Counterfactual Analysis with Artificial Controls: Inference, High Dimensions and Nonstationarity

Recently, there has been growing interest in developing econometric tools to conduct counterfactual analysis with aggregate data when a “treated” unit suffers an intervention, such as a policy change, and there is no obvious control group. Usually, the proposed methods are based on the construction of an artificial counterfactual from a pool of “untreated” peers, organized in a panel data structure. In this paper, we consider a general framework for counterfactual analysis in high dimensions with potentially non-stationary data and either deterministic and/or stochastic trends, which nests well-established methods, such as the synthetic control. Furthermore, we propose a resampling procedure to test intervention effects that does not rely on post-intervention asymptotics and that can be used even if there is only a single observation after the intervention. A simulation study is provided as well as an empirical application where the effects of price changes on the sales of a product is measured.