Effient Estimation of Partially Varying Coefficient Instrumental Variables Models

We study a new class of semiparametric instrumental variables models with the structural function represented by a partially varying coefficient functional form. Under this representation, the models are linear in the endogenous/exogenous components with unknown constant or functional coefficients. As a result, the ill-posed inverse problem in a general nonparametric model with continuous endogenous variables does not exist under this setting. Efficient procedures are proposed to estimate both the constant and functional coefficients. Precisely, a three-step estimation procedure is proposed to estimate the constant parameters and the functional coefficients, we use the partial residuals and implement a nonparametric two-step estimation procedure. We establish the asymptotic properties for both estimators, including consistency and asymptotic normality. More importantly, it is also demonstrated that the constant parameters estimators are efficient, e.g., square root of n-consistent, and the functional coefficient estimators are oracle. A consistent estimation of the asymptotic covariance for both estimators is also provided. Finally, the high practical power of the resulting estimators is illustrated via both a Monte Carlo simulation study and an application to returns to education.