Cointegration and control: Assessing the impact of events using time series data

Control groups can provide counterfactual evidence for assessing the impact of an event or policy change on a target variable. We argue that fitting a multivariate time series model offers potential gains over a direct comparison between the target and a weighted average of controls. More importantly, it highlights the assumptions underlying methods such as difference in differences and synthetic control, suggesting ways to test these assumptions. Gains from simple and transparent time series models are analysed using examples from the literature, including the California smoking law of 1989 and German reunification. We argue that selecting controls using a time series strategy is preferable to existing data-driven regression methods.