Probabilistic population projections with migration uncertainty

Abstract

We produce probabilistic projections of population for all countries based on probabilistic projections of fertility, mortality, and migration. We compare our projections to those from the United Nations' Probabilistic Population Projections, which uses similar methods for fertility and mortality but deterministic migration projections. We find that uncertainty in migration projection is a substantial contributor to uncertainty in population projections for many countries. Prediction intervals for the populations of Northern America and Europe are over 70% wider, whereas prediction intervals for the populations of Africa, Asia, and the world as a whole are nearly unchanged. Out-of-sample validation shows that the model is reasonably well calibrated.Bayesian hierarchical model | international migration | predictive distribution | United Nations | World Population Prospects I n this paper we describe a method for probabilistic projection of population for all countries, with a focus on accounting for uncertainty in projections of international migration. In particular, we are motivated by the needs of the United Nations (UN) Population Division in producing population projections for all countries until 2100 based on projections of fertility, mortality, and migration.A variety of forces contribute to the ebb and flow of international migration. Economic theories at varying levels of granularity indicate that migration flows can arise from individual attempts to maximize income (1, 2), household-level mitigation of risk (3, 4), or differences in global supply and demand for labor (5, 6). Individuals decide to migrate based on an assessment of push and pull factors (7), which may include migration policy (8), geopolitical conflict (9), and quality of the natural environment (10, 11). Networks of migrants provide a feedback mechanism such that migration flows tend to perpetuate themselves over time (12,13). Bijak (14) gives a thorough overview of theories and models of international migration. Despite their acknowledged role in driving migration, our model does not make use of push and pull factors, economic or otherwise, as covariates. Such factors are largely too difficult to predict in the long term to be of use. Instead, we appeal to the inertia of selfperpetuating migration patterns by modeling migration as an autoregressive process.Historically, most methods for projecting population have been deterministic. If the current population is known, broken down by age and sex, and future age-and sex-specific rates are projected for fertility, mortality, and migration, then the cohortcomponent method produces population projections (15). However, the UN Population Division now produces probabilistic projections of population, fertility, and mortality for all countries, but these projections still condition on deterministic migration projections (16, 17). The current methodology in the UN's World Population Prospects (WPP) differs from country to country but typically projects that net migration counts will remain cons...

Demographic Headwinds in Central and Eastern Europe

“…There is more uncertainty about fertility than mortality rates; this in turn implies quite low levels of uncertainty about working-age population (which is more important than total population for our analysis) over the next 15 years. The United Nations does not produce estimates of uncertainty around migration paths, but other analysis suggests that incorporating uncertainty about migration would accentuate the declines in expected population (Azose, Sevcikova, and Raferty 2016). Overall, for the total population of the CESEE region as a whole, the United Nations estimates only a 2½ percent chance that growth rates will not be negative in 20 years' time (Annex Figure 1.3).…”

“…Prediction intervals for population paths for North America and Europe are found to be substantially underestimated when migration uncertainty is not included. Note, however, that the central tendency of migration uncertainty is not the same as for fertility and mortality uncertainty-with the implication that adding uncertainty about migration would tilt error bands downwards (Azose, Sevcikova, and Raferty 2016). On this basis, it would not be correct to infer that the lack of migration uncertainty biases the projections toward being too pessimistic about population prospects in Europe (Annex Figure 1.5).…”

Estimating large correlation matrices for international migration

“…It follows from the demographic balancing equation that the contribution of migration to population change is given by net migration (that is, in-migration minus out-migration.) Probabilistic models exist for both net migration (Azose and Raftery, 2015;Azose et al, 2016) and inand out-migration separately (Wiśniowski et al, 2015). Both of these models are Bayesian hierarchical autoregressive models which treat forecast errors in migration as independent across countries, conditional on model parameters.…”

A Bayesian Semiparametric Approach for Trend–Seasonal Interaction: an Application to Migration Forecasts

“…A possible way to prevent this type of mistakes is to adopt a Bayesian prospective (Bijak, 2010;Bijak and Wiśniowski, 2010;Billari et al, 2014;Azose and Raftery, 2015;Azose et al, 2016) that can condition the future uncertainty on past information and future intuitions, conjugating the 'correspondence to the observed reality' with 'the awareness of multiple perspectives' (Gelman and Hennig, 2017). This more convoluted practice is implemented at the expenses of a closed form solution and the corresponding reliance on numerically intensive algorithms which require an a priori hypothesis about the prior distribution of the structural parameters and an a posteriori sampling of their probability distribution.…”