TY - JOUR AU - Bonfrer,Andre AU - Berndt,Ernst R. AU - Silk,Alvin TI - Anomalies in Estimates of Cross-Price Elasticities for Marketing Mix Models: Theory and Empirical Test JF - National Bureau of Economic Research Working Paper Series VL - No. 12756 PY - 2006 Y2 - December 2006 UR - http://www.nber.org/papers/w12756 L1 - http://www.nber.org/papers/w12756.pdf N1 - Author contact info: Andre Bonfrer Singapore Management University 50 Stamford Road #05-01 Singapore 178899 E-Mail: andrebonfrer@smu.edu.sg Ernst R. Berndt MIT Sloan School of Management 100 Main Street, E62-518 Cambridge, MA 02142 Tel: 617/253-2665 Fax: 617-227-0880 E-Mail: eberndt@mit.edu Alvin Silk Graduate School of Business Administration Harvard University Soldiers Field Boston, MA 02163 Tel: 617-495-6036 E-Mail: asilk@hbs.edu AB - 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. ER -