Counterfactual Analysis and Inference With Nonstationary Data

Ricardo Masini, Marcelo C. Medeiros

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 article, 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, regardless of its existence. 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 nonstandard distribution. Finally, we discuss a test based on resampling which can be applied when there is at least one cointegration relationship or when the data are trend-stationary.

Original languageEnglish (US)
Pages (from-to)227-239
Number of pages13
JournalJournal of Business and Economic Statistics
Issue number1
StatePublished - 2022

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


  • ArCo
  • Cointegration
  • Counterfactual analysis
  • Nonstationarity
  • Policy evaluation
  • Synthetic control


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