A Bootstrap Procedure for Inference in Nonparametric Instrumental Variables

This paper proposes a consistent bootstrap procedure for the test statistic of Santos (2007). The derived bootstrap allows for inference in partially identified nonparametric instrumental variables models. It can be employed to test whether at least one element of the identified set satisfies a conjectured restriction. Possible applications include testing for shape restrictions such as economies of scale and scope as well as building confidence regions for functionals on the identified set, such as the level of the function and its derivative at a point. The obtained procedure is also applicable to a wider class of models defined by a conditional moment restriction, as in Newey & Powell (2003) and Ai & Chen (2003).