The brand switching fraction of promotion effects : unit sales versus elasticity decompositions

Several researchers have decomposed sales promotion elasticities. A key result is that the majority of the sales promotion elasticity, about 74 percent on average, is purportedly due to secondary demand effects (brand switching) and the remainder is due to primary demand effects (timing acceleration and quantity increases). However, studies of unit sales effects suggest that the cross-brand sales effects together are less than half of the own-brand sales effect. Hence, there appears to be a dramatic difference between the relative size of the secondary demand effect based on the one hand on a decomposition of elasticities and on the other hand on a decomposition of unit sales effects. We explore the reason for this paradox and, since the research literature focuses on elasticities, we derive analytical expressions that relate the decomposition of unit sales effects to the elasticity decomposition. We apply these expressions to obtain estimated unit sales effect decompositions from previously reported elasticity decomposition results. We show why the elasticity-based decomposition is not interpretable as a unit sales decomposition, and we find that the unit sales brand switching component is much less than what the elasticity decomposition suggests. Instead of being about 74 percent, it is at most 33 percent on average. Thus, brand switching accounts for a far smaller percent of the unit sales promotion effect than what published results suggest.