Post on 01-Apr-2015
Mortality Projections in Portugal 2008-2060
Joint EUROSTAT – UNECE Work Session on Demographic Projections Lisboa, 28 - 30 April 2010
Edviges Coelho – Instituto Nacional de Estatística - Portugal Graça Magalhães – Instituto Nacional de Estatística - Portugal Jorge Miguel Bravo – Universidade de Évora / CEFAGE-UEJoão Peixoto – Universidade Técnica de Lisboa / ISEG
2
« Introduction
Past Trends and Future Perspectives
Scenarios adopted
Projections Models:
The Poisson-Lee-Carter Model
Model extension with “Limit Life Table”
Empirical results
« «Outline
3
The Portuguese Population Projections 2008- 2060:
Cohort - component method
Starting population – 1st January 2008 Estimates of Resident Population
Introduction
4
Assumptions on future levels of mortality
Recent trends
Scientific studies
National experts’ opinions
International experts’ opinions (EUROSTAT)
Introduction
5
Combination of extrapolative stochastic methods with experts’ judgment
Poisson Lee-Carter Model
Extrapolative method assuming that the future will mirror the past
Poisson Lee-Carter Model with Limit Table
Integrates the experts’ judgment about limits to the decline of
age-specific death rates into the Lee-Carter model.
Mortality Projections Methodology
6
67,9
75,6
74,8
81,9
60
65
70
75
80
85
1980 1985 1990 1995 2000 2005
Males
Females
16,3
13,0
19,8
16,0
10
12
14
16
18
20
22
1980 1985 1990 1995 2000 2005
Males
Females
Mortality Recent Trends
Life expectancy at birth Life expectancy at 65 years
7
The analysis of past trends and experts’ opinions provides the following perspectives for the future:
Increases in the population life expectancy will continue to occur in
the future, but at a slower pace;
Declines in mortality at older ages may also be relevant;
Future gains in infant mortality are expected to be small;
Some improvement in avoidable mortality in young and adult ages,
particularly associated with reduced risk of death from external
causes, particularly among males (attenuation of the accident
hump), can be expected;
The recent trend of narrowing the gap in longevity between men
and women will continue.
Future Perspectives
8
Mortality Assumptions:
Optimistic Scenario:
Future mortality will continue to improve at the same rate as in the recent past.
Moderate Scenario:
Integration of the experts’ perspectives on mortality for the next 50 years
Adopted Scenarios
9
Model:
Optimistic Scenario:
- Poisson Lee-Carter model.
Moderate Scenario:
- Poisson Lee-Carter model with Limit Life Table.
Models
10
«
Let mx,t, be the death rate at age x in year t.
where,
average pattern of mortality by age across
years,
the relative speed of change at each age of mx,t ,
is an index of the level of mortality at time t , and
an error that reflects stochastic influences which
are not captured by the previous terms.
ln ,, txtxxtx km
xx
tx,tk
The Lee - Carter Model
11
«
Let mx,t, be the death rate at age x in year t.
This is a regression framework with no observable quantities on the RHS.
The model is over parameterized To ensure model identification Lee and Carter
(1922) add the following constraints to the parameters:
ln ,, txtxxtx km
The Lee - Carter Model
1max
min
x
xxx 0
max
min
t
tttk
12
«
«
Lee and Carter (1922) : Singular Value
Decomposition
Brouhns, Denuit & Vermunt, 2002: Maximum
Likelihood
Fitting The Lee - Carter Model
13
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
Males
Females
PLC Estimates of x
14
PLC Estimates of and
-40
-30
-20
-10
0
10
20
30
40
1980 1985 1990 1995 2000 2005
Males
Females
0,00
0,01
0,02
0,03
0,04
0 10 20 30 40 50 60 70 80 90
Males
Females
tk xEstimated Estimated tk x
15
PLC Estimates of and forecasts
tk
-200
-150
-100
-50
0
50
1980 1990 2000 2010 2020 2030 2040 2050 2060
Males
Females
16
The decreasing time trend of associated with
positive values of .
The model leads us invariably to asymptotic death
rates approaching zero.
An unlikely scenario according to the experts’ judgment
on the mortality phenomenon for the next 50 years.
x
Lee-Carter with Limit Life Table
tk
17
Limits to the decline of age – specific deaths rates
were imposed through the use of the second mortality
law of Heligman and Pollard (1980).
The limits are defined accordingly to the future
perspectives of mortality behaviour integrating the
opinions of experts.
Lee-Carter with Limit Life Table
18
Lee-Carter with Limit Life Table
Males
-14
-12
-10
-8
-6
-4
-2
0
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
ln (
qxt
)
Heligman Pollard
2007
Females
-14
-12
-10
-8
-6
-4
-2
0
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
ln (
qxt
)
Heligman Pollard
2007
19
PLC Estimates of x
Females
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
Alp
ha
PLC Limit Table
PLC
Males
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
Alp
ha
PLC Limit Table
PLC
20
PLC Estimates of x
Males
0,000
0,005
0,010
0,015
0,020
0,025
0,030
0,035
0,040
0,045
0,050
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
Bet
a
PLC Limit Table
PLCFemales
0,000
0,005
0,010
0,015
0,020
0,025
0,030
0,035
0,040
0,045
0,050
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
Bet
a
PLC Limit Table
PLC
21
PLC Estimates of tk
Males
-50
-40
-30
-20
-10
0
10
20
30
40
1980 1985 1990 1995 2000 2005
kap
pa
PLC Limit Table
PLC
Females
-50
-40
-30
-20
-10
0
10
20
30
40
1980 1985 1990 1995 2000 2005
kap
pa
PLC Limit Table
PLC
22
Males2060
-14
-12
-10
-8
-6
-4
-2
0
0 10 20 30 40 50 60 70 80 90 100
PLC
PLC Limit Table
Females2060
-14
-12
-10
-8
-6
-4
-2
0
0 10 20 30 40 50 60 70 80 90 100
PLC
PLC Limit Table
Mortality Rates Projections 2060
23
Mortality Rates Projections 2060
Males
-14
-12
-10
-8
-6
-4
-2
0
0 10 20 30 40 50 60 70 80 90 100
PLC 2060
PLC Limit Table 2060
2007
Females
-14
-12
-10
-8
-6
-4
-2
0
0 10 20 30 40 50 60 70 80 90 100
PLC 2060
PLC Limit Table 2060
2007
24
75,6
83,5
82,381,9
89,4
87,9
65
70
75
80
85
90
19
80
19
85
19
90
19
95
20
00
20
05
20
10
20
15
20
20
20
25
20
30
20
35
20
40
20
45
20
50
20
55
20
60
estimates projections
age
mortality optimistic scenario - male mortality moderate scenario - male
mortality optimistic scenario - female mortality moderate scenario - female
Life expectancy at birth, by sex and by mortality scenarios,
Portugal, 1980-2060
Mortality – life expectancy
25
100,0 50,0 0,0 50,0 100,0
0
510
15
20
25
30
3540
45
50
55
6065
70
75
80
85
9095
100+
2008 mortality optimistic scenario mortality moderate scenario
Fertility and net migration adopted on the central scenario of PP, moderate and optimistic scenario of mortality
The effects of the two different mortality scenarios on the projected population are particularly visible in the
volume expansion at older ages… a cumulative effect is noticeable in the age pyramid
of population projected for 2060 and particularly at ages
above 60 years.
Population pyramids -1980, 2060
26
More detailed information on the last national exercise can be found at
Statistics Portugal portal www.ine.pt:
http://www.ine.pt/xportal/xmain?xpid=INE&xpgid=
ine_publicacoes&PUBLICACOESpub_boui
=65944632&PUBLICACOEStema=55466&PUBLICACOESmodo=2
http://www.ine.pt/xportal/xmain?xpid=INE&xpgid=
ine_estudos&ESTUDOSest_boui
=65946997&ESTUDOStema=55466&ESTUDOSmodo=2
The future
of Portuguese population? Humm
m…Thank you!