Synthetic Blip Effects: Generalizing Synthetic Controls for the Dynamic Treatment Regime

• URL: http://arxiv.org/abs/2210.11003v1
• Date: Thu, 20 Oct 2022 04:11:20 GMT
• Title: Synthetic Blip Effects: Generalizing Synthetic Controls for the Dynamic Treatment Regime
• Authors: Anish Agarwal, Vasilis Syrgkanis
• Abstract summary: We consider the estimation of unit-specific treatment effects from panel data collected via a dynamic treatment regime. We propose an identification strategy for any unit-specific mean outcome under any sequence of interventions.
• Score: 31.194595148880573
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a generalization of the synthetic control and synthetic interventions methodology to the dynamic treatment regime. We consider the estimation of unit-specific treatment effects from panel data collected via a dynamic treatment regime and in the presence of unobserved confounding. That is, each unit receives multiple treatments sequentially, based on an adaptive policy, which depends on a latent endogenously time-varying confounding state of the treated unit. Under a low-rank latent factor model assumption and a technical overlap assumption we propose an identification strategy for any unit-specific mean outcome under any sequence of interventions. The latent factor model we propose admits linear time-varying and time-invariant dynamical systems as special cases. Our approach can be seen as an identification strategy for structural nested mean models under a low-rank latent factor assumption on the blip effects. Our method, which we term "synthetic blip effects", is a backwards induction process, where the blip effect of a treatment at each period and for a target unit is recursively expressed as linear combinations of blip effects of a carefully chosen group of other units that received the designated treatment. Our work avoids the combinatorial explosion in the number of units that would be required by a vanilla application of prior synthetic control and synthetic intervention methods in such dynamic treatment regime settings.

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