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

– 225 –whereas the ratio <strong>of</strong> female peers does not appear influential. Among the cantonal controls,once again, a higher ratio <strong>of</strong> poor people and more population exhibit a performance decliningimpact for an average student. In contrast to reading, the share <strong>of</strong> residents with at least a highschool degree and the share <strong>of</strong> Protestants are strongly associated with higher test scores.Similar results are obtained in the quantile regressions. For a detailed description <strong>of</strong> theempirical results for the OLS and the quantile regressions, see the Appendix on mathematics,table 9.2Figure 3 illustrates the development <strong>of</strong> the impact <strong>of</strong> direct democracy over the entireconditional test score distribution in the reduced form. Again, the dashed line depicts the OLScoefficient <strong>of</strong> about +2.2, while the continuous line represents the coefficients for allquantiles. <strong>The</strong> confidence interval always crosses the 0-line, indicating that the coefficientnever reaches significance at the 5% level. In contrast to the results for reading, however, aclear upward trend <strong>of</strong> the coefficient is observable, starting with a negative value <strong>of</strong> -6 in thelowest percentile and reaching about +8 in the 90th percentile. <strong>The</strong> H 0 -hypothesis <strong>of</strong> jointlyequal coefficients in the estimated quantiles, however, is not rejected 257 .<strong>The</strong> Structural Form<strong>The</strong> OLS estimate in the structural form reveals a significant performance enhancing effect ontest scores in the structural form (at the 5% level; see table 9.1). <strong>The</strong> size <strong>of</strong> this coefficient isabout 11.6, which in a canton with the theoretically highest level <strong>of</strong> direct democracy <strong>of</strong> 6index points would translate into a sizeable effect <strong>of</strong> about 70 adjusted test score points,almost as large as the standard deviation <strong>of</strong> 80 points in mathematics.<strong>The</strong> quantile regression estimates reveal different sizes <strong>of</strong> impact and varying significancelevels (see table 9.3). In the lower portions <strong>of</strong> the conditional test score distribution, the size<strong>of</strong> the coefficient takes on the small, and thus insignificant, values <strong>of</strong> 1.1 and 5.3. In the 50th,75th, and 90th quantiles, however, direct democracy affects student performanceconsiderably, with maximum test score points <strong>of</strong> 64.5, 76.8, and 148.8 (significant at the 5%,5%, and 0.1% levels, respectively). A test <strong>of</strong> joint nonsignificance reveals that the estimatesare jointly significant at the 1% level, meaning that a test for equality <strong>of</strong> coefficients shouldreveal whether the seeming differences in sizes are statistically significant. <strong>The</strong> test shows257 A pairwise Wald test for equality <strong>of</strong> coefficients does show that some <strong>of</strong> these differences are statisticallysignificant, particularly between the lowest estimated quantile (the 10th) and the two highest (the 75th andthe 90th, respectively). Both, however, are only significant at the 10% level.