Dynamic Causal Inference for Time Series Data
Seminar Series: Kenichiro McAlinn, Temple University.
We generalize the potential outcome framework to time series with a single persistent intervention by defining causal effects on stochastic processes. Interventions in dynamic systems alter outcome levels and can also change evolutionary dynamics, including persistence and transition probabilities. Our framework treats potential outcomes as entire trajectories, enabling causal estimands, identification conditions, and estimators to be formulated directly on path space for multiple independent units. The resulting Dynamic Average Treatment Effect (DATE) characterizes how causal effects evolve through time, averages over a specified distribution of pretreatment histories, and reduces to the classical average treatment effect in the one period case. For observational data, we derive a dynamic inverse probability weighting estimator that is unbiased with known propensity scores under dynamic ignorability and positivity. We also develop inference for contrasts of path functionals, including probabilities of crossing a threshold. For discrete observations with missing data and measurement error, we establish when reconstruction of the mean path recovers the limit under complete observation and when dependence in observation availability leaves additional uncertainty. Simulations show that interventions with identical marginal means and variances can have different crossing probabilities, and that increasing observation density need not remove uncertainty from missing paths. A randomized mask promotion trial in Bangladesh illustrates estimation of dynamic effects for complete pairs, with simultaneous bands and sensitivity analysis for missing data.
