Estimating the effectiveness of permanent price reductions for competing products using multivariate Bayesian structural time series models

TL;DR

This paper develops a multivariate Bayesian structural time series model to estimate the causal impact of permanent price reductions on store brands and competitors, accounting for interference effects within groups, and demonstrates its effectiveness through simulations and real data analysis.

Contribution

It introduces a novel Bayesian approach for causal inference with interference, extending synthetic control methods to handle partial interference within groups.

Findings

The model achieves good frequentist coverage even under misspecification.

It effectively estimates the impact of price changes on sales of affected and competitor brands.

The methodology is implemented in the CausalMBSTS R package.

Abstract

The Florence branch of an Italian supermarket chain recently implemented a strategy that permanently lowered the price of numerous store brands in several product categories. To quantify the impact of such a policy change, researchers often use synthetic control methods for estimating causal effects when a subset of units receive a single persistent treatment, and the rest are unaffected by the change. In our applications, however, competitor brands not assigned to treatment are likely impacted by the intervention because of substitution effects; more broadly, this type of interference occurs whenever the treatment assignment of one unit affects the outcome of another. This paper extends the synthetic control methods to accommodate partial interference, allowing interference within predefined groups but not between them. Focusing on a class of causal estimands that capture the effect both on the treated and control units, we develop a multivariate Bayesian structural time series model for generating synthetic controls that would have occurred in the absence of an intervention enabling us to estimate our novel effects. In a simulation study, we explore our Bayesian procedure's empirical properties and show that it achieves good frequentists coverage even when the model is misspecified. We use our new methodology to make causal statements about the impact on sales of the affected store brands and their direct competitors. Our proposed approach is implemented in the CausalMBSTS R package.