Appendix 2. Robustness checks
Focusing on the robustness checks, in Table 6 the sample has been divided according to the tertile of the economic, social and cultural status index provided by PISA 2015 (ESCS)Footnote 22 –high/medium/low level–. As can be inferred from the results, weekly instruction time does not seem to affect academic achievement in any of the levels of ESCS, with the exception of the high ESCS tertile, but the significance of this coefficient (p-value of 0.085) and its quantitative amount in the context of PISA scale of scores does not seem to indicate an effect of weekly instruction time on academic achievement.Footnote 23 Thus, the null effect obtained in the base model is not the consequence of a compensation of different effects for each ESCS tertile.
The robustness check presented in Table 7 was performed by dividing the Spanish AACC in three groups according to their relative at risk of poverty rate in 2015 (compared to all the AACC), using at risk of poverty rate data provided by INE (2017) for all AACC in 2015, in order to check whether the effect of instruction time per week on children’s academic achievement could be different depending on the relative at risk of poverty group to which AACC belong. Results have corroborated the lack of effect of weekly instruction time on the three groups, which reinforces our main results and indicates that this lack of effect is not the result of a compensation of considering all the three groups in the same regression.
The next robustness check aims at analysing whether grouping students at school according to their ability could influence the results obtained regarding weekly instruction time, in the sense that the effect of weekly instruction time may be different for these groups. Hence, not considering this grouping could entail compensating the differential effect of weekly instruction time on children’s academic achievement in each grouping option, obtaining a lack of effect. Specifically, this time difference between groups could be due to the fact that, for example, children in higher ability groups may be receiving greater amounts of instruction time per week than the rest to take advantage of their better skills or, on the contrary, low ability children may be receiving higher amounts of weekly instruction time to compensate their lack of ability. To perform this check we have divided the sample according to the information provided by the head teacher regarding this grouping; specifically, if the school applies any of these criteria: grouping students by ability into different classes, grouping students by ability within their classes or not grouping students by ability. If we perform a descriptive analysis, we see that the three grouping options present similar amounts of weekly instruction time, so it seems that grouping would not influence a priori the lack of effect of weekly instruction time on academic achievement.
In addition, it is important to highlight that the estimations of this robustness check have been performed using students’ self-reported weekly instruction time, instead of the school average of weekly instruction time. We can thus account for the fact that the differences in the reported amounts of instruction time per week by students may be caused by their grouping. The results for this robustness check are presented in Table 8, and show the lack of effect of weekly instruction time for the three grouping options. This reinforces the argument in favour of averaging students’ self-reported instruction time per week by school in order to reduce reporting errors due to students’ difficulties in recalling it or because of absenteeism. Although we cannot check for absenteeism, as previously argued, this should not affect our results, since attendance is compulsory in secondary education.
The robustness check presented in Table 9 is based on the assumption that weekly instruction may have a nonlinear effect (due to children’s decreasing attention; Bunce et al. 2010) on students’ academic achievement,Footnote 24 so this lack of effect may be due to a specification error. We have specified this nonlinear effect by means of two different strategies: using a squared term for weekly instruction time and its division into three categorical variables according to its distribution. In both cases results hold, so the lack of effect obtained would not be caused by a misspecification of the functional form of the model.
Finally, Table 10 presents the results related to the interaction of weekly instruction time with some measures of school quality provided by the head teacher in the school questionnaire. Specifically, the interacted school quality variables are all derived variables and indexes created by the OECD from other variables in the school questionnaire.Footnote 25 These are: shortage of educational material, shortage of educational staff, proportion of teachers with an ISCED level 5a bachelor qualification, proportion of teachers with an ISCED level 5a masters qualification, proportion of teachers with an ISCED level 6 qualification, student behaviour hindering learning and teacher behaviour hindering learning. The results obtained may be indicating that any of these school quality variables condition the lack of effect of weekly instruction time on children’s academic achievement. Although shortage of educational material is weakly significant, its effect is almost zero in quantity; the same happens with the student behaviour hindering learning index.