Structural Quantile Regression

Quantile Regression Methods for Recursive Structural Equation Models Lingjie Ma and Roger Koenker

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 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 paper appeared in J. of Econometrics, 2006, 471--506. A preprint of the paper is available in pdf. The R code used for the simulations in the paper is available as a tar archive.

Comments are of course always welcome.