Semiparametric instrumental variables estimation

This paper considers a semiparametric regression model in which the error term is correlated with the nonparametric part. A technical difficulty of this semiparametric regression model is that we cannot eliminate the nonparametric part in the two-step estimation procedure of a typical semiparametric regression model. Yet, we can still obtain a semiparametric estimator, called a semiparametric instrumental variables (SIV) estimator, with consistency and asymptotic normality if there exist two sets of instrumental variables satisfying an orthogonality condition. An empirical example of the SIV estimation procedure is discussed.