🤖 AI Summary
This paper addresses the estimation of unit-specific dynamic treatment effects in panel data under multi-stage adaptive interventions: units receive treatments sequentially according to endogenous, time-varying latent variables, with severe time-varying confounding. To tackle this, we extend the synthetic control paradigm to dynamic treatment regimes for the first time, proposing a backward-induction framework—“synthetic blip effects”—that avoids combinatorial explosion and ensures identification under arbitrary intervention sequences. The method builds upon a low-rank latent factor model and overlap assumptions, integrating structural nested mean models, linear dynamic system modeling, and recursive linear combination estimation. Our framework consistently identifies and estimates the average potential outcomes for any target unit under any intervention sequence. It significantly enhances scalability, robustness, and practical applicability of dynamic causal inference in complex, adaptive settings.
📝 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.
