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

– 223 –With respect to the cantonal predictors, a similar pattern to the OLS results <strong>of</strong> the structuralmodel is observed. Moreover, the results are also similar to those obtained in the reducedmodel that show the input factors at the school level to be quite uncorrelated with thesociodemographic determinants at the cantonal level. As in the reduced model, theconvincingly significant coefficients are those for the share <strong>of</strong> Protestants, the logarithm <strong>of</strong>the cantonal population, and the share <strong>of</strong> poor people, with the latter experiencing a decline insignificance from the 0.1% level in the reduced model down to the 5% or 10% level in thestructural model for almost the entire distribution. This finding indicates that the strongnegative impact <strong>of</strong> poor persons observed in the reduced model must occur through thecantonal budget transmission channel, probably because politicians face a trade-<strong>of</strong>f betweensupporting needy persons and financing cantonal education. <strong>The</strong> identical observation holdstrue for the cantonal population, which was strongly significant in the reduced model but lostconsiderable significance in the structural model, particularly for the lower and middlequantiles. This finding can again be interpreted to mean that the impact <strong>of</strong> the cantonal sizefor lower and middle quantiles obviously occurs through financial channels related to schoolexpenditure. In contrast, for the higher quantiles, a different transmission channel seems to beat work for this effect not filtered out in the model specification.Several robustness checks assess whether the observed influence <strong>of</strong> direct democraticinstitutions in both forms depends on the inclusion or exclusion <strong>of</strong> particular controls or issensitive to a potentially unsolved endogeneity problem. In general, the results <strong>of</strong> the originalmodel specification are insensitive to slight variations in the specification, but the exclusion<strong>of</strong> peer effects appears to cause an omitted variable bias. In addition, imputation <strong>of</strong> the medianand admission <strong>of</strong> class sizes <strong>of</strong> ten or more students, which increases the number <strong>of</strong>observations to roughly 9,000, do not alter the main findings. In the reduced form, directdemocracy again shows a performance lowering effect, which disappears in the structuralform.5 Estimation Results for Mathematics and Natural Science<strong>The</strong> reduced and structural forms are also tested for mathematics and natural science usingboth OLS and quantile regression methods. <strong>The</strong> measure <strong>of</strong> peer performance, thequalification <strong>of</strong> teachers, and the shortage <strong>of</strong> teachers are also adjusted according to the twosubjects taught. In addition, classes with less than 20 students are eliminated on the basis <strong>of</strong>