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 – namely, 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 they seldom have access to data on competitive promotions at the customer level. Promotion response models in the literature either have ignored competitive promotions, focusing instead on the focal firm's promotions and sales response, or have considered the ideal situation in which the analyst has access to full information about each firm's sales and promotion activity. The authors propose a random coefficients hidden Markov promotion response model, which takes the competitor's unobserved promotion level as a latent variable driven by a Markov process to be estimated simultaneously with the promotion response model. This enables the authors to estimate cross-promotion effects by imputing the level of competitive promotions. The authors test the proposed model on synthetic data through a Monte Carlo experiment. Then, they 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 show that compared with several benchmark models, the proposed random coefficients hidden Markov model successfully imputes unobserved competitive promotions and, accordingly, reduces biases in the own- and cross-promotion parameters. Furthermore, the proposed model provides better predictive validity than the benchmark models.