Causal Inference in Dynamic Systems

Randomized control trials (RCTs) are the gold standard for causal inference but can be inefficient compared to adaptive designs. A key question is whether adaptive designs can universally outperform RCTs without relying on problem-specific knowledge. We answer this affirmatively in the best-arm identification problem, showing that simple adaptive designs, which sequentially eliminate underperforming arms, universally strictly dominates standard RCTs when there are at least three treatment arms. This dominance is characterized by a notion called efficient exponent, which quantifies a design's statistical efficiency in large populations. Additionally, we derive the maximin elimination-based design, further highlighting that adaptive designs can potentially achieve both efficiency and robustness. This is a joint work with Guido Imbens and Stefan Wager. 

This paper studies the estimation and inference of treatment histories in panel data settings when treatments change dynamically over time.
We propose a method that allows for (i) treatments to be assigned dynamically over time based on high-dimensional covariates, past outcomes and treatments; (ii) outcomes and time-varying covariates to depend on treatment trajectories; (iii) heterogeneity of treatment effects.
Our approach recursively projects potential outcomes' expectations on past histories. It then controls the bias by balancing dynamically observable characteristics. We study the asymptotic and numerical properties of the estimator and illustrate the benefits of the procedure in an empirical application. 

We propose a generalization of the synthetic control and synthetic interventions methodology to the dynamic treatment regime. We consider the estimation of unit-specific treatment effects from panel data collected via a dynamic treatment regime and in the presence of unobserved confounding. That is, each unit receives multiple treatments sequentially, based on an adaptive policy, which depends on a latent endogenously time-varying confounding state of the treated unit. Under a low-rank latent factor model assumption and a technical overlap assumption we propose an identification strategy for any unit-specific mean outcome under any sequence of interventions. The latent factor model we propose admits linear time-varying and time-invariant dynamical systems as special cases. Our approach can be seen as an identification strategy for structural nested mean models under a low-rank latent factor assumption on the blip effects. Our method, which we term "synthetic blip effects", is a backwards induction process, where the blip effect of a treatment at each period and for a target unit is recursively expressed as linear combinations of blip effects of a carefully chosen group of other units that received the designated treatment. Our work avoids the combinatorial explosion in the number of units that would be required by a vanilla application of prior synthetic control and synthetic intervention methods in such dynamic treatment regime settings. 

We propose a causal framework for applications where the outcome of interest is a unit-specific response to events, which first needs to be measured from the data. We suggest a two-step procedure: first, estimate unit-level event studies (ULES) by comparing pre- and post-event outcomes of each unit to a suitable control group; second, use the ULES in causal analysis. We outline the theoretical conditions under which this two-step procedure produces interpretable results, highlighting the underlying statistical challenges. Our method overcomes the limitations of regression-based approaches prevalent in the empirical literature, allowing for a deeper examination of heterogeneity and dynamic effects. We apply this framework to analyze the impact of childcare provision reform on the magnitude of child penalties in the Netherlands, illustrating its ability to reveal nuanced positive relationships between childcare provision and parental labor supply. In contrast, traditional regression-based analysis delivers negative effects, thereby emphasizing the benefits of our two-step approach.