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

60 Pages Posted: 13 Dec 2006 Last revised: 10 May 2021

See all articles by Andre Bonfrer

Andre Bonfrer

Deakin University; Australian National University (ANU)

Ernst R. Berndt

Massachusetts Institute of Technology (MIT) - Sloan School of Management; National Bureau of Economic Research (NBER)

Alvin J. Silk

Harvard Business School

Date Written: December 2006

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.

Suggested Citation

Bonfrer, Andre and Berndt, Ernst R. and Silk, Alvin J., Anomalies in Estimates of Cross-Price Elasticities for Marketing Mix Models: Theory and Empirical Test (December 2006). NBER Working Paper No. w12756, Available at SSRN: https://ssrn.com/abstract=949765

Andre Bonfrer

Deakin University ( email )

Australia

Australian National University (ANU) ( email )

Canberra, Australian Capital Territory 2601
Australia

Ernst R. Berndt (Contact Author)

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

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National Bureau of Economic Research (NBER)

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Alvin J. Silk

Harvard Business School ( email )

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United States
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617-495-8736 (Fax)

HOME PAGE: http://dor.hbs.edu/fi_redirect.jhtml?facInfo=bio&facEmId=asilk

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