Sieve Instrumental Variable Quantile Regression Estimation of Functional Coefficient Models

In this paper, we consider sieve instrumental variable quantile regression (IVQR) estimation of functional coefficient models where the coefficients of endogenous regressors are unknown functions of some exogenous covariates. We approximate the unknown functional coefficients by some basis functions and estimate them by the IVQR technique. We establish the uniform consistency and asymptotic normality of the estimators of the functional coefficients. Based on the sieve estimates, we propose a nonparametric specification test for the constancy of the functional coefficients, study its asymptotic properties under the null hypothesis, a sequence of local alternatives and global alternatives, and propose a wild-bootstrap procedure to obtain the bootstrap p-values. A set of Monte Carlo simulations are conducted to evaluate the finite sample behavior of both the estimator and test statistic. As an empirical illustration of our theoretical results, we present the estimation of quantile Engel curves.