Semiparametrically Efficient Estimation of Conditional Instrumental Variables Parameters

In this paper, I propose a set of parameters designed to identify the slope of structural relationships based on a combination of conditioning on covariates and the use of an exogenous instrument. After giving structural interpretations to these parameters in the context of specific semiparametric models, I derive their efficient influence curves in a fully nonparametric context as well as under imposition of restrictions on the instrument. These influence curves give the semiparametric efficiency bounds for regular asymptotically linear estimators of the parameters and allow the construction of asymptotically efficient estimators. Monte Carlo experiments finally demonstrate the good finite sample performance of such estimators.