  Nonparametric Instrumental Variables (NPIV) analysis is based on a
conditional moment restriction. We show that if this moment condition is even
slightly misspecified, say because instruments are not quite valid, then NPIV
estimates can be subject to substantial asymptotic error and the identified set
under a relaxed moment condition may be large. Imposing strong a priori
smoothness restrictions mitigates the problem but induces bias if the
restrictions are too strong. In order to manage this trade-off we develop a
methods for empirical sensitivity analysis and apply them to the consumer
demand data previously analyzed in Blundell (2007) and Horowitz (2011).
