Quantile regression methods for recursive structural equation models

Abstract

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.

Nonparametric instrumental variables estimation of a quantile regression model

“…Estimators of linear quantile regression models with endogenous right-hand side variables are described by Amemiya (1982), Powell (1983), Chen and Portnoy (1996), Chernozhukov and Hansen (2005a), and Ma and Koenker (2006). Chernozhukov and Hansen (2004) and Januszewski (2002) use such models in economic applications.…”

Tax burden, government expenditures and income distribution in Brazil

“…Ma and Koenker (2006) show that the structural estimator ) , ( Table 3 and Table 4 for 1991 and 2000 respectively, for all deciles (columns 2-9). The results for the second stage structural quantile estimatives containing all variables are presented in Table A in the Appendix.…”

“…Chesher (2003Chesher ( , 2004 has considerably expanded the scope of quantile regression methods for structural models. Ma and Koenker (2006) have considered estimators based on the Chesher identification strategy.…”

“…To briefly describe this control variate approach, proposed by Ma and Koenker (2006), consider the model with conditional quantile functions: where the function )) 0 ( (…”

Testing exogeneity in nonparametric instrumental variables identified by conditional quantile restrictions

“…Koenker (2005) and references therein describe methods for and applications of quantile regression when the explanatory variables are exogenous. Estimators and applications of linear quantile regression models with endogenous explanatory variables are described by Amemiya (1982), Powell (1983), Chen and Portnoy (1996), Januszewski (2002), Hansen (2004, 2006), Ma and Koenker (2006), Blundell and Powell (2007), Lee (2007), and Sakata (2007). Nonparametric methods for quantile regression models are discussed by Chesher (2003Chesher ( , 2005Chesher ( , 2007; Chernozhukov and Hansen (2004; Chernozhukov, Imbens, and Newey (2007); Horowitz and Lee (2007); and Pouzo (2009, 2012).…”