Partial identification of treatment response under complementarity and substitutability

This paper studies partial identification of treatment response when the outcome of an agent is affected heterogeneously by the outcomes, and consequently the treatment statuses, of other agents in the economy. When the sign of the interactions is predicted by the theory, we propose a general approach that allows the use of comparative statics under monotonic treatment response. The paper provides new theoretical results on how the heterogeneous fixed points theorem can be applied to microfound sharp bounds on the distribution of potential outcomes. Through an empirical application we show that our method can produce narrow and meaningful bounds for the response to central bank funding of credit to the real economy, under full endogeneity of, and heterogeneous interdependence among, banks' balance sheet items.