As covariates we used gender, age, mothers and father’s education, the highest value of the International Socio-Economic Index among parents, number of books at home, and grade. Usually, researchers also control for immigrant status; however, there is a negligible number of migrants in the Polish sample. Missing data were imputed using the multiple imputation approach (Royston 2004). Results without any imputation were qualitatively similar, while less precise because of smaller sample sizes.

# <u>Estimates of score change for students in different tracks</u>

Reweighting produces factual and counterfactual distributions, which are balanced in observable characteristics and can be compared across survey cycles. However, it is clear that the performance of Polish students could change for other reasons besides the introduction of comprehensive schooling. The education reform of 1999/2000 modified not only school structure but also curriculum, teacher compensation and many other things. Thus, the test score change cannot be solely attributed to the replacement of old-type tracks in secondary schools by lower secondary schools for 15-year-olds.

To deal with that, our strategy is to assess how the extension of obligatory comprehensive education by one year affected the performance of students in different tracks. More specifically, we are interested in whether students who were in old-type vocational schools in 2000 would have similar scores in 2003 or 2006 in newly established lower secondary comprehensive schools. That could be investigated by matching vocational school students from 2000 with their counterparts in 2003 and 2006. This way an estimate of performance change for students sharing characteristics common in each track can be obtained. Having that, we look at the differential impact of the reform for students who were in different tracks in 2000. The change for vocational school students minus the change for general (or mixed vocationalgeneral) school students could be attributed mainly to the introduction of lower secondary schools. The point is that without the reform 15-year-old students in vocational schools would not have the opportunity to study in general programs; however, students in other tracks had this opportunity despite the reform. Students from general tracks can serve as a control group and the difference in a simulated score change for them and for the former vocational schools students could be attributed to the postponing of vocational education by one year.

Our approach to estimate the differential score change is similar to the differences-indifferences (DD) method. This method compares outcome change in the group of interest (treatment group) with similar change in the control group. DD estimates of treatment effect take into account trends in the whole population that equally affect both groups. In our case, we calculate the difference between the achievement of students in vocational schools in 2000 and similar students in 2003 or 2006, and we subtract it from the difference between scores of secondary general track students in 2000 and their counterparts in 2003 or 2006. Assuming that we are able to match similar students across waves of the PISA study, we can estimate how the reform affected students who without the reform would still be in vocational schools.

To define it formally, we use treatment evaluation nomenclature (see Lee 2005). The treatment is defined as being a 15-year-old student in vocational secondary school ( _szkoła zawodowa_ ) in 2000. The control group is defined as 15-year-olds in general ( _liceum ogólnokształcące_ ) or mixed general-vocational ( _technikum_ ) secondary schools. We have to construct counterfactual groups of students from 2003 or 2006 samples based on their observable characteristics. A crucial assumption is that these observable characteristics constitute the main 11