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Did European fertility forecasts become more accurate  in the past 50 years?

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.

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Did European fertility forecasts become more accurate  in the past 50 years?

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  1. Did European fertility forecasts become more accurate  in the past 50 years? Nico Keilman

  2. 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

  3. 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/

  4. 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)

  5. Scope (cntnd) Forecasts produced by statistical agencies between 1950 and 2002 Compared with actual values 1950-2002

  6. Measuring forecast accuracy absolute forecast error (AE) of TFR |obs. TFR – forec. TFR| accuracy/precision, not bias

  7. 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)

  8. Model  Ffforecast (launch year) effect Pp period effect D(d) duration, parameterized (linear & square root) Cc country effect Vv variant effect

  9. 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

  10. “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)

  11. 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.

  12. 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 0.7 Then 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

  13. TFR No improvement in accuracy since 1975-79 TFR forecasts became worse!

  14. Problems 1. Only fixed effects 2. Autocorrelated residuals 1. Include random effects Mixed model 2. Include AR(1) process

  15. Random effects for countries

  16. For country c, there are nc observations, N = Σcnc. 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

  17. Cov(yc) = σ2I + Zcδ2Zc’

  18. 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

  19. Country st. dev. 0.112 Residual st. dev. 0.258 (Fixed effects residual st. dev. 0.258)

  20. Including random country effects does not change the conclusion based on simple fixed effects model Random period effects?

  21. 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

  22. Calendar year st. dev. 0.167 Residual st. dev. 0.256 (Fixed effects residual st. dev. 0.258)

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

  24. 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

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