Working Paper: NBER ID: w12756
Authors: Andre Bonfrer; Ernst R. Berndt; Alvin Silk
Abstract: We investigate the theoretical possibility and empirical regularity of two troublesome anomalies that frequently arise when cross-price elasticities are estimated for a set of brands expected to be substitutes. These anomalies are the occurrence of: (a) negatively signed cross-elasticities; and (b) sign asymmetries in pairs of cross price elasticities. Drawing upon the Slutsky equation from neoclassical demand theory, we show how and why these anomalies may occur when cross elasticities are estimated for pairs of brands that are substitutes. We empirically examine these issues in the context of the widely used Multiplicative Competitive Interaction (MCI) and Multinomial Logit (MNL) specifications of the fully extended attraction models (Cooper and Nakanishi 1988). Utilizing a database of store-level scanner data for 25 categories and 127 brands of frequently purchased branded consumer goods, we find that about 18% of a total of 732 cross elasticity estimates are negative and approximately 40% of the 366 pairs of cross elasticities are sign asymmetric. Finally, we find that the occurrence of negatively signed cross elasticities can be partially explained by a set of hypothesized relationships between cross-price elasticities and brand share and elasticities of income and category demand.
Keywords: cross-price elasticity; marketing mix models; consumer demand; empirical analysis
JEL Codes: D12; M30
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| brands expected to be substitutes (L67) | negative cross elasticities (D11) |
| one brand's price (D41) | sign asymmetry (D50) |
| relationships between cross-price elasticities and brand share (C29) | observed patterns in the data (C29) |
| relationships between income effects and cross elasticities (H31) | observed patterns in the data (C29) |