Transcript PPT

Session 4:
Projecting the levels of mortality,
fertility and migration
Models and exercises
• Copy folder “Hands-on Exercises” with the
model templates to your computer
Projecting levels of mortality
Overview
Projecting levels of mortality
• Mortality change (and fertility change) are
processes where new behavior is gradually
being adopted by people. It is similar to the
processes of a new product penetrating a
market. In other words: A diffusion process.
• Diffusion processes are often modeled by a
logistic function.
Projecting levels of mortality
The general form of a logistic function can be expressed as
P(t ) 
k
α
β
k
.
1 exp[ (t   )]
Saturation level or asymptote of the diffusion process
Growth rate of the s-curve
Length of time the curve takes to reach the midpoint of the growth trajectory.
For modelling purposes, the logistic function is often simplified, with easier to interpret
parameters:
P(t) 
k
1 exp[ Ln(81) (t  tm )]
t
tm
Midpoint of the growth/diffusion process {   tm }
Δt
Duration for the growth process to proceed from 10 per cent to 90 per cent of the
ln(81)
asymptote (k) { t 
}

This function relates to the general form by substituting
Projecting levels of mortality
Logistic curve - Hypothetical increase of life expectancy
100
Δt=100
K=90
90
Life expectancy (years)
80
70
60
tm=80
50
40
30
0
25
50
75
100
Years
125
150
175
200
Projecting levels of mortality I:
United Nations Model
The demographic process of mortality and fertility decline consists
of two phases: a first phase of accelerating rates of decline that is
followed by a second phase of slowing rates of decline. Such a
two-phase process can be modelled by two logistic functions, one
approaching an upper limit and a second one that approaches a
lower limit.
P(t ) 
k1
k2

1 exp[ Ln(81) (t  tm1)] 1 exp[ Ln(81) (t  tm2 )]
t1
t2
Projecting levels of mortality I:
United Nations Model
Models of annual gains in life expectancy at birth, males
Models of annual gains in life expectancy at birth, females
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
0.0
40
45
Very slow
50
55
Slow pace
60
65
Medium Pace
70
Fast pace
75
80
Very fast
40
45
Very slow
50
55
Slow pace
60
65
Medium Pace
70
Fast pace
75
80
Very fast
Projecting levels of mortality I:
United Nations Model
Model trajectories of gains in life expctancy, low life expectancy, males
85
80
Life expectancy at birth (years)
75
70
65
60
55
50
45
40
35
2000
2010
2020
2030
2040
2050
2060
2070
2080
Year
Very Slow
Slow
Medium
Fast
Very Fast
2090
2100
Projecting levels of mortality I:
United Nations Model
Model trajectories of gains in life expctancy, high life expectancy, males
95
93
Life expectancy at birth (years)
91
89
87
85
83
81
79
77
75
2000
2010
2020
2030
2040
2050
2060
2070
2080
Year
Very Slow
Slow
Medium
Fast
Very Fast
2090
2100
UNPD_MorModel.xlsm
1. Enter description
2. Enter your data
2. Select a model
for each sex
UNPD_MorModel.xlsm
Projected life expectancy at birth
95
90
85
80
75
70
1960
1980
2000
2020
2040
2060
2080
2100
2120
Years
Males
Females
UNPD_MorModel.xlsm
Sex differentials [Female-Male]
6.00
5.00
4.00
3.00
2.00
1.00
0.00
1960
1980
2000
2020
2040
2060
2080
2100
2120
Years
F-M
Projecting level of mortality II:
US Census Bureau Model
• The model in spreadsheet E0LGST.xls
interpolates and extrapolates life expectancies
at birth, by sex. The program fits a logistic
function to 2 to 17 life expectancies at birth,
given the upper and lower asymptotes.
E0LGST.xls
Input data for E0LGST.xls
•Table number [“Table 123”]
•Country name and Year [“Poplandia: 1960 and 1980”]
•Lower asymptote [leave default]
•Upper asymptote [leave default]
•2-17 data points of observed life expectancy
•Dates for life expectancy [Decimal years: 1960.5 for midyear]
•Values for male, female life expectancy
•Sex ratio at birth [male births per female births]
•Start year for listing results
•Sources of input data
E0LGST.xls
1. Enter description
2. Enter observed
life expectancies
3. Enter parameter
4. Retrieve projection
(Automatic update)
E0LGST.xls
COUNTRY: YEARS
1. Life Expectancy by Sex
90
85
80
75
70
65
60
55
50
1940
1960
1980
2000
2020
Male
Female
2040
2060
2080
E0LGST.xls
COUNTRY: YEARS
2. Sex Differential in Life Expectancy
7.00
6.50
6.00
5.50
5.00
4.50
4.00
1940
1960
1980
2000
2020
2040
2060
2080
Hands-on exercise: Mortality
• Make yourself familiar with the Excel
templates
–
E0LGST.xls [USBC]
– UNPD_MorModel.xls/UNPD_MorModel.xlsm [UNPD]
• Prepare a projection using a target level of life
expectancy or a typical rate of change.
• Validity check I: Sex-differentials in e0
Hands-on exercise: Mortality
• Validity check II: Explore ways to ensure that
the projected trends are compatible with past
trends.
Projecting levels of fertility
Overview
Projecting levels of fertility I:
United Nation Model
• Applies a similar model as for mortality.
• Not the level itself, but the rates of changes
are modeled
• Incorporates the observation that during the
demographic transition, fertility first changed
slowly, then accelerated and finally
decelerated
UNPD_FerModel.xls
1. Enter description
2. Enter data
3. Select a model
UNPD_FerModel.xls
Projected TFR
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
2000
2010
2020
2030
2040
2050
2060
2070
2080
2090
2100
2110
Projecting level of fertility II:
US Census Bureau Model
The model in spreadsheet TFRLGSTNew.xls interpolates and
extrapolates life expectancies at birth, by sex. The program fits a
logistic function to 2 to 17 life expectancies at birth, given the
upper and lower asymptotes.
TFRLGSTNew.xls
Input data for TFRLGSTNew.xls
•Table number [“Table 123”]
•Country name and Year [“Poplandia: 1960 and 1980”]
•Lower asymptote [leave default]
•Upper asymptote [leave default]
•2-17 data points of observed TFR
•Reference dates for TFR [Decimal years: 1960.5 for midyear]
•Values for TFR
•Start year for listing results
•Sources of input data
TFRLGSTNew.xls
1. Enter description
2. Enter observed
TFR
3. Enter parameter
4. Retrieve projection
(Automatic update)
TFRLGST.xls
COUNTRY: YEARS
1.
Total Fertility Rates
7.00
6.50
6.00
Total fertility rate
5.50
5.00
4.50
4.00
3.50
3.00
2.50
2.00
1940
1960
1980
2000
2020
Year
2040
2060
2080
TFRLGSTNew.xls
COUNTRY: YEARS
2.
Input/Output TFR's
7.00
6.50
6.00
5.50
5.00
4.50
4.00
3.50
3.00
2.50
2.00
1955.0
1960.0
1965.0
1970.0
1975.0
Reported
1980.0
Logistic
1985.0
1990.0
1995.0
Hands-on exercise: Fertility
• Make yourself familiar with the Excel
templates
–
TFRLGSTNew.xls [USBC]
– UNPD_FerModel.xls/UNPD_FerModel.xlsm [UNPD]
• Prepare a projection using a target level of
Total Fertility or a typical rate of change.
• Validity check I: Explore ways to ensure that
the projected trends are compatible with past
trends.
Excursion: Test data
• Spectrum comes with a complete database of
national estimates and projections for all
countries (WPP2010).
• The data are formatted into time series for
single years, and into single years of age.
• How to obtain the data?
Spectrum: Step 1
Spectrum: Step 2
Spectrum: Step 3
Spectrum: Step 4
Spectrum: Step 5
Spectrum: Step 6
Spectrum: Step 7.1
Spectrum: Step 7.2
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