Differences-in-Differences with multiple Treatments under Control

Roller, Marcus; Steinberg, Daniel (January 2023). Differences-in-Differences with multiple Treatments under Control (CRED Research Paper 41). Bern: CRED - Center for Regional Economic Development

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Numerous quasi-experimental identification strategies making use of the differencein-
differences setup suffer from multiple treatments which can be separated into
sequential and simultaneous treatments. While for causal inferences under sequential
treatments a staggered difference-in-differences approach might be applied, for
causal inferences under simultaneous treatments the standard differences-indifferences
approach is normally not applicable. Accordingly, we present an adjusted
differences-in-differences identification strategy that can neutralize the effects of
additional treatments implemented simultaneously through the definition and the
specific composition of the control group and an amended common trend assumption.
Even though the adjusted difference-in-differences strategy identifies the average
treatment effect on the treated, we also show that the adjusted strategy is capable of
identifying the average treatment effect under stronger common trend assumptions
and the absence of interaction effects between the treatments.

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