Inferring causal impact using Bayesian structural time-series models
Venue
Annals of Applied Statistics, vol. 9 (2015), pp. 247-274
Publication Year
2015
Authors
Kay H. Brodersen, Fabian Gallusser, Jim Koehler, Nicolas Remy, Steven L. Scott
BibTeX
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 assess
to what extent different campaigns have contributed to an incremental lift in 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 model inversion, 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 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.
