Abstract for Aman Ullah
Title: Local Linear GMM Estimation of Functional Coefficient IV Models with an Application to
Estimating the Rate of Return to Schooling (Liangjun Su, Irina Murtazashvili, Aman Ullah)
School of Economics, Singapore Management University (ljsu@smu.edu.sg)
Department of Economics, Drexel University, Philadelphia (im99@drexel.edu)
Department of Economics, University of California, Riverside (aman.ullah@ucr.edu)
Abstract: We consider the local linear GMM estimation of functional coefficient models with a
mix of discrete and continuous data and in the presence of endogenous regressors. We establish
the asymptotic normality of the estimator and derive the optimal instrumental variable that
minimizes the asymptotic variance-covariance matrix among the class of all local linear GMM
estimators. Data-dependent bandwidth sequences are also allowed for. We propose a
nonparametric test for the constancy of the functional coefficients, study its asymptotic
properties under the null hypothesis as well as a sequence of local alternatives and global
alternatives, and propose a bootstrap version for it. Simulations are conducted to evaluate both
the estimator and test. Applications to the 1985 Australian Longitudinal Survey data indicate a
clear rejection of the null hypothesis of the constant rate of return to education, and that the
returns to education obtained in earlier studies tend to be overestimated for all the work
experience.
JEL Classifications: C12, C13, C14
Key Words: Discrete variables; Endogeneity; Heterogeneity; Functional coefficient; Local linear
GMM estimation; Optimal instrumental variable; Schooling.