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.

翻译：近年来，营销组合模型（MMMs）——即营销效果的整体层面模型——重新受到学界关注。这类模型通常包含非线性效应，并或明或暗地假设营销效果随时间变化。本文证明，非线性效应与时间效应往往无法通过标准营销组合数据进行识别：虽然某些数据模式可能暗示非线性效应，但这些模式同样可能出现在包含营销效果动态变化的更简单模型中。这种识别缺失问题具有重要影响，因为非线性效应与动态效应本质上指向截然不同的最优营销资源配置方案。我们通过理论推演与仿真模拟检验该识别问题，深入探究两类模型产生混淆的确切条件。在此过程中，我们引入一种灵活的贝叶斯非参数模型，该模型既能灵活模拟不同数据生成过程，又能对其进行参数估计。研究表明，当存在自相关营销变量时——这在实践中尤为常见，特别是考虑到广泛使用存量变量来捕捉广告长期效应的情况——两类效应的混淆尤其容易发生。我们通过对真实世界营销组合数据的多项实证应用阐明这些观点，揭示该混淆问题在实际应用中的普遍性。最后，我们展示营销人员如何通过设计战略性操纵支出的实验来确定模型形式，从而避免此类混淆。