stochastic population forecasts for the united kingdom emma wright & mita saha office for...
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Stochastic population forecasts for the United Kingdom
Emma Wright & Mita Saha
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-2006
• Results on GAD website and National Statistics Online
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
Mil
lio
ns
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 Population2006-based principal and variant projections
56
60
64
68
72
76
80
84
88
92
1981 1991 2001 2011 2021 2031 2041 2051
Year
Mill
ion
s
Principal projection Single component variant Combination variant
H Pop
L Pop
Principal
LLLM
HF
LF
Estimates Projections HLHM
ONS Stochastic forecasting project
• AimTo develop a model that will enable the degree of
uncertainty in UK national population projections to
be specified
• Approach– Express fertility, mortality and migration assumptions in
terms of probability distributions
– Generate random values from these probability distributions to produce predictive distributions for any projection result
Probability distributions
How can we estimate future probability distributions?
Three approaches:• Analysis of accuracy of past projections• 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 distributionsfor the ONS model
• Expert opinion - NPP expert advisory group questionnaire
• Past projection errors - GAD historic projections database
Expert Opinion
• National Population Projections Expert Advisory Group (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 sample paths
Random walk with drift model:
Driver(T)=
Driver(T-1) + ValueDriver(T) + DriftDriver(T)
UK TFR250 sample paths with 67% confidence intervals
-
0.50
1.00
1.50
2.00
2.50
3.00
3.50
1971 1981 1991 2001 2011 2021 2031
Year
TF
R
67% confidence interval from test scenario
67% confidence interval from expert opinion
UK TFRProbability distribution v 2006-based assumptions
0.5
1.0
1.5
2.0
2.5
3.0
1971 1981 1991 2001 2011 2021 2031 2041 2051
Year
TF
R
Projections
95% high
67% high
Median
67% low
95% low
Estimates
High fert
Principal
Low fert
UK male period life expectancy at birth Probability distribution
65
70
75
80
85
90
95
1971 1981 1991 2001 2011 2021 2031 2041 2051
Year
Lif
e ex
pec
tan
cy (
year
s)
Projections
95% high
67% high
Median
67% low
95% low
Estimates
UK net migration Probability distribution
-200
0
200
400
600
1971 1981 1991 2001 2011 2021 2031 2041 2051Year
Th
ou
san
ds
Projections
95% high
67% high
Median
67% low
95% low
Estimates
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
120A
ge
(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
120A
ge
(ye
ars)
Population (thousands)
95%predictiveinterval
67%predictiveinterval
Median
Males Females
Provisional results: UK total dependency ratioPredictive intervals
400
500
600
700
800
900
1971 1981 1991 2001 2011 2021 2031 2041 2051
Year
Dep
end
ants
per
th
ou
san
d p
erso
ns
of
wo
rkin
g a
ge
Projections95% high
67% high
Median
67% low
95% low
Estimates
Provisional results: Probability of the number of children in the UK exceeding the SPA population
0%
10%
20%
30%
40%
50%
2007 2012 2017 2022 2027 2032 2037 2042 2047 2052
Year
Per
cen
tag
e p
rob
abil
ity
Illustrative probabilities
Based on current provisional assumptions, there is a….
• 48% chance that TFR will exceed replacement level
• 9% chance that male period life expectancy at birth will exceed 90 yrs
• 20% chance that there will be negative annual net migration
• 2% chance that the population will fall below the 2006 base level
… at some point between 2006 and 2056.
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
Estimates of the UK TFR in 2049/2050Median and 80% confidence intervals
1.0
1.5
2.0
2.5
3.0
TF
R
ONSUPE VID
Quality Assurance
• Prof Phil Rees (University of Leeds)
• Prof Nico Keilman (University of Oslo)
• Prof Wolfgang Lutz (Vienna Institute of Demography)
• ONS Methodology Directorate
Future plans
• ONS plans to publish a set of 2006-based stochastic forecasts for the UK as ‘Experimental Statistics’ during 2009
• If you would like to feed in any comments on this work, please e-mail: