In order to inspect the possible contribution of schools to skill production, we replace the school fixed effects with a proxy for school performance (SKILL −isc,G6 ) in a variant of the model. This measure is computed by taking the leave-out mean of the sixth-grade skill scores of a school in a certain year.11 In addition, we include a wide range of student characteristics (Zisc,G6): students’ age, sex, and migration background, household type, and family size.12 Last, we include year fixed effects (δc,G6) in the model, which control for differences between years in sixth-grade performance. ϵisc,G6 is the idiosyncratic error term. In this model, coefficient β1 represents the estimate of the relationship of sixth-grade skill level and its initial counterpart in an earlier grade. β2 quantifies the association between the student’s skill level and parental education. Given that our model takes the student’s initial skill level into account, the coefficient captures the extent to which parental education relates to the student’s skill advancement throughout primary education. In other words, it estimates advancement differences throughout primary education of students with varying levels of parental education. We estimate changes in the disparities by sex and migration background in a similar way by analyzing the respective coefficients of these variables. 11If there are less than ten observations from one school in one cohort, we do not include this school performance measure. 12We also add a control for repeating a grade and we include a dummy to control for the delayed end-of-term test in 2020. 57
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