Counterfactual Analysis and Inference with Nonstationary Data

Abstract

Recently, there has been growing interest in developing econometric tools to conduct counterfactual analysis with aggregate data when a single “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/synthetic counterfactual from a pool of “untreated” peers, organized in a panel data structure. In this paper, we investigate the consequences of applying such methodologies when the data comprise integrated processes of order 1, I(1), or are trend-stationary. We find that for I(1) processes without a cointegrating relationship (spurious case) the estimator of the effects of the intervention diverges, resulting in the rejection of the null hypothesis of no effects regardless of its existence with probability approaching 1. Although spurious regression is a well-known concept in time-series econometrics, they have been ignored in most of the literature on counterfactual estimation based on artificial/synthetic controls. For the case when at least one cointegration relationship exists, we have consistent estimators for the intervention effect albeit with a non-standard distribution. However, even in this case, the test of no intervention effect is extremely oversized if nonstationarity is ignored. Finally, we discuss a test based on re-sampling which can be applied when there is at least one cointegration relationship or when the data is trend-stationary.