Did European fertility forecasts become more accurate in the past 50 years?
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Did European fertility forecasts become more accurate in the
past 50 years?
Nico Keilman
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Background
Data assembled in the framework of the UPE project “Uncertain population of Europe”
Stochastic population forecasts for each of the 17 EEA countries + Switzerland
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Analysed empirical forecast performance of subsequent population forecasts in 14 European countries
Predictive distribution of (errors in) fertility, mortality, migration
http://www.stat.fi/tup/euupe/
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Scope
Official forecasts in 14 European countries: Austria, Belgium, Denmark, Finland, France, Germany/FRG, Italy, Luxembourg, Netherlands, Norway, Portugal, Sweden, Switzerland, United Kingdom
Focus on Total Fertility Rate (TFR)
(#ch/w)
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Scope (cntnd)
Forecasts produced by statistical agencies between 1950 and 2002
Compared with actual values 1950-2002
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Measuring forecast accuracy
absolute forecast error (AE) of TFR
|obs. TFR – forec. TFR|
accuracy/precision, not bias
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Total Fertility Rate in 14 countries
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
1945 1955 1965 1975 1985 1995
ch/w
Portugal
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average absolute forecast errors in TFR by year in which forecast was made (forecast launch)
0.0
0.2
0.4
0.6
0.8
1.0
1950-54
1955-59
1960-64
1965-69
1970-74
1975-79
1980-84
1985-89
1990-94
1995-99
2000+
forecast launch
erro
r (c
h/w
)
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average absolute forecast errors inTFR by forecast duration
0.0
0.2
0.4
0.6
0.8
1.0
0 5 10 15 20 25 30
duration (years)
erro
r (c
h/w
)
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Regression model to explain AE
Independent variables:• launch year• forecast duration• forecast year (year to which forecast applies)• country• forecast variant• stability in observed parameter (slope & trend)
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Model
Ff forecast (launch year) effect
Pp period effect
D(d) duration, parameterized (linear & square root)
Cc country effect
Vv variant effect
, , , , 1 2 , , , ,( ) . .f p d c v f p c v f p d c vAE K F P D d C V STDEV SLOPE
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Perfect multicollinearity
forecast year = launch year + forecast duration
solution:
- duration effect parameterized
- effects of forecast year and launch year were grouped into five-year intervals
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“Panel”, but strongly unbalanced
Repeated measurements for each
- country
- launch year
- calendar year
but many missing values
http://folk.uio.no/keilman/upe/upe.html
e.g. Italy (165), Denmark (1014)
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Estimation results for errors in Total Fertility Rate (TFR) forecasts
The dependent variable is ln[0.3+abserror(TFR)]. The figure shows estimated forecast effects in a model that also controls for period, duration, country, and forecast variant. Launch years 2000-2001 were selected as reference category for the forecast effects. R2 = 0.578, N = 4847.
TFR-errors: Estimated forecast effects and 95% confidence intervals
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
1950-54
1955-59
1960-64
1965-69
1970-74
1975-79
1980-84
1985-89
1990-94
1995-99
2000-01
launch year
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Interpretation of estimated forecast effects
The forecast effect Ff for launch years f equals
ln[0.3 + AE(f)] – ln[0.3 + AE(ref)]
with AE(ref) the error for the reference launch years 2000-2001.
AE(ref) arbitrary -- Choose 0.7Then AE(f) = exp(Ff) – 0.3 and estimated forecast effects vary between 0.4 (1975-79)
and 1.13 ch/w (1965-69) -- relative to 0.7 in 2000-2001
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TFR
No improvement in accuracy since 1975-79
TFR forecasts became worse!
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Problems
1. Only fixed effects
2. Autocorrelated residuals
1. Include random effects
Mixed model
2. Include AR(1) process
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Random effects for countries
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For country c, there are nc observations, N = Σc nc.
yc is the (nc x 1) data vector for country c, c = 1, 2, …, m.
yc = Xcβ + Zcbc + ec.
β is an unknown (p x 1) vector of fixed effects
Xc is a (nc x p) matrix with ind. variables for country c
bc is an unknown r.v. for the random effect, bc ~ N(0,δ2)the variance δ2 is the same for all countries
Zc is a (nc x 1) vector [1 1 … 1]’
ec is a (nc x 1) vector of intra-country errors,
ec ~ N(0, σ2I), assuming iid residuals
bc and ec are independent
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Cov(yc) = σ2I + Zcδ2Zc’
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Estimated forecast effects Mixed Fixed
F65-69 0.327 (.0787) 0.328 (0.0788) F70-74 -0.094 (.0701) -0.094 (0.0701)F75-79 -0.298 (.0626) -0.299 (0.0626)F80-84 -0.281 (.0553) -0.281 (0.0553)F85-89 -0.232 (.0486) -0.233 (0.0486)F90-94 -0.199 (.0444) -0.199 (0.0444)F95-99 -0.131 (.0420) -0.132 (0.0420)F00-02 0 0
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Country st. dev. 0.112
Residual st. dev. 0.258
(Fixed effects residual st. dev. 0.258)
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Including random country effects does not change the conclusion based on simple fixed effects model
Random period effects?
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Estimated forecast effects Mixed Fixed
F65-69 0.405 (.0818) 0.581 (0.0325) F70-74 -0.037 (.0936) 0.128 (0.0310)F75-79 -0.250 (.0721) -0.106 (0.0305)F80-84 -0.246 (.0656) -0.119 (0.0306)F85-89 -0.206 (.0599) -0.103 (0.0318)F90-94 -0.183 (.0550) -0.099 (0.0341)F95-99 -0.122 (.0499) -0.060 (0.0368)F00-02 0 0
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Calendar year st. dev. 0.167
Residual st. dev. 0.256
(Fixed effects residual st. dev. 0.258)
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Conclusion
Random effects for country or calendar year do not change conclusion that forecast accuracy became worse since 1970s
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Next
Include AR(1) in (fixed effects) model
Estimate AR(1) parameter ρ from residuals
Transform data (e.g. Cochrane/Orcutt or Prais/Winsten) and re-estimate model