A Hierarchical Bayes Error Correction Model to Explain Dynamic Effects of Price Changes

Abstract

The authors put forward a sales response model to explain the differences in immediate and dynamic effects of promotional prices and regular prices on sales. The model consists of a vector autoregression rewritten in error-correction format which allows to disentangle the immediate effects from the dynamic effects. In a second level of the model, the immediate price elasticities, the cumulative promotional price elasticity and the long-run regular price elasticity are correlated with various brand-speciffic and category-speciffic characteristics. The model is applied to seven years of data on weekly sales of 100 different brands in 25 product categories. We find many significant moderating effects on the elasticity of price promotions. Brands in categories that are characterized by high price differentiation and that constitute a lower share of budget are less sensitive to price discounts. Deep price discounts turn out to increase the immediate price sensitivity of customers. We also find significant effects for the cumulative elasticity. The immediate effect of a regular price change is often close to zero. The long-run effect of such a decrease usually amounts to an increase in sales. This is especially true in categories characterized by a large price dispersion, frequent price promotions and hedonic, non-perishable products.

Keywords: sales, vector autoregression, marketing mix, promotional and regular price, short and long-term effects, hierarchical bayes

JEL Classification: M, C44, M31