Before revision:  Our procedure delivers sharp bounds for the identified set of counterfactuals (i.e. without parametric assumptions about the distribution of unobservables) as the neighborhoods become large . Over small neighborhoods , we relate our procedure to a measure of local sensitivity which is further characterized using an influence function representation. We provide a suitable sampling theory for plug-in estimators and apply our procedure to models of strategic interaction and dynamic discrete choice.
After revision:  Our procedure delivers sharp bounds for the identified set of counterfactuals over large neighborhoods and has connections with local approaches to sensitivity analysis over small neighborhoods. We propose plug-in estimators and apply our procedure to models of strategic interaction and dynamic discrete choice.