A Dynamic Bayesian Model for Causal Inference with Mediation

Many marketing research projects aim not only to estimate the causal effect of an intervention but also to understand the mechanism by which the intervention affects outcomes. However, existing causal inference methods, such as difference-in-differences and synthetic control, do not include mediation analysis, nor do existing mediation analysis methods address unobserved confounders. The authors therefore propose an integrative, scalable framework for performing mediation analysis while estimating causal treatment effects with panel data. The proposed method decomposes the causal effect of an intervention into indirect effects, transmitted through the model’s mediators, and a direct effect, not transmitted through the mediators. Simulation studies confirm that the proposed method correctly identifies the direct, indirect, and total treatment effects and outperforms existing causal inference methods in inferential quality. Two real-world applications yield further insights. For Washington state’s 2010 soda tax, despite a persistent, negative indirect effect on sales through inflated prices, the tax’s total effect is transient, due to a direct effect that was initially negative but became positive later on, offsetting the price effect. In the case of U.S. newspaper paywall adoption, paywalls decreased newspaper circulation through increased print prices, but a direct spillover effect dominated the indirect price effect. Moreover, newspaper size positively moderated the spillover effect, such that only large newspapers enjoyed the positive spillover effect and therefore larger circulation