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.

本文提出了一种基于扩散回归状态空间模型的方法，用于推断经济学干预措施对于市场结果指标的因果影响，相较于差异 - 差异方案，该模型有助于灵活适应多种变异来源，并在模拟和实际数据上进行了验证。