Dynamic causal inference with time series data

We generalize the potential outcome framework to time series with an intervention by defining causal effects on stochastic processes. Interventions in dynamic systems alter not only outcome levels but also evolutionary dynamics – changing persistence and transition laws. Our framework treats potential outcomes as entire trajectories, enabling causal estimands, identification conditions, and estimators to be formulated directly on path space. The resulting Dynamic Average Treatment Effect (DATE) characterizes how causal effects evolve through time and reduces to the classical average treatment effect under one period of time. For observational data, we derive a dynamic inverse-probability weighting estimator that is unbiased under dynamic ignorability and positivity. When treated units are scarce, we show that conditional mean trajectories underlying the DATE admit a linear state-space representation, yielding a dynamic linear model implementation. Simulations demonstrate that modeling time as intrinsic to the causal mechanism exposes dynamic effects that static methods systematically misestimate. An empirical study of COVID-19 lockdowns illustrates the framework’s practical value for estimating and decomposing treatment effects.

💡 Research Summary

The paper extends the classic Rubin potential‑outcome framework from static, single‑time‑point outcomes to full stochastic processes, thereby providing a principled way to conduct causal inference when interventions affect not only the level of an outcome but also its evolution over time. Each unit’s outcome is modeled as a trajectory ({Y_t(z)}_{t=0}^T) under treatment ((z=1)) and control ((z=0)). The authors define the Dynamic Average Treatment Effect (DATE) as the time‑varying expectation (\tau_t = E