The future development of population size and structure is of importance since planning in many areas of politics and business is conducted based on expectations about the future makeup of the population. Countries with both decreasing mortality and low fertility rates, which is the case for most countries in Europe, urgently need adequate population forecasts to identify future problems regarding social security systems as one determinant of overall macroeconomic development. This contribution proposes a stochastic cohort-component model that uses simulation techniques based on stochastic models for fertility, migration and mortality to forecast the population by age and sex. We specifically focus on quantifying the uncertainty of future development as previous studies have tended to underestimate future risk. The results provide detailed insight into the future population structure, disaggregated into both sexes and 116 age groups. Moreover, the uncertainty in the forecast is quantified as prediction intervals for each subgroup. The underlying models for forecasting the demographic components have been developed in earlier studies and rely on principal component time series models. Since the proposed model is fully probabilistic, it offers a wide range of information, not only identifying the most probable course of the population but also a vast number of possible scenarios for future development of the population and quantifying their respective likelihoods. The model is applied to forecast the population of Germany until 2040. 2 The results indicate a larger future population for Germany compared to the population predicted in studies conducted before 2015. The driving factors are lower mortality, higher fertility and higher net migration as derived by us statistically in contrast to widely used qualitative assumptions. The present study shows that the increase in population is mainly due to a larger proportion of older individuals.

This contribution proposes a simulation approach for the indirect estimation of age-specific fertility rates (ASFRs) and the total fertility rate (TFR) for Germany via time series modeling of the principal components of the ASFRs. The model accounts for cross-correlation and autocorrelation among the ASFR time series. The effects of certain measures are also quantified through the introduction of policy variables. Our approach is applicable to probabilistic sensitivity analyses investigating the potential outcome of political intervention. A slight increase in the TFR is probable until 2040. In the median scenario, the TFR will increase from 1.6 in 2016 to 1.68 in 2040 and will be between 1.46 and 1.92 with a probability of 75%. Based on this result, it is unlikely that the fertility level will fall back to its extremely low levels of the mid-1990s. Two simple alternate scenarios are used to illustrate the estimated ceteris paribus effect of changes in our policy variables on the TFR.

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Population projections serve various actors at subnational, national, and international levels as a quantitative basis for political and economic decision-making. Usually, the users are no experts in statistics or forecasting and therefore lack the methodological and demographic background to completely understand methods and limitations behind the projections they use to inform further analysis. Our contribution primarily targets that readership. Therefore, we give a brief overview of different approaches to population projection and discuss their respective advantages and disadvantages, alongside practical problems in population data and forecasting. Fundamental differences between deterministic and stochastic approaches are discussed, with special emphasis on the advantages of stochastic approaches. Next to selected projection data available to the public, we show central areas of application of population projections, with an emphasis on Germany.

Substantiated knowledge of future demographic changes that is derived from sound statistical and mathematical methods is a crucial determinant of regional planning. Of the components of demographic developments, migration shapes regional demographics the most over the short term. However, despite its importance, existing approaches model future regional migration based on deterministic assumptions that do not sufficiently account for its highly probabilistic nature. In response to this shortcoming in the literature, our paper uses age- and gender-specific migration data for German NUTS-3 regions over the 1995–2019 period and compares the performance of a variety of forecasting models in backtests. Using the bestperforming model specification and drawing on Monte Carlo simulations, we present a stochastic forecast of regional migration dynamics across German regions until 2040 and analyze their role in regional depopulation. The results provide evidence that well-known age-specific migration patterns across the urban-rural continuum of regions, such as the education-induced migration of young adults, are very likely to persist, and to continue to shape future regional (de)population dynamics.