Abstract

Abstract 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. In order to allocate a given budget optimally, for example, an advertiser must determine the incremental contributions that different advertising campaigns have made to web searches, product installs, or sales. This paper proposes to infer causal impact on the basis of a diffusion-regression state-space model that predicts the counterfactual market response 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 the time-varying influence of contemporaneous covariates, i.e., synthetic controls. Using a Markov chain Monte Carlo algorithm for posterior inference, we illustrate the statistical properties of our approach on synthetic data. We then demonstrate its practical utility by evaluating the effect of an online advertising campaign on search-related site visits. We discuss the strengths and limitations of our approach in improving the accuracy of causal attribution, power analyses, and principled budget allocation.