Regional Probabilistic Fertility Forecasting by Modeling Between-Country Correlations.

AbstractBACKGROUNDThe United Nations (UN) Population Division constructs probabilistic projections for the total fertility rate (TFR) using the Bayesian hierarchical model of Alkema et al. (2011), which produces predictive distributions of the TFR for individual countries. The UN is interested in publishing probabilistic projections for aggregates of countries, such as regions and trading blocs. This requires joint probabilistic projections of future country-specific TFRs, taking account of the correlations between them.OBJECTIVEWe propose an extension of the Bayesian hierarchical model that allows for probabilistic projection of aggregate TFR for any set of countries.METHODSWe model the correlation between country forecast errors as a linear function of time invariant covariates, namely whether the countries are contiguous, whether they had a common colonizer after 1945, and whether they are in the same UN region. The resulting correlation model is incorporated into the Bayesian hierarchical model's error distribution.RESULTSWe produce predictive distributions of TFR for 1990-2010 for each of the UN's primary regions. We find that the proportions of the observed values that fall within the prediction intervals from our method are closer to their nominal levels than those produced by the current model.CONCLUSIONSOur results suggest that a substantial proportion of the correlation between forecast errors for TFR in different countries is due to the countries' geographic proximity to one another, and that if this correlation is accounted for, the quality of probabilistic projections of TFR for regions and other aggregates is improved.(ProQuest: ... denotes formulae omitted.)1. IntroductionThe United Nations (UN) Population Division produces population estimates and projections for all countries every two years and publishes them in the biennial World Population Prospects (WPP). These projections are used by UN agencies and governments for planning, monitoring development goals, and as inputs to climate change and other models. They are also widely used by social and health science researchers and the private sector. The UN produces these population forecasts by projecting countries' age- and sex-specific fertility, mortality, and migration rates, and combining them to obtain age- and sex-specific population sizes using the standard cohort component method.In this paper we focus on the fertility component. Country fertility in a given time period is summarized by the period total fertility rate (TFR), which is the average number of children a woman would bear if she lived past the end of the reproductive age span and at each age experienced the age-specific fertility rate of the given country and time period. Projections of future TFR are decomposed using forecasted age schedules to obtain projections of age-specific fertility rates.The WPP reports three projection variants (low, medium, and high) for the population and vital rates based on expert opinion and models of historical patterns. The low and high variants correspond to TFR half a child below and above the medium value, respectively. One drawback of these projections is that the range given by the low and high variants has no probabilistic interpretation and hence does not reflect meaningful uncertainty in the forecasts.For the 2010 WPP (United Nations 2011), the UN used as its medium projection the predictive median of TFR from a Bayesian hierarchical model developed by Alkema et al. (2011). We refer to this model as the "current model". This model produces predictive probability distributions of each country's TFR, although the distributions were not used in the 2010 WPP. The model is based on the demographic transition, where countries move from high birth and death rates to low birth and death rates, and is composed of three phases: before, during, and after the fertility transition. …