Developing stochastic population forecasts for the United Kingdom:Progress report and plans for future work

Emma Wright

Office for National Statistics

National population projections

• Dependent on assumptions about future levels of fertility, mortality and migration which are reviewed every two years

• Latest projections based on the population at

mid-2008

• Results on the ONS website

Uncertainty in population projections

• Demographic behaviour is inherently uncertain

• Any set of projections will inevitably be proved wrong to a greater or lesser extent

Past UK population projections

50

55

60

65

70

75

80

1966 1976 1986 1996 2006 2016 2026 2036 2046 2056

Year

Milli

ons

Actual 1971-based 1977-based 1989-based

1998-based 2004-based 2006-based

Mean projection error by age groupPast UK projections

-30%

-20%

-10%

0%

10%

20%

30%

0-4

5-9

10-1

4

15-1

9

20-2

4

25-2

9

30-3

4

35-3

9

40-4

4

45-4

9

50-5

4

55-5

9

60-6

4

65-6

9

70-7

4

75-7

9

80-8

4

85+

Age group

% E

rro

r

-30%

-20%

-10%

0%

10%

20%

30%

5 years ahead 10 years ahead 25 years ahead

Principal & variant projections

• Principal projections - based on assumptions thought to be the best at the time they are adopted

• Variant projections – plausible alternative scenarios, NOT upper or lower limits.

• Limitation - principal and variant projections are deterministic, no measure of probability

Total UK Population2008-based principal and variant projections

50

55

60

65

70

75

80

85

90

95

100

105

110

115

1981 2001 2021 2041 2061 2081Year

Millio

ns

P

HF

LF

LMLL

HLHM

LP

HPProjected

ONS Stochastic forecasting project

• AimTo develop a model that will enable the degree of uncertainty in UK national population projections to be specified

• ApproachExpress fertility, mortality and migration assumptions in terms of their assumed probability distributions

Probability distributions

How can we estimate future probability distributions?

Three approaches:• Analysis of past projection errors• Expert opinion• Time series analysis

No ‘right’ answer – subjective judgement

Model Drivers

• Fertility – Total Fertility Rate

• Mortality – Male and female period life expectancy at birth

• Migration – Total net migration

Deriving probability distributions for the ONS model

• Expert opinion - NPP expert advisory panel questionnaire

• Past projection errors - GAD historic projections database

Expert Opinion

• National Population Projections Expert Advisory Panel (set up via BSPS):

David Coleman Phil Rees Mike Murphy Robert Wright John Salt John Hollis

• Expressed opinions on the most likely levels and 67% confidence intervals for TFR, period life expectancy at birth and net migration in 2010 and 2030.

Generating drivers

Overall model

Pt = Pt-1 + Bt – Dt + Mt

Random walk with drift (RWD) model:

Drivert = Drivert-1 + Valuet + Driftt

UK TFRPrediction intervals v 2006-based assumptions

1.0

1.5

2.0

2.5

1971 1976 1981 1986 1991 1996 2001 2006 2011 2016 2021 2026 2031

Year

TFR

Median

Prediction Interval 67%

Actual and PrincipalNPP

Variant NPP

Expert Average 67% CI

projections

UK male period life expectancy at birth Prediction intervals v 2006-based assumptions

65

70

75

80

85

90

1971 1976 1981 1986 1991 1996 2001 2006 2011 2016 2021 2026 2031

Year

EOLBMales(years)

Median

Prediction Interval 67%

Actual and PrincipalNPP

Variant NPP

Expert Average 67% CI

projections

UK net migration Prediction intervals v 2006-based assumptions

-200

-100

0

100

200

300

400

500

1971 1976 1981 1986 1991 1996 2001 2006 2011 2016 2021 2026 2031

Year

Net Migration

(thousands)

Median

Prediction Interval 67%

Actual and PrincipalNPP

Variant NPP

Expert Average 67% CI

projections

Program

• Based on cohort component model

• UK only

• Random numbers generated

• Age distributions

• 5,000 simulations

• 2006-2056 projection period

Provisional results UK age structure 2031

800 600 400 200 0 200 400 600 800

0

10

20

30

40

50

60

70

80

90

100

110

120

Ag

e

(ye

ars

)

Population (thousands)

95%predictiveinterval

67%predictiveinterval

Median

Males Females

Provisional resultsUK age structure 2056

800 600 400 200 0 200 400 600 800

0

10

20

30

40

50

60

70

80

90

100

110

120

Ag

e (

year

s)

Population (thousands)

95%predictiveinterval

67%predictiveinterval

Median

Males Females

Limitations

• Do not know true probability distributions

• Validity of results wholly dependent on assumptions underlying model

• Inflated sense of precision

• Communicating results and limitations may be a challenge

• BUT….if aware of the limitations, then stochastic forecasting can be a useful approach

Future plans

• Use of time series approach

• Deriving probability distributions

• The RWD model

• Correlations

• Net migration

• Age Distributions

Questions?

If you would like to feed in any comments on this work, please e-mail:

natpopproj@ons.gov.uk