Background

Fig 1 shows considerable regional variations in COVID-19 vaccine uptake. This has also been found in other countries. Most of the studies on the regional variation in COVID-19 vaccine uptake are based on the USA. [21] find more variation across counties than states and [22] find more variation in vaccination levels across postal codes within cities than between cities. A common source of variations in COVID-19 vaccinations in the US is racial disparities. However, the findings are mixed: [22] find higher vaccination rates in areas with a high share of white or Asian people and [23] find lower vaccination rates in regions with a high share of Black people. These findings differ from the results of [24] who find that minorities, defined as all persons except white, non-Hispanic, have a positive impact on vaccination rates, and from the results of [2] who finds that regions with a high share of non-Hispanic white residents have lower vaccination rates. Political affiliation has also been associated with vaccine uptake, where counties with a large proportion of Republican voters have lower vaccine uptake [2, 23]. Other socio-demographic and socio-economic factors which have also been related with the regional variation in vaccine uptake include the share of population below the poverty line, the share of uninsured persons, the share without internet access and the share of younger persons, where higher shares are associated with lower vaccination rates, and the share of persons with a college degree, the share of older persons and per capita income, where higher levels are associated with higher vaccination rates [2, 21–24].

Some of these factors associated with COVID-19 uptake also correlate with compliance or non-compliance with other COVID-19 preventive measures. Political affiliation is mostly found to be associated with the compliance or non-compliance with COVID-19 preventive measures, where Democrats in the USA are more welcoming to measures such as social distancing [25–27]. Poverty [28] and the share of younger population [29] have been associated with lower compliance with social distancing.

For Germany, [30] find considerable variations in vaccination rates between federal states: states in West Germany have higher vaccination rates than those in East Germany. They also find that support for the populist right-wing political party, Alternative for Germany (AfD), is correlated with lower vaccination rates at the state level. Among the studies done on regional variations in COVID-19 vaccinations, only a few, such as [23] and [24], have tried to explain the variations. All in all, with an adjusted R² of about 76–79% these studies can explain a considerable share of variation in vaccination rates in the USA by observable characteristics. Our study contributes to the literature by bringing in a new perspective from not only a different country but a country with a different health care system.

Our paper also adds to a growing field of health economic research on regional variations in the health care market. Strong regional variations have been found in many dimensions across different countries. Differences have been found in health [31], health expenditures [32–38], access to healthcare [39], medical services utilization [40–45], and productivity in the health care sector [46]. These differences may be linked to the variation in vaccine uptake. [23] find that counties with more health facilities have higher vaccination rates. They argue that a lack of these health facilities may have resulted in the delay or loss of opportunity to vaccinate in some regions.

We study regional variations in the share of at least double-vaccinated persons in Germany using administrative data on all vaccinated doses in all 400 German counties until December 2022. Using a host of potentially relevant socio-economic variables (guided from determinants found in the previous literature) we can explain about 52 per cent of regional variations in vaccination on county level and 72 per cent on federal state level. Major explanatory factors are demographic characteristics, levels of education, and further preferences proxied by political party vote shares. To get an idea of what might account for the remaining part, we describe the federal state level distribution in selected “soft” factors and document that individuals in federal states with lower vaccination rates, on average, report to be less risk averse, have less trust in the German government and scientists, and are more likely to believe in conspiracy theories regarding the origins of the Corona virus. While our study design is not able to provide any causal evidence and, thus, does not allow to immediately derive policy recommendations, it adds to our knowledge on the picture of regional variations in health care.

Vaccination rates

Our main dependent variable is the share of individuals with at least two vaccinations against the Corona virus. It is based on freely accessible and continuously updated data from the German Robert Koch Institute (RKI) [47] that publishes data on the universe of daily vaccinated doses per age group on the level of the 400 German counties. German counties can either be rural areas (Landkreis, N = 293) or single larger cities (Kreisfreie Stadt, N = 107). The RKI vaccination data are assigned to the county where the vaccination took place and not where the vaccinated individual lives. In principle, individuals can freely choose where to get vaccinated and it may be possible that they get vaccinated in neighbouring counties. In particular, it seems to be frequently done that individuals in rural areas get vaccinations in the next bigger cities where larger vaccination centers had been installed.

Fig 2 shows the number of second corona vaccinations—usually defined as “complete vaccination protocol”—per inhabitant of the corresponding county until end of December 2022, calculated as follows: where c is the county, SV_c is the sum of second vaccination doses carried out in county c until end of 2022, and I_c is the number of inhabitants living in county c. The left panel shows the map of the 400 German counties where darker colors imply larger shares of vaccinated people and lighter ones imply lower shares. A striking pattern are the small dark dots, mainly in the south of Germany. These are larger cities completely surrounded by rural counties. Often, individuals from these rural counties got their vaccination in the larger cities, leading to an overestimation of actual vaccination rates in these cities and an underestimation in the rural areas. To account for this, we manipulate the data in the following way: for the 36 cases of cities completely surrounded by one rural county, we assign both the same vaccination rate of the sum of vaccination doses divided by the sum of inhabitants in city and rural county. S1 Table in the Supporting Information lists all these counties. The resulting regional distribution of the share is shown in the right panel of Fig 2. In our baseline analysis, we will work with this outcome variable, that is, based on partly merging certain counties. Robustness checks with the original variable, however, yield results of similar magnitude, implying that crossing county boarders do not completely drive the results.

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Fig 2. Share of 2nd vaccination per inhabitant.

Left panel: Original data; Right panel: Cities merged with rural counties. Data from the Robert Koch Institute. Number of second Corona vaccinations per county until December 2022, divided by inhabitants per county. The left panel uses the original data from 400 counties. The right panel presents average numbers for 36 pairs of cities surrounded by rural counties, see text for explanations. The basemap bases on data from GeoBasis-DE / BKG (2022), dl-de/by-2–0 (www.govdata.de/dl-de/by-2-0), https://gdz.bkg.bund.de/index.php/default/digitale-geodaten/verwaltungsgebiete/verwaltungsgebiete-1-5-000-000-stand-31-12-vg5000-12-31.html.

https://doi.org/10.1371/journal.pone.0296976.g002

The mean share of individuals with two Covid vaccinations is 0.75, close to the German average reported in Fig 2, the standard deviation is 0.15. Five counties (cities) have a share larger than one while the five counties with lowest numbers have rates between 0.34 and 0.41. In robustness checks we will exclude these 10 counties. The map reveals strong variations in Corona vaccinations in Germany, both across federal states (marked by the bold borders), thereby repeating the pattern from Fig 1, as well as within states. North-West Germany has a significantly higher number of counties with larger vaccination rates than the other parts of Germany. Particularly the eastern states (Thuringia, Saxony, Brandenburg) and southern states (Baden-Wuerttemberg, Bavaria) have many counties with less than 70% vaccination coverage.

Pool of variables on the county level

We obtain county level demographic and socio-economic variables from the INKAR database [48]. INKAR is an interactive online atlas of the Federal Institute for Research on Building, Urban Affairs and Spatial Development (BBSR), containing about 600 indicators, which enable rural-urban comparisons and analyses over the last decades. INKAR provides current regional statistics on socially important topics such as education, demography, job market, economy, accommodation, transportation, and the environment.

For the regressions, we consider those variables that are associated with vaccine uptake or hesitancy. As variations in the age structure could influence the variation in vaccinations given that older age groups were initially given preference over others when the vaccines were made available, we take into account differences in the demography by considering the age structure and also include the share of male persons, the share of non-natives, the share of people in need of long-term care, life-expectancy and fertility rate.

Previous exposure of counties to the COVID-19 pandemic might affect the willingness to vaccinate. Thus, we account for the cumulative sum of COVID-19 infections per county until December 2020, that is, at the time vaccination campaigns started. Moreover, since the spread of the COVID-19 virus is through the air, the living situation is likely to have an impact on its spread which in turn could have an influence on vaccination uptake. We, therefore, include variables that refer to the housing conditions such as the share of residential buildings, the different apartment sizes based on the number of rooms, per capita living space and the share of apartments in residential buildings.

Further potentially contributing factors to the rate of vaccine uptake are the location and its economy, education, political affiliation and healthcare accessibility. Thus, we consider the rurality, the distance to centers, net commuting and cadastral area as well as gross earnings, taxes, debts, GDP, unemployment rate and the share of people receiving minimum social security benefits, as well as the number of pupils, university students, and different educational levels of employees. In addition, we include the share of voter turnout and the votes for the different political parties and medical supply by taking into account the number of hospital beds and physicians, and the distance to the nearest pharmacy. All variables are listed in Table 1 below.

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Table 1. Descriptives.

https://doi.org/10.1371/journal.pone.0296976.t001

Further variables measured on the federal state level for supplementary analyses

On the individual level, different aspects and types of trust were identified as determinants of vaccination [49, 50]. Therefore, in supplementary analyses described below, we also consider four questions from the 10th wave of the European Social Survey (ESS) [51] and the German Socio-Economic Panel (SOEP) [52]—the most prominent and long-running German representative household data set. SOEP is based on about 22,000 participants and the latest wave was carried out in 2020. The German part of the ESS covers around 8,700 participants, interviews regarding the questions below took place between 2021 and 2022. Both data sets are on the individual level but only representative for the federal state, not the county level. Therefore, we use these individual level data but present averages on federal state level as suggestive complementary evidence.

We consider four questions:

• How do you see yourself: Are you generally a person who is very willing to take risks or do you try to avoid taking risks? 0 (not at all willing to take risks) to 10 (very willing to take risks). (Source: SOEP)
• Please tell me on a score of 0–10 how much you personally trust each of the institutions I read out. 0 means you do not trust an institution at all, and 10 means you have complete trust: Germany’s parliament? (Source: ESS)
• Please tell me on a score of 0–10 how much you personally trust each of the institutions I read out. 0 means you do not trust an institution at all, and 10 means you have complete trust: Scientists. (Source: ESS)
• Please tell me how much you agree or disagree with the following statement: Coronavirus is the result of deliberate and concealed efforts of some government or organization. Disagree strongly (1)—Agree strongly (5) (Source: ESS, answer categories recoded by the authors)

Basic approach

To fix ideas, consider the following linear regression model: (1) where c stands for the county. Further let:

y_c = COVID-19 vaccinations per inhabitant,

X_1c = Vector of demographic characteristics,

X_2c = Vector of variables reflecting previous Corona cases and housing conditions,

X_3c = Vector of variables reflecting area and local economy,

X_4c = Vector of educational levels,

X_5c = Vector of political preferences,

X_6c = Vector of supply of medical services,

u_c = error term.

In Section Pool of variables on the county level and Table 1 below, we list a number of variables for these six blocks. In total, we have a pool of 48 potential variables that may enter the regression equation. Since we do not aim to perform a causal analysis but to maximize explanatory power in a prediction sense, we use a data-driven approach to select variables from the pool of K = 48 variables. The approach is in the spirit of [53], here adapted to increase the explanatory power of the model. To be specific, we apply the following pre-processing procedure:

1. Start with K bivariate regressions of y_c on each of the variables from the pool of potential variables. Store the K values of adjusted R².
2. Take the variable that leads to the largest adjusted R² and put it into the set X_lin. Let L be the number of variables in X_lin. After this step, we have L = 1.
3. Perform K − L regressions of y_c on X_lin and each of the remaining K − L variables not in X_lin. Store the K − L adjusted R².
4. Take the variable that leads to the largest increase in the adjusted R² compared to the regression from the previous step. Put in into the set X_lin.
5. Repeat the steps 3 and 4 until no further variable increases the adjusted R².
6. Generate all H possible bivariate interactions of the variables in X_lin after step 5. This is an additional pool of potential variables.
7. Repeat the procedure from steps 3 to 5. Now, start with H regressions of y_c on X_lin and one of the H interactions. Proceed as before where you put selected interactions into the vector X_int and regress y_c on X_lin and X_int until no further interaction increases the adjusted R².

The regressions then use the vectors X_lin and X_int. Both are composed of selected variables from the above-mentioned blocks X_1c to X_6c. Allowing for many possible variables and their interaction means to have more potential variables than observations. In the data science literature, this is a common problem. Our solution to this, outlined above, is the “forward stepwise selection” discussed in Chapter 6 of [54].

Spatial interdependencies

Note that this subsection is taken almost word by word from [38]. The error term u_c formulated in Eq (1) is probably not distributed independently over the individual counties. Rather, exogenous shocks in one county can be assumed to have knock-on effects in neighbouring counties. It is therefore likely that the error terms are correlated with each other spatially. To take this into account, we formulate the error term as (2) where m_cj represents the weighting factor for the effect of a shock in county j on county c. Formulated more compactly, we get u = ρMu + ε where u is the vector of all error terms (dimension 400 × 1), M is the weighting matrix (400 × 400) and ε the vector of errors whose elements are assumed not to correlate with each other. The lower the spatial distance between two counties, the stronger the correlation of the error terms should be. In the definition of the weighting matrix this is achieved by the fact that the weights for adjacent counties are greater than for more distant ones. For M, we use an inverse distance matrix, in which the inverse of the distances between the county centroids are used as elements and the main diagonal contains zeros. The shape files of the counties from the Federal Agency for Cartography and Geodesy (as of 1.1.2022) were used to calculate the distances and transferred into Stata format with the help of the Stata programme shp2dta. We follow [55] and normalize the elements with the eigenvalue standardisation, in which every element is divided by the largest module of the eigenvalues of M (see [56], for a discussion of the normalisation procedures).

Furthermore, it can be assumed that the vaccination rates themselves are also subject to spatial interdependencies. It is conceivable, for example, that local vaccination initiatives have positive spill over effects from one county to another. Moreover, the issue of differences between vaccination location and home county may lead to negative spatial interdependence in the outcome variable. In a more general model in the tradition of [57]’s spatial model or the expanded spatial autoregressive model with spatial autoregressive disturbances (SARAR, [58]), the following variant is estimated: (3) Here W is again a weighting matrix. We define the matrix W as a contiguity matrix where only the contingent counties are taken into account and the weights for all others are set at 0. To estimate the parameters β, ρ und λ we use the Stata module sppack, which contains both the estimator for the model formulated above (spreg) and the programme for creating the weighting matrix (see [59]).

To be specific, we run the following spatial regression model: (4) where

This spatial regression model is also used for the variable selection described above.

A compact approach to present the results

For an easier understanding of how much of the differences between federal states can be explained, we then turn to a more compact approach. We perform a step-wise regression. We start with a regression on a constant only, go on with a regression on a constant and variables from vector X_1c, then add X_2c, and so on. All regressions follow the spatial-econometric approach of Eq (2) and the variable selection procedure. However, when using block X_1c only, only variables from this block are in the pool of potential variables. The same applies when block X_1c and X_2c are used and so on. After each regression, we store the residuals and calculate the federal state averages of the residuals. The standard deviation of these average residuals should be smaller the larger the explanatory power of our model is. The results are presented in Table 3.

Baseline results

Table 1 provides the descriptive statistics of the pool of variables on the level of the 400 counties. Table 2 shows the regression results of the model with the highest predictive power according to the spatial regression model outlined in Section Spatial interdependencies and the variable selection procedure outlined in Section Basic approach. The table includes the chosen variables and interactions. Both ρ and λ are negative. This most likely reflects the definition of the outcome variable, capturing vaccinations where they took place, not where individuals live. This possibly induces a negative correlation in vaccination rates across neighboring counties. The spatial model takes this into account. However, ρ is not significantly different from zero and λ is small in magnitude. All in all, spatial correlations do not seem to play a large role in this application.

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Table 2. Regression results.

https://doi.org/10.1371/journal.pone.0296976.t002

Note that Table 2 reports coefficients but not marginal effects of certain characteristics. The many interactions make the interpretations of the coefficients complicated. However, many of the baseline coefficients (though not all) go into the expected directions. For instance, the share of individuals over 65 years and previous exposure to the COVID pandemic (measured by COVID cases) have a positive baseline coefficient, while the share of voters for right populist parties (AfD) has a negative coefficient. A higher share of individuals with academic degree goes along with more vaccinations, indicating a positive relationship between education and vaccination. The share of women is positively associated with vaccination rates but the relationship is not statistically significant. All in all, with an R² of 0.52 we can explain more than half of the variation on county level using variables on the socio-demographic structure.

Table 3 reports the results of the approach outlined in Section A compact approach to present the results where we stepwise include variables in order to understand their share of explained variation in Corona vaccinations. A regression of the COVID vaccinations on only demographics has an R² of 19% and can reduce the standard deviation of the residuals by 48% at the federal state level. Previous COVID exposure and housing increases the share to 54%. Variables for area and economy increase it further to 65%. Education, politics and supply of medical services do not add much, once the other variables are controlled for, but ultimately 52% of the variation on county level and 72% on federal state level can be explained by our observable characteristics. Of course, these single numbers also depend on the ordering of the blocks but the total number after all blocks are included is invariant to the ordering.

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Table 3. Reduction in variation.

https://doi.org/10.1371/journal.pone.0296976.t003

Robustness checks

Table 4 reports results from robustness checks. These follow the same estimation protocol as above but do not split up the results by different blocks of variables and merely show results for all blocks X_1c to X_6c. We first run the regressions with 390 observations where the ten counties with largest and smallest vaccination rates are dropped. We cannot rule out that these are still strongly affected by differences in vaccination location and place of residence. Moreover, we use the original RKI data without merging numbers for 36 county-pairs (see Section Data). The results are basically the same when we drop the 10 outliers. Using the original data, we receive a very large R² of 84. However, we tend to have more trust in the baseline specification.

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Table 4. Robustness checks.

https://doi.org/10.1371/journal.pone.0296976.t004

Potential remaining factors measured at the federal state level

The variables used in the previous analysis cannot fully explain the regional variation in differences in COVID-19 vaccination. Therefore, this subsection provides examples of variables that can be expected to be associated with vaccination but for which data are not available at county level.

Fig 3 reports the sample means in the different federal states of the four answers concerning risk willingness, trust in Germany’s parliament, trust in scientists and the belief that COVID was deliberately created. For the sake of presentation, we color the number of the four states with highest vaccination rates (see Fig 1) in green and the four states with the lowest vaccination rates in red. Specifically, the four states with lowest vaccination rates also form a consistent group of highest or lowest ranked states in these four panels (with one exception). In these states, individuals tend to be more risk loving, have less trust in the German parliament and scientists in general, and are more likely to believe that the Corona virus was deliberately created. Bavaria and Mecklenburg-West Pomerania, the states that rank 5 and 6 from the bottom of vaccination status, also broadly rank in this range in the four answers. It is less consistent with the states with highest vaccination rates. By and large, however, they rank on the other extreme also in these four questions. Hence, Fig 3 offers additional explanatory factors for regional variations in vaccination rates.

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Fig 3. Federal state-level differences in risk preferences and selected statements.

Sample means by federal states presented. MV stands for Mecklenburg-West Pomerania, TH = Thuringia, BB = Brandenburg, RP = Rhineland Palatinate, SL = Saarland, NI = Lower Saxony, SH = Schleswig-Holstein, Saxony-A. = Saxony-Anhalt, NRW = North Rhine-Westphalia, BW = Baden-Wuerttemberg. Upper left panel: Source: SOEP; Other panels: Source: ESS.

https://doi.org/10.1371/journal.pone.0296976.g003