Heterogeneity and Non-Constant Effect in Two-Stage Quantile Regression

Heterogeneity in how some independent variables affect a dependent variable has become a major topic of study in econometrics and statistics. In this respect, this paper addresses the question of constant versus non-constant effect through quantile regression modeling. For linear quantile regression under endogeneity, it is often believed that the fitted- value setting (i.e., replacing endogenous regressors with their exogenous fitted-values) implies constant effect (that is: the coefficients of the covariates do not depend on the considered quantile, except for the intercept). Here, it is shown that, under a weakened instrumental variable restriction, the fitted-value setting can allow for non-constant effect, even though only the constant-effect coefficients of the model can be identified. An application to food demand estimation in 2012 Egypt shows the practical potential of this approach.