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# Jahrbücher für Nationalökonomie und Statistik

### Journal of Economics and Statistics

Editor-in-Chief: Winker, Peter

Ed. by Büttner, Thiess / Riphahn, Regina / Smolny, Werner / Wagner, Joachim

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# Population Projection for Germany 2015–2050 on Grid Level (RWI-GEO-GRID-POP-Forecast)

Philipp Breidenbach
/ Matthias Kaeding
/ Sandra Schaffner
Published Online: 2018-07-06 | DOI: https://doi.org/10.1515/jbnst-2017-0149

## 1 Introduction

The demographic structure in Germany changes due to low fertility rates and increased life expectancy. Focusing on the natural development, Germany faces a shrinking and aging population. Expected migration flows will weaken these effects but it is not predicted to turn around. These developments are recorded by the German Federal Statistical Office in their German-wide projection (Destatis 2015a) for the years up to 2060. Depending on underlying assumptions, the population will shrink to about 70 million people in 2060 and the share of people over 65 years will increase from 21 % to about 32 %. These expected developments have substantial effects for various major fields of economic policy. Public finances as well as the labor market and the demand for public services and infrastructure are highly affected by the decrease and aging of the population.

By definition, these German-wide projections disregard the wide variety of demographic change on lower regional levels as these projections are only available on administrative levels like Federal State or county. The demographic structure on lower levels is quite heterogeneous, which implies that Federal State and county are too large to capture regional heterogeneity adequately. Especially for child care or elderly-care services, supply of medical care or local transport services areas below the county level serve the right delineation to describe local needs. Up to now, there is a lack of such data which offer a nationwide consistent demographic projection based on reliable data sources for small scaled areas.

To fulfill the need for such data, the Research Data Centre Ruhr at RWI (FDZ Ruhr) has developed a demographic projection based on grid data. The grids are defined as 1×1 kilometer squares which cover Germany in spatially equal units. In comparison to common administrative data, synthetic grid data offer major advantages: (1) Grid data can be easily transformed into administrative regions. (2) Spatial grids are time-independent, unlike e. g., German counties or zip codes. (3) Grid data can be efficiently stored, analyzed and linked with other data types (4) The grids offer a high spatial resolution to uncover heterogeneities in less dense populated areas, despite German counties or zip code areas.

This report summarizes the underlying method of this grid-based population projection for Germany from 2015 to 2050, based on main assumptions from Destatis (2015a). The assumptions consider birth probabilities, life-expectancy, net migration and expected changes in fertility, mortality and migration. The projection is based on grid-level population data, the RWI-GEO-GRID (RWI/microm 2017), described in Breidenbach and Eilers (2018). The grid level projection is comparable to the official in its aggregation but it accounts for the substantial spatial variation.

The paper is organized as follows. Section 2 gives a detailed overview of the data, the applied methodology and the underlying assumptions. The results in Section 3 show that our projection is in line with existing nationwide projections of the Federal Statistical Office and give some insights into the data. Section 4 sums up the scopes of the data and discusses the limitations. Section 5 gives information on the data availability.

## 2 Data

The population projection is based on population data on the 1km2 grid level from the RWI-GEO-GRID, a dataset containing population information disaggregated by gender and age. Age is divided into 17 age intervals. 2 These data are available for 216 831 populated 1km2 grid-cells 1 as defined under the ETRS89 Lambert Azimuthal Equal-Area projection coordinate reference system (Annoni 2003).

For forecasting purposes, the underlying population data presented in age intervals are transformed into a population cohort for every age-year. As the last age interval (75,infinity) has no information on the maximum age in this group, the age distribution is treated as truncated at 100 years. The RWI-GEO-GRID contains the number of people ${N}_{g,s,2015}^{i}\text{\hspace{0.17em}}$in 2015 by sex [s] for age interval [i] in grid g=1, …, 216 831. However, the number of inhabitants ${N}_{g,s,2015}^{a}$ for each age [a] is needed. Therefore, a meaningful transformation of the given intervals into age-years is applied. Note that

${N}_{g,s,2015}^{i}=\sum _{a\phantom{\rule{thickmathspace}{0ex}}in\phantom{\rule{thickmathspace}{0ex}}i}{N}_{g,s,2015}^{a}.$

Define

${w}_{g,s,2015,a}:=\text{\hspace{0.17em}}\frac{{N}_{g,s,2015}^{a}}{{N}_{g,s,2015}^{i}},$

than

${N}_{g,s,2015}^{a}={w}_{g,s,2015,a}\phantom{\rule{thickmathspace}{0ex}}x\phantom{\rule{thickmathspace}{0ex}}{N}_{g,s,2015}^{i},$

so that the population data can be transformed into age-years given an estimate for ${w}_{g,s,2015,a}$. This fraction is taken from administrative county-level data which are available in age-year resolution up to the age of 85. The estimator for ${w}_{g,s,2015,a}\text{\hspace{0.17em}}$is given by the county-specific fraction $\frac{{N}_{county,s,2015,a}}{{N}_{county,\text{\hspace{0.17em}}s,\text{\hspace{0.17em}}2015}^{i}}$

of the county in which the majority of the area of the grid cell g is located. This method assumes that the real fraction of each age-year within an age-interval is fixed on the county level. For ages above 85, German wide fractions of ages are used for all grid cells, as no population numbers are available in age-year resolution for counties.

This prepared database offers a good starting point for the projection algorithms. Basically two algorithms are at work, the main one projects the non-newborn population in each year (i. e. age>0), the other one projects the newborns for each year which can naturally not be derived by the lower age-year in the past year (t-1). The non-newborn population N is estimated as ${N}_{g,s,t}^{a}={N}_{g,s,t-1}^{a-1}-{D}_{g,s,t-1}^{a-1}+\text{\hspace{0.17em}}{M}_{g,s,t}^{a}$

for each grid g, sex s and year t=2016, …, 2050 at the age-years a=1, …, 100. D denotes the number of deceased persons and M denotes net migration. For notational clarity, no distinction between estimated or known entities is made. The number of deceased people is calculated by the life-expectancy and its expected development over time. The migration in each age group comes from the expected total migration for each year. These assumptions are described in the following paragraphs.

## 2.1 Life expectancy

It is assumed that life expectancy increases over time. The probability of death is predicted using the popular Lee and Carter (1992) method, which can be viewed as the benchmark method. The following model is assumed for the probability of death q, conditional on surviving up to the age a −1: $\text{E}\left[log\left({q}_{s,t,a}\right)\right]={\alpha }_{s,a}\phantom{\rule{thinmathspace}{0ex}}+{b}_{s,a}\phantom{\rule{thinmathspace}{0ex}}{\gamma }_{s,t}.$

The parameter ${\alpha }_{s,a}\text{\hspace{0.17em}}$represents the mean life-expectancy of gender s and age-year a at time t, ${\gamma }_{s,t}$ represents the overall level of mortality at time t, for gender s which is adjusted by the gender- and age-specific coefficient ${b}_{s,a}.\text{\hspace{0.17em}}\mathrm{F}\mathrm{o}\mathrm{r}\text{\hspace{0.17em}}{\gamma }_{s,t,n}\text{\hspace{0.17em}}$a random walk with drift is assumed. The German-wide death rates are projected to fall between 2015 and 2050 for almost each age-year (Figure 1). Exceptions can only be seen for men above the age of 90. The underlying parameters are estimated using observed German-wide death rates from Destatis (2015c). Estimation is carried out using the R-package forecast (Hyndman et al. 2014).

Source: Estimated from the Lee and Carter (1992) model. Note: The reported death rates imply an increasing life expectancy for women from about 83.33 (men: 77.69) in 2015 to 86.93 (men: 82.80) in 2050.
Figure 1:

Annual death rate and arising life expectancy. Death rate by sex and age-year.

Specific death rates on lower regional levels are not used in the projection. These variations in death rates are assumed to stem from worse health conditions in (former) employment and former differences in the medical care system. We assume that these differences in death rates will vanish over time.

## 2.2 Net migration

Net migration is defined as the difference between immigrants and emigrants. The net migration was driven by several trends during the last years (Figure 2). Before the start of the financial crisis in 2008, Germany was characterized by very low or even negative net migration. Afterwards, the rather strong German recovery compared to other European countries and the large immigration flows due to the refugee crisis turned the net migration highly positive. Based on these very different developments expectations on future migration are hard to make. Our projection assumes a sequential decrease of net migration from the observed value of 1.13 million people in 2015 to 150 000 in 2020 (Figure 2). This value is approximated from the median net-migration inflow before the migration wave from 2001 to 2015 (142 645). In line with the German-wide projection by the German Federal Statistical Office, the net migration stays constant afterwards. Our long-term migration is right in between the two scenarios which Destatis (2015a) applies (migration surplus of 100 000 or 200 000 per year). However, the short-run projection is much higher since the projection of Destatis (2015a) was made just in the beginning of the big refugee inflow. The age structure of the migrants is assumed to be constant over time and is derived from Destatis (2015a). Since there is no information on future regional distribution of the migration, the regional migration surpluses are based on the existing population. The net migration inflow is separated to each grid by its share of the total population.

Source: Destatis (2016a) for historical data – own assumptions for future values.
Figure 2:

Net migration flows. Historical data up to 2013, assumed data up to 2050. In 1 000 persons.

Future intra-German flows are ignored in this projection since there is no reliable estimation on the extent and direction of these future flows. Since the underlying movements on such small spatial levels are a result of wages, unemployment, housing prices and connectivity and there are no long-term small area predictions on these parameters, a resilient projection cannot cover these parameters. Constant flow parameters can instead be added by users (e. g. assuming that urbanization trends relocate a share of a certain population group from each rural to each urban area). The projection can highlight the basic natural development in terms of an aging and mostly decreasing population which can be compensated by good local competitiveness or be accelerated by a bad policy.

The projected number of newborns is based on the female population aged between 16 and 49, which is assumed to be the period of birth-giving age: ${N}_{g,s,t}^{0}=fractio{n}_{s}^{}\ast \text{\hspace{0.17em}}\sum _{a=16}^{49}{N}_{g,female,t}^{a}\phantom{\rule{thinmathspace}{0ex}}{P}_{g,t}^{a},$

where fractions 3 is the mean fraction of births of sex s for the years 1980 to 2015. The age-specific fertility rate p of women at age a at time t and grid g must be simulated.

## 2.3 Age-specific fertility rates

It is assumed that fertility rates vary over time and space. Regional differences are accounted for by using county-specific birth rates, obtained from Destatis (2015b). These differences in fertility rates are expected to be persistent. Figure 3 illustrates the variation for Germany on county-level showing higher fertility rates in East German states and lower rates on average in western parts. The rate varies from 1.07 children per women to 1.79.

Source: Computation based on Destatis (2015b).
Figure 3:

Birth rates on county level. Expected number of birth per woman.

Furthermore, it is assumed that the age of women with the highest probability of giving birth shifts from 31 in the year 2015 to 33 in the year 2028 and remains on this level afterwards. We assume that the number of births per woman increases from 1.5 in the year 2015 sequentially to 1.6 in the year 2028 and stays constant in the years 2029 to 2050. This assumption is in line with Destatis (2015a). Figure 4 shows a sample of resulting fertility rates for each age-year of women between 16 and 49 for 2015 and 2050.

Source: Destatis (2015b) – own assumptions for future values.
Figure 4:

Probability of childbearing. By age of women for 2015 and 2050.

## 3 Results

The result section is intersected in two main strands. Before some stylized facts and maps are presented, the long-term trends in the age structure of the aggregated German projection results are compared to the results of Destatis (2015a). As the Destatis (2015a) projections can be seen as the gold-standard of German population projections, a similarity can raise the credibility. Destatis (2015a) computes different scenarios, we use “Variant 2: Continued trend based on higher immigration” as reference: This version assumes the highest level of net migration, matching the observed net migration in the most recent years somewhat better than the other variants.

On the aggregated level, the German population is decreasing in size, as more people are dying than being born or migrate to Germany. Figure 5 compares the total population by sex for each projected year until 2050. The trends shown in both projections are similar, beginning with a trend of increasing population (due to migration). There is a turnaround around the years 2020/2025 with an ongoing decrease of population. While our projection starts with a slightly lower number of inhabitants, the two projections intersect quickly around 2017 and our data project a higher population afterwards. While our data indicate 0.7 % less population in the underlying data, we project 2.6 % more inhabitants for 2050.

Source: Computation based on Destatis (2015a).
Figure 5:

Projected Population 2015 to 2050. Comparison of Destatis (2015a) and RWI-GEO-GRID-Forecast by sex, in million.

These differences stem from different assumptions on migration. The reference scenario of Destatis (2015a) assumes a lower level of migration for the years up to 2020. We assume a net migration surplus of 3.87 million in the years 2015 until 2020, resulting in 1.62 million more migrants until 2020 compared to Destatis (2015a). Furthermore, we project a slightly lower level of migration for the ongoing years afterwards (150 000 migrants per year compared to 200 000). Due to recent migration waves which could not be taken into account by Destatis (2015a) as their figures were defined before the migration accelerated noticeably, our assumption seems to be plausible.

Since our projection shows quite sophisticating results compared to Destatis (2015a), we proceed with some further summarizing statistics especially on the spatial variation of our results. Figure 6 shows the mean age for Germany in 2015, 2033 and 2050. There is a considerable difference in age structure between East and West Germany; the mean age is around two years higher in East Germany. For the year 2033, this stays approximately constant while the mean age is shifted upwards.

While the information presented yet can also be extracted from existing data especially on the county level (BBSR 2015), Figure 7 gives an impression on the detailed information provided by our data. The map shows the old-age dependency ratio, the ratio of the number of people aged 65 and above divided by the number of people aged between 15 and 65 (working age population) for Berlin in 2015 and 2050. At the starting point in 2015, the ratio varies from 7 % to about 35 % derived by a few exceptions. In 2050, the mean ratio is significantly higher and converges between the grids. 4

Some information on the municipality-developments are listed in Table 1. Those ten municipalities with the highest population gains and losses are shown as well as those with the strongest developments in the old-age dependency ratio. Municipalities with less than 5 000 inhabitants (in 2015) are ignored since their gains and losses in percentage are prone to be driven by outliers. The data show substantial changes due to natural demographic changes. The most shrinking municipalities loose more than 25 % percent of their population. Eastern German municipalities dominate this snapshot. Contrary, the municipalities with the highest gains of inhabitants are dominated by universities.

Table 1:

Population changes on municipality level. Municipalities with largest losses and gains.

## 4 Scopes and limitations

This article presents the RWI-GEO-GRID-POP-Projection (FDZ Ruhr am RWI, 2017) – a population projection up to 2050 based on 1×1km-grid data. This is the first nationwide projection considering spatial heterogeneity on such a detailed level. The data are based on the RWI-GEO-GRID which contain population information for detailed age groups. Projections are mostly in line with the German-wide projection from the German Federal Statistical Office (Destatis 2015a). Fertility rates are regionalized as we assume that there are persistent regional differences in the probability of having children. We do not assume that differences in life expectancy are persistent over time as they massively reflect former employment which were harmful to health and former different medical services which are not assumed to be persistent.

We assume that migrants distribute along the distribution of the total population. Future intra-German flows are ignored in this projection since there is no reliable estimation on the extent and direction of these future flows. Since the underlying movements on such small spatial levels are a result of wages, unemployment, housing prices and connectivity and there are no long-term small area predictions on these parameters, a resilient projection cannot cover these parameters. Constant flow parameters can instead be added by users (e. g. assuming that urbanization trends relocate a share of a certain population group from each rural to each urban area).

Nevertheless, the projection can give a solid base on natural population development until 2050. Comparing our results with the German-wide projection offer sophisticating results. Differences in predicted total population can be explained by different assumptions on migration while our migration assumptions have taken recent migrant waves into account.

Our results suggest an aging society and shrinking population in Germany. Migration can slow down (but not stop) this development. These trends differ substantially between regions. A snapshot on remarkable developments on municipality level show decreases up to 29 % on the one side and a gain in population of 21 % from 2015 to 2050 on the other side.

The dataset can be merged with basically all datasets which contain precise geographical information (longitude/latitude or grid information). These data – as well as other grid information e. g. provided by the RWI-GEO-GRID – can revalue existing datasets when they are merged as so-called context data. Moreover the data can be aggregated to higher ordered regional entities. We have positive experience with aggregation on zip code or municipality level. The data also promise new insights into demographic development on the municipality level since it is the first German wide projection on this level.

Regarding the research potential, these data allow research directly focused on demographic developments e. g. the provision and location of local infrastructures that should be planned regarding the local demographic trends.

## 5 Data availability

The data are available as a scientific use file (SUF) for scientific, non-commercial, research. The data is stored efficiently using a wide format, where the rows are given by the combination of grid cell, sex and age and the columns are the forecasted population numbers. 5 The data can be obtained as a Stata® dataset (data), R dataset (rds), Excel (xlsx) or csv. Data access requires a signed data use agreement. Only researchers of scientific institutions are eligible to apply for data access to the SUF. The SUF can be used at the workplace of the users. Upon request, we can provide snapshots of the data or data on higher aggregated regional levels as public use file for non-scientists.

Data access is provided by the Research Data Centre Ruhr at the RWI – Leibniz-Institute for Economic Research (FDZ Ruhr). Data access can be applied for online at http://fdz.rwi-essen.de/application.html. The application form includes a brief description and title of the project, cooperation, department, expected duration of data usage as well as further participants in the project.

## References

• Annoni (2003), European Reference Grids. Proposal for a European Grid System. Workshop Proceedings and Recommendations. EUR Report 21494 EN. Google Scholar

• BBSR (2015), Die Raumordnungsprognose 2035 Nach Dem Zensus. In BBSR-Analysen Kompakt 05/2015. Google Scholar

• Breidenbach, P., L. Eilers (2018), RWI-GEO-Grid: Socio-economic data on grid level. Jahrbücher für Nationalökonomie und Statistik (forthcoming). Google Scholar

• Destatis (2015a), Bevölkerung Deutschlands Bis 2060. 13. Koordinierte Bevölkerungsvorausberechnung. Wiesbaden, Statistisches Bundesamt. Google Scholar

• Destatis (2015b), Geburten: Lebendgeborene nach Geschlecht, Nationalität und Alter der Mütter. Google Scholar

• Destatis (2015c), Sterbetafel (Periodensterbetafel): Deutschland, Jahre, Geschlecht, Vollendetes Alter. Google Scholar

• Destatis (2016a), Wanderungen: Wanderungen zwischen Deutschland und dem Ausland 1991 bis 2015. Google Scholar

• FDZ Ruhr am RWI (2017), Population Forecast. RWI-GEO-GRID. Version: 1. RWI – Leibniz-Institut für Wirtschaftsforschung. Datensatz. http://doi.org/10.7807/pop:forecast:suf:v1

• Hyndman, R.J., H. Booth, L. Tickle, J. Maindonald (2014), Demography: Forecasting mortality, fertility, migration and population data. R package version 1.18. Google Scholar

• Lee, R.D., L.R. Carter (1992), Modeling and Forecasting US Mortality. Journal of the American Statistical Association 87(419): 659–671.

• RWI; microm (2017), Socio-economic data on grid level (Wave 5). Population by age and gender. RWI-GEO-GRID. Version: 1. RWI – Leibniz-Institut für Wirtschaftsforschung. Datensatz. http://doi.org/10.7807/microm:einwGeAl:V5

• Wood, S.N. (2006), Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC, Boca Raton. Google Scholar

## Footnotes

• 2

i=[0,2],…,[6,9],[10,14],[15,17],[18,19],[20,24],[25,29],…,[65,74],[75,infinity),

• 1

About 40 % of the grid cells covering Germany are not populated.

• 3

The mean fractions of births are: fractionfemale: 48.6633 % and fractionmale: 51.3367 %.

• 4

Especially for the case of Berlin, the ignored inner-German migration will change the results. However, such inflows will intensify the small-scaled variation, making such grid data more important.

• 5

See http://fdz.rwi-essen.de/doi-detail/id-107807popforecastsufv1.html for meta data registered with the DOI. The meta data as related publications are updated regularly.

Published Online: 2018-07-06

Citation Information: Jahrbücher für Nationalökonomie und Statistik, ISSN (Online) 2366-049X, ISSN (Print) 0021-4027,

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