Probabilistic projection of subnational total fertility rates

Background: We consider the problem of probabilistic projection of the total fertility rate (TFR) for subnational regions. Objective: We seek a method that is consistent with the UN’s recently adopted Bayesian method for probabilistic TFR projections for all countries and works well for all countries. Methods: We assess various possible methods using subnational TFR data for 47 countries. Results: We find that the method that performs best in terms of out-of-sample predictive performance and also in terms of reproducing the within-country correlation in TFR is a method that scales each national trajectory from the national predictive posterior distribution by a region-specific scale factor that is allowed to vary slowly over time. Conclusions: Probabilistic projections of TFR for subnational units are best produced by scaling the national projection by a slowly time-varying region-specific scale factor. This supports the hypothesis of Watkins (1990, 1991) that within-country TFR converges over time in response to country-specific factors, and thus extends the Watkins hypothesis to the last 50 years and to a much wider range of countries around the world. Contribution: We have developed a new method for probabilistic projection of subnational TFR that works well and outperforms other methods. This also sheds light on the extent to which within-country TFR converges over time.