Uncertain population forecasts
Nico Keilman
Department of Economics, University of Oslo
Main points
• Uncertainty in forecasts of certain population
variables surprisingly large
• Forecasts for the young and the old age groups are
the least reliable
• Forecast errors increase as forecast interval
lengthens
• European forecasts have not become more accurate
during the past 2-3 decades
• Traditional forecasts with their high and low
scenarios do not give a correct impression of
uncertainty  probabilistic forecasts
Focus
National forecasts in industrialized countries
(to a large extent)
Where does uncertainty manifest
itself?
Forecasts of:
• Total population
• Age structure
• Fertility
• Mortality
• Migration
Measuring uncertainty
Empirical findings – historical forecasts evaluated
against actual population numbers (ex post facto)
Total population size fairly accurate
Forecasts of population size
- all countries of the world
- made by the UN, the World Bank, and the US
Census Bureau between 1972 and 1994
were too high by, on average,
- 0.8 %, 5 years ahead
- 2.4 %, 15 years ahead
- 3.5 %, 25 years ahead
Characteristic age pattern
Errors in age structure forecasts
Europe
Percentage errors in age structure forecasts for Europe
UN forecasts 1968-1990
20 %
5 years ahead
15 %
10 years ahead
forecasts too high
15 years ahead
10 %
5%
0%
-5 %
-10 %
forecasts too low
-15 %
-20 %
0-4
10-14
20-24
30-34
40-44
age group
50-54
60-64
70-74
80+
United Kingdom - men
Percentage errors in age structure forecasts for the UK,
GAD forecasts 1971-1994, men
30 %
10 years ahead
20 %
15 years ahead
forecasts too high
20 years ahead
10 %
0%
-10 %
forecasts too low
-20 %
-30 %
0-4
10-14
20-24
30-34
40-44
50-54
age groups
60-64
70-74
80-84 85+
United Kingdom - women
Percentage errors in age structure forecasts for the UK,
GAD forecasts 1971-1994, women
30 %
10 years ahead
20 %
15 years ahead
forecasts too high
20 years ahead
10 %
0%
-10 %
forecasts too low
-20 %
-30 %
0-4
10-14
20-24
30-34
40-44
50-54
age groups
60-64
70-74
80-84 85+
• Young age groups  fertility
• Old age groups  mortality
Uncertain Population of Europe (UPE)
Joint work with Juha Alho, Harri Cruijsen, Maarten Alders, Timo Nikander, Din Quang Pham
Evaluated historical accuracy of population forecasts
- national agencies in 14 European countries
- 1950-2000
One (of several) source of information for probabilistic
forecasts
European forecasters have under-predicted
gains in life expectancy:
- by 2.3 years of life for forecasts 15 years ahead
- by 4.5 years of life for forecasts 25 years ahead
Average error in life expectancy forecasts
National population forecasts, 14 European countries, 1950-2000
2
years
0
-2
-4
-6
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Forecast duration (years)
European forecasters have predicted too high
fertility:
- by 0.2 children per woman for 15 years ahead
- by 0.4 children per woman for 25 years ahead
Average error in fertility forecasts
National population forecasts, 14 European countries, 1950-2000
0.5
children per woman
0.4
0.3
0.2
0.1
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Forecast duration (years)
European forecasters have predicted too low levels
of migration:
- by 1 per thousand of population for 6-8 years ahead
- by 3 per thousand of population for 18-25 years ahead
Average errors in net migration forecasts
National population forecasts, 14 European countries, 1950-2000
1
per thousand
0
-1
-2
-3
-4
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Forecast duration (years)
Why uncertain?
• Data quality
• Social science predictions
• No accurate behavioural theory
• Rely on observed regularities instead
• Problems when sudden trend shifts occur
 assumption drag
Assumption drag: fertility
Fertility assumptions for West Germany,
forecasts by Federal St. Office, 1952-1998
average no. of children per woman
3.0
2.5
2.0
1.5
1.0
0.5
0.0
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
(observed fertility: black solid line,
fertility forecasts: dashed coloured lines)
2000
Assumption drag: mortality
Life expectancy assumptions for men, Netherlands,
forecasts by Statistics Netherlands 1965-1997
76
75
74
years
73
72
71
70
69
68
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
(observed life expectancy: black solid line,
life expectancy forecasts: dashed coloured lines)
Forecast accuracy has NOT improved
over the last 25 years
Error indicator for TFR forecasts, 14 countries
The graph shows estimated forecast effects in a model that also controls for period,
duration, country, and forecast variant. Log of absolute error in TFR is dependent
variable.
Estimates in black, 95% confidence intervals in red. Launch years 1950-54 are
reference category for the forecast effects.
R2 = 0.704, N = 4847
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
195054
195559
196064
196569
197074
197579
198084
launch year
198589
199094
199599
200001
Error indicator for e0 forecasts, 14 countries
The graph shows estimated forecast effects in a model that predicts the log of absolute
error in e0. The model controls for period, duration, country, sex, and forecast variant.
Estimates in black, 95% confidence intervals in red. Launch years 1950-54 are reference
category for the forecast effects.
R2 = 0.722, N = 5562.
NB No data for launch years 1955-59
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.4
-0.5
-0.6
1950- 1955- 1960- 1965- 1970- 1975- 1980- 1985- 1990- 1995- 200054
59
64
69
74
79
84
89
94
99
01
launch year
Three problems related to
deterministic population forecasts
1. Wide margins for some variables, narrow margins for
others
Example: Old Age Dependency Ratio
(OADR) for Norway in 2060
Source: 2005-based forecast of Statistics Norway
High Middle Low
|H-L|/M
millions
%
POP67+
1.55
1.33
1.13
31
POP20-66
4.03
3.39
2.83
36
OADR
0.38
0.39
0.40
4 (!)
Problems … (cntd)
2. Too narrow margins in the short run,
too wide margins in the long run
Problems …
3. A limited number of variants, without probability
statements, leave room for politically motivated
choices.
Views about the demographic future
have changed over time
TFR assumptions for 18 EEA+
countries, 2045-2049
Averages across countries
2.1
UN: United Nations
ES: Eurostat
UPE: Uncertain Population of Europe
children/woman
2.0
1.9
1.8
1.7
1.6
UN
1994
UN
1996
UN
1998
UN
2000
UN
2002
UN
2004
ES
1995
Organisation and base year
ES
1999
ES
2004
UPE
2004
Life expectancy assumptions for 18
EEA+ countries, 2045-2049 Men
Averages across countries
90
UN: United Nations
ES: Eurostat
UPE: Uncertain Population of Europe
yrs
85
80
75
UN
1994
UN
1996
UN
1998
UN
2000
UN
2002
UN
2004
ES
1995
Organisation and base year
ES
1999
ES
2004
UPE
2004
Net migration assumptions for 18 EEA+
countries, 2045-2049
Averages across 18 EEA+ countries (UN, UPE),
across 15 EU-15 countries (Eurostat)
3.5
UN: United Nations
ES: Eurostat
UPE: Uncertain Population of Europe
per thousand of population in 2000
3.0
2.5
2.0
1.5
1.0
0.5
0.0
UN
1998
UN
2000
UN
2002
UN
2004
ES
1995
ES
1999
Organisation and base year
ES
2004
UPE
2004
Implications
• Forecast users should be informed about the
reliability of the future population numbers
• Historical errors just a first step
• Expected errors for the current forecast 
probabilistic forecasts
UPE: probabilistic forecasts for 18 European
countries.
See http://www.stat.fi/tup/euupe/
UPE probabilistic projection of total population size,
United Kingdom, 2000-50
85
80
85
2010
UPE
ONS
80%L median 80%H
59.7 60.5
61.3
62.1
ONS mid-2006
80
60.6
millions
75
70
75
2006-based official ONS/GAD
principal projection
70
65
65
60
60
UPE 80%prediction
interval
UPE probabilistic projection
(median)
55
55
2000
2010
2020
2030
year
2040
2050
Age pyramid UK 2050,
age
median (black), 80% prediction interval (red)
95+
90-94
85-89
80-84
75-79
70-74
65-69
60-64
55-59
50-54
45-49
40-44
35-39
30-34
25-29
20-24
15-19
10-14
5-9
0-4
4000
Men
3000
Women
2000
1000
0
1000
numbers in thousands
2000
3000
4000
Age pyramid UK 2030,
age
median (black), 80% prediction interval (red)
95+
90-94
85-89
80-84
75-79
70-74
65-69
60-64
55-59
50-54
45-49
40-44
35-39
30-34
25-29
20-24
15-19
10-14
5-9
0-4
4000
Men
3000
Women
2000
1000
0
1000
numbers in thousands
2000
3000
4000
Forecast users should be prepared
for the unexpected
- use buffers?
- flexibility?
- risk aversion?
Users should check whether overpredictions are more
costly, or less costly, than underpredictions
Loss function
Forecasters should educate the users, cf.
- weather forecasts: EPS (Ensemble Prediction
System) Meteograms: series of Box plots
- inflation and interest rate forecasts: uncertainty fans
Bank of Norway’s forecast of future interest rate (%) with uncertainty fan
30% 50% 70% 90%
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
2005
2006
2007
Source: Norges Bank
2008
2009
2010