We suggest two nonparametric approaches, based on kernel methods and orthogonal series, respectively, to estimating regression functions in the presence of instrumental variables. For the first time in this class of problems we derive optimal convergence rates, and show that they are attained by...

In the last decade a growing body of research has studied inference on partially identified parameters (e.g., Manski, 1990, 2003). In many cases where the parameter of interest is realvalued, the identification region is an interval whose lower and upper bounds may be estimated from sample data....