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

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## Abstract

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## 1. Introduction

## 2. Background

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

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

## 3. Data and Methods

#### 3.1. Data

- ${c}_{y,a,g}$ 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.

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

#### 3.2. Methods

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

- $ln\left(\right)$ 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.

- ${l}_{y,a,g,d}$ 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.

- $\mathbf{P}$ is the time-series matrix (3 × 100) of principal components;
- $\mathbf{\Lambda}$ is the matrix of eigenvectors (100 × 100; also loadings) computed based on the covariance matrix of $\mathcal{L}$.

#### 3.2.2. Projection of Estimates for Care Demand and LTCI Expenses

- (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.

**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)

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

- 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.

- ${\widehat{\pi}}_{k,a,g,d}$ 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

## 4. Results

**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.

## 5. Discussion and Conclusions

- 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.

## Supplementary Materials

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

a | Age |

ASSCR | Age- and sex-specific care rate |

ASSSCR | Age-, sex-, and severity-specific care rate |

B | Population |

bil | Billion |

$\mathit{\beta}$ | Vector of coefficients |

c | Care rate |

C | Care beneficiary |

CI | Credible interval |

c.p. | ceteris paribus |

d | Care degree |

Destatis | German federal statistical office |

$exp\left(\right)$ | Euler’s number to the power of () |

g | Gender |

GPV | Gesetzliche Pflegeversicherung |

HMD | Human Mortality Database |

k | Category of care |

K | Total annual costs |

$\kappa $ | Average annual cost per patient |

l | Logistically transformed care rate |

$\mathcal{L}$ | Logistically transformed care rate time-series matrix |

$ln\left(\right)$ | Natural logarithm of () |

LTC(I) | Long-term care (insurance) |

mil | Million |

$\mathbf{\Lambda}$ | Loadings matrix |

$\mathbf{P}$ | Principal component time-series matrix |

PC(A) | Principal component (analysis) |

PfWG | Pflege-Weiterentwicklungsgesetz |

PI | Prediction interval |

pinoc | Persons in need of care |

PSG | Pflegestärkungsgesetz |

$\mathit{\pi}$ | Vector of probabilities of claiming specific category of care |

t | Trajectory |

$\mathbf{x}$ | Vector of predictors |

u | Unit cost |

y | Year |

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**Figure 1.**Persons in need of care in Germany according to care statistics for 1999–2021 (official and age-standardized to 2021) (sources: GENESIS-Online (2024a); Human Mortality Database (2022); authors’ computation and illustration).

**Figure 2.**Populationin Germany by age group below 75 years and gender until 2021 with forecasts for 2022–2050, medians, and 75% prediction intervals (sources: Human Mortality Database (2022); Sarajan et al. (2024); authors’ computation and illustration).

**Figure 3.**Population in Germany by age group over 74 years and gender until 2021 with forecasts for 2022–2050, medians, and 75% prediction intervals (sources: Human Mortality Database (2022); Sarajan et al. (2024); authors’ computation and illustration).

**Figure 4.**Loadings of LTC Index by age, gender, and severity (source: authors’ computation and illustration).

**Figure 8.**Projections for costs of statutory long-term care insurance by scenario until 2050, adjusted to 2020 prices (sources: GENESIS-Online (2024b, 2024c); 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 |

**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 |

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**MDPI and ACS Style**

Vanella, P.; Wilke, C.B.; Heß, M.
Long-Term Care in Germany in the Context of the Demographic Transition—An Outlook for the Expenses of Long-Term Care Insurance through 2050. *Econometrics* **2024**, *12*, 28.
https://doi.org/10.3390/econometrics12040028

**AMA Style**

Vanella P, Wilke CB, Heß M.
Long-Term Care in Germany in the Context of the Demographic Transition—An Outlook for the Expenses of Long-Term Care Insurance through 2050. *Econometrics*. 2024; 12(4):28.
https://doi.org/10.3390/econometrics12040028

**Chicago/Turabian Style**

Vanella, Patrizio, Christina Benita Wilke, and Moritz Heß.
2024. "Long-Term Care in Germany in the Context of the Demographic Transition—An Outlook for the Expenses of Long-Term Care Insurance through 2050" *Econometrics* 12, no. 4: 28.
https://doi.org/10.3390/econometrics12040028