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International Workshop on Population Projections using Census Data. 14 – 16 January 2013 Beijing, China. Session IV: Projecting the levels of mortality, fertility, and migration. Projecting life expectancy at birth Projecting total fertility Projecting international net-migration. - PowerPoint PPT Presentation
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International Workshop on
Population Projectionsusing Census Data
14 – 16 January 2013Beijing, China
Session IV:Projecting the levels of mortality, fertility,
and migration
• Projecting life expectancy at birth• Projecting total fertility• Projecting international net-migration
http://unstats.un.org/unsd/demographic/meetings/wshops/China2013/list_of_docs.htm
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
• 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 mortalityThe general form of a logistic function can be expressed as
( ) 1 exp[ ( )]kP t t
.
k Saturation level or asymptote of the diffusion process α Growth rate of the s-curve β 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:
( )(81)1 exp[ ( )]m
kP tLn t tt
tm Midpoint of the growth/diffusion process { mt } Δt Duration for the growth process to proceed from 10 per cent to 90 per cent of the
asymptote (k) { ln(81)t }
This function relates to the general form by substituting
0 25 50 75 100 125 150 175 20030
40
50
60
70
80
90
100
Logistic curve - Hypothetical increase of life expectancy
Years
Life
expe
ctan
cy (y
ears
)
tm=80
Projecting levels of mortality
K=90Δt=100
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.
1 2
1 21 2
( ) (81) (81)1 exp[ ( )] 1 exp[ ( )]m m
k kP t Ln Lnt t t tt t
40 45 50 55 60 65 70 75 800.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Models of annual gains in life expectancy at birth, males
Very slow Slow pace Medium PaceFast pace Very fast
40 45 50 55 60 65 70 75 800.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Models of annual gains in life expectancy at birth, females
Very slow Slow pace Medium PaceFast pace Very fast
Projecting levels of mortality I: United Nations Model
2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 210035
40
45
50
55
60
65
70
75
80
85Model trajectories of gains in life expctancy, low life expectancy, males
Very Slow Slow Medium Fast Very Fast
Year
Life
exp
ecta
ncy
at b
irth
(yea
rs)
Projecting levels of mortality I: United Nations Model
2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 210075
77
79
81
83
85
87
89
91
93
95Model trajectories of gains in life expctancy, high life expectancy, males
Very Slow Slow Medium Fast Very Fast
Year
Life
exp
ecta
ncy
at b
irth
(yea
rs)
Projecting levels of mortality I: United Nations Model
UNPD_MorModel.xlsm
2. Enter your data
2. Select a model for each sex
1. Enter description
UNPD_MorModel.xlsm
1960 1980 2000 2020 2040 2060 2080 2100 212070
75
80
85
90
95
Projected life expectancy at birth
Males Females
Years
UNPD_MorModel.xlsm
1960 1980 2000 2020 2040 2060 2080 2100 21200.00
1.00
2.00
3.00
4.00
5.00
6.00
Sex differentials [Female-Male]
F-M
Years
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
4. Retrieve projection(Automatic update)
2. Enter observed life expectancies
3. Enter parameter
E0LGST.xls
1940 1960 1980 2000 2020 2040 2060 208050
55
60
65
70
75
80
85
90
COUNTRY: YEARS
Male Female
1. Life Expectancy by Sex
E0LGST.xls
1940 1960 1980 2000 2020 2040 2060 20804.00
4.50
5.00
5.50
6.00
6.50
7.00
COUNTRY: YEARS
2. Sex Differential in Life Expectancy
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
2000 2020 2040 2060 2080 2100 21200.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
Projected TFR
Projecting level of fertility II:US Census Bureau Model
• The model in spreadsheet TFRLGSTNew.xls interpolates and extrapolates Total Fertility Rates (TFR). The program fits a logistic function to 2 to 17 TFRs, 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
4. Retrieve projection(Automatic update)
2. Enter observed TFR
3. Enter parameter
TFRLGST.xls
1940 1960 1980 2000 2020 2040 2060 20802.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
6.50
7.00
COUNTRY: YEARS
Year
Tota
l fer
tility
rate
1. Total Fertility Rates
TFRLGSTNew.xls
1955.0 1960.0 1965.0 1970.0 1975.0 1980.0 1985.0 1990.0 1995.02.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
6.50
7.00
COUNTRY: YEARS
Reported
2. Input/Output TFR's
Hands-on exercise: Fertility
• Make yourself familiar with the Excel templates– TFRLGST.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.
Projecting levels of Migration
Overview
Projecting levels of Migration• International migration is the most challenging part of a
population projection exercise: – Reliable data on the number of immigrants and emigrants are
often not available– Migration exhibits strong fluctuations that make extrapolations
difficult, if not untenable. – Not possible to calculate meaningful demographic rates
(exposure/occurrence rates) for immigration and net migration. • International (net) migration is often formulated in terms
of absolute numbers. Because if its irregular fluctuations, (net) migration is often kept constant over time.
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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