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

Inferring causal impact using Bayesian structural time-series models