Treatment response with social interactions: Partial identification via monotone comparative statics

This paper studies (nonparametric) partial identification of treatment response with social interactions. It imposes conditions motivated by economic theory on the primitives of the model, that is, the structural equations, and shows that they imply shape restrictions on the distribution of potential outcomes via monotone comparative statics. The econometric framework is tractable and allows for counterfactual predictions in models with multiple equilibria. Under three sets of assumptions, we identify sharp distributional bounds on the potential outcomes given observable data. We illustrate our results by studying the effect of police per capita on crime rates in New York state.