Bayesian probabilistic population projections for all countries

Abstract

Projections of countries' future populations, broken down by age and sex, are widely used for planning and research. They are mostly done deterministically, but there is a widespread need for probabilistic projections. We propose a bayesian method for probabilistic population projections for all countries. The total fertility rate and female and male life expectancies at birth are projected probabilistically using bayesian hierarchical models estimated via Markov chain Monte Carlo using United Nations population data for all countries. These are then converted to age-specific rates and combined with a cohort component projection model. This yields probabilistic projections of any population quantity of interest. The method is illustrated for five countries of different demographic stages, continents and sizes. The method is validated by an out of sample experiment in which data from 1950-1990 are used for estimation, and applied to predict 1990-2010. The method appears reasonably accurate and well calibrated for this period. The results suggest that the current United Nations high and low variants greatly underestimate uncertainty about the number of oldest old from about 2050 and that they underestimate uncertainty for high fertility countries and overstate uncertainty for countries that have completed the demographic transition and whose fertility has started to recover towards replacement level, mostly in Europe. The results also indicate that the potential support ratio (persons aged 20-64 per person aged 65+) will almost certainly decline dramatically in most countries over the coming decades.

Fig. 1.

Bayesian probabilistic population projections for Brazil, 2010–2100: major population indicators. Left, Top to Bottom: total fertility rate; total population; potential support ratio (20–64 population/65+ population). Right, Top to Bottom: female life expectancy; male life expectancy; joint predictive distribution of female and male life expectancy for 2010–2015, 2050–2055 and 2095–2100. The Bayesian predictive distributions are shown in red: median—solid; 80% prediction interval—dashed; 95% prediction interval—dotted. The UN WPP 2010 projection is shown as a solid blue line. The typical trajectory is shown as a solid gray line.

Fig. 2.

Bayesian probabilistic population projections for selected age groups for Brazil, 2010–2100.

Fig. 3.

Probabilistic population pyramid projections for Brazil, 2010–2100. The predictive median is shown by the black boxes. The 80% predictive intervals are shown in green and the 95% intervals in yellow. The 2005–2010 population distribution is shown by the purple horizontal lines. Left: population numbers. Right: proportions by age for each sex.

Fig. 4.

Aggregated population projections with 80% and 95% prediction intervals, UN WPP 2010 projection and UN variants for major UN regions, 2010–2100. The probabilistic population projections are based on the assumption of statistical independence between the forecast errors of different countries.