Given a set of baseline assumptions, a breakdown frontier is the boundary between the set of assumptions which lead to a specific conclusion and those which do not. In a potential outcomes model with a binary treatment, we consider two conclusions: First, that ATE is at least a specific value...

A breakdown frontier is the boundary between the set of assumptions which lead to a specific conclusion and those which do not. In a potential outcomes model with a binary treatment, we consider two conclusions: First, that ATE is at least a specific value (e.g., nonnegative) and second that the...

One of the perceived advantages of difference-in-differences (DiD) methods is that they do not explicitly restrict how units select into treatment. However, when justifying DiD, researchers often argue that the treatment is "quasi-randomly" assigned. We investigate what selection mechanisms are...