Is 3/4 of the Sales Promotion Bump Due to Brand Switching? No, it is 1/3

Several researchers have decomposed sales promotion elasticities based on household scanner panel data. A key result is that the majority of the sales promotion elasticity, about 74 percent on average, is attributed to secondary demand effects (brand switching) and the remainder to primary demand effects (timing acceleration and quantity increases). We demonstrate that this result does not imply that if a brand gains 100 units in sales during a promotion the other brands in the category lose 74 units (74 percent). We offer a complementary decomposition measure based on unit sales. This measure shows the ratio of the current cross-brand unit sales loss to the current own-brand unit sales gain during promotion, and we report empirical results for this measure. We also derive analytical expressions that transform the elasticity decomposition into a decomposition of unit sales effects. These expressions show the nature of the difference between the two decompositions. To gain insight into the magnitude of the difference, we apply these expressions to previously reported elasticity decomposition results. We find that on average about one third of the unit sales increase is attributable to losses incurred by other brands in the same category (i.e., they lose 33 units). Thus, secondary demand effects account for a far smaller percent of the unit sales promotion effect than has been inferred from elasticity decomposition results. We find that the difference is due to the manner in which the two decomposition measures deal with the category expansion that occurs during a promotion. One interpretation is that the elasticity decomposition yields a gross measure of brand switching, in the sense that category sales are held constant. The unit sales decomposition yields a net measure of brand switching: it accommodates the category expansion effect that applies to both promoted and nonpromoted brands in the models