Open Access
March 2015 Inferring causal impact using Bayesian structural time-series models
Kay H. Brodersen, Fabian Gallusser, Jim Koehler, Nicolas Remy, Steven L. Scott
Ann. Appl. Stat. 9(1): 247-274 (March 2015). DOI: 10.1214/14-AOAS788


An important problem in econometrics and marketing is to infer the causal impact that a designed market intervention has exerted on an outcome metric over time. This paper proposes to infer causal impact on the basis of a diffusion-regression state-space model that predicts the counterfactual market response in a synthetic control that would have occurred had no intervention taken place. In contrast to classical difference-in-differences schemes, state-space models make it possible to (i) infer the temporal evolution of attributable impact, (ii) incorporate empirical priors on the parameters in a fully Bayesian treatment, and (iii) flexibly accommodate multiple sources of variation, including local trends, seasonality and the time-varying influence of contemporaneous covariates. Using a Markov chain Monte Carlo algorithm for posterior inference, we illustrate the statistical properties of our approach on simulated data. We then demonstrate its practical utility by estimating the causal effect of an online advertising campaign on search-related site visits. We discuss the strengths and limitations of state-space models in enabling causal attribution in those settings where a randomised experiment is unavailable. The CausalImpact R package provides an implementation of our approach.


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Kay H. Brodersen. Fabian Gallusser. Jim Koehler. Nicolas Remy. Steven L. Scott. "Inferring causal impact using Bayesian structural time-series models." Ann. Appl. Stat. 9 (1) 247 - 274, March 2015.


Published: March 2015
First available in Project Euclid: 28 April 2015

zbMATH: 06446568
MathSciNet: MR3341115
Digital Object Identifier: 10.1214/14-AOAS788

Keywords: advertising , Causal inference , counterfactual , difference in differences , econometrics , market research , observational , synthetic control

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.9 • No. 1 • March 2015
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