These results, however, demonstrate the contemporaneous positive relationship between varying skills, suggesting that if students succeed in augmenting one of their skills, this increase is associated with an increase in the other skills. Numerous potential explanations may underpin this particular finding. On the one hand, these skills may complement each other. Strong language comprehension skills are essential for understanding mathematical problems. With respect to testing, this is even more important if textual problems are employed to assess math skills. On the other hand, skills may require other foundational skills, such as problem-solving skills, critical thinking, logical reasoning, and analytical thinking. Students who manage to develop in one of these areas are likely to benefit from this in other domains. This also holds for study habits, motivation and received parental support, which are beneficial for success in all skills. On top of these potential explanations, also test formats, teachers, and schools may have a functional role in the relationship between multiple skills. 4.4.2 Results of the panel VAR model While the contemporaneous relationships are informative, they fail to capture the time dimension in the interaction between skills. To investigate dynamic interdependencies between reading, spelling, and math skills, we estimate the panel VAR(1) model, as described in Section 4.3.2.13 Table 4.3 summarizes the estimation results for this panel VAR model, where the column variables are regressed on the lags of the row variables. 13We also test whether reading, spelling, and math skills Granger-cause each other with a Granger causality test. Table C.1 in the appendix shows that we find bidirectional Granger causality between reading, spelling, and math skills. 95
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