Before revision:  Unfortunately, if the researcher allows for an arbitrarily small failure of instrumental validity then the failure of such a smoothness condition is generally not testable and in fact one cannot identify any upper bound on the magnitude of the failure. To address these problems we propose an alternative method in which the structural function is treated as partially identified .
After revision:  However, we show that in general the smoothness assumptions cannot be confirmed empirically. In response, we treat the structural function is treated as partially identified .