Inference in Nonparametric Instrumental Variables with Partial Identification

This paper develops methods for hypothesis testing in a nonparametric instrumental variables (IV) setting within a partial identification framework. I construct and derive the asymptotic distribution of a test statistic for the hypothesis that at least one element of the identified set satisfies a conjectured restriction. This procedure can be used to test for features of the model that may be identified even when the true model is not. This framework can also be employed to construct confidence regions for functionals of the elements of the identified set, such as consumer surplus and price elasticity of demand at a point. I apply this procedure to study Engel curves for gasoline and ethanol in Brazil. For both ethanol and gasoline I fail to reject that there are log-linear Engel curves in the identified set. In addition, I derive confidence regions for the level and slope of the Engel curves at the sample average as well as for the compensated variation associated with a price change in gasoline.