Estimating Promotion Response When Competitive Promotions Are Unobservable

This study addresses a problem commonly encountered by marketers who attempt to assess the impact of their sales promotions: the lack of data on competitive marketing activity. In most industries, competing firms may have competitive sales data from syndicated services or trade organizations, but seldom have access to data on competitive promotions except, if any, at a high level of aggregation; competitive promotion data are rarely available at the customer level. Promotion response models in the literature either have ignored competitive promotions focusing on the focal firm’s promotions and sales response or have considered the ideal situation where the analyst has access to full information about each firm’s sales and promotion activity. We propose a random-coefficients hidden Markov promotion response model, which takes the unobserved promotion level (i.e., promotion or no promotion) by competitors in the same product category as a latent variable driven by a Markov process to be estimated simultaneously with the promotion response model. This allows us to estimate cross-promotion effects by imputing the level of competitive promotions, even though these promotions are not directly observable. First, we test the proposed model on synthetic data through a Monte Carlo experiment. Then, we apply and test the model to actual prescription and sampling data from two main competing pharmaceutical firms in the same therapeutic category. The two tests clearly show that, in comparison with several benchmark models, our randomcoefficients hidden Markov model (HMM) successfully imputes competitive promotions when they are completely missing and, accordingly, reduces biases in the own and cross promotion parameters. Furthermore, our model provides better predictive validity than the benchmark models.