| This dissertation consists of two essays. The first essay considers the quartile regression methods for recursive structural equation models. Two classes of quantile regression estimation methods for the recursive structural equation models of Chesher (2003) are investigated. A class of weighted average derivative estimators based directly on the identification strategy of Chesher is contrasted with a new control variate estimation method. The latter imposes stronger restrictions achieving an asymptotic efficiency bound with respect to the former class. An application of the methods to the study of the effect of class size on the performance of Dutch primary school students shows that (i) reductions in class size are beneficial for good students in language and for weaker students in mathematics, (ii) larger classes appear beneficial for weaker language students, and (iii) the impact of class size on both mean and median performance is negligible.;The second essay explores the heterogeneous peer effects in Dutch primary schools by employing a series of percentiles of classmates achievement distribution as the peers outcome measurement and the quantile regression estimation method. It is found that better performance by lower attainment peers has a significant positive effect on performance of all students in both language and math. This effect is most pronounced at the lower conditional quantiles of the performance distribution, but persists even into the upper tail. In contrast, better performance by high-achieving classmates, has a somewhat more modest effect on language performance, while for math, it has little or no effect on weaker students, but does have strong positive effect on students in the upper tail of the conditional distribution. The findings imply that mixing diverse students may be an efficient policy for the improvement of language performance, tracking appears desirable for the improvement of students' math performance. |
