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!