We present basic descriptive statistics for all variables in wave 1 (grade 5) in Table 1.
Because of the sample-selection process, which we outlined above, our analysis sample comprised a specific subpopulation of the initial sample. This is reflected in the reduced number of cases, and it produces a very selective sample with regard to some key aspects. For example, the average parental education is rather high; almost half of all children have parents with a higher education degree. Only 27% of the children have parents with a degree lower than upper-secondary education, and 84% of the children attend the academic track.
The last two columns of Table 1 display the mean values of each variable separately by school track. The differences in these values indicate that the individual characteristics of the students in the two tracks differ somewhat, which can also cause differences in the patterns related to the adjustment of aspirations. To adjust for these compositional differences, we applied propensity score matching to isolate school-track effects. The table also highlights the differences in the three school-level variables, which we used as mediators to explain potential differences between the two tracks. They show that the different tracks indeed provide different learning environments with regard to social and cognitive environments. The share of highly educated parents, the share of students with aspirations for a higher-education degree, and the average competences are clearly higher in the academic track.
Effects of School Tracks
First, we calculated a propensity-score model to match pupils in grade 5. With this logistic model, we estimated for each pupil the propensity to attend the academic track as a function of the model’s covariates (cf. Table 6 in the appendix). As covariates, we included the pretreatment control variables described in Sect. 3.2. Based on the propensity scores, we identified a region of common support that comprises highly comparable pupils in different school tracks. Figure 1 displays the distributions of the propensity scores by school track.
As expected, high propensities to attend the academic track are more common among pupils who actually attend the academic track. However, we do find high propensity scores even among the students attending the nonacademic track. We selected a region of common support to ensure that enough observations with similar propensity scores from each comparison group entered the analysis. A simple numerical rule is to use the overlap between the treatment and the control groups. However, if the range of propensity scores is similar but the shapes of the distributions strongly differ between the two groups, regions can exist with very weak common support. To avoid this, we selected only propensity scores that would ensure a density exceeding 3% in both distributions. Through restricting the region of common support, we made sure that the two groups were actual comparable and that pupils without any “matches” in the other group were removed. The selected region of common support is indicated by the dashed vertical lines in Fig. 1. Pupils falling outside that range were not included in the subsequent analyses on school-track effects. For this part of the analyses, this left us with an analytical sample of 1063 observations.
As a first descriptive analysis, we compared the development of aspirations over time between the two school tracks for all pupils within the selected range of common support. Figure 2 displays the percentages of pupils with aspirations for higher-education eligibility across the five survey waves from grades 5 to 9, including 95% confidence intervals. There are no further control variables or adjustments for any of the following figures (Figs. 2, 3, 4, 5, and 6), as they should demonstrate the purely descriptive development of aspirations from grades 5 to 9.
We see that the trajectories clearly differ between tracks. While aspirations for higher-education eligibility are constantly high in the academic track, the share drops significantly even just 1 year after entrance into secondary education in the nonacademic track (about 15 percentage points). This downward trend continues over the following years and is about 24 percentage points lower in grade 9. Since the confidence bars never overlap, we can assume that this difference is statistically significant. This descriptive finding is in accord with hypothesis H1a. However, as we pointed out above, the result can be partially driven by differences in the compositions of individual student characteristics between the two tracks, which is why we now turn to models that are adjusted by the propensity scores.
In addition to the descriptive analyses shown in Fig. 2, we included the propensity scores as a sole control variable to take into account the differences between the two comparison groups. Table 2 presents the results in the columns labelled M0. Since the dependent variable is binary and we computed logistic models, we report average partial effects (APEs), which facilitate a clear interpretation (therefore, no constant is computed). Even after controlling for the propensity scores (M0), we observe that significantly more pupils in the academic track than in the nonacademic track report aspirations for higher-education eligibility in grades 6 and 9. In grade 6, the APE is 0.074. This means that pupils in the academic track have a 7.4–percentage point higher probability to hold aspirations for higher-education eligibility than pupils in other school tracks. In grade 9, the respective value amounts to 17.4 percentage points. This again supports hypothesis H1a. If the propensity scores were able to account for all pretreatment differences between these pupils, one could refer to this as the causal effect of tracking on aspirations. However, since we were able to control only for observable characteristics, we consider it an approximation to a causal effect.
In a next step, we were interested to what extent the differences between the tracks were due to differences in learning environments. For that reason, we added the school-level mediators to the models (share of students with high aspirations and share of students with highly educated parents and average academic competences). To estimate the extent to which those variables would be able to account for the differences between the two tracks, we proceeded as follows: We started from the reduced model (M0) without any of the mediating variables and then compared it to a model that includes the mediators (M1). For linear models (for example, OLS regressions), this procedure is straightforward, and coefficients can be compared across models to assess the degree of mediation, which is reflected in the relative change of the coefficient of the treatment variable (in our case, the school track attended). However, in nonlinear binary models, this is not possible in the same way since the coefficients can also change across models due to scaling effects, even in the absence of any “true” mediation. This can lead to false conclusions. This issue is taken care of by the KHB decomposition technique (Karlson et al. 2012). We appled this method using the Stata package khb to compute the degree of mediation (Kohler et al. 2011). We present a reduced and a full model and display the difference between their academic-track coefficients. When this difference is statistically significant, our mediators can be considered to account for the differences between the school tracks. In addition, we decomposed the total mediation, which allows us to assess the influence of all mediators separately. We present mediation analyses for differences in aspirations in grades 6 and 9. The standard errors are clustered by school. The results are shown in Table 2.
After the addition of the mediator variables in the full model (M1), the coefficient of the academic school track decreases from 7.4 to about 1.6 percentage points in grade 6 (also note that the statistical significance of the effect vanishes). By comparing the coefficients between models M0 and M1, we can calculate the relative reduction. Together, the three mediators account for about 79% of the difference in aspirations between the school tracks. When we consider the separate contributions of the mediators in the bottom part of the table, we see that, in particular, average competences and aspirations account for the differences between tracks, while the percentage of highly educated parents contributes little in addition.
In grade 9, the mediators account for only about 50% of the differences in aspirations between the two tracks. While the school-level aspirations again explain a large fraction of the difference, the contributions of the other two mediators are different from the grade 6 analysis. The percentage of highly educated parents now accounts for a substantial fraction of the gap, while average academic competences at the school level do not contribute at all to the explanation. Recall, however, that the mediators were measured in grade 5. It might be possible that the results are influenced by changes in the learning environments that we did not fully capture with our measurement. Yet, because our indicators of learning environments’ characteristics account (at least partially) for the differences in the development of aspirations between school tracks, we find support for our hypothesis H1b.
Association Between Social Background and Aspirations
For the following analyses, we employed a different design than before. We started again with a descriptive analysis to visualise how aspirations develop for pupils of different social background over time. Figure 3 pictures this development without any controls. Social background refers to parents’ highest educational degrees. Especially for the least educated group, aspirations drop significantly over time. In this group, the share of pupils with aspirations for higher-education eligibility decreases from 100% in grade 5 to about 89% in grade 9. Because the confidence intervals do not overlap with those of the other groups, we can assume that the differences are statistically significant. This conforms to our hypothesis H2a. The differences between the two other groups are rather small and not statistically significant.
In the next step, we computed the mediation models. We considered the same school-level mediators as before, but we also included the track (academic track or any nonacademic track) as an additional binary mediator. Since we did not rely on a matching model, we included control variables (because we did not apply any common support restrictions, the case numbers are slightly larger). The control variables are the same that we used for the assignment model in our matching analysis, except for place of residence (east/west) due to empty cells.Footnote 2 We employed a nested design to trace the explanatory contributions of different sets of variables. The first model only includes parents’ education. The second model adds all control variables. The third model adds the school-track variable. The fourth and final model adds the three school-level mediators. Table 3 displays the results for grade 6, and Table 4 displays the results for grade 9. In addition, the last column of the tables displays the relative contribution of each variable from model 4 to the explanation of the aspiration gap between students with parents with less than higher-education eligibility and students with parents with a higher-education degree.
Note that in this analysis, parents with a higher-education degree are the reference group. Considering the differences in aspirations in grade 6, model 1 just mirrors the results from Fig. 3. We see that the aspirations for higher-education eligibility in grade 6 are 1.8 percentage points lower for students from low-educated families compared with students from highly educated families. However, this difference in the drop of aspirations is not statistically significant. Yet, adding control variables and the mediators for tracks and learning environments both contribute to a reduction of the coefficient. The variables in model 4 account for 79% of the initial difference, of which about 46 percentage points are due to influences of the tracks and learning environments. While the differences in grade 6 are small and not statistically significant, the situation is different in grade 9. Table 4 presents the findings.
First, we see a statistically significant effect between parents with higher education and parents with less than upper-secondary education in model 1. Children in the latter group have a 5.6–percentage point lower probability to hold high aspirations in grade 9 than children from academically educated parents. This gap in aspirations still amounts to 4.6 percentage points when control variables in model 2 are added. Introducing the track variable in model 3 leads to a further reduction of the coefficient to 3.7 percentage points. This means that participation in different school tracks provides a partial explanation of why children of low educated families adjust their aspirations more often in a downward direction than do children of academically educated families. Adding the three school-level mediators in model 4 does not lead to a substantial further reduction of the coefficient. Our model is not able to account for the remaining gap of 3.1 percentage points. In total, model 4 accounts for about 45% of the difference in aspirations between students from low and highly educated families, 34 percentage points of which are due to influences of school tracks and our measures of school-level learning environments. Note that, in model 4, the school-track variable still accounts for 21% of the gap. This means that our measures of learning environment do not fully capture the differences between the tracks. On the other hand, these school-level factors also account for differences within tracks.
In support of our hypothesis H2b, these results indicate that the more pronounced downward adjustment of educational aspirations that we observe for students from less educated families is at least partially attributable to their more frequent exposure to learning environments that are assumed to provide less simulation for academic ambitions.
Heterogeneous School-Track Effects
To complete our analyses, we considered whether the school-track effects on aspirations differ by social background. We display the development of aspirations for four groups, which were created from the interaction between track attended (academic or nonacademic) and parents’ education. To simplify the interpretation, we omitted the group of pupils with parents with upper-secondary education as their highest level of education. For each grade, we computed arithmetic means and 95% confidence bands. No control variables or restrictions were imposed for these descriptive analyses. The results are depicted in Fig. 4.
In support of our hypothesis H3, the figure displays a clear interaction effect. While pupils attending the academic track have consistently high aspirations, regardless of their social background, we see pronounced social differences within the nonacademic track. Even though both social groups show declining rates of aspirations for higher-education eligibility, the decline is much more pronounced for pupils with low-educated parents. While among the pupils with highly educated parents about 88% still hold aspirations for higher-education eligibility in grade 9, the respective share is as low as 67% for pupils with low-educated parents. Since the confidence bands do not overlap, we can assume that this difference is statistically significant at the 5% level.
To corroborate the robustness of our findings, we conducted a large number of additional sensitivity checks. First, we repeated our analyses with imputed data using multiple imputation with chained equations (Azur et al. 2011). While we cannot reproduce all statistics because the khb command is not fully compatible with imputed data, the main patterns of our findings are highly similar and lead to the same conclusions. In the imputed models, we always observe a strong reduction of the main effects through the mediators, just as in the nonimputed models. Hence, we believe that selective dropout of students is not a main driver behind our findings. Second, we tested whether the change of individual competences is another confounder. Because of the nature of the data, we can add this variable only in the wave 5 models since there are no test data available in wave 2. For these models, we computed the relative change in ability ranks for each pupil. For example, if a pupil has a relative rank of percentile 70 in wave 1 and a percentile of 75 in wave 5, we can conclude that this pupil has improved his or her relative rank over time. However, adding this variable as a further control variable does not affect the results or conclusions in any substantive way.
Finally, when we focus on realistic instead of idealistic aspirations, we argued above that the effects might be even stronger. Our empirical tests (cf. Figs. 5 and 6) are in line with this expectation. When repeating the analyses from Table 2 (left panel, grade 6), we observed a difference of 27 percentage points before adding the mediators and a difference of 1.6 percentage points afterwards. This is a reduction of about 94%, which underscores that effects become more pronounced when realistic aspirations are investigated instead of realistic ones.