International Workshop on Population Projections using Census Data

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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