Title: Accounting for Uncertainty About Past Values In Probabilistic Projections of the Total Fertility Rate for All Countries,
Abstract: Since the 1940s, population projections have in most cases been produced
using the deterministic cohort component method. However, in 2015, for the
first time, in a major advance, the United Nations issued official
probabilistic population projections for all countries based on Bayesian
hierarchical models for total fertility and life expectancy. The estimates of
these models and the resulting projections are conditional on the UN's official
estimates of past values. However, these past values are themselves uncertain,
particularly for the majority of the world's countries that do not have
longstanding high-quality vital registration systems, when they rely on surveys
and censuses with their own biases and measurement errors. This paper is a
first attempt to remedy this for total fertility rates, by extending the UN
model for the future to take account of uncertainty about past values. This is
done by adding an additional level to the hierarchical model to represent the
multiple data sources, in each case estimating their bias and measurement error
variance. We assess the method by out-of-sample predictive validation. While
the prediction intervals produced by the current method have somewhat less than
nominal coverage, we find that our proposed method achieves close to nominal
coverage. The prediction intervals become wider for countries for which the
estimates of past total fertility rates rely heavily on surveys rather than on
vital registration data.