Synthetic Blips: Generalizing Synthetic Controls for Dynamic Treatment Effects

Anish Agarwal, Sukjin Han, Dwaipayan Saha, Vasilis Syrgkanis and Haeyeon Yoon

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Abstract: 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. Using unique Korean firm-level panel data, we estimate individualized dynamic treatment effects and optimal allocation rules in the context of financial support for exporting firms.

Date: 2022-10, Revised 2026-09
New Economics Papers: this item is included in nep-ecm
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