Abstract. 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.

Abstract. 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.

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In finance there is growing interest in quantile regression with the particular focus on value at risk and copula models. In this paper, we first present a general interpretation of quantile regression in the context of financial markets. We then explore the full distributional impact of factors on returns of securities and find that factor effects vary substantially across quantiles of returns. Utilizing distributional information from quantile regression models, we propose two general methods for return forecasting and portfolio construction. We show that under mild conditions these new methods provide more accurate forecasts and potentially higher value-added portfolios than the classical conditional mean method.return forecast, quantile regression, portfolio construction,

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