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Good forecasts for future fertility developments are of high importance in political planning, especially regarding measures in social insurance. Fertility is the main driver of demographic change, since small fertility rates lead to a shrinking population and together with decreasing mortality rates to an aging of the population structure. Which means an increasing stock of elder people, who have to be financed by less people in the working ages. Parametric time series models based on a quasi-three principal component model are fitted to the age- and sex-specific fertility rates (ASSFR). Age-specific migration, represented by a migration index derived from a previous principal component analysis (PCA), is used as a predictor variable to take into account its impact on fertility. Simulations of Wiener processes are used for estimating the future distributions of each ASSFR as well as the Total Fertility Rate (TFR). The forecast shows, ceteris paribus, a further increase in the TFR, with increases in the ASSFR for older women and decreasing ones for younger females. A test based on squared residuals shows that the model gives better forecast accuracy than the most commonly used methods in Germany. The modeling approach performs better than common projection and forecast methods in Germany while integrating the often discussed link between migration and fertility into a forecasting model. Next to the detailed and stochastic quantification of age-specific fertility it includes the gender of newborns, which allows for easy implementation into regular population updating through a stochastic cohort-component model.

Demographic change is one of the greatest challenges faced by Germany as well as a large part of Europe today. One of the main drivers of this change is the low fertility level, often referred to as the Total Fertility Rate (TFR), since the early 1970s. Therefore, on the one hand, while the total population is expected to decline, on the other hand, the relative share of the elderly in the total population is expected to increase. This poses a great challenge for the society in a wide range of aspects, most notably in the statutory pension fund. Therefore, it is important to gain an understanding of the future demographic development, in our case, the course of the TFR. Official forecasts often assume that the TFR will remain at a low level of 1.4 in the long run, which was already proven wrong in the publication of the 2014 data, which shows a TFR of 1.47. However, separate analysis of age-specific fertility lead to expected increases of the future TFR. This study presents a stochastic projection of the TFR based on econometric-statistical modeling of age-specific fertility rates over principal components. Simulation techniques not only generate the expected future TFR until the year 2040, but also provide point-wise prediction intervals which cover the future TFR with a probability of 95\% annually based on the current data set. The age-specific structure of the modeling procedure gives a detailed insight of the future development of the reproductive behavior for women in Germany, and therefore, is very informative with regard to possible political intervention with the scope of increasing the TFR. Moreover, the flexible structure of the model allows more sophisticated estimations of future outcome of certain political measures.

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.

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. 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.

Internationale Migration ist eines der gesellschaftlich am kontroversesten diskutierten Themen. Kritiker einer offenen Migrationspolitik sehen hohe Immigrationszahlen als großes Risiko für die Sicherheit und warnen vor möglichen Verdrängungseffekten am Arbeitsmarkt, während die Befürworter u.a. argumentieren, dass internationale Migration aus demografischer Sicht eine große Chance sei, die Folgen des Demografischen Wandels durch eine Erhöhung und Verjüngung der Bevölkerung auszubremsen und vor allem das Arbeitskräfteangebot in vom Fachkräftemangel bereits betroffenen Wirtschaftsbereichen zu erhöhen. Aus diesen Gründen ist es umso wichtiger, eine sachliche Diskussion auf Basis empirischer Ergebnisse zu führen. Eine quantitative Diskussionsgrundlage bildet in diesem Zusammenhang eine Prognose der zukünftigen Migrationsströme für Planungen in der Politik und dem Unternehmenskontext, was bisher nur unzureichend durchgeführt wird. Hierfür stellen wir einen Modellansatz für die Prognose der internationalen Nettomigration zwischen Deutschland und dem Ausland, differenziert nach Geschlecht, Alter und Nationalitätsgruppen, vor. Der Beitrag liefert stochastische Prognosen der zukünftigen Nettomigrationen auf Basis eines Hauptkomponenten-Zeitreihenmodells. Bei diesem Verfahren bilden Prognoseintervalle die Unsicherheit über die zukünftige Entwicklung ab.

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.

Since 2013, more than two million refugees have arrived in Germany and have been allocated across federal states and districts according to legal policies. A steadily increasing number of refugees is now entering the German labor market, albeit under varying economic and demographic contexts. However, regional differences in refugees' labor market integration have received little attention both retrospectively and particularly prospectively, given the projected population decline across Germany. Addressing this apparent shortcoming in the literature, we collect data on refugee arrivals by gender, nationality, approval rates, and regional allocation from 1995 to 2019. Applying principal component analysis and time series analysis, we first analyze past patterns of refugee migration to Germany and project both arrivals and regional allocations by gender and nationality until 2030. Then, combining the collected migration figures for German labor market regions and official labor market statistics, we investigate past regional employment effects from 2008 to 2019. Next, we calculate corresponding future employment effects conditional on our projected refugee figures, our estimation results, and official regional demographic forecasts until 2030. Our findings suggest that refugee migration does not affect German labor market regions equally, but instead has and will continue to lead to distinct regional employment effects. Moreover, the labor market integration differs by gender and origin of the refugees. Consequently, the interaction of regional employment effects with projected population change gives rise to different regional mitigation potentials in view of the upcoming population decline.

The COVID-19 pandemic has affected all areas of our lives. Among other outcomes, the academic literature and popular media both discuss the potential effects of the pandemic on fertility. As fertility is an important determinant of population development and population forecasts are important for policy decisions and planning, we need to address to which extent fertility forecasts performed before the pandemic still apply. Using Monte Carlo forecasting based on principal components of fertility rates, we quantify the effects of the pandemic on fertility for 22 countries and discuss whether forecasts made prior to the pandemic need adjustment based on more recent data. Among the studied countries, 14 countries show no significant effect of the pandemic at all, while six countries have significantly lowered numbers of births in comparison to counterfactual trajectories that assume that past trends will hold. These countries are primarily in the Mediterranean and East Asia. For Finland and South Korea, there is statistical evidence for increased fertility in the early phases of the pandemic. In all cases with statistically significant fertility differentials caused by the pandemic, reproductive behavior normalized quickly. Therefore, we find no evidence for long-term effects of the pandemic on fertility, leading to the conclusion that pre-pandemic fertility forecasts still apply.

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 di erent approaches to population projection and discuss their respective advantages and disadvantages, alongside practical problems in population data and forecasting. Fundamental di erences 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

Demographic aging puts social insurance systems under immense pressure as frailty risks increase with age. The statutory long-term care insurance in Germany (GPV), whose society has been aging for decades due to low fertility and decreasing mortality, faces massive future pressure. The present study presents a stochastic outlook on long-term care insurance in Germany until 2045 by forecasting the future number of frail persons who could claim insurance services by severity level with theory-based Monte Carlo simulations. The simulations result in credible intervals for age-, sex- and severity-specific care rates as well as the numbers of persons for all combinations of age, sex and severity by definition of the GPV on an annual basis. The model accounts for demographic trends through time series analysis and considers all realistic epidemiological developments by simulation. The study shows that increases in the general prevalence of disabilities, especially for severe disabilities, caused by the demographic development in Germany are unavoidable, whereas the influence of changes in age-specific care risks does not affect the outcome significantly. The results may serve as a basis for estimating the future demand for care nurses and the financial expenses of the GPV.

Die zukünftige Entwicklung der lokalen oder regionalen Bevölkerung ist für kommunale Planungen von großer Bedeutung. Diese zentrale Rolle erfordert, dass kleinräumige Bevölkerungsprojektionen auf entsprechend valider Methodik beruhen. Der vorliegende Beitrag gibt einen Überblick zu ebensolchen methodischen Ansätzen und spiegelt diese mit Erfahrungsberichten aus der kommunalen Planung. Dabei werden die Herausforderungen und Potenziale, die in der Umsetzung kleinräumiger Bevölkerungsprojektionen zu finden sind, illustrativ diskutiert. Der Beitrag leitet daraus Empfehlungen ab, wie eine bessere Informationsbasis für kleinräumige Bevölkerungsprojektionen aussehen könnte und wie sich die Projektionen methodisch ausbauen ließen.

Industrialised economies are experiencing a decline in mortality alongside low fertility rates - a situation that puts social security systems under severe pressure. Population ageing is associated not only with longer periods of pension claims but also smaller cohorts eventually entering the labour market. This threatens the sustainability of pay-as-you-go social security systems for implementing or further improving appropriate reform measures; adequate forecasts of the future population structure are needed. We propose a probabilistic approach to forecast the number of pensions in Germany up to 2040. Our model considers trends in population development, labour force participation, and early retirement, as well as the effects of pension reforms. Principal component analysis is used to manage the high degree of complexity involved in forecasting trends in old-age and disability pension claims, which arises because of cross-correlations between old-age and disability pension rates, different age groups, and gender. Time series methods enable the inclusion of autocorrelations of the pension rate time series in the model. Monte Carlo simulation is used to quantify future risk. The latter is an important feature of our model, as the future development of the population and, eventually, the pension claims and the financial burden resulting from those claims, are highly stochastic. The model predicts that, in the median trajectory, the number of old-age pensions will increase by almost 5 million between 2017 and 2036, alongside increases in the number of disability pensions by 2036. These numbers take account of the increase in legal retirement ages as part of the 2007 pension reform. After the mid-2030s, however, a moderate decrease can be expected. The results show a clear need for further reforms, especially in the medium term.