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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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  • Andre Bonfrer & Ernst R. Berndt & Alvin Silk, 2006. "Anomalies in Estimates of Cross-Price Elasticities for Marketing Mix Models: Theory and Empirical Test," NBER Working Papers 12756, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:12756
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    References listed on IDEAS

    1. 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.
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    6. 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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    8. 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.
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    Cited by:

    1. Barth, Anne-Kathrin & Heimeshoff, Ulrich, 2012. "How large is the magnitude of fixed-mobile call substitution? Empirical evidence from 16 European countries," DICE Discussion Papers 49, University of Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
    2. Dikgang, Johane & Muchapondwa, Edwin, 2013. "Conservation Fees in the Kgalagadi Transfrontier Park between Botswana and South Africa in the Presence of Land Restitution," Discussion Papers dp-13-09-efd, Resources For the Future.
    3. Banerjee, Dyuti S. & Chatterjee, Ishita, 2014. "Exploring Stackelberg profit ordering under asymmetric product differentiation," Economic Modelling, Elsevier, vol. 36(C), pages 309-315.
    4. Mensah, Justice Tei & Adu, George, 2015. "An empirical analysis of household energy choice in Ghana," Renewable and Sustainable Energy Reviews, Elsevier, vol. 51(C), pages 1402-1411.
    5. Savorelli, Luca, 2012. "Asymmetric cross-price effects and collusion," Research in Economics, Elsevier, vol. 66(4), pages 375-382.
    6. Barth, Anne-Kathrin & Heimeshoff, Ulrich, 2014. "What is the magnitude of fixed–mobile call substitution? Empirical evidence from 16 European countries," Telecommunications Policy, Elsevier, vol. 38(8), pages 771-782.
    7. Vogelsang, Ingo, 2010. "The relationship between mobile and fixed-line communications: A survey," Information Economics and Policy, Elsevier, vol. 22(1), pages 4-17, March.

    More about this item

    JEL classification:

    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • M30 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - General

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