Early Careers of Graduates from Private and Public Universities in Germany: A Comparison of Income Differences Regarding the First Employment

Research estimating the outcomes of higher education in Germany has widely ignored the private educational sector. This study focuses on labour market returns in terms of the income of graduates from private higher education institutions in Germany. Using data from the National Education Panel Study (NEPS) the results of the Bayesian regression analysis indicate a moderate wage premium for private students compared to students who are enrolled in public higher education institutions regarding the first employment. Despite the predominant role of public universities in Germany, graduates of private higher education institutions receive similar advantages on the labour market as their counterparts in other countries, although private education in other countries is more prestigious.


Introduction
Private education is a rapidly growing phenomenon in the German market for higher education. Every year, a steadily increasing number of students invest in private education to get a head start in the labour market in terms of finding profitable entry-level positions. Despite the importance of these investment decisions for individual careers, there is no evidence, if the prospects of above-average starting salaries hold for the German case.
In this study, we explore the differences in the predominant labour market return, which is monthly gross income, between alumni of private and public universities and universities of applied sciences in Germany. The private higher education sector in 1 3 Germany is a rather new development and as a result, little is known about the success of German private students. Currently, only 9% of German students are enrolled in private educational institutions, but the number is rising continuously. For instance, back in 1995 this share of students was only one percent (Federal Statistical Office 2019). There is a great body of literature in other countries estimating the wage premium for private enrolled students, but despite its economic importance within the European market for higher education, this is the first study for Germany thus far. The German higher education sector is different to other countries: Many of the German high quality and elite universities are public universities. Access to German universities is usually linked to high school graduation grades only. Many other fields of study do not have admission criteria at all. Furthermore, unlike in many other OECD countries, German public universities charge relatively low or no tuition fees. In this setting, opting for costly private education despite freely available public education is only rational given strong held beliefs that superior service quality in private institutions provides better educational outcomes and can confer an advantage to the competition in the labour market.
The question whether enrolment in a private institution pays off in terms of aboveaverage salaries is not only important to the students or their parents who pay for the costly education. It is also an essential question for the government, which operates most of the German universities and universities of applied sciences. Despite the fact that in Germany, in general, no tuition fees apply to public higher education, social inequality still plays a major role pertaining to the accessibility of the tertiary education system. Students from backgrounds characterized by less socio-economic capital are less likely to pursue a bachelor's degree (e.g. Shavit & Blossfeld, 1993). This socially unequal situation could become more pronounced, if private education, which usually causes tuition fees, becomes the norm rather than the exception in the German higher education system. Private higher education bares the signs of a potentially disruptive innovation. According to Bower and Christensen (1996), a disruptive innovation matures in the shadow of an established system until it is ready to supersede the status quo. In the beginning, the disruptive innovation is attractive to only a small fraction of consumers. Private education is costly and therefore perceived as inferior for the majority. However, if it offers significant advantages over public higher education, for instance in terms of labour market returns, it might unlock its disruptive potential and transform the higher education system. Moreover, many state universities in Germany fail to occupy certain niches and to address target groups such as working people. Private universities in particular focus on custom-made study programs or offer alternatives to fields of study that are in high demand at state universities, such as psychology (Wissenschaftsrat, 2012b). The privatisation of the university market could further increase the connection between social status and educational success. Social inequality inevitably becomes more severe if only members of socio-economically privileged groups can afford access. Consequently, we want to investigate the question whether there is a noticeable wage premium for graduates of private universities in Germany.
In the next section, we will discuss related international research with a special focus on German study results and the particularities of the German higher education sector. Subsequently, we describe the datasets and the used variables. In the following section, we explain our analysis strategy and present the results of our models. Finally, we discuss our findings in the light of recent research and point out some limitations of our analysis.

Related Research and Theoretical Background
To date, most research regarding the labour market outcomes for alumni of private institutions stems especially from the U.S. and the U.K. The widely privatized higher education sector in those countries explains this deep interest. Theoretical frameworks are mainly based on human capital theory and the assumption that students take the expected costs, returns and the feasibility of other alternatives into consideration during their choice of study. In particular, the choice of an expensive private university is justified by the usually higher expected returns after graduation and a higher accumulation of human capital (Botelho & Pinto, 2004). Early research in this field suggested clear income gains for alumni of private universities compared to students enrolled in public universities (Brewer et al., 1996;Brunello & Cappellari, 2008;Daniel et al., 1997).
Based on those early findings it could be assumed that privileged students are more likely to enrol in a private elite university due to their financial possibilities and their educational background. Even after controlling for this selectivity, there is still much evidence for higher labour market returns for attendees of private colleges: Brewer et al. (1999) have found evidence for higher economic returns after graduating from a private institution after controlling for selectivity due to socio-economic status. Moreover, their findings suggest that the returns have increased over time in the labour market. Dale and Krueger (2002) compared students with similar abilities, who were accepted at the same or comparable private and public colleges. Regarding the selectivity, they could not find significant effects on earnings, but there is a notable wage premium for students of elite colleges with higher tuition fees, indicating that the amount of tuition fees are a quality characteristic of colleges. Moreover, students from low-income and less-educated families earned more if they attended private colleges. A replication of this study by Dale and Krueger (2011) showed similar results and a clear wage premium for black and Hispanic students, who attended a private college. More recent research from the U.S. shows the following results: Cellini and Chaudhary (2014) used a fixed-effects approach to control for individual characteristics and found out that alumni of private for-profit 2-year colleges generate income gains of additional 4 percent per year of education compared to similar public 2-year college students. Furthermore, alumni of private universities are more likely to be employed. Chetty et al. (2017) also prove a selectivity-corrected higher income for elite private colleges alumni compared to other alumni of other colleges. In mainland Europe, private universities are relatively new and therefore little research exists on them, but research from Italy, which is probably more comparable to the German higher education sector, shows also a clear wage premium for students of private universities (Brunello & Cappellari, 2008). Research from Poland shows that private students in Poland also have advantages, such as a higher income or a shorter job search time, but these advantages decrease significantly once controlling for pre-study work experience (Zając et al., 2018).

Private Higher Education in Germany
Previous research results from the Anglo-Saxon region cannot be transferred easily to the German higher education system. Private universities in the U.S. or U.K. are often highly selective, with a high research performance and a corresponding reputation. To maintain this standard, many of the private universities have to charge high tuition fees. The structure of private universities in Germany is oriented towards other standards and target 1 3 groups: The majority of German private universities consist of small universities of applied sciences with a narrow scope of subjects (Wissenschaftsrat 2012b). Elite universities in the German private university sector constitute rather the exception than the norm. Furthermore, there is also a small share of very large distance learning universities with many departments. Official figures on the admission rates of private universities in Germany are unfortunately not available which is why we cannot make any statements about the selectivity of German private HEIs. Moreover, the direct competition with public-funded institutions forces private universities to fill niches and to provide courses that are not or only insufficiently covered by public universities. For example, private universities are increasingly offering study courses for part-time students or subjects that are still inadequately covered by state universities, such as health sciences (Wissenschaftsrat 2012b). 1 Unlike in the Anglo-Saxon regions, German private HEIs do not offer associate degrees or other special short-term programs. Private universities must meet the same standards for accreditation as public universities and offer the same degrees, which entitle graduates of private universities to the same advanced degree programs as those of public universities (Wissenschaftsrat, 2012a).
It is often theorized that the strong competition on the university market leads to higher efficiency. The high-cost pressure makes private universities efficient in the allocation of their resources, while the lower requirements make private universities more flexible (Cellini & Chaudhary, 2014;Platz & Holtbrügge, 2016). As a result, teaching becomes more innovative and student satisfaction is at the forefront. One mechanism that results from competitive pressure is a higher service orientation and significantly better quality of supervision, as this helps to set oneself apart from the state-supported competitors and to achieve a high level of student satisfaction (Hasan et al., 2008;Sumaedi et al., 2011). According to private universities, good support and high service levels lead to low dropout rates and efficient studies. Moreover, private institutions offer practical training with close contact to the industry and plenty of career services. According to a study by Platz and Holtbrügge (2016) one of the main reasons for attending a private university instead of a public university lies in the employability. Herrmann (2019a) provides similar results by showing that German students attend expensive private universities because of the good career prospects and the feasibility of the studies. Further, there was no evidence of a severe selection in favour of students with a higher educational background at private universities. Private universities are also much more flexible than public universities in terms of admission requirements or other study regulations and provide higher education access for employed students, which usually make up a large group of the students enrolled in private institutions (Bildungsbericht, 2018). Thus, the reasons to attend a private university in Germany differ considerably from those in the United States or the U.K. Hence, the students enrolled in private universities in Germany may not have the same advantages private students in other countries have.
Our research question therefore is: Are there substantial differences in income pertaining to entry level positions between alumni of German private and public universities?

Data
We build our analyses on the National Education Panel Study (NEPS), a large-scale education survey program of first-year-students in Germany. This data comes with the advantages of covering students from all federal states and encompassing graduates from private higher education.
For the following analyses, we use data from 12 th wave of the Scientific Use File of the starting cohort 5 (first-year-students) of the National Education Panel (NEPS) (Aschinger et al., 2011). First semester students of the winter semester 2010/11 were recruited from a nationwide and representative university sample. From the identified universities, fields of study were drawn whose students were to be surveyed (stratified-cluster-sample). A total of 17,910 cases were validly realised in the first wave (Steinwede & Aust, 2012). The survey takes place twice a year, always online and alternately by telephone. 2 For our analyses, we exclude not-for-profit ecclesiastical colleges due to their very different target groups. Further, we use information particularly from all students who have already obtained a degree and reported to have a first job. Usually, this is about 3-5 years after the first survey, depending on the type of degree(s) a student obtained. The vast majority complete a master's degree after the bachelor's degree, so graduation is usually after 5 years of the first survey wave or later.
Due to panel attrition, this sample is rather selective. It is plausible to suppose that especially the more successful students are more likely to take part in the NEPS for such a long time (Liebeskind & Vietgen, 2017). After approx. 5 years of panel duration and the reduction of the sample to the relevant target persons (see section Data Preparation for details), 1757 students enrolled in public universities and 77 students from private universities persons remain in the sample.

Data Preparation
We use full and part-time students, who report to have a first job position. We preclude students who earn less than 450 Euro 3 and whose first position is characterized by a training character, like internships, traineeships, or legal clerkships, from our analyses. Such internships and training phases are often mandatory and therefore not comparable with a regular employment. To adequately capture entry-level positions, we exclude students who reported having started their job position before they even had started their studies. Our analyses rely on the first reported employment episodes of these panels, i.e. all those not in employment after graduation (unemployed, child-rearing periods, etc.) are not taken into account. Accordingly, only persons who have been successful on the labor market are included in the models.

Variables
We measure students' gross income by taking their reported first salary in Euro per month. Graduates reported their income with varying precision. Therefore, we group the income variable into 100 Euro categories.
Further, we use the obtained degree of qualification and the field of study as control variables, because it is very likely that these variables have a substantial effect on income. For the same reason we additionally control for the type of university and prior work experience. Moreover, we include the migration background, the educational status of the parents, age and gender in our analyses to control for the influence of demographic differences.
We include a variable which indicates whether a higher education institution has a private or public sponsorship to examine our research question.

Imputation Method
We assume a missing-at-random-mechanism pertaining to the 18% missing values in the data. For reasons of computational efficiency, we rely on single imputation using the classification-and-regression-trees algorithm as implemented in the MICE package for R (Van Buuren et al., 2007). We diagnosed the results of the imputation using VIM (Kowarik & Templ, 2016).

Results
In this section, we present descriptive results as well as regression models pertaining to our target variable income.

Descriptive Results
We show the summary statistics in Table 1 (see appendix). The NEPS sample consists of 1757 students enrolled in public universities and 77 students from private universities. We show kernel density plots for our dependent variable in Fig. 1. The income distribution has a mean of 2729 Euro (see Fig. 1). As mentioned above, we explicitly focus on graduates, who have already started their careers. Hence, the data we show in Fig. 1 does neither contain unemployed or marginally employed graduates nor graduates currently pursuing internships or similar positions. Since we are interested in the isolated effect of graduation on starting salaries, Fig. 1 does not show students who already were employed since the time before the start of their studies and did not change positions after graduating. Due to the different group sizes of private and public students, we additionally checked the distribution of the dependent variable income in both groups. The mean income for public students is 2694 Euro and the mean income for private students is slightly higher with 3312 Euro per month. The variances were comparable with a standard deviation of 11.76 for public and 12.61 for private students.

Analysis Strategy
We use Bayesian statistics for our income estimation, because the Bayesian approach yields credible intervals around the coefficient estimates, which have a more intuitive interpretation than confidence intervals. Furthermore, this approach enables us to additionally regularize the models by means of weakly informative prior distributions. Regularization helps preventing the models from overfitting and therefore improves the external validity of our estimation. In a nutshell, Bayesian statistics is quite similar to maximum likelihood estimation, with the main difference being the additional use of a priori distribution. This prior p(θ) represents our beliefs concerning the true parameter value θ. Equation (1) shows that the evidence from the observed data y, the likelihood p(y|θ), gets weighted by this prior beliefs.
This weighting is a strong analogy to human learning, as we all have our prior beliefs which we update whenever we encounter novel information (data) on a subject. Unlike maximum likelihood estimation, Bayesian methods produce posterior distributions p(θ|y) proportional to the product of the likelihood and the prior (Eq. 1), answering the question which parameter values would be most likely, given the observed data y (Hoff, 2010). When the prior beliefs are strong, it takes strong evidence coming from observed data to overcome them. We utilize this property when we regularize some of our models. Specifically, we impose weakly informative prior distributions which favour the assumption that our covariates are likely to have no effect on the outcome to obtain more conservative estimates. Apart from this subtle differences, Bayesian methods and maximum likelihood estimation are known to produce almost the same estimates when p(θ) carries little information. Therefore, we present all of our results using uninformative prior distributions first before we continue regularizing our models.
Since we cannot go into further detail regarding Bayesian statistics we highly recommend e.g. Peter D. Hoff (2010): A first course in Bayesian statistical methods for further reading. For detailed information on distributions please see appendix.

Models
We modelled income using the R package 'brms' (Bürkner, 2017; which provides an interface from R to the probability modelling language Stan (Carpenter et al. 2017). We sampled all models for 4000 iterations and examined them for convergence. We diagnosed all models by means of posterior predictive checks and inspected them for misspecifications. Figure 2 shows the NEPS model with an uninformative prior (M1) and regularized with weakly informative standard normally distributed priors (M2). We use once uninformative priors on the coefficients to show how the NEPS data behaves without additional information (M1). The results are comparable to maximum likelihood estimates. As an add-on, we show the results also using weakly informative priors centred at 0 to obtain more conservative estimates (M2). For a closer look at all estimated models see Tables 2 in the appendix. We present 89% highest posterior density intervals around our estimates (Makowski et al., 2019).
Overall, the dot-whisker plot (Solt et al., 2018) shows that the results from Models 1 and 2 are highly congruent (Fig. 2). In this situation, the weakly informative standard normally distributed prior had almost no influence on the posterior distribution. In light of the size of the finally estimated coefficients these standard normal distributions where very vague, as we expected coefficient values a-priori to be in the range between + 1.0 and −1.0 with a probability of 68 percent. Hence, we can restrict our elaboration to results from Model 1, which we obtained using uninformative priors on the coefficients. The Bayesian-R 2 for Model 1 is 0.28, as it is for Model 2 (Gelman et al., 2019).
Pertaining to our main predictor variable of interest, we find that private sponsorship of higher education has a positive impact on graduates' gross income (Estimate (M1) = 0.11) in contrast to public institutions. This means private students show a 111 Euro higher median value of earnings before taxes than public students (exp(0.11) × 100 = 111.62). On average private students earn about 175 Euro more each month compared to public students ((exp(0.11 + (1/2) 2 ) × 100 = 175.06).
We proceed with presenting the effects of the remaining covariates to develop a holistic picture of the effects on income. For the exact estimates please see Table 2.
Training before the studies and the related work experience seems to bring a small wage gain (Est. (M1) = 0.08). Attending a university does not seem to have a positive effect on the salary compared to a graduate of a university of applied sciences (Estimate (M1) = −0.03).
The reference category in fields of study is "Linguistics and Cultural Studies". Compared to those students, sport students are likely to earn more, but the effect is not substantial and negligibly small (Est. (M1) = 0.01). Again, the estimates are quite uncertain due to a small number of cases in this category. The results for "Law, Social and Economic Sciences" are clearer: They tend to earn more than cultural or linguistic graduates (Est. (M1) = 0.31). For "Natural Sciences and Mathematics" applies almost the same: They earn more compared to culture or language students, even if only a little (Est. (M1) = 0.09). "Medicine and Health Sciences" have a very high wage premium compared to cultural and linguistic studies (Est. (M1) = 0.54). "Agricultural, Forest, Nutritional sciences" earn slightly higher salaries, but the effect does not differ substantially from the linguistic and cultural students (Est. (M1) = 0.08). This might be due to the various fields of study in this category. Graduates of "Engineering Sciences" have much higher salaries compared to alumni of linguistics and cultural studies (Est. (M1) = 0.38). Students of "Art Sciences" probably earn less than linguistic and cultural students, but the effect is not substantially different from zero (Est. (M1) = −0.09).
The results for training qualification or type of the degree must be compared to the reference category "Bachelor's degree". Students with a master's degree have a slightly higher probability to earn more compared to students who obtained only a bachelor's degree (Est.  Table 2 for the intercepts and family specific parameters graduates from medicine, law and teachers' profession. Due to an oversampling of teachers in the NEPS sample, this effect might be biased and underestimates the wage premium in this category. Diploma and Magister graduates earn a little more (Est. (M1) = 0.09) in comparison to bachelor degrees, artistic degrees earn less compared to bachelor degrees, but this estimate is very uncertain due to a very small number of observations as shown by the wide credible interval. The results of the Demographics of the alumni show that compared to men, women have a higher probability of earning less (Estimate (M1) = −0.18).The educational level of the father does not have any substantial impact on the wage after graduation (Higher secondary school: Estimate (M1) = −0.04; University: Estimate (M1) = −0.01), whereas a highly educated mother has a positive influence on the first income after graduation (University: Estimate (M1) = 0.06). After a closer look at the age of the students, there is no evidence indicating a difference regarding income in the first job after graduation (Est. (M1) = 0.0). The same applies to the migration background (Est. (M1) = −0.01).

Discussion
This study contributes to research regarding private higher education and the success of graduates of private higher educational institutions compared to public universities. We find higher incomes for graduates of private universities and universities of applied sciences in Germany. Our investigation contributes to higher education research in at least three ways: First, our results show that the income of private students is higher than the income of public students and adds support to the findings of previous studies in other countries like the U.S. (Brewer et al., 1999;Dale & Krueger, 2011) and Italy (Brunello & Cappellari, 2008). Despite the idiosyncratic setting of the only recently established German private higher education sector, embedded in an environment characterized by world-class public universities with little to no tuition fees and no apparent self-selection of overly ambitious students to private universities (Herrmann, 2019b), we arrive at similar findings as in studies covering private education in higher education systems with a long-standing tradition. Research from other countries suggests that the better labour market outcomes for private students are due to a higher socio-economic status, who can afford high quality education more easily and have access to elite alumni networks (Chetty et al., 2017;Brunello & Cappellari, 2008;Zając et al., 2018). This result is all the more surprising, since this argumentation is rather not valid for the German higher education sector because private higher education institutions in Germany are rarely elite universities and previous studies do not support this assumption for Germany (Herrmann, 2019a). However, we think it is more likely that other reasons play a role here: We suppose that on the one hand, this can be some kind of compensation for the higher tuition costs for private students (Brewer et al., 1999). On the other hand, it can be interpreted as a reward for the firm-specific knowledge the students already have gained during their practise-phase(s) (Weich et al., 2017). This experience likely leads to an advantageous negotiating position. Moreover, it is not implausible that the income advantage will disappear in the long run. The advantage that private students gain through practical phases or company contacts can presumably be made up for by public students in a short time.
Second, our results provide evidence for the human capital considerations of students. The job perspectives and salary gains seem to partially compensate for the higher tuition fees for the private institution. There actually is a higher return of income after graduation, which is in line with the reasoning of Botelho and Pinto (2004) who argue that closer contacts to companies, like it is the case in the private higher education sector, lead to a higher employment probability.
In addition, our study has practical implications: Although private education is a frequently covered issue in media (e.g. Lock, 2017;FAZ, 2020) there are no adjusted analyses for private higher education alumni yet. With the present study, we contribute to close this information gap. In our models, we condition income on common explanatory variables, enabling the reader to properly estimate expected income by simply inserting available information into the equations. The Bayesian framework, which we deliberately utilize for our analyses, increases interpretability for the broader readership, as it produces intuitive models with straightforward probability interpretations pertaining to the uncertainty in the regression coefficients. Considering the higher cost and the rather small benefits of private education, in line with rational choice theory of education we imagine, prospective students might be interested in the additional information we provide as part of their decisionmaking process.
Our analyses have implications for the policy of higher education institutions in Germany: Educational outcomes and labour market returns show a positive income effect for those students who graduate from private higher education institutions. Therefore, private education can increase the dependency between socioeconomic background and educational opportunities. In terms of disruptive innovation theory, the higher labour market returns of private higher education could lead to an increasing demand for private education and eventually result in an unintended system change in the long run (Bower & Christensen, 1996). Policymakers and public institutions in Germany should be aware of this and maybe adapt the curriculums accordingly, strengthen contacts to regional employers and provide innovative teaching and learning formats to continuously attract good applicants. Ideally, if private and public higher education institutions learn from each other, healthy competition will emerge, with the result that innovation will not divide the German higher education system and lead to further social inequality, but will remain competitive in the international context and provide access to education for anyone, regardless of one's socioeconomic background.

Limitations and Further Research
Some limitations have to be considered when interpreting the results: The data quality especially in terms of private education in Germany needs improvement. The NEPS started with a private higher education institution oversampling and is a representative educational data source for Germany, but it has to deal with the same problems as all long-term panel surveys. High attrition over the years and a self-selection bias in favour of the more successful students is a common problem. Due to the low willingness of private universities to participate, private students-despite the oversampling-are probably somewhat underrepresented in the NEPS (Zinn et al., 2017). In addition, the data are based on self-reportings, which may lead to biased results or incomplete information. In general, it would be highly desirable to improve the data situation in Germany regarding the whereabouts and the study success of private students. Especially longitudinal administrative data of the higher education institutions, like e.g. the Swedish LISA database (Statistics Sweden, 2020) would provide many opportunities for further in-depth research. More detailed analyses at the subject level cannot be performed with the available data, but would certainly be very informative.
Moreover, our study is limited to early careers. We cannot fully exploit the potential of a panel survey and utilize a longitudinal analysis, because we do not have enough (reliable) information over a longer period for all of the students. A longitudinal analysis would be suitable to investigate whether the salary advantage is still maintained with additional years of professional experience. It is even likely that with the increasing professional experience of public students, the effect disappears and public students catch up with their private competitors. In addition, we excluded right-censored data from our analyses, which means we analysed only graduates who successfully landed a job until the date of the survey.
Further, a comparison of private and public students under different labour market conditions would be desirable to answer the question, if the high investment still pays back under poor labour market conditions (e.g. a worldwide recession due to an economic crisis). In that case, this could be an advantage for the "cheaper" public graduates.
Furthermore, the firm-specific human capital can also be a disadvantage: The sometimes very special skills and training often apply to the infrastructure of only one or at least a few companies. Reorientation towards other employers could therefore be difficult. Especially in times of an economic crisis, this could be an advantage for the more theoretically trained graduates of public institutions.