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
80
75
Millions
70
65
60
55
50
1966
1976
1986
1996
2006
2016
2026
2036
2046
Year
Actual
1971-based
1977-based
1998-based
2004-based
2006-based
1989-based
2056
30%
30%
20%
20%
10%
10%
0%
0%
Age group
5 years ahead
10 years ahead
25 years ahead
85+
80-84
75-79
70-74
65-69
60-64
55-59
50-54
45-49
40-44
35-39
30-34
-30%
25-29
-30%
20-24
-20%
15-19
-20%
10-14
-10%
5-9
-10%
0-4
% Error
Mean projection error by age group
Past UK projections
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 Population
2006-based principal and variant projections
92
H Pop
88
HF
HM
HL
84
80
Projections
Estimates
Millions
Principal
76
LL
LM
LF
72
68
L Pop
64
60
56
1981
1991
2001
2011
2021
2031
2041
2051
Year
Principal projection
Single component variant
Combination variant
ONS Stochastic forecasting project
• Aim
To 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 distributions
for 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 TFR
250 sample paths with 67% confidence intervals
3.50
67% confidence
interval from test
scenario
3.00
67% confidence interval
from expert opinion
2.50
TFR
2.00
1.50
1.00
0.50
1971
1981
1991
2001
Year
2011
2021
2031
UK TFR
Probability distribution v 2006-based assumptions
3.0
95% high
2.5
Estimates
Projections
67% high
High fert
2.0
TFR
Principal
Median
Low fert
1.5
67% low
95% low
1.0
0.5
1971
1981
1991
2001
2011
Year
2021
2031
2041
2051
UK male period life expectancy at birth
Probability distribution
95
95% high
90
67% high
Estimates
Projections
Life expectancy (years)
Median
85
67% low
80
95% low
75
70
65
1971
1981
1991
2001
2011
Year
2021
2031
2041
2051
UK net migration
Probability distribution
600
95% high
Estimates
Projections
400
Thousands
67% high
200
Median
67% low
0
95% low
-200
1971
1981
1991
2001
2011
Year
2021
2031
2041
2051
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
Males
Females
120
110
100
90
Age (years)
80
95%
predictive
interval
70
60
67%
predictive
interval
50
40
30
Median
20
10
0
800
600
400
200
0
200
400
Population (thousands)
600
800
Provisional results
UK age structure 2056
Females
Males
120
110
100
90
Age (years)
80
95%
predictive
interval
70
60
67%
predictive
interval
50
40
Median
30
20
10
0
800
600
400
200
0
200
400
Population (thousands)
600
800
Provisional results: UK total dependency ratio
Predictive intervals
Dependants per thousand persons of working age
900
800
Estimates
95% high
Projections
67% high
700
Median
600
67% low
95% low
500
400
1971
1981
1991
2001
2011
Year
2021
2031
2041
2051
Provisional results: Probability of the number of
children in the UK exceeding the SPA population
50%
Percentage probability
40%
30%
20%
10%
0%
2007
2012
2017
2022
2027
2032
Year
2037
2042
2047
2052
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 2049/2050
Median and 80% confidence intervals
3.0
TFR
2.5
2.0
1.5
1.0
UPE
ONS
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:
natpopproj@ons.gov.uk