The Impact of Direct Democracy on Society - Universität St.Gallen

– 215 –weighted likelihood estimate <strong>of</strong> a student's performance that is a weighted average <strong>of</strong>correctly answered responses, with the weights reflecting the level <strong>of</strong> difficulty <strong>of</strong> thequestion (HAMBLETON and SWAMINATHAN 1985, WARM 1989). <strong>The</strong> matching <strong>of</strong> schools andstudents also makes it possible to construct classroom-based peer variables.<strong>The</strong> national study sample is preferred over the original PISA sample for two reasons: first, itcovers almost all cantons 245 ; second, the administration <strong>of</strong> the questionnaires to completeclasses instead <strong>of</strong> age groups allows the construction <strong>of</strong> peer group/class mate predictors.Moreover, even though there exists an extension ('the French sample') to the national studydataset that covers only French-speaking regions 246 , the national study oversampled studentsfrom the German-speaking cantons <strong>of</strong> Bern, Zürich, and St. Gallen. <strong>The</strong>refore, to prevent anoverrepresentation, both datasets are merged and all observations with missing values deleted.In a second step, to prevent endogeneity in the peer group variables, all students who attendedtest language classes with less than 20 peers are also excluded. <strong>The</strong> mean <strong>of</strong> the reading testscore was originally normalized at 500, with a standard deviation <strong>of</strong> 90 for the whole nationaldataset, but because <strong>of</strong> the deletion process, the new mean is about 530, with a standarddeviation <strong>of</strong> approximately 80 based on a final sample <strong>of</strong> 3,411 observations. For moredescriptive statistics also for the other two test subjects, see tables 11.3 and 11.4 <strong>of</strong> theAppendix.3.4 MethodologyBoth the reduced and the structural model are estimated using two different econometricmethods. <strong>The</strong> first approach uses ordinary least squares (OLS) and corrects the standard errors<strong>of</strong> the coefficients for heteroscedasticity. It also assumes that students who attend identicalschools share common factors both at the school and cantonal level – for example, condition245 No observations exist from the cantons Appenzell Innerrhoden and Uri. To the author's knowledge, there isno educational institute providing a ninth-grade education in the first canton.246 <strong>The</strong> extension dataset differs from the national sample solely in that entire classes were administered thequestionnaires, whereas in the national sample, students were drawn randomly from selected classes. <strong>The</strong>original dataset included 4,833 students in 105 schools belonging to both samples. For the data, thecodebooks, and further information, see SIDOS 2000 (2004). A more detailed description <strong>of</strong> data sources forthe determinants <strong>of</strong> education can be found in the Appendix (table A.7). This table also provides informationon the chosen base categories. <strong>The</strong> procedure <strong>of</strong> normalization follows that for the international PISA sample(FERTIG 2003).