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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 identifiable from standard marketing mix data: while certain data patterns may be suggestive of nonlinear effects, such patterns may also emerge under simpler models that incorporate dynamics in marketing effectiveness. This lack of identification is problematic because nonlinearities and dynamics suggest fundamentally different optimal marketing allocations. We examine this identification issue through theory and simulations, wherein we explore the exact conditions under which conflation between the two types of models is likely to occur. In doing so, we introduce a flexible Bayesian nonparametric model that allows us to both flexibly simulate and estimate different data-generating processes. 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.

Understanding individual customers' sensitivities to prices, promotions, brands, and other marketing mix elements is fundamental to a wide swath of marketing problems. An important but understudied aspect of this problem is the dynamic nature of these sensitivities, which change over time and vary across individuals. Prior work has developed methods for capturing such dynamic heterogeneity within product categories, but neglected the possibility of correlated dynamics across categories. In this work, we introduce a framework to capture such correlated dynamics using a hierarchical dynamic factor model, where individual preference parameters are influenced by common cross-category dynamic latent factors, estimated through Bayesian nonparametric Gaussian processes. We apply our model to grocery purchase data, and find that a surprising degree of dynamic heterogeneity can be accounted for by only a few global trends. We also characterize the patterns in how consumers' sensitivities evolve across categories. Managerially, the proposed framework not only enhances predictive accuracy by leveraging cross-category data, but enables more precise estimation of quantities of interest, like price elasticity.