Identification of causal intensive margin effects by difference-in-difference methods

This paper discusses identification of causal intensive margin effects. The causal intensive margin effect is defined as the treatment effect on the outcome of individuals with a positive outcome irrespective of whether they are treated or not (always-takers or participants). A potential selection problem arises when conditioning on positive outcomes, even if treatment is randomly assigned. We propose to use difference-in-difference methods - conditional on positive outcomes - to estimate causal intensive margin effects. We derive sufficient conditions under which the difference-in-difference methods identify the causal intensive margin effect in a setting with random treatment.