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Endogeneity and Heterogeneity in a Probit Demand Model: Estimation Using Aggregate Data

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  • Pradeep K. Chintagunta

    () (Graduate School of Business, University of Chicago, 1101 East 58th Street, Chicago, Illinois 60637)

Abstract

Two issues that have become increasingly important while estimating the parameters of aggregate demand functions to study firm behavior are the of marketing activities (typically, price) and across consumers in the market under consideration. Ignoring these issues in the estimation of the demand function parameters can lead to biased and inconsistent estimates for the effects of marketing activities. Endogeneity and heterogeneity have achieved prominence in large measure because of the increasing popularity of logit models to characterize demand functions using data. The logit model accounts for purchase incidence and brand choice by including a “no-purchase” alternative in the consumer's choice set. This allows for category sales to change as a function of the marketing activities of brands in the category. There are three issues with using the logit model with the no-purchase option to characterize demand when studying competitive interactions among firms. (1) The marketing literature dealing with brand choice behavior at the consumer level has found that the IIA restriction is not appropriate, as each brand in the choice set is more similar to some brands than it is to others. (2) Studies have found that the purchase incidence decision is distinct from the brand choice decision. Hence, it may not be appropriate to model the no-purchase decision as just another alternative in the choice set with the IIA restriction holding across all brands and the no-purchase option. (3) Even if the distinction between the purchase incidence and brand choice decisions is accounted for via, for example, a nested logit specification, accounting for the purchase incidence decision with aggregate data requires assumptions for computing the share of the no-purchase alternative which is otherwise unobserved. In this paper, we propose a probit model as an alternative to the logit model to specify the aggregate demand functions of firms competing in oligopoly markets. The probit model avoids the IIA property that affects the logit model at the individual consumer level. Furthermore, the probit model can naturally account for the distinction between the purchase incidence and brand choice decisions due to the general covariance structure assumed for the utilities of the alternatives. We demonstrate how the parameters of the proposed model can be estimated using aggregate time series data from a product market. In the estimation, we account for the endogeneity of marketing variables as well as for heterogeneity across consumers. Our results indicate that both endogeneity as well as heterogeneity need to be accounted for even after allowing for a non-IIA specification at the individual consumer level. Specific to our data, we also find that ignoring endogeneity has a bigger impact on the estimated price elasticities than ignoring the effects of heterogeneity. A comparison of the elasticities obtained from the probit model with those from the corresponding logit specification indicates that the of elasticities obtained from the probit model across brands is larger than that obtained from the logit. The results have implications for issues such as firm-level pricing. In addition to specifying a probit model and providing comparisons with the logit model, the paper also addresses the third issue raised above. We propose a simple alternative to the purchase incidence/brand choice specification by decomposing the demand for a brand into a category demand equation and a conditional brand choice share equation. We provide a comparison of results from this specification to those from the specification that includes the no-purchase alternative and find that estimated elasticities are sensitive to the specification used. We also estimate the demand function parameters using a traditional specification such as the double-logarithmic model. Here, we find that the estimated elasticities could be signed in such a manner as to be not useful for firm-level pricing decisions. One of the key limitations of the proposed model is that while it accounts for the purchase incidence and brand choice decisions of households, it does not account for differences across consumers in their purchase quantities. The model and analysis are best suited for product categories in which consumers typically make single-unit purchases. Another limitation is more practical in nature. While recent advances have been made in computing probit probabilities, it could nevertheless be a challenge to do so when the number of alternatives is large.

Suggested Citation

  • Pradeep K. Chintagunta, 2001. "Endogeneity and Heterogeneity in a Probit Demand Model: Estimation Using Aggregate Data," Marketing Science, INFORMS, vol. 20(4), pages 442-456, December.
  • Handle: RePEc:inm:ormksc:v:20:y:2001:i:4:p:442-456
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    File URL: http://dx.doi.org/10.1287/mksc.20.4.442.9751
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    References listed on IDEAS

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    Cited by:

    1. Sungho Park & Sachin Gupta, 2012. "Handling Endogenous Regressors by Joint Estimation Using Copulas," Marketing Science, INFORMS, vol. 31(4), pages 567-586, July.
    2. Greg M. Allenby & Thomas S. Shively & Sha Yang & Mark J. Garratt, 2004. "A Choice Model for Packaged Goods: Dealing with Discrete Quantities and Quantity Discounts," Marketing Science, INFORMS, vol. 23(1), pages 95-108, June.
    3. Juan C. Gázquez-Abad & Manuel Sánchez-Pérez, 2009. "Factors influencing olive oil brand choice in Spain: an empirical analysis using scanner data," Agribusiness, John Wiley & Sons, Ltd., vol. 25(1), pages 36-55.
    4. Haaf, C. Grace & Morrow, W. Ross & Azevedo, Inês M.L. & Feit, Elea McDonnell & Michalek, Jeremy J., 2016. "Forecasting light-duty vehicle demand using alternative-specific constants for endogeneity correction versus calibration," Transportation Research Part B: Methodological, Elsevier, vol. 84(C), pages 182-210.
    5. Edlira Shehu & Tim Prostka & Christina Schmidt-Stölting & Michel Clement & Eva Blömeke, 2014. "The influence of book advertising on sales in the German fiction book market," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 38(2), pages 109-130, May.
    6. Steven M. Shugan, 2002. "In Search of Data: An Editorial," Marketing Science, INFORMS, vol. 21(4), pages 369-377.
    7. Steven M. Shugan, 2005. "Comments on Competitive Responsiveness," Marketing Science, INFORMS, vol. 24(1), pages 3-7.
    8. Juanjuan Zhang & Peng Liu, 2012. "Rational Herding in Microloan Markets," Management Science, INFORMS, vol. 58(5), pages 892-912, May.
    9. Marcus Tamm & Harald Tauchmann & Jürgen Wasem & Stefan Greß, 2007. "Elasticities of market shares and social health insurance choice in germany: a dynamic panel data approach," Health Economics, John Wiley & Sons, Ltd., vol. 16(3), pages 243-256.
    10. Peter Ebbes & Dominik Papies & Harald J. van Heerde, 2011. "The Sense and Non-Sense of Holdout Sample Validation in the Presence of Endogeneity," Marketing Science, INFORMS, vol. 30(6), pages 1115-1122, November.
    11. Avi Goldfarb & Qiang Lu & Sridhar Moorthy, 2009. "Measuring Brand Value in an Equilibrium Framework," Marketing Science, INFORMS, vol. 28(1), pages 69-86, 01-02.
    12. Tchumtchoua, Sylvie & Dey, Dipak, 2007. "Semiparametric Bayesian Estimation of Random Coefficients Discrete Choice Models," Research Reports 149208, University of Connecticut, Food Marketing Policy Center.
    13. Xueming Luo, 2009. "Quantifying the Long-Term Impact of Negative Word of Mouth on Cash Flows and Stock Prices," Marketing Science, INFORMS, vol. 28(1), pages 148-165, 01-02.
    14. Steven M. Shugan, 2004. "Endogeneity in Marketing Decision Models," Marketing Science, INFORMS, vol. 23(1), pages 1-3.
    15. Paulo Albuquerque & Bart J. Bronnenberg, 2009. "Estimating Demand Heterogeneity Using Aggregated Data: An Application to the Frozen Pizza Category," Marketing Science, INFORMS, vol. 28(2), pages 356-372, 03-04.
    16. Peter Ebbes, 2007. "A non-technical guide to instrumental variables and regressor-error dependencies (in Russian)," Quantile, Quantile, issue 2, pages 3-20, March.
    17. S. Sriram & Pradeep K. Chintagunta & Ramya Neelamegham, 2006. "Effects of Brand Preference, Product Attributes, and Marketing Mix Variables in Technology Product Markets," Marketing Science, INFORMS, vol. 25(5), pages 440-456, September.
    18. Raphael Thomadsen, 2007. "Product Positioning and Competition: The Role of Location in the Fast Food Industry," Marketing Science, INFORMS, vol. 26(6), pages 792-804, 11-12.
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    20. Pinar Karaca-Mandic, 2011. "Role of complementarities in technology adoption: The case of DVD players," Quantitative Marketing and Economics (QME), Springer, vol. 9(2), pages 179-210, June.
    21. repec:eee:ijrema:v:32:y:2015:i:2:p:164-178 is not listed on IDEAS

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