Here, we provide an overview of the German educational system (primary and secondary education). In grades 1 to 4 (which span an average age range of 6–7 to 10–11 years), pupils attend primary school. Based on their performance in primary school, pupils are then sorted into one of the four qualitatively different tracks (Eckhardt 2017). For each pupil, the grade four teacher makes a recommendation, which is either binding or non-binding depending on the federal state, regarding which secondary education track the pupil should be enrolled in based on his or her general academic achievement and development potential. The five-year lower secondary school track (Hauptschule), which prepares pupils for low-skilled service or manual work, is the least demanding. The six-year intermediate track (Realschule) provides pupils with vocational training in skilled white-collar or service occupations. The nine-year upper secondary school track (Gymnasium) prepares pupils to obtain the qualifications needed to enter university (Abitur), and is regarded as the most prestigious. Furthermore, most federal states have introduced comprehensive schools (Gesamtschulen) in addition to the tracked tripartite school system. These comprehensive schools can be seen as another approach to making the secondary school system more permeable. While comprehensive schools usually offer all three of the school-leaving certificates issued by the traditional tripartite school system, students can continue from one level to the next level given adequate performance. Thus, a comprehensive school can combine several tracks within one institution, and enable students to move between the tracks. In general, the hierarchy of the schools’ performance requirements is as follows, from lowest to highest: Hauptschule, Realschule, Gesamtschule, Gymnasium.

After the final year of elementary school (grade four), the class teacher gives a track recommendation for each pupil that is based on the teacher’s overall impression of the pupil’s abilities and competences, including the child’s social and soft skills and potential for further development.

As was explained above, even when a child is a low performer, the parents may be motivated to overrule the teacher’s recommendation and to enrol the child in the academic track; i.e., in the school track that is associated with the best outcomes and the highest wage premiums. It has always been possible for parents to choose to enrol their child in a less demanding track (for example, the teacher recommends the academic track, but the parents select the intermediate track instead). Recently, parents have been given the option to overrule the teacher’s decision and select a more demanding track for their child (for example, the teacher recommends the intermediate track, but the parents choose the academic track instead). In our analyses, we refer to a situation in which a child was enrolled in the academic track (Gymnasium) in grade five, and had received a teacher’s recommendation to do so, as a match. Conversely, we refer to a situation in which a child was enrolled in the academic track, but had received a teacher’s recommendation to enrol in a less demanding track in grade four (i.e., the parents overruled the recommendation), as a mismatch. Children who were not enrolled in the academic track in grade five are not of interest for our study, and are not considered in the theoretical expectations or analyses.

In order to clarify which social classes tend to accept a mismatch condition, the concept of primary and secondary effects of Boudon (1974) can be applied. Boudon argued that educational inequality is caused primarily by two factors. First, he noted, socially disadvantaged children tend to have lower academic performance than other children, including lower grades and standardised achievement test results (primary effects). Boudon attributed this lower performance to socially disadvantaged families being less able to invest in their children’s education by, for example, providing them with individual early support or tutoring. He also identified secondary effects related to educational decisions. Boudon argued that compared to their more advantaged counterparts, children from disadvantaged backgrounds are less likely to achieve high educational qualifications even when their academic performance levels are the same, and are therefore more likely to choose the lower schooling tracks. He explained this tendency by observing that socially disadvantaged families often regard attending the Gymnasium as a comparatively long and costly educational route with a lower probability of success. This view has been further supported by the concept of relative risk aversion, which posits that children must primarily reproduce the social status of their parents (Breen and Goldthorpe 1997; Esser 1999). Thus, children from the higher social strata are expected to at least secure eligibility to enrol in higher education, as this is seen as the only way for the parents to achieve their desired level of status; whereas children from disadvantaged families are not expected to earn more than a lower diploma (Stocké 2007). Thus, the motivation to attend the Gymnasium is often not educational in nature (Schulze et al. 2009; Sewell and Shah 1968). If this is the case, which children belong to the group of pupils who have to ignore the teacher’s recommendation to enrol in the Gymnasium, rather than in a lower track? Since the recommendation should be based primarily on the child’s academic performance, and not on his or her social class affiliation, these individuals are likely to be low-performing students who have not achieved the required grade point average. Based on the primary effects argument, this group should include many socially disadvantaged children, as well a few children who are more socially advantaged. Nevertheless, based on the secondary effects argument, it may be assumed that among the children in this group, the more socially advantaged children (and their parents) in particular are motivated to ignore the teacher’s recommendation that the child enrol in a lower secondary track, and thus proceed to enrol in the Gymnasium. Furthermore, it is known that compared to their more socially advantaged counterparts, socially disadvantaged families tend to be less informed about the education system, and to rely more on teacher recommendations (Harazd and van Ophuysen 2008). Based on this argumentation, the following research hypothesis can be formulated: parents who overrule the teacher’s recommendation that their child enrol in a less demanding track by sending their child to the Gymnasium tend to belong to the higher social classes (Hypothesis 1).

This expectation is supported by previous research. For example, it is known that in Germany, social origin influences the probability of transitioning to the Gymnasium, even when controlling for the actual performance (Ditton and Krüsken 2006; Stubbe and Bos 2008); and that children from socially disadvantaged families are less likely to receive a recommendation to attend the Gymnasium, even if their performance is equal to that of their more socially advantaged counterparts (Dumont et al. 2014; Maaz et al. 2008). These effects are also stronger in federal states without a binding teacher recommendation (Gresch et al. 2010), which means that in these states, the parents often overrule the teacher’s recommendation. Overall, the secondary effects appear to be responsible for almost 60% of the educational inequality that arises in the transition to upper secondary school (Neugebauer 2010). Other studies have also concluded that parents from the higher social strata are especially like to ignore undesirable recommendations, whereas parents from the lower social strata are more likely to accept them (Ditton et al. 2005; Harazd 2008). This discrepancy can also be attributed to evidence indicating that social position and educational aspirations are positively correlated. Therefore, it may be assumed that socially disadvantaged families are less likely to want their children to attend the Gymnasium in the first place (Haunberger and Teubner 2008). In order to go beyond the results of these previous studies, the following analyses will extend the window of observation by several years, as longer running panel data have recently become available. In contrast to either cross-sectional studies or panel analyses with only two waves, including a large number of survey waves allows us to trace the development of children over a longer period of time, which has several advantages. First, the problem of outliers and errors is reduced since the total number of data points is larger. Second, it makes it easier to recognise general trends over time (like up- or downward trends), and thus to draw more robust inferences. For example, it is possible that pupils with a mismatch condition have abilities that are comparable to those of pupils without a mismatch condition at the beginning of secondary education, but that the gap in performance between these two groups widens as the pupils progress. These diverging trends can be studied in detail only when several time points are included. Thus, our study has an advantage over previous studies, which often drew conclusions from a smaller number of points in time. Clearly, the more data that are available, the more precisely we can investigate the general development of pupils.

In light of the considerations outlined above, the following question arises: How does a mismatch condition – that is, enrolling in the academic schooling track without a teacher’s recommendation – affect a child’s subsequent educational achievement and success? Does a child with such a mismatch have lower chances of successfully completing the academic track? How do indicators of a child’s success in life, such as his or her well-being and academic performance, as well as other relevant factors, such as the enjoyment of reading, develop over time? First, there is evidence that from the outset, children with a mismatch have lower academic performance than their classmates in the academic track (Klicpera et al. 1993; Stern 2008). This seems logical, as previous differences in the academic performance of these two groups is the main reason for the mismatch. It can, therefore, be assumed that these children do not meet the performance standards of the Gymnasium, or at least have below-average performance. If these children are unable to overcome their academic shortcomings, they may have to repeat the grade or even transfer to another type of school. Ultimately, these pupils are generally found at the lower end of the intra-class performance distribution, which is communicated to them by, among other things, the grades they achieve (Pfost et al. 2018). These observations can be further explained by the big-fish-little-pond effect. It is well known that for students, their own class is the most important reference group, and the comparison with their classmates has a particularly large impact on their academic self-concepts (Möller and Trautwein 2015; Zeinz and Köller 2006). Pupils whose performance is poor relative to that of the reference group are, therefore, negatively influenced (Köller 2004). Based on these findings, we can expect to observe that students who attend the Gymnasium without a teacher’s recommendation will, on average, have worse academic outcomes than their classmates (Hypothesis 2). This working hypothesis is supported by previous findings, and serves as a starting point for the following analyses (Klicpera et al. 1993; Stern 2008). Furthermore, it can be assumed that the negative effects of a mismatch are ultimately caused by inadequate school performance, since performance is regularly tested and communicated by grades (Hypothesis 3). A pupil with unsatisfactory results will find herself at the lower end of the performance distribution, and will also face the problem of not being able to advance to the next school year, which is an objective measurement of failure that can cause the pupil to experience stress, to develop negative attitudes towards schooling, or to develop low self-esteem.

The empirical analyses we use to test our hypotheses are based on data from the German National Education Panel Study (NEPS) (Blossfeld et al. 2011).² The NEPS has been collecting longitudinal individual data (panel data) in a multicohort sequence design since 2008. For the present study, we use the starting cohort 3 (data version 8-0-0), which includes secondary school students who have been surveyed annually since the fifth grade; i.e., the first grade of secondary school. The target population for the starting cohort 3 consists of all children in Germany who were enrolled in fifth grade in Germany in the 2010/2011 school year. At the time the analyses were performed, information was available for grades five to nine; i.e., a total of five survey waves were conducted between 2010 and 2016. These prospectively collected individual data cover a range of relevant dimensions, such as competence development, grades, and health; but also socio-demographic variables, such as social origin, as measured by the educational degrees of the parents and their ISEI classification. Thus, the NEPS data are well-suited for the purposes of the present study. The teachers’ recommendations in the fourth grade are also available.

The total sample consists of 5,753 students enrolled in the fifth grade of secondary school. This sample is additionally restricted. First, pupils from federal states that had a binding teacher recommendation at the time of the first selection (the transition to secondary education) were removed from the sample, because in such cases, the teacher’s decision could not be ignored, and a mismatch was, therefore, not possible. These federal states were Bavaria, Baden–Württemberg, Bremen, Saxony and Thuringia (i.e., five out of the 16 federal states, which underlines the general trend in Germany towards abolishing the binding character of the teacher’s recommendation). This leaves 3,345 pupils. In addition, the states of Berlin and Brandenburg are excluded because in these states, the first selection takes place in the sixth grade. Children who attended a special needs school (Förderschule) are also excluded, since it can be assumed that our theoretical concepts do not fully apply to them. This leaves a sample of 2,790 children for analyses in wave 1 (raw sample).

As explained above, theoretically, students at both the academic track schools (Gymnasium) and the comprehensive schools (Gesamtschulen) can earn the qualifications needed to enter higher education (Abitur). In the data, it is not always possible to distinguish which types of comprehensive schools provide this option, and which do not. Therefore, all analyses were carried out twice. In the first definition, only the academic track schools provide this option; while in the second version, both academic track and comprehensive schools are analysed together, and are considered to be equivalent. By using this approach, very precise effects can be estimated. Note that the second form of operationalisation always contains a larger number of cases. The variable of interest, mismatch, is binary, and is operationalised as follows: if a child in grade five attends either the Gymnasium (or a comprehensive school, depending on the operationalisation) despite not having a teacher’s recommendation to enrol in this track, this is classified as a mismatch (coded 1); whereas if a child attends the Gymnasium after having received the corresponding recommendation, there is no mismatch (coded 0).

The social background is operationalised in accordance with Boudon’s theory of the two effects via the highest school-leaving qualifications the parents achieved, as doing so enables us to directly measure whether a particular school type can reproduce the parents’ school-leaving qualifications. While there are other options available for operationalising social background (e.g., Erikson–Goldthorpe–Portocarero class scheme (EGP) or International Socio-Economic Index of Occupational Status (ISEI)), in the context of the German system – in which the educational degrees students earn are decisive for their subsequent life course, since these qualifications have a gatekeeping function that allow students to enrol in specific educational tracks – using these qualifications seems most appropriate, as each degree has a clear and inherent meaning. If information on the school-leaving qualifications achieved by both parents is available, the higher of the two degrees is used (principle of dominance). To create categories of approximately equal size, they are operationalised as follows: no degree, lower (Hauptschulabschluss) or intermediate degree (Mittlere Reife) (1), any higher education eligibility (Fachabitur or Abitur), (2) and any higher education degree (3). For the sake of simplicity, social background and parental educational qualifications are sometimes considered equivalent in the further analyses, even if the two concepts are not identical. Parental social status is measured by the highest ISEI (International Socio-Economic Index of Occupational Status) level, which includes additional information on the occupational status of the parents. These variables are included as control variables in the longitudinal models.

The objective academic competence or performance of students is measured by standardised competence tests, which the NEPS conducts in grades five, seven and nine. The tests cover competences in mathematics, reading skills and orthography. Reading competence is tested via 32 items in a partial credit model (Pohl et al. 2012). Mathematics competence is calculated from 24 items, which include aspects such as counting, spatial thinking, form and probability (Duchhardt and Gerdes 2012). As these different areas of competence are highly correlated, for the sake of simplicity, a single performance score is generated, which has a high Cronbach’s Alpha (an Alpha in each wave greater than 0.86). Since the competences are only measured three times over the five ways, they are imputed in the two missing waves by averaging the two adjacent measurement points, if both were available. Further information on the competence measures of the NEPS can be found in the data manual (Fuß et al. 2019). As a second performance indicator, we use the school grades achieved in the subjects of mathematics and German from the annual reports. These grades are, in turn, combined into a single score by means of simple averaging. The German grade system ranges from one (best grade) to six (worst grade), so lower values indicate a higher performance. As both grades and objective competences were z-standardised by wave, the results can be interpreted in standard deviations. This approach also removes any growth and time effects from the data, which is beneficial for the following analyses.

Well-being is measured by general life satisfaction, and is generated from six Likert-scaled individual items (Alpha always greater than 0.76), which have already been tested in previous studies (TNS Infratest Sozialforschung 2009).³ This variable will be referred to as general well-being, and is available in all five waves (von Collani and Herzberg 2003). The subjectively perceived health status of each pupil is measured on a scale of zero (“very poor”) to four (“very good”), and is taken from the pupil questionnaires. As another indicator of general well-being and health, each pupil’s self-reported days of absence from school in the past four weeks are selected. Values above the 99th percentile (corresponding to more than 15 days of absence) have been removed from this item to avoid distortions due to outliers. We assume that pupils with health problems will have a higher number of days absent from school. The enjoyment of reading is measured using six different Likert-scaled items (Möller and Bonerad 2007), and indicates how much a child enjoys reading (Alpha always greater than 0.85). This variable is selected to measure the child’s subjective interest in reading. The age of the children is measured in years in wave 1. The absolute age of the child is used to capture his or her overall cognitive development, which might be confounding if the parents sent the child to school earlier or later than the other children.

It is important to note that in the analyses, a hierarchical data structure exists, as up to five data points are available for one person. In the longitudinal analyses, this clustering must be taken into account in order to estimate standard errors correctly. In addition, missing information is imputed to the extent possible in order to increase the effective number of cases. Multiple imputation with chained equations (MICE) is utilised. In each case, 40 imputations are generated after a burn-in of 60 iterations (Allison 2001). Common diagnostic criteria for imputations, such as convergence, were examined and approved. Some statistics about the total number of imputed values and convergence are presented in the appendix (Table A.1 and Figures A.1 and A.2). It should be noted that analyses that do not make use of any imputation procedures report basically the same results and conclusions. Thus, we are confident that the imputation does not disturb or bias the analyses in any way.

First, purely descriptive statistics are reported for all of the relevant variables in order to get a general impression of the distribution of the variables. Then, a first cross-sectional model is used to test how social origin and mismatch are related. The sample includes all children in grade five who did not receive an academic track recommendation (n=1008), and may, therefore, have ignored it. This enables us to test which of these children nevertheless enrolled in the academic track. The dependent variable is binary coded (academic track/comprehensive school=1, other school type=0). The key explanatory variable is social origin, measured by the highest parental educational certificate with three levels.

In all of the subsequent analyses, only those children who actually enrolled in the Gymnasium in the fifth grade are included (n=862 in schooling year five). This enables us to test what effects a mismatch had on a child’s outcomes. Multilevel growth curve models are utilised to take the data structure into account. The dependent variables are the probability of remaining in the academic track (retention rate), competences and grades, well-being, self-assessed health, days absent from school in the last four weeks, and the enjoyment of reading. Depending on the scaling of the dependent variable, different statistical models are used, which are described in more detail below. All graphs contain 95% confidence bars to test for significant differences between groups. Unlike most other growth curve models, we use a different parametrisation, since the number of waves was low, and all of the pupils were interviewed at virtually the same point in time. This approach allows for a very flexible estimation of effects, and does not require us to make assumptions about the functional form of the temporal developments of outcomes.

In the final mediation analysis, we examine whether the group differences in outcomes between the pupils with and without a mismatch can be explained by their competences or grades. Longitudinal panel regressions with random effects are utilised. By employing a nested model design, the strength of the mediation can be assessed.

Since spurious correlations are always possible in studies using observational data, these should be mitigated or eliminated by including relevant control variables. The following variables were selected as potential confounders: the gender of the child, the child’s migration background (both parents born in Germany/one parent born abroad/both parents born abroad), ⁴ the highest parental educational level, the highest parental ISEI level, the age of the child, whether the parents were living together (including whether the parents were divorced, widowed or single) and the federal state where the school was located. It should be noted that due to the data protection regulations for the NEPS, we are not allowed to publish regression coefficients that were computed for the federal states; thus, these coefficients are not included in the output tables.

All calculations are computed in Stata 16.1, using, among other programs, the user program mimrgns, which is needed to calculate the average margin effects for the imputations (Klein 2014).

To test how social origin was associated with a mismatch, binary logistic regressions are performed (Table 2). For each operationalisation, two models are computed, one without controls and one with all control variables added. Unlike all of the following analyses, these analyses include children enrolled in the fifth grade in all types of schools who did not receive a teacher’s recommendation to enrol in the academic track. Average marginal effects (AMEs) are reported. It should be noted that parental social status, measured via the ISEI level, is not included in these models, as this variable is strongly correlated with parental education, and its inclusion would undermine the effect of the education variable.

In the models without the controls added, we find a positive and statistically significant effect. For example, the results show that compared to parents with lower levels of education, parents with a university degree whose children were enrolled in the academic track (strict operationalisation) were 8.3 percentage points more likely to enrol their child in the academic track despite not having received a teacher’s recommendation to do so. The results for the alternative definition of academic track that includes comprehensive school are similar. However, our conclusions change as soon as controls are added. In the strict operationalisation, a big part of the effect vanishes and the significance is lost, while the trend is still the same. When the alternative definition of the academic track that includes comprehensive schools is applied, the effect becomes smaller, but is still significant. Taken together, we conclude that the effect is reduced somewhat after the controls are added; that there is still a clear trend in both forms of operationalisation; and that highly educated parents are, on average, more prone to enrol their child in the academic track despite not having received a recommendation to do so.

In the following analyses, mismatch status is the central explanatory variable. Multilevel growth curve models are calculated in which an interaction between the wave dummy and the mismatch variable is inserted (Rabe-Hesketh and Skrondal 2012). The educational trajectories can thus be modelled in a very flexible way, and allow for a clear graphical representation. First, we investigate whether students with a mismatch are more likely to drop out of the academic track than students who received a teacher’s recommendation to enrol (retention rate). For this purpose, a binary variable that indicates whether or not a student was enrolled in the academic track in a given wave is created. By design, this share was 100% in grade five. The entire trajectories are depicted in Figure 1. Each model includes the previously introduced control variables. Complete regression tables are available in the appendix (Table A.2).

The trend is quite clear. Pupils with a mismatch tended to drop out more often than the pupils who received the recommendation. In the strict operationalisation, this effect is huge, and is more than 15 percentage points in wave nine. When the alternative definition of academic track that includes comprehensive schools is applied, the effect is smaller (more than five percentage points), but is still statistically significant. Additional tests for the difference between the two lines indicate that the difference is actually statistically significant on the 5% level from grade seven onwards (not depicted). These results are in line with previous findings (Tiedemann and Billmann-Mahecha 2010).

In the next model, the trajectories of objective competences and school grades are analysed. Linear models are estimated, since the outcomes are measured continuously and are approximately normally distributed. The models include the same control variables as before to account for spurious correlations. To allow for a clearer interpretation, the model shows not the predicted outcomes, but the differences between the two groups (match/mismatch). This means that for the objective competences, a positive number represents an advantage for the pupils with a match, while for the grades, a negative number indicates an advantage for these pupils (since lower grades indicate better performance in the German system, with one being the best grade and six being the worst). This interpretation makes it convenient to test for statistical significance. As long as the zero line is not touched by the confidence bars, the difference is significant on the 5% level. The results are shown in Figure 2, and the complete regression tables are presented in the appendix (Table A.3).

When we look at the results for the objective competences (upper row), we can see that the differences are always positive, and that zero is never touched by the confidence bars. This means that pupils with a match status always display higher objective competences. The gap between the two groups is rather constant over time, and lies between 0.4 and 0.5 standard deviations. The difference between the two forms of operationalisation is rather small, while the effects are stronger in the alternative definition of academic track that includes comprehensive schools. The same overall conclusions can be reached for subjective grades (lower row). While the signs are reversed due to the coding scheme, the meaning is the same. The pupils with a mismatch condition always had worse outcomes; that is, numerically higher grades.

The models for the other four outcomes are built identically. The predicted outcomes are reported for both groups (Figure 3 and 4), and complete regression tables are shown in the appendix (Table A.4). Again, the results are visualised separately for both operationalisations.

As we can see, there are virtually no differences between the matched and the mismatched pupils using the strict operationalisation. For both outcomes, satisfaction and enjoyment of reading, the confidence intervals clearly overlap. The picture is quite different when the alternative definition of the academic track that includes comprehensive schools (right side of the figure) is employed: i.e., we see clear gaps for both satisfaction and enjoyment, which indicate significant group differences. Here, we observe that pupils in the mismatch condition have lower levels of satisfaction and of enjoyment of reading.

With respect to the two final outcomes, the general health of the child and the days the child was absent from school in the last four weeks, we do not see any group differences at all, regardless of the form of operationalisation. These findings lead us to conclude that there is no association between the mismatch status and these two outcomes after controlling for various potentially confounding variables, which are the same as those used in the previous models.

Since the previous analyses indicate that there are significant group differences in levels of satisfaction and of enjoyment of reading, the question of whether these differences can be attributed to differences in performance, which are clearly present, arises. To investigate this question, mediation models can be applied. Again, both forms of operationalisation are used for the outcomes of satisfaction and enjoyment of reading. The models are built as follows. The first model includes the treatment (mismatch) and all controls. The second model adds both variables of performance (objective performance and grades). If the coefficients of the treatment status change, a mediation effect is present. To test this statistically, the Sobel test is applied to each model (Hayes 2018). If the coefficients are found to be statistically significant, this proves that a mediation effect is present. Results are presented in Table 3.

When interpreting the results from the strict operationalisation, we notice that the models also indicate that there is no effect of mismatch status in these findings. However, we see that the sign of the coefficient changes after the mediators are included. The mediator variables are highly significant (for satisfaction, only grades; for enjoyment, both grades and objective performance). Applying the Sobel test revealed that there is indeed a mediation effect, and that the coefficients are highly significant. However, since the baseline effect of mismatch is not significant, the total share mediated is probably very small, and these findings should, therefore, be interpreted with caution. The outcomes are clearly different when the alternative definition of academic track that includes comprehensive schools is used. Here, the mismatch variable is highly significant and negative, which suggests that there is a negative effect for pupils with a mismatch. This was also clear from the previous analyses. When the mediators are added, the coefficient of mismatch is no longer significant, which indicates that a mediation effect is present. The mediating variables are again highly significant. As the Sobel test results are highly significant as well, we can conclude that a mediation effect is present, and that the performance differences between the two groups can explain why the pupils with a mismatch status had worse outcomes.