Did European fertility forecasts become more accurate  in the

past 50 years?

Nico Keilman

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

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/

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)

Scope (cntnd)

Forecasts produced by statistical agencies between 1950 and 2002

Compared with actual values 1950-2002

Measuring forecast accuracy

absolute forecast error (AE) of TFR

|obs. TFR – forec. TFR|

accuracy/precision, not bias

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

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

)

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

)

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)

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

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

“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)

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

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

TFR

No improvement in accuracy since 1975-79

TFR forecasts became worse!

Problems

1. Only fixed effects

2. Autocorrelated residuals

1. Include random effects

Mixed model

2. Include AR(1) process

Random effects for countries

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

Cov(yc) = σ2I + Zcδ2Zc’

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

Country st. dev. 0.112

Residual st. dev. 0.258

(Fixed effects residual st. dev. 0.258)

Including random country effects does not change the conclusion based on simple fixed effects model

Random period effects?

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

Calendar year st. dev. 0.167

Residual st. dev. 0.256

(Fixed effects residual st. dev. 0.258)

Conclusion

Random effects for country or calendar year do not change conclusion that forecast accuracy became worse since 1970s

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