We consider the local linear GMM estimation of functional coe cient 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.
Discrete variables, Endogeneity, Heterogeneity, Functional coefficient, Local linear GMM estimation, Optimal instrumental variable, Schooling
Econometrics | Economics | Education
Journal of Business and Economic Statistics
Taylor and Francis
SU, Liangjun; MURTAZASHVILI, Irina; and ULLAH, Aman.
Local Linear GMM Estimation of Functional Coefficient IV Models with Application to the Estimation of Rate of Return to Schooling. (2013). Journal of Business and Economic Statistics. 31, (2), 184-207. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/1435
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