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Anomalies in Estimates of Cross-Price Elasticities for Marketing Mix Models: Theory and Empirical Test

  • Andre Bonfrer
  • Ernst R. Berndt
  • Alvin Silk

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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 12756.

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Date of creation: Dec 2006
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Handle: RePEc:nbr:nberwo:12756
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  1. Raj Sethuraman & V. Srinivasan & Doyle Kim, 1999. "Asymmetric and Neighborhood Cross-Price Effects: Some Empirical Generalizations," Marketing Science, INFORMS, vol. 18(1), pages 23-41.
  2. Aviv Nevo, 2003. "Measuring Market Power in the Ready-to-Eat Cereal Industry," Microeconomics 0303006, EconWPA.
  3. David Besanko & Sachin Gupta & Dipak Jain, 1998. "Logit Demand Estimation Under Competitive Pricing Behavior: An Equilibrium Framework," Management Science, INFORMS, vol. 44(11-Part-1), pages 1533-1547, November.
  4. Little, John D. C., 1998. "Integrated measures of sales, merchandising, and distribution," Working papers WP 3997-98., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  5. Allenby, G.M. & Rossi, P.E., 1988. "There Is No Aggregation Bias: Why Macro Logit Models Work," Papers 88-62, Chicago - Graduate School of Business.
  6. Andrew Ainslie & Peter E. Rossi, 1998. "Similarities in Choice Behavior Across Product Categories," Marketing Science, INFORMS, vol. 17(2), pages 91-106.
  7. Vincent R. Nijs & Marnik G. Dekimpe & Jan-Benedict E.M. Steenkamps & Dominique M. Hanssens, 2001. "The Category-Demand Effects of Price Promotions," Marketing Science, INFORMS, vol. 20(1), pages 1-22, September.
  8. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, vol. 6(4), pages 345-354, August.
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