An Empirical Model of Advertising Dynamics

Abstract

We develop a model of dynamic advertising and apply it to the problem of optimal advertising scheduling through time. In many industries we observe advertising pulsing, whereby firms systematically switch advertising on and off at a high-frequency. The previous literature has explained such patterns through an S-shaped sales response to advertising, and long-run effects of advertising on demand (advertising carry-over). We extend a discrete choice based demand system to allow for a threshold in the effect of advertising (a special form of an S-shape) and for advertising carry-over. Demand without a threshold and no long-run advertising effect is a special, testable case of our proposed model. We estimate the demand system using an easy to implement partial maximum likelihood estimator. We then solve for dynamically optimal advertising under the estimated demand system. We allow for oligopolistic competition among firms, using the Markov perfect equilibrium (MPE) concept to solve for the outcome of the repeated game. An analytic solution of the model is infeasible, and we thus solve for equilibrium advertising using numerial dynamic programming techniques. The flexibility provided by the numerical solution method allows us to improve on the existing literature, which has placed strong restrictions on the demand models for which supply side policies can be obtained, and mostly considered only two competitors. We apply our model to the case of advertising in the Frozen Entree product category. The demand estimates provide evidence for a threshold effect in the sales-response to advertising as well as advertising carry-over. The threshold is robust to functional form assumptions on the impact of advertising on demand. The demand estimates imply that firms should pulse in equilibrium. On average, the optimal advertising policies yield a moderate profit improvement over the profits under observed advertising.