Local Linear GMM Estimation of Functional Coefficient IV Models With an Application to Estimating the Rate of Return to Schooling
提出一种局部线性GMM方法估计含内生变量的函数系数模型，推导了最优工具变量，并构造了检验系数是否恒定的非参数检验。应用于1985年澳大利亚纵向调查数据，发现教育回报率并非恒定，且以往研究可能高估了各工作经验水平下的回报。
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.