Marketing Dynamics: A Primer on Estimation and Control

摘要

This primer provides a gentle introduction to the estimation and control of dynamic marketing models. It introduces dynamic models in discrete- and continuous-time, scalar and multivariate settings, with observed outcomes and unobserved states, as well as random and/or time-varying parameters. It exemplifies how various dynamic models can be cast into the unifying state space framework, the benefit of which is to use one common algorithm to estimate all dynamic models. The primer then focuses on the estimation part, which answers questions such as: how much is the sales elasticity of advertising? How much sales lift can managers expect for a certain level of price promotion? What is the best sales forecast for the next quarter? The estimation relies on two principles: Kalman filtering and the likelihood principle. The Kalman filter recursively infers the means and covari-ances of an unobserved state vector as the observed outcomes arrive over time. This evolution of moments is then embedded in the likelihood function to obtain parameter estimates and their statistical significance. Next, the primer elucidates the control part, which answers questions such as: how much should managers spend on advertising over time and across regions? What is the best promotional timing and depth? How should managers optimally respond to competing brands' actions and resulting outcomes? The control part relies on the maximum principle and the optimality principle. Pontryagin's maximum principle allows managers to determine the optimal course of action (for example, the optimal levels and timing of advertising spends or price promotions) to attain a specified goal, such as profit maximization. Bellman's optimality principle, on the other hand, offers insights into optimal course correction when implementing the best plan as the state of a system varies dynamically and/or stochastically. Finally, the primer presents three examples on the application of optimal control, differential games, and stochastic control theory to marketing problems, and illustrates how to discover novel insights into managerial decision-making.