Semiparametric efficiency for DiD frameworks without parallel trends

Develop semiparametric efficient influence functions and corresponding efficient estimators for Difference-in-Differences-like frameworks that do not rely on parallel trends assumptions, including synthetic Difference-in-Differences and related methods, by deriving efficiency bounds and estimation procedures under their identification structures.

Background

The paper’s semiparametric efficiency results are derived under parallel trends and no-anticipation assumptions. In contexts where parallel trends are implausible, researchers use alternative estimators such as synthetic DiD or recent methods that relax parallel trends. Extending semiparametric efficiency theory to those identification strategies would provide variance bounds and optimal estimators analogous to what is developed here under parallel trends.

The authors explicitly state that building semiparametric efficient estimators for non-parallel-trends frameworks is not addressed and is deferred to future research, framing a concrete methodological development problem.