Your MMM is Broken: Identification of Nonlinear and Time-varying Effects in Marketing Mix Models

Abstract

Recent years have seen a resurgence in interest in marketing mix models (MMMs), which are aggregate-level models of marketing effectiveness. Often these models incorporate nonlinear effects, and either implicitly or explicitly assume that marketing effectiveness varies over time. In this paper, we show that nonlinear and time-varying effects are often not separately identifiable: while certain data patterns may be suggestive of nonlinear effects, such patterns may also emerge under simpler models with time-varying effects. Moreover, problematically, these two types of effects may suggest fundamentally different optimal marketing allocations. We examine this identification issue through theory and simulations, describing the conditions under which conflation between the two types of models is likely to occur. We show that conflating the two types of effects is especially likely in the presence of autocorrelated marketing variables, which are common in practice, especially given the widespread use of stock variables to capture long-run effects of advertising. We illustrate these ideas through numerous empirical applications to real-world marketing mix data, showing the prevalence of the conflation issue in practice. Finally, we show how marketers can avoid this conflation, by designing experiments that strategically manipulate spending in ways that pin down model form.

Keywords: marketing mix models, aggregate response models, dynamics, nonlinear models, identification, Bayesian nonparametrics