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A mathematical reformulation of the reference price

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  • Kevin Dayaratna

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  • P. Kannan
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    Abstract

    Reference prices have long been studied in applied economics and business research. One of the classic formulations of the reference price is in terms of an iterative function of past prices. There are a number of limitations of such a formulation, however. Such limitations include burdensome computational time to estimate parameters, an inability to truly account for customer heterogeneity, and an estimation procedure that implies a misspecified model. Managerial recommendations based on inferences from such a model can be quite misleading. We mathematically reformulate the reference price by developing a closed-form expansion that addresses the aforementioned issues, enabling one to elicit truly meaningful managerial advice from the model. We estimate our model on a real world data set to illustrate the efficacy of our approach. Our work is not only important from a modeling perspective, but also has valuable behavioral and managerial implications, which modelers and non-modelers alike should find useful. Copyright Springer Science+Business Media, LLC 2012

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    File URL: http://hdl.handle.net/10.1007/s11002-012-9192-3
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    Bibliographic Info

    Article provided by Springer in its journal Marketing Letters.

    Volume (Year): 23 (2012)
    Issue (Month): 3 (September)
    Pages: 839-849

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    Handle: RePEc:kap:mktlet:v:23:y:2012:i:3:p:839-849

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    Web page: http://www.springerlink.com/link.asp?id=100312

    Related research

    Keywords: Reference price; Logit choice models; Logistic regression; Non-iterative estimation; Heaviside step function; Maximum likelihood estimation; Finite mixture models; Misspecified models;

    References

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    1. Heath, Timothy B & Chatterjee, Subimal & France, Karen Russo, 1995. " Mental Accounting and Changes in Price: The Frame Dependence of Reference Dependence," Journal of Consumer Research, University of Chicago Press, University of Chicago Press, vol. 22(1), pages 90-97, June.
    2. Winer, Russell S, 1986. " A Reference Price Model of Brand Choice for Frequently Purchased Products," Journal of Consumer Research, University of Chicago Press, University of Chicago Press, vol. 13(2), pages 250-56, September.
    3. Bruce G. S. Hardie & Eric J. Johnson & Peter S. Fader, 1993. "Modeling Loss Aversion and Reference Dependence Effects on Brand Choice," Marketing Science, INFORMS, INFORMS, vol. 12(4), pages 378-394.
    4. Praveen K. Kopalle & Ambar G. Rao & João L. Assunção, 1996. "Asymmetric Reference Price Effects and Dynamic Pricing Policies," Marketing Science, INFORMS, INFORMS, vol. 15(1), pages 60-85.
    5. Wolfgang Jank & P. K. Kannan, 2005. "Understanding Geographical Markets of Online Firms Using Spatial Models of Customer Choice," Marketing Science, INFORMS, INFORMS, vol. 24(4), pages 623-634, December.
    6. Peter M. Guadagni & John D. C. Little, 1983. "A Logit Model of Brand Choice Calibrated on Scanner Data," Marketing Science, INFORMS, INFORMS, vol. 2(3), pages 203-238.
    7. P. K. Kannan & Gordon P. Wright, 1991. "Modeling and Testing Structured Markets: A Nested Logit Approach," Marketing Science, INFORMS, INFORMS, vol. 10(1), pages 58-82.
    8. Kamins, Michael A & Dreze, Xavier & Folkes, Valerie S, 2004. " Effects of Seller-Supplied Prices on Buyers' Product Evaluations: Reference Prices in an Internet Auction Context," Journal of Consumer Research, University of Chicago Press, University of Chicago Press, vol. 30(4), pages 622-28, March.
    9. Marcus Cunha Jr. & Jeffrey D. Shulman, 2011. "Assimilation and Contrast in Price Evaluations," Journal of Consumer Research, University of Chicago Press, University of Chicago Press, vol. 37(5), pages 822 - 835.
    10. Briesch, Richard A, et al, 1997. " A Comparative Analysis of Reference Price Models," Journal of Consumer Research, University of Chicago Press, University of Chicago Press, vol. 24(2), pages 202-14, September.
    11. Janiszewski, Chris & Lichtenstein, Donald R, 1999. " A Range Theory Account of Price Perception," Journal of Consumer Research, University of Chicago Press, University of Chicago Press, vol. 25(4), pages 353-68, March.
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