Dynamical Systems Theory for Causal Inference with Application to Synthetic Control Methods

Yi Ding, Panos Toulis

Abstract: In this paper, we adopt results in nonlinear time series analysis for causal inference in dynamical settings. Our motivation is policy analysis with panel data, particularly through the use of “synthetic control" methods. These methods regress pre-intervention outcomes of the treated unit to outcomes from a pool of control units, and then use the fitted regression model to estimate causal effects post-intervention. In this setting, we propose to screen out control units that have a weak dynamical relationship to the treated unit. In simulations, we show that this method can mitigate bias from “cherry-picking" of control units, which is usually an important concern. We illustrate on real-world applications, including the tobacco legislation example of \citet{Abadie2010}, and Brexit.