New forecast: Population decline postponed in Europe

Can We Rely on Projections of the Immigrant Population? The Case of Norway

Demographic forecasters must be realistic about how well they can predict future populations, and it is important that they include estimates of uncertainty in their forecasts. Here we focus on the future development of the immigrant population of Norway and their Norwegian-born children ("second generation"), grouped by three categories of country background: 1. West European countries plus the United States, Canada, Australia, and New Zealand; 2. Central and East European countries that are members of the European Union; 3. other countries. We show how to use a probabilistic forecast to assess the reliability of projections of the immigrant population and their children. We employ the method of random shares using data for immigrants and their children for 2000-2021. We model their age- and sex-specific shares relative to the whole population. Relational models are used for the age patterns in these shares, and time series models to extrapolate the parameters of the age patterns. We compute a probabilistic forecast for six population sub-groups with immigration background, and one for non-immigrants. The probabilistic forecast is calibrated against Statistics Norway's official population projection. We find that a few population trends are quite certain: strong increases to 2060 in the size of the immigrant population (more specifically those who belong to country group 3) and of Norwegian-born children of immigrants. However, prediction intervals around the forecasts of immigrants and their children by one-year age groups are so wide that these forecasts are not reliable.

Probabilistic population forecasting: Short to very long-term

Population forecasts are used by governments and the private sector for planning, with horizons up to about three generations (around 2100) for different purposes. The traditional methods are deterministic using scenarios, but probabilistic forecasts are desired to get an idea of accuracy, assess changes, and make decisions involving risks. In a significant breakthrough, since 2015, the United Nations has issued probabilistic population forecasts for all countries using a Bayesian methodology that we review here. Assessment of the social cost of carbon relies on long-term forecasts of carbon emissions, which in turn depend on even longer-range population and economic forecasts, to 2300. We extend the UN method to very-long range population forecasts by combining the statistical approach with expert review and elicitation. While the world population is projected to grow for the rest of this century, it will likely stabilize in the 22nd century and decline in the 23rd century.

Spatio-Temporal Patterns of County Population Shrinkage and Influencing Factors in the North-South Transitional Zone of China

Population is the foundation of socio-economic development. However, continued population shrinkage has made the problem of unbalanced and insufficient regional development more prominent, threatening human well-being. How to solve the contradiction between population shrinkage and regional development has become an urgent scientific problem. Therefore, taking a typical underdeveloped mountainous region, the North-South Transitional Zone of China, as an example, we analyzed the spatial and temporal evolution of regional population shrinkage from 2000 to 2020, classified the types of regional population shrinkage, and revealed the key influencing factors and driving mechanisms for the formation of population shrinkage patterns in poor mountainous counties. The results showed that: (1) From 2000 to 2020, the number of counties in the North-South Transitional Zone of China with population shrinkage grew, and the degree of shrinkage increased. The shrinking counties were mainly municipal counties, and the shrinkage types were mainly continuous shrinkage and expansion followed by shrinkage. (2) Spatially, the shrinking counties had significant and strengthening spatial autocorrelation, with obvious characteristics of the contiguous shrinkage of county units, and the shrinkage center of gravity and shrinkage agglomeration areas showed an evolutionary trend of shifting from east to west. The shrinking counties had obvious divergence in both the "east-west" and "north-south" directions. (3) Natural factors had an endogenous rooting role, while human factors had a strong driving role, and the impact of different influencing factors varied significantly. (4) The formation and evolution of the spatial pattern of county population shrinkage was subject to the synergistic effect of natural factors and human factors. The interaction between natural and human factors had a non-linear enhancement effect and a two-factor enhancement effect. The results of this study are expected to provide a scientific basis for coordinating regional human-land relations in order to optimize population-flow governance and sustainable regional development in the North-South Transitional Zone and less-developed regions of China.

ACCOUNTING FOR UNCERTAINTY ABOUT PAST VALUES IN PROBABILISTIC PROJECTIONS OF THE TOTAL FERTILITY RATE FOR MOST COUNTRIES

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 extends the UN model for projecting future total fertility rates 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 extant method (which does not account for this source of uncertainty) have somewhat less than nominal coverage, we find that our proposed method achieves closer 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, especially in high fertility countries.

Regional Probabilistic Fertility Forecasting by Modeling Between-Country Correlations

BACKGROUND

The United Nations (UN) Population Division produces probabilistic projections for the total fertility rate (TFR) using the Bayesian hierarchical model of Alkema et al. (2011), which produces predictive distributions of the TFR for individual countries. The UN is interested in publishing probabilistic projections for aggregates of countries, such as regions and trading blocs. This requires joint probabilistic projections of future country-specific TFRs, taking account of the correlations between them.

OBJECTIVE

We propose an extension of the Bayesian hierarchical model that allows for probabilistic projection of aggregate TFR for any set of countries.

METHODS

We model the correlation between country forecast errors as a linear function of time invariant covariates, namely whether the countries are contiguous, whether they had a common colonizer after 1945, and whether they are in the same UN region. The resulting correlation model is incorporated into the Bayesian hierarchical model's error distribution.

RESULTS

We produce predictive distributions of TFR for 1990-2010 for each of the UN's primary regions. We find that the proportions of the observed values that fall within the prediction intervals from our method are closer to their nominal levels than those produced by the current model.

CONCLUSIONS

Our results suggest that a substantial proportion of the correlation between forecast errors for TFR in different countries is due to countries' geographic proximity to one another, and that if this correlation is accounted for, the quality of probabilitistic projections of TFR for regions and other aggregates is improved.

Probabilistic forecasting using stochastic diffusion models, with applications to cohort processes of marriage and fertility

In this article, we show how stochastic diffusion models can be used to forecast demographic cohort processes using the Hernes, Gompertz, and logistic models. Such models have been used deterministically in the past, but both behavioral theory and forecast utility are improved by introducing randomness and uncertainty into the standard differential equations governing population processes. Our approach is to add time-series stochasticity to linearized versions of each process. We derive both Monte Carlo and analytic methods for estimating forecast uncertainty. We apply our methods to several examples of marriage and fertility, extending them to simultaneous forecasting of multiple cohorts and to processes restricted by factors such as declining fecundity.

Probabilistic projections of the total fertility rate for all countries

We describe a Bayesian projection model to produce country-specific projections of the total fertility rate (TFR) for all countries. The model decomposes the evolution of TFR into three phases: pre-transition high fertility, the fertility transition, and post-transition low fertility. The model for the fertility decline builds on the United Nations Population Division's current deterministic projection methodology, which assumes that fertility will eventually fall below replacement level. It models the decline in TFR as the sum of two logistic functions that depend on the current TFR level, and a random term. A Bayesian hierarchical model is used to project future TFR based on both the country's TFR history and the pattern of all countries. It is estimated from United Nations estimates of past TFR in all countries using a Markov chain Monte Carlo algorithm. The post-transition low fertility phase is modeled using an autoregressive model, in which long-term TFR projections converge toward and oscillate around replacement level. The method is evaluated using out-of-sample projections for the period since 1980 and the period since 1995, and is found to be well calibrated.