Long-Term Care in Germany in the Context of the Demographic Transition—An Outlook for the Expenses of Long-Term Care Insurance through 2050

Abstract

Demographic aging results in a growing number of older people in need of care in many regions all over the world. Germany has witnessed steady population aging for decades, prompting policymakers and other stakeholders to discuss how to fulfill the rapidly growing demand for care workers and finance the rising costs of long-term care. Informed decisions on this matter to ensure the sustainability of the statutory long-term care insurance system require reliable knowledge of the associated future costs. These need to be simulated based on well-designed forecast models that holistically include the complexity of the forecast problem, namely the demographic transition, epidemiological trends, concrete demand for and supply of specific care services, and the respective costs. Care risks heavily depend on demographics, both in absolute terms and according to severity. The number of persons in need of care, disaggregated by severity of disability, in turn, is the main driver of the remuneration that is paid by long-term care insurance. Therefore, detailed forecasts of the population and care rates are important ingredients for forecasts of long-term care insurance expenditures. We present a novel approach based on a stochastic demographic cohort-component approach that includes trends in age- and sex-specific care rates and the demand for specific care services, given changing preferences over the life course. The model is executed for Germany until the year 2050 as a case study.

1. Introduction

Demographic aging, which is caused by low fertility rates and increasing life expectancies Vanella and Deschermeier (2020) is resulting in a steeply growing number of older people in need of care in many regions all over the world Harper (2015). Germany, whose total fertility rate has been below replacement level for over half a century Vanella and Deschermeier (2019) and whose life expectancy has been mostly increasing for the last sixty years Destatis (2024b), has witnessed steady population aging for decades Vanella and Deschermeier (2020). Hence, policymakers and other stakeholders have, for years, been discussing how to fulfill the rapidly growing demand for care workers and finance the rising cost of long-term care Bowles (2015).

To make informed decisions and take well-planned action to address these two challenges, we need solid and reliable knowledge of how the demand for care workers, as well as the expenses for the German statutory long-term care insurance (LTCI) system, will develop Bowles (2015). Understanding future cost implications allows policymakers to adequately allocate resources and plan for the sustainability of long-term care infrastructure Rothgang et al. (2012). Moreover, this information is essential for the development of effective social policies and insurance mechanisms. Investigating the future cost of long-term care in Germany is vital for ensuring the sustainability of the long-term care system and—in particular, statutory LTCI Bowles (2015); Zhang et al. (2020)—as well as fostering the development of effective policies and services to meet the needs of an aging population.

There are several drivers of the future costs of LTCI. First, the future size and structure of the population play major roles, as described above. Ceteris paribus (c.p.), care risks in both dimensions, overall and according to severity, increase at higher ages (see Section 3.1). Secondly, morbidity trends affect how age- and sex-specific care risks change over time; for instance, medical advances, work conditions, or nutrition can lead to decreasing morbidities Vanella et al. (2020). Thirdly, the definitions and coverage rates of care needs determine how representative care rates are for the underlying care risks. For instance, stricter official eligibility rules concerning care benefits are associated with lower disability prevalence and care rates. Increased and more thorough testing naturally decreases the difference between the actual prevalence of diseases and known cases Rajgor et al. (2020), which holds for disabilities as well. In our context, this means that an increased number of eligibility tests for care benefits decreases the share of latent disabilities, i.e., the bias of care rates relative to the actual shares of disabled persons who are theoretically in need of care decreases. For the case of Germany, we return to those points in more detail in Section 3.1. Fourthly, the chosen type of care benefit influences the associated costs, as, for instance, inpatient care in a nursing home is, from the standpoint of statutory LTCI, more expensive than exclusively monetary support (see Section 3.2.2). The choice of a specific care service is affected by a variety of factors, such as personal preferences (e.g., does the dependent individual prefer to stay at home rather than living in a nursing home? Lehnert et al. (2018)), the respective family structures (e.g., are there children willing and able to care for their parents? Bowles (2015)), and infrastructural factors (e.g., are there available care workers that can provide outpatient care? Destatis (2024a)). Fifthly, the unit costs (for instance, monthly or annually) of the received care service obviously play a role in the overall costs. These are primarily a political choice Bowles (2015).

The study at hand contributes to the literature in two ways. First, we suggest a novel forecast model for the costs of long-term care that combines (stochastic) demographic forecasting with projections of morbidity trends represented via age-, sex-, and severity-specific care rates (ASSSCRs), a term coined by Vanella et al. (2020). The resulting projections of individuals that claim care benefits are then merged with projections of the distributions of the provided care types, which are, in turn, multiplied by unit costs to derive projections of total costs. Secondly, the model is used to project the expenses of statutory LTCI in Germany until the year 2050, taking the abovementioned cost drivers into account. Whereas the available data do not yet allow for a fully stochastic forecast, we present a semi-probabilistic approach (from a stochastic population forecast conducted in an earlier study) that is more informative than LTCI projections available thus far for Germany.

The remainder of this study has the following structure. First, we provide a short outline of the structure of the German statutory long-term care insurance (Gesetzliche Pflegeversicherung, GPV) system and its major reforms with regard to its past expenses. We then provide a short overview of previous approaches to LTCI (cost) forecasting, with a focus on Germany, to show the connection to our approach. Section 3 summarizes the data used in our projection and presents the model. Section 4 shows the most important results from our projection for the expenses of the GPV until 2050. Finally, Section 5 discusses the model’s results and limitations, outlining further research needs and potentials.

2. Background

2.1. Structure and Major Reforms of German Statutory Long-Term Care Insurance

Given the aging of the population and the associated increase in morbidities and long-term care risks, Germany introduced statutory LTCI (GPV) in 1995 to support those being affected by the need for care directly or indirectly (via their family members) Bowles (2015). GPV supports a variety of care services, such as complete (e.g., living at a nursing home) or partial (e.g., only staying at a nursing home at night) inpatient care, professional outpatient care, or purely monetary support (e.g., financial support or digital services for children) for caring relatives (see, e.g., Siegl (2024) for a thorough overview). The GPV support for an individual depends on the services demanded by disabled persons and their relatives and on the severity of the respective disabilities. Some of the amounts are flat rates that each individual may request, while others are only upper limits that need to be assigned to concrete services. A detailed overview of the services and associated amounts in EUR exceeds the scope of this section. However, interested readers can find more information on that (albeit in German) in, e.g., Siegl (2024).

GPV has been adjusted various times since its introduction. The major improvement has been a process that began in 2001 with the passing of the Pflegeleistungs-Ergänzungsgesetz, which acknowledged that GPV services until that point had only been targeting persons with physical disabilities. Therefore, the reform aimed to offer wider support to individuals with mental disabilities, especially dementia. However, the new regulation did not have a major impact, which is why further reforms followed, such as the Pflege-Weiterentwicklungsgesetz (PfWG) of 2008. Among other goals, the PfWG was intended to foster the establishment of a better consulting infrastructure for affected individuals with the aim of easier access to LTC support Rothgang et al. (2009). The most important reform has been the Zweites Pflegestärkungsgesetz (PSG II), which was introduced in 2016, by which the original definition of severities was significantly overhauled. Instead of three care levels (Pflegestufen), five care degrees (Pflegegrade) were introduced. Whereas dementia had been acknowledged as a side effect only in the context of long-term care prior to the reform, a diagnosis of dementia has ensured eligibility for care benefits since PSG II was introduced Vanella et al. (2020). In Section 3.1, we show the quantitative effects of the mentioned reforms.

2.2. Approaches for Projection of Long-Term Care Demand and Associated Costs

Given the degree of population aging, future demand for long-term care is expected to increase just due to the larger number of elderly cohorts present in the population. However, so far, the link between increasing life expectancy, on the one hand, and health status and, thus, the potential need for care, on the other hand, has not been clearly and empirically determined. Do medical advances that allow for longer life expectancies lead to additional years spent mainly in bad health with high needs for care (the so-called medicalization thesis, going back to Gruenberg (1977))? Or do they lead to additional years mostly spent in good health with the need for care arising later in life (the so-called morbidity compression thesis, going back to Fries (1980))? Most likely, a mix of both hypotheses is true, as suggested, e.g., by Kane et al. (1990). According to the latter, the majority of people with increased life expectancies live healthier lives, while some spend their additional life years entirely in illness and, thus, in need of care. In this study, we follow a modest status quo approach, holding care rates constant by age, as well as an alternative approach that extrapolates the development of care rates from recent years. In the literature, methodological approaches to LTCI cost forecasting go back to Schmähl and Rothgang (1996), who presented a first projection of the future expenditures of GPV until the year 2030 as a response to its introduction in 1995 (see Section 2.1). The authors illustrated the complexity of the forecast problem and suggested decomposition using a population projection of the German federal statistical office (Destatis) for the underlying future population, which they multiplied by age- and sex-specific care probabilities by care level, following the then-definition, which had been previously estimated based on survey data. They adjusted this projection to estimates for the frail population by multiplying it by the share of the total population insured by GPV. Drawing on survey data, the authors estimated the shares of the frail population by type of care benefit. The results of these steps where then multiplied by cost units by care level and type of care, which were derived from the legal frameworks.

The Schmähl–Rothgang approach was improved by Bowles (2015), who conducted a series of scenario analyses that simulated GPV expenditures under varying assumptions on demographic development, linking care rates to assumed life expectancy improvements following the Sullivan method (see Sullivan (1971)). Moreover, Bowles included several scenarios for the future population potentially available to provide informal care given several labor market scenarios. Finally, the author investigated policy scenarios aimed at changing the distribution of care among the care types and changing financial strategies.

The named studies refer to the old definition of care levels instead of care degrees, as pictured in Section 2.1. Our approach, in essence, follows Bowles; however, we suggest improvements to his approach. First, we include our own stochastic population forecast that appropriately covers both the empirical trends and the uncertainty in the future population size and structure. An improved prediction of the future population size and structure is of major importance, since demographics form the strongest driver of care need Vanella et al. (2020). However, the official deterministic projections for Germany have been shown to achieve low predictive performance in comparison to eventual population development on a large scale Vanella and Deschermeier (2020), which is associated with an unreliable informational basis when conducting forecasts of future long-term care demand. Secondly, our projection is based on the definition of care in place since 2016, as first employed by Vanella et al. (2020). We use the currently available care data (until 2021) and check two different scenarios for the development of ASSSCRs (status quo against empirical extrapolation) based on the present data. This appears imperative, since the re-definition of long-term care from levels to degrees, as presented in Section 2.1, did not only change the way care needs are defined. Remuneration for beneficiaries of GPV services varies significantly by care degree (see Section 3.2.2). Therefore, an accurate forecast of future costs for LTCI requires reliable forecasts for both the population and the corresponding care rates by severity. Moreover, we quantify probabilities to claim a specific type of care benefit (purely financial, exclusively outpatient, partially inpatient, or exclusively inpatient), employing a multivariate generalized linear model. We will provide more detail on the methods in Section 3.2.

3. Data and Methods

3.1. Data

The data used for this study consist of national population and long-term care (LTC) data for Germany. Population estimates by gender and years of age (0, 1, …, 109, 110+) for 1 January, 2000–2022 are provided in the Human Mortality Database (2022) (HMD). The raw data originate from Destatis. The raw population data from Destatis exhibit a significant structural break in the year 2011, when they were corrected after the census survey. The HMD data are adjusted according to Klüsener et al. (2018), avoiding a structural break in the analysis.

Data on persons in need of care (pinoc) by five-year age group and type of care benefit received are available biennially for 15 December, 1999–2021 in the Destatis database GENESIS-Online (2024a). Figure 1 illustrates the official sum of pinoc over that period in Germany.

The black line shows a monotonous and progressive increase in the pinoc throughout the observed period. Discussions on the future demand for long-term care primarily revolve around population aging (e.g., Destatis (2010)). As a first investigation of this demographic effect, we adjusted the trend for changes in the age and sex structure of the population. In addition to the pinoc, Figure 1 shows a blue, dashed line that is an age- and sex-standardized curve computed as in, e.g., Eurostat (2013). For this, we first computed annual age- and sex-specific care rates (ASCRs) by dividing the number of persons receiving care benefits in each stratum by the corresponding population estimates as follows:

$$c_{y,a,g}:={\displaystyle \frac{C_{y,a,g}}{B_{y,a,g}}},$$

(1)

where

• $c_{y,a,g}$ is the care rate for year $y\in (1999,2001,\dots ,2021)$ among individuals in age group a and of gender g;
• $C_{y,a,g}$ represents individuals receiving care benefits on 31 December, year y, in age group a and of gender g; and
• $B_{y,a,g}$ is the population estimate for 31 December, year y, in age group a of gender g.

Secondly, we computed the hypothetical individuals in need of care for each year, age group, and gender under the assumption of a population structure as on 31 December 2021.

$${\widehat{C}}_{y,,a,g}=c_{y,a,g}\times B_{2021,a,g}.$$

(2)

Thirdly, these values were cumulated to compute the blue curve in Figure 1 as follows:

$${\widehat{C}}_y=\sum _{a=1}^{20}\sum _0^1{\widehat{C}}_{y,a,g},$$

(3)

where

• $g=0$ denotes males and $g=1$ denotes females; and
• $a=1:\mathrm{age}0-4,a=2:\mathrm{age}5-9,\dots ,a=20:\mathrm{age}95+.$

Drawing from the theoretical connection between mortality and morbidity developments (Vanella et al. (2020)) and long-term trends in mortality decreases observed in Germany since the second half of the 20th century Destatis (2024b), we would expect long-term c.p. decreases in LTC risks Vanella et al. (2020) for the blue curve in Figure 1. This, indeed, appears to be the case until the year 2005. However, after that, the trend shifts, and the age- and sex-adjusted curve increases. This shows that demography is not the only driver of the the pinoc increases. Another conclusion from that is that morbidity trends appear to have a minor impact in the German case. Increases in the demographically standardized curve after 2005 can be tracked to increases in assessments of care need among outpatients—a process that was especially stressed after the introduction of the PfWG in 2008, which aimed to allow a larger share of pinoc to receive statutory financial support, especially those being treated at home Kimmel et al. (2009); Wagner (2010). Figure 1 exhibits very steep increases since 2017 that are connected with a change in care need definitions as described in Section 2.1 Destatis (2022).

For further analyses described in Section 3.2, we computed ASSSCRs for the applicable years, i.e., 2017, 2019, and 2021, following the suggestion of Vanella et al. (2020). The data on long-term beneficiaries by age, gender, degree of severity, and type of benefit received for the years 2017, 2019, and 2021 are provided in GBE-Bund (2024), a joint database maintained by Destatis and the Robert Koch Institute. The population data are identical to the HMD data presented earlier Human Mortality Database (2022). For interested readers, we provide the ASSSCRs computed from those two data sources in File S1 in an analyzable form. We checked the data for consistency and representivity. As a result, we decided to aggregate ages of 0–49 years into one age group to avoid biased estimates.

Population projections deliver indispensable input data for LTC projections (see, e.g., Bowles (2015); Vanella et al. (2020)). In that regard, our projection refers to a stochastic population forecast for Germany that was developed by Vanella and Deschermeier (2020) and refined and updated recently by Sarajan et al. (2024) as an input for an epidemiological projection model. The authors of that study provided their data for our paper. Figure 2 and Figure 3 illustrate the resulting population forecasts with median and 75% prediction intervals (PIs) by age and gender stratification, consistent with our projection model.

The most apparent conclusions from those figures are, first, that the population of older people, as illustrated in Figure 3, in the long term, is very likely to increase further. Secondly, the future population structure is marked by major waves that can be tracked over the course of time. The most apparent wave is the so-called baby boomer generation that was born around the mid-1960s Vanella and Deschermeier (2019) and corresponds to the age group most affected by care risks (around age 70 and older Vanella et al. (2020)) in the 2030s. A more thorough analysis of the population trends’ impact on LTC is presented in Section 4. In the following subsection, we describe how the population forecast flows into our forecast model for LTC costs.

3.2. Methods

3.2.1. Projection of Age-, Sex- and Severity-Specific Care Rates

From the descriptive investigation in Section 3.1, we learned that, next to demographic developments, the major drivers of the pinoc trend are the testing for and the definition of care needs. From the standpoint of forecasting, this means that extrapolation of trends based on classical time-series analysis of the present data does not lead to good predictions for the future demand for care.

In Section 1, we presented the most important drivers of LTCI expenses. In that regard, the primary driver is the population’s demographic development Bowles (2015). As presented in Section 3.1, our projection includes the latter according to a recent stochastic population forecast by Sarajan et al. (2024), as illustrated in Figure 2 and Figure 3. Next, morbidity trends factor into the developments of age-specific care rates. However, those are not directly observable in the data. Bowles (2015) suggested the inclusion of those in projection models by merging the Sullivan method linked to the projection of life expectancy with a projection of the care rates. Vanella et al. (2020) developed a forecast approach that included their suggestion for theory-based Monte Carlo simulation, given the lack of representative historical data for Germany. However, their projection failed to cover the developments of the ASSSCRs ex post (see File S1), since morbidity trends are largely superimposed by changes in the testing and definition of care need, the third factor mentioned earlier. From this, we understand that the direct treatment of morbidity trends in a GPV projection is currently less reasonable.

However, for our projection, we consider the impact of more testing on the care rates based on a scenario simulation under two assumptions. Under the status quo scenario, we hold the ASSSCRs fixed at their 2021 values. As an alternative, we construct a mid-term trend scenario that extrapolates the trends observed for the period of 2017–2021 over the forecast horizon. We present the approach below. First, our model includes 20 (ten age groups and two genders) ASSSCR time series. This implies a relatively highly dimensional forecast problem that needs to consider collinearity between the ASSSCRs as well. For instance, care risks increase with age for all genders Vanella et al. (2020). Moreover, disability risks have a similar trending behavior for different age groups Vanella et al. (2022), i.e., cross-correlations among age-specific care risks are high, as can be seen in File S1. Cross-correlations of care risks over different degrees of disability are observable as well. For instance, more severe care degrees (4 and 5) become more prevalent at very high ages over 90 years, whereas the less severe care degrees (1 and 2) have a negative tendency for that age group Vanella et al. (2020). Principal component analysis (PCA) is an established method to cope with both high dimensionality and multicollinearity in forecast problems. For instance, Vanella et al. (2022) applied PCA for a joint forecast of old age and disability pension rates in Germany. PCA involves singular value decomposition of the covariance (or correlation) matrix of the underlying time-series matrix Vanella and Deschermeier (2020). In our study, we performed PCA for the covariance matrix of the logistically transformed ASSSCRs for the years 2017, 2019, and 2021. The logistic transformation keeps eventual simulations within a realistic range of values, as first suggested by Vanella and Deschermeier (2019) for the forecasting of age-specific fertility rates. In our case, we implemented two conditions in our data. First, we defined $(0;1)$ as the allowed range for the overall care rate in each age–gender stratum. We made sure that no age- or sex-specific care rates over all care degrees exceeded those bounds by excluding the ASSSCRs for care degree 1 from PCA, instead including the overall care rates. The transformation for the first 20 columns (the overall care rates for each of the ten age groups and the two genders) of the care rate matrix is, therefore,

$$l_{y,a,g,.}:=ln\left({\displaystyle \frac{c_{y,a,g,.}}{1-c_{y,a,g,.}}}\right),$$

(4)

where

• $ln\left(\right)$ is the natural logarithm of the argument;
• $l_{y,a,g,.}$ is the logistically transformed care rate for year y, age group a, and gender g over all care degrees; and
• $c_{y,a,g,.}$ is the care rate for year y, age group a, and gender g over all care degrees.

For care degrees 2–5 (columns 21–100), we restricted the value range to $(0;1/3)$, roughly corresponding to the empirical extreme values for the observed data.

$$l_{y,a,g,d}:=ln\left({\displaystyle \frac{c_{y,a,g,d}}{1/3-c_{y,a,g,d}}}\right),$$

(5)

where

• $l_{y,a,g,d}$ is the logistically transformed care rate for year y, age group a, gender g, and care degree d; and
• $c_{y,a,g,d}$ is the care rate for year y, age group a, gender g, and care degree d.

Therefore, care degree 1 is modeled indirectly as the difference between the sum of all care rates and the sum of all care rates for degrees 2–5 for each age–gender stratum. For instance, the ASSSCR for males aged over 89 years in care degree 1 for year 2021 is modeled as

$$c_{2021,10,0,1}=c_{2021,10,0,.}-\sum _{d=2}^5{c}_{2021,10,0,d}.$$

This way, we make sure that our model cannot predict negative values for the ASSSCRs, and the overall care rate is not predicted to be over 100%. Based on these data, PCA is performed as follows:

$$\mathbf{P}=\mathcal{L}\mathbf{\Lambda },$$

(6)

where

• $\mathbf{P}$ is the time-series matrix (3 × 100) of principal components;
• $\mathcal{L}$ is the time-series matrix (3 × 100) of logistically transformed care rates according to Equations (4) and (5); and
• $\mathbf{\Lambda }$ is the matrix of eigenvectors (100 × 100; also loadings) computed based on the covariance matrix of $\mathcal{L}$.

The computation of $\mathbf{\Lambda }$ exceeds the goals of our paper. It suffices to say that the PCs are linear combinations of the original variables that are uncorrelated and aggregate the majority of the variation of the original matrix in very few PCs. They are presented in descending order according to the variation they explain in the ASSSCRs Vanella and Deschermeier (2020). In our case, the first PC explains about 97% of the variation in the logit-ASSSCR time-series matrix. Therefore, it is sufficient to analyze time-series trends in the care rates based on the first PC, which we label as the LTC Index. Figure 4 shows the loadings of the LTC Index. The symbols refer to the median ages of each age group but hold for the complete age groups. For instance, a red dot at age 24.5 refers to the loading for the complete age group of 0–49 years.

The loadings show strong correlations over all dimensions of age, gender, and care degree. Therefore, an increase in the LTC Index is, for instance, associated with similar c.p. decreases for the majority of strata. Interestingly, high care degrees in the older age groups exhibit mostly positive loadings next to strongly negative loadings for the total care rates and the low-to-moderate severities, i.e., increases in the LTC Index would be associated with c.p. decreases in the overall care rates and less severe disabilities, whereas more severe disabilities would be more prevalent in those age groups. In the context of Figure 5, which shows short time series of the LTC Index, we can draw some conclusions for that observation.

We see a negative trend in the LTC Index, i.e., overall increases for the care rates, consistent with Figure 1. However, more severe disabilities, which we identify by care degrees 4 and 5, show a decreasing trend in the older age groups. This may be a small indicator of decreasing morbidities in the aging population in the context of increasing longevity, as hypothesized by Vanella et al. (2020). However, this observation has to be treated with extreme caution, since the time series, thus far, only cover three points in time. Next to the time series of the LTC Index, Figure 5 illustrates its projections according to the status quo and trend scenarios. As mentioned above, the status quo scenario simply holds the index and, therefore, the ASSSCRs, at the 2021 level. Therefore, this scenario measures the isolated c.p. effect of the demographic transition on LTCI expenses. The trend scenario, on the other hand, extrapolates the trend observed over the period of 2017–2021 into the future. After graphical inspection, a logarithmic trend appeared reasonable, which we fit to the data. Obviously, three observations are insufficient to create a good forecast. Therefore, this trend should only be understood as an extreme scenario that illustrates the development of the ASSSCRs if the trends observed since 2017 were to persist in the long term. Qualitatively speaking, we might expect the future development to lie somewhere between these two scenarios. However, the available data do not allow for quantification of probabilities of occurrence of future scenarios in good conscience. PCA generates a number of PCs that corresponds to the number of original time series, i.e., in our case, 100. The remaining 99 PCs are simply assumed to remain constant over the forecast horizon, which is a common assumption for this kind of forecast model Vanella and Deschermeier (2020).

From the PC projections presented in Figure 5, we can derive projections for the ASSSCRs by replacing $\mathbf{P}$ with the PC projection matrix in each trajectory (say, ${\mathbf{P}}_{\mathbf{t}}$) in Equation (6), solving for ${\mathcal{L}}_{\mathbf{t}}$ as follows:

$${\mathbf{P}}_{\mathbf{t}}={\mathcal{L}}_t\mathbf{\Lambda }\iff {\mathcal{L}}_{\mathbf{t}}={\mathbf{P}}_{\mathbf{t}}{\mathbf{\Lambda }}^{-\mathbf{1}},$$

(7)

with ${\mathcal{L}}_{\mathbf{t}}$ denoting the projection matrix of the logistically transformed ASSSCRs (29 × 100). Next, we derive the projections of the ASSSCRs in each scenario by plugging the values of the first 20 columns of ${\mathcal{L}}_{\mathbf{t}}$ for $l_{y,a,g,.}$ into Equation (4) and columns 21–100 for $l_{y,a,g,d}$ into Equation (5) and solving for $c_{y,a,g,.}$ and $c_{y,a,g,d}$, respectively. This leads to the following projections for the total care rates:

$$l_{y,a,g,.,t}=ln\left({\displaystyle \frac{c_{y,a,g,.,t}}{1-c_{y,a,g,.,t}}}\right)\iff c_{y,a,g,.,t}={\displaystyle \frac{exp\left(l_{y,a,g,.,t}\right)}{1+exp\left(l_{y,a,g,.,t}\right)}},$$

(8)

and the following for the ASSSCRs for care degrees 2–5:

$$l_{y,a,g,d,t}=ln\left({\displaystyle \frac{c_{y,a,g,d,t}}{1/3-c_{y,a,g,d,t}}}\right)\iff c_{y,a,g,d,t}={\displaystyle \frac{exp\left(l_{y,a,g,d,t}\right)}{3+3exp\left(l_{y,a,g,d,t}\right)}}.$$

(9)

Based on Equations (8) and (9), we can then compute the projections of the ASSSCRs for care degree 1 as follows:

$$c_{y,a,g,1,t}=c_{y,a,g,.,t}-\sum _{d=2}^5{c}_{y,a,g,d,t}$$

(10)

3.2.2. Projection of Estimates for Care Demand and LTCI Expenses

Having computed the projections for the ASSSCRs, we merge those with the population forecast presented in Section 3.1 by multiplying the population in each age–sex group by the corresponding ASSSCR in each trajectory. Sarajan et al. (2024) estimated 1000 trajectories for the population, each of which we merged with our two scenarios for the ASSSCRs, resulting in 2000 trajectories overall. In trajectory t, the pinoc estimate for age group a of gender g and for care degree d in year y is, therefore,

$$C_{y,a,g,d,t}=c_{y,a,g,d,t}·B_{y,a,g,t}.$$

(11)

In Section 4, we present results from that simulation.

To estimate the future costs for LTCI, we need to estimate the type of care service demanded and provided in the future. As this depends on both the personal preferences of the pinoc and their families’ and the infrastructural abilities to supply those (see Section 1), we cannot really predict this for the future. In addition, we have to consider a potential mismatch between the demand for care and the infrastructural supply, resulting in a potential demand–supply gap. We could potentially make assumptions on that in a projection. However, we chose to keep the extent of assumptions in the model to a minimum level, sticking to the information drawn from the data. Therefore, we used the available data on care benefits by age, gender, and care degree for the years 2017, 2019, and 2021 to check for associations of the demographic and epidemiological characteristics of the patients with regard to the care service they receive. The data allow for a distinction of care benefits into the following four major categories:

• (Full) inpatient care in nursing homes;
• Partial inpatient care (normally either daytime or nighttime);
• Professional outpatient care at the patients’ homes;
• Exclusive monetary benefits for patients who are cared for by family and friends.

For interested readers, we provide those numbers as count data in File S2. To maximize the information from the data, we constructed a prediction model for the probabilities of receiving a specific type of care benefit given a patient’s age, gender, and care degree, which we also adjusted for previously observed temporal aspects.

In the context of genome analysis, Zhang et al. (2017) compared the performance of several multivariate generalized linear models when fitted to simulated data. The authors provided the accompanying R package, MGLM, which we used for our analysis. We followed their suggestion and tested the models regarding their fit to our four possible outcomes of types of care via maximum likelihood estimation. In our specific case, the only model that led to (plausible) estimators (more on that in Section 4) was a Dirichlet multinomial regression model. Here, an individual’s (i) probability distribution of being estimated to belong to each category k (receive a specific care service), given their specific demographic and epidemiological characteristics, is Thorsén (2014)

$${\pi }_k\left({\mathit{x}}_{\mathit{i}}\right)={\displaystyle \frac{exp\left({{\mathit{\beta }}_{\mathit{k}}}^T{\mathit{x}}_{\mathit{i}}\right)}{{\sum }_{j=1}^{4}exp({{\mathit{\beta }}_{\mathit{j}}}^T{\mathit{x}}_{\mathit{i}})}}.$$

(12)

Equation (12) expresses the probability (${\pi }_{\kappa }$) of requesting a specific care service, with $\kappa$ being one of the following four categories:

• Full inpatient care;
• Partial inpatient care;
• Outpatient care;
• Exclusively monetary support.

${\mathit{x}}_{\mathit{i}}$ is a vector of predictors for an individual (i), with $\mathit{x}$ comprising the following variables:

• The logarithmized median age in years for each age group;
• A gender dummy taking a value of 0 for males and 1 for females;
• Care degree dummies for degrees 2–5, with care degree 1 being the reference;
• Temporal dummies for the years 2019 and 2021, with year 2017 being the reference year.

${\mathit{\beta }}_{\mathit{\kappa }}$ is the corresponding coefficient vector of the predictors ($\mathbf{x}$) for category $\kappa$. Therefore, ${\pi }_1-{\pi }_4$ sum to one, assigning an individual’s probabilities of requesting each of the four categories of care. The estimators for the model, derived via maximum likelihood estimation, are presented in Section 4. We then used the model fit to estimate shares of each care degree for each age–sex group. We used those to calculate age-, sex-, and severity-specific average cost estimates. Costs for the GPV are highly individual, therefore, it is not possible to provide general unit costs. Instead, the GPV offers a maximum volume of service given the patients’ care degree and demanded types of benefits. Siegl (2024) provided a thorough overview of the range of services with associated costs. From those, we derived calculatory unit costs by care degree and type of care service according to our four categories.

The (annual) average unit cost for an individual of age a, gender g, and care degree d (${\kappa }_{a,g,d}$) is

$${\kappa }_{a,g,d}=\sum _{k=1}^4{\widehat{\pi }}_{k,a,g,d}·u_{k,d},$$

(13)

where

• ${\widehat{\pi }}_{k,a,g,d}$ is the estimated share of individuals of age a, gender g, and care degree d who receive care benefit k as estimated by model (12); and
• $u_{k,d}$ is the unit cost for care category k and care degree d according to

  Table 1. Annual per patient unit costs by severity and chosen care service [EUR] (sources: Siegl (2024); authors’ computation and illustration).

  Care Degree/Benefit	Inpatient	Partial Inpatient	Outpatient	Exclusively Monetary
  1	1500	2886	2886	2886
  2	10,740	14,540	15,404	10,256
  3	16,644	21,848	23,456	13,148
  4	22,800	25,616	27,608	15,452
  5	25,560	30,212	32,672	17,636

  .

Then, we multiplied our projections of age-, sex-, and severity-specific pinoc according to Equation (11) by the unit costs (${\kappa }_{a,g,d}$) according to Equation (13) for each scenario, which resulted in the following overall annual cost estimates for LTCI for each trajectory:

$$K_{y,t}=\sum _{a=1}^{10}\sum _{g=0}^1\sum _{d=1}^5{\kappa }_{a,g,d}·C_{y,a,g,d,t}$$

(14)

Finally, we adjusted those projections to the official GPV expenses in 2021, similar to the original approach proposed by Schmähl and Rothgang (1996). This was necessary, since our calculations obviously did not perfectly resemble the total costs but, rather, represent the relative development of the costs over time. First, as mentioned earlier, unit costs cannot perfectly simulate the exact costs. Secondly, whereas the care statistics refer to all pinoc in Germany, our GPV expenses only refer to individuals being insured by statutory LTCI, not those being privately insured. The results of our projections are presented in Section 4.

4. Results

Figure 6 presents the pinoc projections by severity until 2050 by morbidity scenario. The green curves represent the naive status quo scenario for the ASSSCRs. Therefore, the green curves represent the isolated c.p. effect of the demographic development on the pinoc curves. Based on the 1000 population trajectories computed by Sarajan et al. (2024), we derived a median trajectory and lower and upper bounds of 75% credible intervals (CIs). The red curves show the corresponding simulations under the trend scenario, which extrapolates the trends observed in the ASSSCRs over the horizon of 2017–2021.

We see that the projections are relatively robust and do not depend as much on the morbidity scenario for severe care degrees 4 and 5. However, for care degrees 1–3, the assumption on the development of the care rates is of major importance for the pinoc estimates, especially for care degree 1. In the status quo scenario, the overall number of pinoc slightly increases in the median from close to 5 million in 2021 to 5.7 million in 2050. In the trend scenario, we expect a strong increase to 14.7 million individuals in 2050.

Those numbers were combined with the estimated unit costs, as explained in Section 3.2.2. The coefficients of our Dirichlet multinomial model according to Equation (12) are given in

Table 2. Coefficients of the Dirichlet multinomial model for estimation of care-type shares (source: authors’ computation and illustration).

Predictor/Benefit	Inpatient	Partial Inpatient	Outpatient	Exclusively Monetary
intercept	−2.81	−5.30	5.82	−19.92
ln(age)	0.94	1.19	−0.58	−1.96
female	0.84	0.65	0.82	0.66
care degree 2	1.03	0.99	−0.19	32.57
care degree 3	1.97	1.70	−0.34	32.33
care degree 4	2.71	2.06	−0.38	32.05
care degree 5	2.80	1.40	−0.63	31.15
year 2019	0.05	0.24	0.21	0.29
year 2021	−0.10	0.09	0.15	0.35

.

The exact coefficients are not easily interpreted. However, the direction of the effects is easily understood. For instance, a positive coefficient for ln(age) is associated with a c.p. increase in the share of the respective care type with increasing age. The negative coefficient in this case for pure monetary benefits means that older patients, c.p., have a decreasing probability of demanding exclusively financial benefits. This is plausible, since older patients typically receive support from professional care workers (see File S2). All of the coefficients are highly statistically significant based on the Wald test, with p values close to zero.

Figure 7 illustrates the projected demand for specific care services in thousands of individuals. Readers should pay attention to the varying scales of the ordinates. Again, the results mirror the high sensitivity to effects of the morbidity assumptions on the development of the care rates. In particular, the projections for outpatient services and purely monetary benefits are very difficult to predict, since they are more dependent on the number of individuals that have lighter disabilities, which is more difficult to predict, as illustrated earlier.

Figure 8 presents the costs for GPV since 1995 and projected to 2050. For comparability, the data are inflation-adjusted to 2020 prices. Overall, we see a significant long-term increase, especially since 2008, as discussed in Section 3.1. In comparison to Figure 6, the monetary differences between the two scenarios are less distinct. This is because the major differences in the pinoc curves originate from care degree 1, which has a rather minor impact on the expenses. Depending on the morbidity scenario, the GPV expenses are expected to increase, inflation-adjusted to 2020, from EUR 50.7 billion to EUR 57.3 billion or EUR 109 billion from 2021–2050, respectively. The corresponding 75% CIs range from EUR 44.7 billion to EUR 71.7 in the status quo scenario and from EUR 85.5 billion to EUR 137.5 billion in the trend scenario.

5. Discussion and Conclusions

The present study pursued two objectives. First, we suggested a novel approach for long-term forecasting of LTCI expenses that allows for the inclusion of demographic and epidemiological trends and different care definitions in the model. Our approach manages high dimensionalities and correlations in the data, which allows for the inclusion of both common and opposing trends in care rates over demographic and epidemiological dimensions. Moreover, the model allows for the inclusion of future uncertainty in forecasts based on various approaches, including either deterministic scenario analyses; stochastic Monte Carlo simulations; or mixed forms, such as randomizations from ensemble models. Moreover, our model suggests the use of multivariate generalized linear models—in our case, a Dirichlet multinomial model that estimates the differences in demand for specific care services based on the patients’ demographic and epidemiological characteristics. Secondly, we presented an updated projection of the GPV expenses for Germany, which had not been previously done to that degree of detail and based on these data for Germany. Therefore, our paper offers valuable insights for both scientists interested in the improvement of forecast models for social and, especially, long-term care insurance and planners interested in the fiscal outlook for Germany.

We have seen that, based on the future demographic development of Germany, the future expenses for LTCI are highly probable to increase further. However, those are highly affected by a variety of other factors, such as morbidities in the elderly population and care definitions, which are not predictable based on the available data, since there has been a variety of reforms over the last two decades that do not allow for the construction of consistent time series that could serve as a quantitative basis for time-series models. We approached this by computing two major scenarios for the care rates. Therefore, it is important to note that the results presented in our paper are not forecasts but, rather, projections under specific assumptions. Future data will allow for the incorporation of more trends in the data in the models—for instance, with regard to the care rates or the distributions of specific care services by stratum. This way, we expect to be able to construct improved forecasts based on the models developed here that will present more reliable data for future planning of public economics. Including socio-economic factors (such as personal migratory histories or education Frohn and Obersneider (2020)) that may affect eventual care risks could serve as a possible extension of our approach and could be included in the model through further stratification. However, German care statistics, thus far, do not provide the needed degree of detail on the socio-economic backgrounds of pinoc. Regarding the care statistics, the impact of the COVID-19 pandemic on pinoc and care rates represents another point of discussion. We cannot completely rule out potential bias in the 2021 data due to COVID-19-associated excess mortality. However, a major effect appears unlikely, since Germany reacted quickly to isolate vulnerable population groups, such as retirement and care home residents. As a result, COVID-associated mortality in Germany was relatively low in care homes Sepulveda et al. (2020).

Given the projected increase in the number of beneficiaries requiring long-term care by 2050, policymakers must urgently take proactive steps to ensure the sustainability and accessibility of GPV. Key areas of focus should include the following:

• Strengthening workforce capacity: To meet the rising demand, it is crucial to invest more in the recruitment and training of skilled care professionals, as well as improve working conditions to attract and retain staff in the sector Seyda et al. (2021).
• Ensuring financial sustainability: Reforming the financing model of long-term care insurance is essential to prevent financial strain on future generations. This may involve adjusting contribution rates, increasing state subsidies, or even addressing a similar multipillar perspective of a public–private provision mix as in pension economics (see, e.g., Vanella et al. (2022)).
• Further promoting home-based care: Expanding support for home-based and community care options can help to reduce pressure on institutional care facilities while promoting still greater autonomy for the elderly and their families.

In fact, Germany already addressed these issues in its latest reform of May 2023 (Pflegeunterstützungs- und –entlastungsgesetz (PUEG); see e.g., BMG (2023)); it will now be crucial to see whether the newly set incentives will work as expected.

Finally, there are two additional policy fields that have, so far, received less attention in the public debate. First, the use of digital solutions, such as telemedicine and assistive technologies, is not being encouraged on a larger scale, although it may enhance the efficiency and quality of care while, at the same time, alleviating some of the burden caregivers are confronted with BMG (2024). Secondly, more cooperative structures among health, social, and housing sectors would be helpful to ensure an integrated approach to elder care, where infrastructure and services are well-coordinated and more responsive to the growing needs of the population. Both policy fields could contribute considerable to better address the challenges posed by an aging population and increased care demands.