Instrumental variable methods for recovering continuous linear functionals

This paper develops methods for estimating continuous linear functionals in nonparametric instrumental variable problems. Examples of such functionals include consumer surplus and weighted average derivatives. The estimation procedure is robust to a setting where the underlying model is not identified but the linear functional is. In order to attain such robustness, it is necessary to employ a partially identified nuisance parameter. We address this problem by consistently estimating a unique element of the identified set for nuisance parameters which we then use to construct a asymptotically normal estimator for the desired linear functional.