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Since the 1940s, population projections have in most cases been producedusing the deterministic cohort component method. However, in 2015, for thefirst time, in a major advance, the United Nations issued officialprobabilistic population projections for all countries based on Bayesianhierarchical models for total fertility and life expectancy. The estimates ofthese models and the resulting projections are conditional on the UN's officialestimates of past values. However, these past values are themselves uncertain,particularly for the majority of the world's countries that do not havelongstanding high-quality vital registration systems, when they rely on surveysand censuses with their own biases and measurement errors. This paper is afirst attempt to remedy this for total fertility rates, by extending the UNmodel for the future to take account of uncertainty about past values. This isdone by adding an additional level to the hierarchical model to represent themultiple data sources, in each case estimating their bias and measurement errorvariance. We assess the method by out-of-sample predictive validation. Whilethe prediction intervals produced by the current method have somewhat less thannominal coverage, we find that our proposed method achieves close to nominalcoverage. The prediction intervals become wider for countries for which theestimates of past total fertility rates rely heavily on surveys rather than onvital registration data.

Accounting for Uncertainty About Past Values In Probabilistic Projections of the Total Fertility Rate for All Countries