Trading Scope for Credibility in Difference-in-Differences

Abstract

When parallel trends fails for some treated cohorts but not others, the average treatment effect on the treated (ATT), an average over all of them, is exactly the target that becomes hard to recover. We propose changing the estimand rather than defending it. The credible-subpopulation local ATT (LATT) is the effect for the subpopulation of cohorts whose parallel trends is credible, and it is point-identified under parallel trends for the selected cohorts alone, a weaker requirement that can hold when the ATT's fails. It is estimated by reweighting standard group-time effects toward those cohorts, and paired with honest sensitivity bounds on the residual violation that a pre-trend screen cannot rule out. The method's advantage grows with how informative pre-trends are about post-treatment violations, as simulations confirm. In an application, a significantly positive pooled estimate of the shale boom's effect on local house prices proves to rest on cohorts already trending before onset, and the credible subpopulation reveals no effect.