Ortega and Poncela 2005 — Joint Forecasts of Southern European Fertility Rates

Summary

Published in the International Journal of Forecasting 21(3): 539–550 (2005) by Ortega and Poncela (Universidad Autónoma de Madrid); circulated earlier as a working paper. The paper asks whether jointly modelling total fertility rate (TFR) time series for four Southern European countries (Portugal, Spain, Greece, Italy) using Non-Stationary Dynamic Factor Models (DFM) yields better fertility forecasts than univariate autoregressive integrated moving average (ARIMA) methods. The answer is no for one-year-ahead forecasts — where ARIMA excels — but yes for horizons of 3, 5, and 10 years, with root mean squared error (RMSE) reductions of roughly one-third compared to naive forecasts at 10-year horizons.

Key Claims

• The four Southern European countries share one clearly non-stationary common factor (a random walk) capturing the shared dramatic fertility decline from the 1970s through 2000 — a transition that moved these countries from the highest TFR in Europe around 1950 to the lowest by 1998. A possible second borderline-stationary first-order autoregressive (AR(1)) factor captures timing differences and rank reversals among countries.
• Factor model (DFM): $\text{TFR}_t = P \times f_t + n_t$, where $f_t$ follows a non-stationary (random walk) or stationary AR(1) process, $P$ is the factor loading matrix, $n_t$ are country-specific AR idiosyncratic residuals. Estimated by maximum likelihood via the expectation-maximization (EM) algorithm. One-factor model (F1) and two-factor model (F2) both considered.
• Forecasting comparison: naive (last value = random walk), ARIMA(p,1,0) with and without trend (ARI/ARIT), Integrated Random Walk (IRW) unobserved-component models, vs. F1 and F2. Evaluated by RMSE with base years 1978–1999 and horizons 1–10.
• At horizon 1: ARI performs best (mean RMSE ≈ 5.1); factor models offer no gains over ARIMA at the very short term. At horizon 3: F2 best (mean RMSE 9.6 vs. 17.5 naive). At horizon 10: F2 wins decisively (mean RMSE 34.0 vs. 47.6 naive vs. 139.7 ARIT).
• ARIMA with constant trend (ARIT) fails catastrophically at 10-year horizons because linear drift extrapolation is inappropriate for fertility series, which undergo nonlinear transitions.
• Explicit limitation: restricted to TFR trends only, ignoring cohort fertility, parity distribution, and postponement (Kohler and Ortega 2002). This demonstrates forecast improvement from joint modelling, not a full stochastic forecast with uncertainty quantification.
• Gains from joint modelling grow with the forecast horizon because the common trend in other countries carries information about future trends in any one country even when contemporaneous co-movement is imperfect.

Concepts Introduced or Extended

• Stochastic Fertility Forecasting
• Tempo Effects in Fertility

Entities Mentioned

• José Antonio Ortega
• Pilar Poncela

Quotes

"We restrict ourselves to a limited subset of information, TFR trends, while ignoring other sources relevant for future fertility, including cohort fertility levels, the parity distribution of women, or patterns of postponement (Kohler and Ortega, 2002). Therefore, the goal is restricted to improving upon univariate forecasting based on this limited information set."

"There are no gains from joint forecasts for one period ahead TFR forecasts where ARIMA models fare well, but the gains become important for longer horizons (3, 5 and 10 years ahead)."

My Take

A technically clean demonstration that exploiting cross-country commonality in fertility trends improves long-range TFR forecasting. The main finding — factor model gains over univariate methods increase with the forecast horizon — is intuitive: the shared long-run trajectory becomes more informative relative to short-run idiosyncratic noise as the horizon lengthens. The paper's honest acknowledgment of what it ignores (cohort, parity, postponement — the K-O framework) is commendable. It appeared in the International Journal of Forecasting (2005) after circulating as a working paper. The ARIMA-with-trend (ARIT) collapse at 10-year horizons is a useful reminder that imposing linear drift on a non-stationary fertility series is dangerous. Complement to the K-O framework: where K-O addresses quantum measurement and tempo correction, this addresses joint-country forecast improvement using shared trend information.