  Difference-in-differences is based on a parallel trends assumption, which
states that changes over time in average potential outcomes are independent of
treatment assignment, possibly conditional on covariates. With time-varying
treatments, parallel trends assumptions can identify many types of parameters,
but most work has focused on group-time average treatment effects and similar
parameters conditional on the treatment trajectory. This paper focuses instead
on identification and estimation of the intervention-specific mean - the mean
potential outcome had everyone been exposed to a proposed intervention - which
may be directly policy-relevant in some settings. Previous estimators for this
parameter under parallel trends have relied on correctly-specified parametric
models, which may be difficult to guarantee in applications. We develop
multiply-robust and efficient estimators of the intervention-specific mean
based on the efficient influence function, and derive conditions under which
data-adaptive machine learning methods can be used to relax modeling
assumptions. Our approach allows the parallel trends assumption to be
conditional on the history of time-varying covariates, thus allowing for
adjustment for time-varying covariates possibly impacted by prior treatments.
Simulation results support the use of the proposed methods at modest sample
sizes. As an example, we estimate the effect of a hypothetical federal minimum
wage increase on self-rated health in the US.
