Dynamic causal inference with time series data

TL;DR

This paper extends causal inference to time series data by defining effects on entire trajectories, allowing for dynamic treatment effect estimation and providing methods for observational data and scarce treatment scenarios.

Contribution

It introduces a framework for causal inference on stochastic process trajectories, including estimands, identification, and estimators for dynamic effects.

Findings

Dynamic effects differ from static estimates in simulations.

The proposed estimator is unbiased under certain assumptions.

Application to COVID-19 data demonstrates practical utility.

Abstract

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.