Modeling Potentially Time-Varying Effects of Promotions on Sales

A commonly applied modeling tool for the analysis of promotional effects on weekly sales data is a linear regression model. Usually, such a model includes 0/1 dummy variables for promotions, where weeks with a promotion get a value of 1. When these variables are included in a model with parameters which are constant over time, the market researcher implicitly makes two important but rather restrictive assumptions. The first is that anytime a dummy variable takes a value of 1 and the relevant parameter is significant, there is a non-zero effect of promotion on sales. The second is that this effect is constant across all weeks. In many practical cases however, one may conjecture that the effects of promo- tion are not constant over time. Therefore, we propose a new and rather parsimo- nious econometric model for the purpose of measuring the effects of promotions, while allowing for time-variation in these effects. The main idea is that promotions can (but not necessarily) lead to positive and suddenly large values of sales in the same week, and that they can perhaps lead to large negative values in the week there-after, if there is a, what is called, post-promotion dip. We discuss representation and interpretation of the model, and we outline the maximum likelihood parameter estimation method. Simulation results suggest that the estimation method is quite reliable and that the distribution of the estimator is approximately normal. We illustrate the model in substantial detail on two sets of empirical data in order to indicate its practical usefulness