Optimized Random-Combinations of Total Fertility Rates and Life Expectancies at Birth for Probabilistic Population Projections

Many studies indicate that Total fertility rates (TFR(t)) are negatively correlated with life expectancies at birth (e0(t)). We found that complete random-combinations of TFR(t) and e0(t) would result in about 24% and 22.2% of improbable combinations in probabilistic population projections (PPPs) for developing and developed countries, respectively, namely, high (or low) TFR(t) combined with high (or low) female e0(t). Thus, we propose optimized random-combinations of probabilistically projected TFR(t) and e0(t) for PPPs, and we use different strategies of the optimized randomcombinations across developing and developed countries due to different empirical patterns observed. As illustrative applications, we conducted PPPs for 11 developing countries (Brazil, China, Indonesia, Madagascar, Pakistan, Philippines, Saudi Arabia, Singapore, Sri Lanka, Thailand, Viet Nam), and 6 developed countries (Canada, France, Italy, Japan, the United Kingdom, the United States), using our proposed optimized random-combinations of probabilistically projected TFR(t) and e0(t). We found that optimized random-combinations largely reduce percentages of improbable combinations of TFR(t) and e0(t) and substantially narrow the prediction intervals width compared to complete random-combinations in both developing countries and developed countries. This is important in a real-world practical sense since it would substantially improve the accuracy of PPPs, which are useful for socioeconomic planning. The present study is part of our ongoing research program on probabilistic households and living arrangement projections (PHPs) that builds upon and is consistent with the UNPD PPPs. The PHPs are useful for various studies of healthy aging and sustainable development.