –Formula
RF(x,t) - Exponential Decay Characterized by two age-dependent parameters. α(x) denotes the value to be asymptotically approached when t ends to infinite, while fn is the percentage of the total fall (1- α(x)) assumed to occur in n years.
Two set of tables 80 and 92 series (1979-82 and 1991-94 experiences, respectively) for annuitants and pensioners.
1. 80 Series - n was fixed at value of 20 and f20 at 0.6 for all ages. And α(x) is expressed as:
Methods Used for Mortality Improvement Factor
ntn xfxxtxRF /)](1[)](1[)(),(
),(0,, txRFqq xtx
0.5, 6010( ) , 60 110
1001, 110
xxx x
x
5Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
CMIB Methods –Formula
2. “92” Series - n remained fixed at 20 but f20 values linearly from 0.45 to 0.71 between ages 60 to 110, below 60 and above 110, constant values with the values already mentioned apply. And α(x) and fn are expressed as the following:
Methods Used for Mortality Improvement Factor
ntn xfxxtxRF /)](1[)](1[)(),(
),(0,, txRFqq xtx
0.13, 60110( ) 1 0.87 , 60 110
501, 110
xxx x
x
20
0.55, 60(110 ) 0.55 ( 60) 0.29( ) , 60 110
500.29, 110
xx xf x x
x
6Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
Other Actuarial Method Specifications1. Define Factor2. Determine “standard” rate for trend
a) Ratio of the mortality to the previous year’s mortalityb) Most Recent Mortality Ratec) Mean
3. Methodsa) Arithmetic averageb) Meanc) Geometric averaged) Weighted average
Methods Used for Mortality Improvement Factor
7Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
1. Data Source2. Lee-Carter Model3. Model Analysis
Lee-Carter Model
8Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
HMD: Human Mortality Database is a population data that it is administrated by UC Berkley
US population data from HMD period 1933 – 2006 is used to demonstrate Lee-Carter Method.
Mortality – Data Source
9Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
Region Source CalYr # of CalYr ProjPeriod # of ProjYrJapan HMD 1947-08 62 1979-08 30
Taiwan HMD 1970-08 39 1970-08 39USA HMD 1933-06 74 1977-06 30
KoreaKorean
Population Statistics
1983-03 21 1983-03 21
Lee-Carter’s Extrapolating Method1. Project age pattern and to measure uncertainty2. SVD to Solve the age-specific parameters as well
as the preliminary mortality index3. ARIMA (0,1,0) a random walk with a drift to
project mortality index
Mortality Trend – Methodology overview
10Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
General Model (1)
Where, is the central mortality rate for age x for year t; ax and bx are parameters dependent only on age x; kt is factor to be modeled as a time series; and the error term, is assumed to have mean zero and standard deviation .
Mortality Trend - Lee-Carter Method
, ,ln( )x t x x t x tm a b k ,x tm
,x t
11Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
Re-Write Model as (2)
Where, is the general shape across age of the mortality schedule; the bx profile tells us which rates decline rapidly and which rates decline slowly in response to changes in kt ( )
Mortality Trend - Lee-Carter Method
,x x ta b k
x tm e xae
,ln x t tx
d m dkbdt dt
12Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
The model (1) cannot be fitted by simple regression methods;
It allows for several solutions.
To deal the above, Use SVD, and bx and kt is normalized to sum to unity and
to zero respectively.
Mortality Trend - Lee-Carter Method
13Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
SVD Let A be order nxm, then there are unitary matrices U and V, of order n and m respectively, such that , where F is a rectangular diagonal matrix of order mxn,
With Fii = µi. The numbers µi are called the singular values of A. They are all real and positive, and they can be arranged so that
Where r is the rank of the matrix. V* is a conjugate transpose.
Lee-Carter Method – SVD overview
1 0
0 0rF
1 2 0r
14Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
SVD applied to ln(mx,t),(3)
Or (4)
Note that, V (and also U) is real number, so the conjugate transpose V* is equal to the transpose V’.
Mortality Trend - Lee-Carter Method
', ')ln( TTFVUm nntx
r
iiiitx tvxum
1, )()()ln(
15Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
Singular values – US 1933-2006
The first singular value is larger
Mortality Trend - Lee-Carter Method
Mu Male Female Both1 195.40 214.09 203.58 2 5.91 4.48 5.33 3 2.34 1.96 1.97 4 1.09 0.95 0.89 5 0.81 0.67 0.65 6 0.55 0.53 0.44 7 0.43 0.37 0.38 8 0.38 0.32 0.31 9 0.29 0.23 0.27 10 0.20 0.22 0.18
16Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
Use the first singular value component
(5)
The portion of the total temporal variances explained by the first SV component is all over 99%, that seemed captured important of data. The second singular value didn’t seemed add much value.
Mortality Trend - Lee-Carter Method
txtx tvxum ,111, )()()ln(
Mu Male Female Both1 0.9989 0.9994 0.9992 2 0.9998 0.9999 0.9999
17Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
18
Mortality Trend -Lee-Carter Method
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
SVD to Solve {ax}, {bx} and {kt},(6)
(7)
Mortality Trend -Lee-Carter Method
txxtxtx kbaBAm )ln( ,
t
tt
xtxx T
BABA
Ta 1
T
BBAk t
t
tx
xt
xx
x
t
xtxx A
Ak
aBAb
19Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
20
Fitted Values of {ax} and {bx} for 1933-2006 from equation (7) above,
Mortality Trend -Lee-Carter Method
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
A second stage of estimation of kt, whereby the kt’s are recalculated from the equation, (8)
Taking the estimated {ax} and {bx} as fixed from equation (7).
Note that: there is no closed form solution for equation (8) above. (Newton method is employed)
Mortality Trend -Lee-Carter Method
ˆˆ( ) [ ( , ) exp( )]x t xD t N x t a k b
21Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
Take an initial kt1 equation along with {ax} and {bx} from equation (7) above, the following vector is employed for the Newton’s method to obtained the 2nd stage k
Re-write the equation (8) above,
(9)The Jacobian matrix for equation (9) is,
The first order Taylor series becomes:
(10)
Mortality Trend -Lee-Carter Method
0)()()(),(),()( 1)()()()()()(
ii
XbTkXai
XBTkXaii TkTkeXbTXNeTXNTD ii
)()()(),()()( XbTkXaeTXNTDTF
)()(),()( )()()( TkeXbTXNTJ XbTkXa
22Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
After iterated equation (10) to find solution kt for equation (8). ARIMA(0,1,0) time series model that a random walk with drift is found to be a good fit, for the mortality index kt, That is,
(11)
Mortality Trend -Lee-Carter Method
1t t tk c k u
23Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
From the kt formula (11),
Summing up the above,
Mortality Trend -Lee-Carter Method
)1()1(
121
1
mtmtmt
ttt
ttt
uCkk
uCkkuCkk
1
01
1 m
jjtjt kk
mC
24Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
the projection of the kt into the i years from the current year t, (12)
Equation (12) implies, the quantity for the error term is,
Mortality Trend -Lee-Carter Method
1
0
i
jjttit uiCkk
iu
i
jjt
1
0
25Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
26
Lee-Carter Model fit Example – US
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
27
Lee-Carter Model fit Example – US
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
Lee-Carter Model fit Example – US
The error Term Analysis Recall that the error is assumed to follow a
normal distribution with mean 0 and standard deviation . The should not be too much different across ages.
,x t
28Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
29
Lee-Carter Model fit Example – US
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
30
Lee-Carter Model fit Example – US
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
31
Lee-Carter Model fit Example – US
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
32
Lee-Carter Model fit Example – US
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
Lee-Carter Model fit Example – US
33
Age Male Female Both5-9 2.4414 2.6466 2.4852
10-14 2.4132 2.6748 2.478120-24 1.9795 2.3692 2.088830-34 1.9380 2.2244 2.020740-44 1.7267 1.9751 1.803350-54 1.4564 1.7044 1.540460-64 1.1943 1.4324 1.282470-74 0.9447 1.1412 1.023880-84 0.6848 0.8267 0.746790-94 0.4383 0.5204 0.4761
(1-Exp(bxC))*100
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
Singular values
The first singular value is larger for all three countries (Japan, Taiwan, and US)
Mortality Trend -Lee-Carter Method
SV Japan Taiwan US SV Japan Taiwan USµ1 189.985 147.231 195.399 µ1 206.401 161.933 214.087 µ2 6.329 3.600 5.912 µ2 5.858 2.766 4.483 µ3 2.758 2.092 2.341 µ3 3.831 1.490 1.956 µ4 1.168 1.262 1.090 µ4 1.166 0.765 0.946 µ5 0.687 0.672 0.806 µ5 0.780 0.639 0.672 µ6 0.626 0.517 0.549 µ6 0.462 0.521 0.526 µ7 0.561 0.389 0.428 µ7 0.388 0.443 0.367 µ8 0.428 0.342 0.382 µ8 0.289 0.368 0.322 µ9 0.327 0.268 0.286 µ9 0.238 0.311 0.227 µ10 0.271 0.264 0.197 µ10 0.205 0.254 0.219
Male Female
34Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
Use the first singular value component
(5)
The portion of the total temporal variances explained by the first SV component is all over 99%, that seemed captured important of data.
Mortality Trend -Lee-Carter Method
txtx tvxum ,111, )()()ln(
Japan Taiwan US Japan Taiwan US0.9986 0.9991 0.9989 0.9988 0.9995 0.9994
Male Female
35Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
36
Mortality Trend -Lee-Carter Method
1947
1951
1955
1959
1963
1967
1971
1975
1979
1983
1987
1991
1995
1999
2003
2007
-20
-15
-10
-5
0
5
10
15
20
25
30 k1
k1
1947195
1195
5195
9196
3196
7197
1197
5197
9198
3198
7199
1199
5199
9200
3200
7
-0.800
-0.600
-0.400
-0.200
0.000
0.200
0.400
0.600
0.800
1.000 k2k2
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
37
-8.0
-7.5
-7.0
-6.5
-6.0
-5.5
-5.0
-4.5
-4.0
-3.5
-3.0
1947
1949
1951
1953
1955
1957
1959
1961
1963
1965
1967
1969
1971
1973
1975
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
2007
Log D
eath
Rat
e
Japan Male Actual and Fitted Death Rate (log Scale)
60-64Approx 60-6440-44Approx 40-4420-24Approx 20-24
Lee-Carter Model fit Example – Japan Male
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
Mortality Improvement – Selected Age
38
Age Japan Korea Taiwan US Japan Korea Taiwan US5-9 4.28 5.79 3.67 3.64 6.75 6.25 5.08 2.32
20-24 3.63 5.15 3.08 2.82 6.14 5.91 4.61 2.0430-34 3.54 4.79 2.90 2.76 5.81 5.64 4.37 1.9240-44 3.14 4.13 2.58 2.50 5.23 5.10 3.93 1.7150-54 2.66 3.53 2.24 2.15 4.58 4.46 3.40 1.4770-74 1.74 2.23 1.43 1.40 3.20 2.86 2.15 1.0080-84 1.20 1.38 1.02 1.02 2.23 1.68 1.50 0.74
FemaleMale
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
39
Korean has the highest improvement however the mortality rates are mostly higher than other regions for most ages;
US mortality has the lowest improvement.
Mortality Improvement for Some Regions
0 5-915-
1925-
2935-
3945-
4955-
5965-
6975-
7985-
8995-
99 1050.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0 Male Mortality Improvement by Age
JapanKoreaTaiwanUS
0 5-915-
1925-
2935-
3945-
4955-
5965-
6975-
7985-
8995-
99 1050.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0 Female Mortality Im-provement by Age
JapanKoreaTaiwanUS
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
40
a. Leading Cause of Deathb. Mortality Trend for cause of death Datac. Mortality Rates change by calendar year,
type of underwriting, age, sex, Cause of Death etc.
Short Term Mortality Trend
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
41
a. Japan: mortality and % of the number of deaths by cause were provided by age, sex, and type of underwriting for each year from 2001 to 05. The mortality and the number of death for leading cause of death by sex and type of underwriting for years from 1992 to 2005.
b. Korea: Mortality Rates by age for leading cause of day by age and sex; and the mortality for study period
c. Taiwan: mortality by sex and medical examination from year 1982 to 2000.
Short Term Mortality Trend
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
42
Leading Cause of Death and the additional Data Used in this analysis
Leading Cause of Death
Region Current Prior Current PriorJapan Neoplasm Neoplasm 2001-05 1997-98Korea Neoplasm Accident 2000-02 1996-98China Accident N/A 2000-03 N/ATaiwan N/A Accident N/A 1995-99
Leading Cause of death Study Period
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
43
Leading Cause of DeathCause of Death - Japan
2001-05Cause Med NonMed Med NonMed Male FemaleMalignant Neoplasm 42.61 36.14 47.52 45.62 41.70 47.06 Heard Disease 10.39 11.26 9.05 8.61 10.51 8.94 Cerebrovascular 6.89 7.36 8.54 8.71 6.95 8.58 Suicide 7.00 8.53 4.34 5.64 7.22 4.65 Accident 4.39 6.55 3.26 4.41 4.70 3.54 Subtotal 71.28 69.84 72.72 72.99 71.08 72.78
1997-98Cause Med NonMed Med NonMed Male FemaleMalignant Neoplasm 41.28 38.51 44.40 42.21 40.61 43.53 Heard Disease 11.93 13.86 10.85 12.17 12.40 11.38 Cerebrovascular 8.18 9.17 10.66 11.13 8.42 10.85 Suicide 5.39 4.20 3.95 4.68 5.10 4.24 Accident 6.60 6.52 4.49 4.55 6.58 4.52 Subtotal 73.38 72.26 74.35 74.74 73.11 74.52
Male Female Combined
Male Female Combined
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
44
Number of Death Age distributionCause of Death - Japan
0
2
4
6
8
10
12
14
16
18
20
0-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79
Japan Cause of Death Percent by Age
M.N.H.D.C.D.S.C.A.D.
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
45
0
2
4
6
8
10
12
2005 Male Med Mortality by Age
M.N.
0.0
0.1
0.2
0.3
0.4
0.5
0-4
5-9
10-1
415
-19
20-2
425
-29
30-3
435
-39
40-4
445
-49
50-5
455
-59
60-6
465
-69
70-7
475
-79
0-79
2005 Male Med Mortality by Age
S.C.
0.0
0.5
1.0
1.5
2.0
2.52005 Male Med Mortality by Age
H.D.C.D.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0-4
5-9
10-1
415
-19
20-2
425
-29
30-3
435
-39
40-4
445
-49
50-5
455
-59
60-6
465
-69
70-7
4
2005 Male Med Mortality by Age
A.D.
Japan Cause of Death – Mortality Per 1,000
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
Leading Cause of DeathCause of Death - Korea
Cause of Death 5thEMT 4thEMT 5thEMT 4thEMT 5thEMT 4thEMTNeoplasm 29.9 21.5 28.8 28.6 32.4 23.7Injury & Poisoning 29.1 34.3 14.8 23.6 26.7 31Circulatory 19.3 16 21.2 19.5 20.2 17.1Digestive 8.7 9.7 7.8 4.7 8.7 8.1Subtotal 87 81.5 72.6 76.4 88 79.9
CombinedFemaleMale
46Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
47
Number of Death Age DistributionCause of Death - Korea
0 1-4 5-9 10-14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-59 80-84 85+0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
Korea 5th EMT Major Cause of Death Distribution
Neoplasm Injury & Poisoning
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
Taiwanese 5 leading Cause of Death
Cause of Death - Taiwan
Cause Male Female BothMalignant Neoplasm 24.93 30.51 26.55 Accident 26.15 20.15 24.41 Circulatory 10.23 10.24 10.23 Digestive System 8.95 4.99 7.80 Mental and Nervous 7.97 7.12 7.72 Subtotal 78.23 73.01 76.72
48Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
49
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Japan Mortality Per 1000 by Fiscal Year
Male Med Male NonMed Female Med Female NonMed
Mortality Trend – Japan
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
50
0.50
1.05
1.60
2.15
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Malignant Neoplasm - Mortality Per 1,000
Male Med Male NonMed Female Med Female NonMed
Japan Mortality – Cause of Death
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
51
Japan Mortality – Cause of Death
0.65
0.85
1.05
1.25
1.45
1.65
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Malignant Neoplasm - Mortality Per 1,000
Male Female Med NonMed
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
52
Japan Mortality – Cause of Death
0.100.150.200.250.300.350.400.450.500.550.60
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Heart Disease - Mortality Per 1,000
Male Med Male NonMed Female Med Female NonMed
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
53
0.05
0.10
0.15
0.20
0.25
0.30
0.35
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Cerebrovascular - Mortality Per 1,000
Male Med Male NonMed Female Med Female NonMed
Japan Mortality – Cause of Death
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
54
Japan Mortality – Cause of Death
0.05
0.10
0.15
0.20
0.25
0.30
0.35
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Suicide - Mortality Per 1,000
Male Med Male NonMed Female Med Female NonMed
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
55
Japan Mortality – Cause of Death
0.00
0.05
0.10
0.15
0.20
0.25
0.30
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Accident - Mortality Per 1,000
Male Med Male NonMed Female Med Female NonMed
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
Improvement/Deteriorate (+/-) Percent
Mortality Trend – Japan
1997-05Cause Med NonMed Med NonMed Male FemaleM.N. (1.91) 5.79 (1.85) 2.80 (0.06) (0.04) H.D. (1.61) 6.91 (0.75) 5.92 0.48 1.67 C.D. 0.32 8.07 1.26 5.67 2.22 3.18 S.C. (0.07) (0.28) (0.34) 2.90 0.42 1.03 A.D. 2.44 4.78 1.53 5.34 3.18 3.26 Total (1.63) 5.10 0.94 2.33 0.06 0.94
CombinedMale Female
56Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
Improvement comparison to Population:
Mortality Improvement – Japan
57
Industry Population (Age 20-69)1998-05 1933-08 1979-08
Male 3.27% 3.28% 2.95%Female 3.61% 3.85% 4.99%
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
Korea EMT Improvement Factor
Mortality Trend – Korea
From To Male Female EMT Period Male Female3rd EMT 4thEMT 4.88 6.36 3rd 1988-1992 2.972 1.624 4th EMT 5th EMT 1.14 1.08 4th 1996-1998 2.093 1.025 5th EMT 6th EMT 1.25 4.21 5th 2000-2002 2.000 0.982 4th EMT 6th EMT 1.19 2.43 6th 2003-2005 1.926 0.863
Period Factor Percent Korea EMT Mortality Per 1,000
58Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
59
1.00
1.50
2.00
2.50
3.00
3.50
4.00
198219831984198519861987198819891990199119921993199419951996199719981999
Taiwan Mortality Per 1,000 by Calendar YearMale Female
Mortality Trend –Taiwan
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
Mortality Trend - Taiwan
Figure2 Taiwanese Aggregate Mortality by Type of Underwriting
Taiwan Aggregate Mortality
0
1
2
3
4
5
6
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
Calendar Year
Mor
talit
y Pe
r 1,0
00
Medical Non-Med
60Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
Compare Industry Improvement to Population
*Population result is for Age 20-69
Mortality Improvement Comparison
61
Industry Population*Japan 1992-05 1998-05 1979-08
Male 1.18% 3.27% 2.95%Female 1.69% 3.61% 4.99%
Korea 1988-05 1996-05 1970-08Male 3.05% 1.19% 4.16%Female 4.42% 2.43% 5.02%
Taiwan 1982-99 1988-99 1970-08Male 3.45% 3.74% 2.18%Female 4.28% 4.16% 2.72%
Methods Lee-Carter Model Model fit/Analysis/Result Industry Trend Study
62
1. Lee-Carter Method modeled the uncertainty of the reduction factor while other methods didn’t;
2. The reduction factor is vary by age and sex;3. The reduction factor is also vary by projection
year;4. The reduction factor vary by region;5. The industry mortality improvement is usually
smaller than the population’s improvement.
Conclusion
63
Questions??