strong). It is very implausible that errors in the two scores are correlated. For instance, both tests are administered on a different day with no overlapping items, which minimizes day-specific errors (e.g., variability in external distractions, children’s energy level, etc.) and eliminates familiarity-related measurement error. We may not completely eliminate all potential sources of measurement error. Therefore, we should interpret our findings as lower bound estimates. 3.4.3 Sixth-grade achievement gap We then continue to examine sixth-grade achievement gaps between various groups and the extent to which they are formed before and during primary education. These gaps may arise in early childhood before formal schooling begins or during schooling, as children’s backgrounds influence their educational development and learning. Our empirical strategy identifies the contributions of both sources to the sixth-grade achievement gap. First, we inspect the overall sixth-grade achievement gap using a similar model as model 3.3, but where we do not include an independent skill variable. In this model, the estimate for a specific student characteristic (e.g., β2 for parental education) represents the achievement gap of this group compared to the reference category. Next, we take the ratio of the learning advancement difference among groups to the total sixth-grade achievement gap. This ratio indicates how much a student’s background helps or hinders their educational development during primary school, relative to the total achievement gap with peers at the end of primary education. 59
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