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DYNAMIC CAUSAL INFERENCE: METHODOLOGICAL FOUNDATIONS AND APPLICATIONS
Schaffe-Odeleye, Tanique
Schaffe-Odeleye, Tanique
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2025-05
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https://doi.org/10.34944/nsyx-cg55
Abstract
This dissertation develops and discusses a potential outcomes causal inference framework for time series data from a foundational perspective. Causal inference, in the potential outcomes setting, is understood to be the effect of an intervention on outcomes. This intervention is what delineates causal inference from inference of association. In classical causal inference, the potential outcomes– bivariate outcomes on whether the unit receives an intervention or not– are atemporal, meaning that each unit has pre-determined outcomes that are instantaneously realized when that unit receives the intervention, or not. Randomized inference, such as randomized control trials, then defines an ideal situation for causal inference in this setting by averaging out biases that may arise from confounding effects. Much of the causal inference literature has been centered around developing methods to overcome problem settings that deviate from this ideal situation, such as propensity score analysis for when the interventions are not randomized, but are within the atemporal framework of potential outcomes. In generalizing the potential outcomes framework to time series data, the temporal nature of the data poses unique problems that have not been sufficiently addressed in the literature. For one, the core assumptions that the potential outcomes are bivariate and atemporal are violated. In a time series setting, even if the instantaneous outcomes are determined, observations continue as time progresses, with the effect itself potentially changing over time. While there have been many methods proposed for specific problems that use time series data, existing methods rely on strong assumptions that reflect the atemporal nature of the classical potential outcomes setting. As these methods are not developed from a solid foundation of temporal potential outcomes, they are often ad hoc, lack clear estimands, and result in poor modeling choices.
We propose a generalization of the potential outcome causal inference framework to estimate treatment effects in a time series context. Using stochastic process theory, we define the causal estimand for time series; the dynamic average treatment effect (DATE). The proposed DATE is defined through randomized inference, where the randomness is not only in the treatment assignment, but the potential temporal paths a unit can take. For observational data, we propose a dynamic inverse probability weighting estimator and show its unbiasedness and consistency. We use the dynamic linear model (DLM) where there are few, or one, treatment series. We show that the dynamic linear model is the best approximation of the dynamic average treatment effect in terms of quadratic loss. The flexibility and the adaptability of this framework provide a firm foundation for handling causal inference with time series data.
Chapter 1 introduces the motivation and related works in the field. In Chapter 2, a preliminary discussion differentiates time series data from i.i.d. data by exploring the complexities of time series data. The causal estimand within the potential outcome framework is the subject of Chapter 3. We use this to create estimators for specific cases and show that, in terms of quadratic loss, the dynamic linear model best approximates the dynamic average treatment effect. Chapter 4 provides the simulations study. We examine unemployment and Covid-19 lockdowns in Chapter 5 by applying economic data to the established framework. Chapter 6 employs the framework to determine the effect of drug policy on Australia’s depression medication. Chapter 7 uses the framework of public health data to assess the effect of lockdown on hospitalizations. In Chapter 8, we extend the framework to financial data to access publication on return anomalies. Finally, Chapter 9 concludes the dissertation with open questions and a discussion of potential future research.
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