Tanique Schaffe-Odeleye, Kōsaku Takanashi, Vishesh Karwa, Edoardo M. Airoldi, Kenichiro McAlinn
arXiv 31 Jan 2026 · Statistics — Methodology
arXiv:2602.00836 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Bojinov, Iavor and Shephard, Neil (2019) Time series experiments and causal estimands: exact randomization tests and trading | 1.000 | 6 | 4 | 100% |
| 2 | Bojinov, Iavor and Rambachan, Ashesh and Shephard, Neil (2021) Panel experiments and dynamic causal effects: A finite population perspective | 0.843 | 3 | 3 | 100% |
| 3 | Ikeda, N and Watanabe, S (1989) Stochastic differential equations and diffusion processes | 0.811 | 4 | 2 | 100% |
| 4 | K. Li and G. Tierney and C. Hellmayr and M. West (2024) Compositional dynamic modelling for counterfactual prediction in multivariate time series | 0.737 | 3 | 2 | 100% |
| 5 | Abadie, Alberto and Diamond, Alexis and Hainmueller, Jens (2010) Synthetic control methods for comparative case studies: Estimating the effect of California’s tobacco control program | 0.644 | 2 | 2 | 100% |
| 6 | R. Prado and M. West (2010) Time Series: Modelling, Computation & Inference | 0.405 | 1 | 1 | 100% |
| 7 | Revuz, Daniel and Yor, Marc (1999) Continuous Martingales and Brownian motion | 0.405 | 1 | 1 | 100% |
| 8 | Rogers, L Chris G and Williams, David (2000) Diffusions, Markov processes, and martingales: Itô calculus | 0.405 | 1 | 1 | 100% |
| 9 | S. Frühwirth-Schnatter (1994) Data augmentation and dynamic linear models | 0.405 | 1 | 1 | 100% |
| 10 | M. West and P. J. Harrison (1997) Bayesian Forecasting & Dynamic Models | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 28 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | When are time series predictions causal? The potential system and dynamic causal effects | 0.405 | 1 | 1 |