Synthetic Blips: Generalizing Synthetic Controls for Dynamic Treatment Effects

Understand

We propose a generalization of the synthetic control methods to the setting with dynamic treatment effects, in which each unit receives multiple treatments sequentially, according to an adaptive policy that depends on a latent, endogenously time-varying confounding state.

• Under a low-rank latent factor model assumption, which admits linear time-varying and time-invariant dynamic triangular systems as special cases, we develop an identification strategy for any unit-specific mean outcome under any sequence of interventions.
• Our method, which we term synthetic blips, is a backward induction process in which the blip effect of a treatment at each period for a target unit is recursively expressed as a linear combination of the blip effects of other units that received the designated treatment, avoiding the combinatorial donor requirements of naive synthetic control extensions.
• We provide easy-to-implement estimation algorithms that yield consistent estimators.