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In this paper, we adopt results in nonlinear time series analysis for causalinference in dynamical settings.~Our motivation is policy analysis with paneldata, particularly through the use of "synthetic control" methods. Thesemethods regress pre-intervention outcomes of the treated unit to outcomes froma pool of control units, and then use the fitted regression model to estimatecausal effects post-intervention. In this setting, we propose to screen outcontrol units that have a weak dynamical relationship to the treated unit. Insimulations, we show that this method can mitigate bias from "cherry-picking"of control units, which is usually an important concern. We illustrate onreal-world applications, including the tobacco legislation example of\citet{Abadie2010}, and Brexit.

Dynamical systems theory for causal inference with application to synthetic control methods