reference groups for students tested in 2000. We match using propensity score _P_<sup>_2000_</sup> = _P_ ( _T_ =2000| _X_ ), reflecting the propensity to be in the PISA 2000 sample. Two propensity scores need to be estimated. One measuring a propensity of being in a vocational school in 2000 for students tested in 2003 or 2006, and the other for being in a general (or mixed vocationalgeneral) school in 2000 for students tested in 2003 or 2006. Thus, we have the propensity score for treated units (vocational school students)<sup>_P_</sup> _T_ 2000 and the propensity score for controls _PC_ 2000 (students in other tracks), both reflecting the propensity of being sampled in 2000 for students sampled in 2003 or 2006.

Let us now define _Y_<sup>_1_</sup> as the score of students separated into tracks in secondary schools in 2000 and _Y_<sup>_0_</sup> as the score for students tested in 2003 or 2006. Now, the DD estimator could be defined by: 1 1 In this equation _E_ ( _Y_ | _D_  )1 and _E_ ( _Y_ | _D_  0) are directly observed in the data, but 0 2000 0 2000 _E_ ( _Y_ | _PT_ , _D_  )1 and _E_ ( _Y_ | _PC_ , _D_  0) have to be constructed from 2003 or 2006 PISA samples using propensity scores. We first estimate the performance change for students in each type of secondary school in 2000 and their matched counterparts in 2003 or 2006. Then we compare these performance changes across students from different tracks. The difference between performance gains of students in the former vocational track and for students in other tracks is the differences-in-differences estimator of the impact of abolishing the vocational curriculum for 15-year-olds. This estimator reflects the causal impact of the reform under the crucial assumption that the score change for students in the general track would be the same without the reform. This assumption is not directly testable, however. For general track students the curriculum did not change in a fundamental way, while other changes affected them as much as they did other students.

Propensity scores were estimated using logit regressions. Two kinds of propensity score matching were then employed: nearest neighbor matching 1-to-1 matching and kernel matching. The first method matches to each treated observation one control observation with the closest value of the propensity score. The kernel method constructs values for matched counterparts by weighting control observations by their proximity in the propensity score to the treated observation, using a kernel function (we used Epanechnikov kernel with bandwidth 0.6; see Becker and Ichino 2002 for details of the Stata procedure used). In both methods a common support restriction was imposed, which means that if propensity score distribution does not overlap at the bottom or top of the distribution, then observations with extreme propensity score values will not be considered. This restriction rarely affects the results in our case, but guarantees that proper matches were drawn from the 2003 and 2006 samples.

Finally, we need to decide which covariates to balance across surveys or use to draw counterparts of 2000 students in different tracks from 2003 and 2006 data. An obvious limitation here is availability of control variables which are identically defined across waves of PISA. Fortunately, PISA collects crucial variables reflecting student socio-economic background, including the HISEI index (highest of mother or father international socio-economic index), mother and father ISCED education level, and number of books at home; in addition, student gender, age, grade they attended at the time of PISA survey, and family structure, were also used as covariates. Some of these indicators, mainly HISEI index, parental education levels, and 13