IDEAS home Printed from
   My bibliography  Save this article

A Constructive Approach to Estimating Pure Characteristics Demand Models with Pricing


  • Jong-Shi Pang

    () (Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, California 90089)

  • Che-Lin Su

    () (The University of Chicago Booth School of Business, Chicago, Illinois 60637)

  • Yu-Ching Lee

    () (Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801)


Discrete-choice demand models are important and fundamental tools for understanding consumers’ choice behavior and for analyzing firms’ operations and pricing strategies. In these models, products are often described as a vector of observed characteristics. A consumer chooses the product that maximizes her utility, assumed to be a function of the observed product characteristics and the consumer’s preference over these product characteristics. One central task in the demand estimation literature is to infer, based on observed data, consumers’ preferences on product characteristics. We consider such an estimation problem for pure characteristics models, a class of random coefficients demand models without the idiosyncratic logit error term in a consumer’s utility function. The absence of the logit error term and the use of numerical integration to approximate the integral in aggregate market shares lead to a nonsmooth formulation of approximated market share equations. As a result, solving the approximated market share equations and estimating the model by using existing methods proposed in the econometrics literature remain computationally intractable. To overcome this difficulty, we first characterize consumers’ purchase decisions by a system of complementarity constraints. This new characterization leads to smooth approximated market share equations and allows us to cast the corresponding generalized method of moments (GMM) estimation problem essentially as a quadratic program with linear complementarity constraints, parameterized by an exponential, thus nonlinear, function of the structural parameter on price. We also extend this estimation framework to incorporate an endogenous pricing mechanism that captures the competitive profit maximization behavior of the producing firms. We provide existence results of a solution for the GMM estimator and present numerical results to demonstrate the computational effectiveness of our approach.

Suggested Citation

  • Jong-Shi Pang & Che-Lin Su & Yu-Ching Lee, 2015. "A Constructive Approach to Estimating Pure Characteristics Demand Models with Pricing," Operations Research, INFORMS, vol. 63(3), pages 639-659, June.
  • Handle: RePEc:inm:oropre:v:63:y:2015:i:3:p:639-659

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Gustavo Vulcano & Garrett van Ryzin & Richard Ratliff, 2012. "Estimating Primary Demand for Substitutable Products from Sales Transaction Data," Operations Research, INFORMS, vol. 60(2), pages 313-334, April.
    2. Jean‐Pierre Dubé & Jeremy T. Fox & Che‐Lin Su, 2012. "Improving the Numerical Performance of Static and Dynamic Aggregate Discrete Choice Random Coefficients Demand Estimation," Econometrica, Econometric Society, vol. 80(5), pages 2231-2267, September.
    3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    4. Che‐Lin Su & Kenneth L. Judd, 2012. "Constrained Optimization Approaches to Estimation of Structural Models," Econometrica, Econometric Society, vol. 80(5), pages 2213-2230, September.
    5. Roger Wets, 1999. "Statistical estimation from an optimization viewpoint," Annals of Operations Research, Springer, vol. 85(0), pages 79-101, January.
    6. Kalyan Talluri & Garrett van Ryzin, 2004. "Revenue Management Under a General Discrete Choice Model of Consumer Behavior," Management Science, INFORMS, vol. 50(1), pages 15-33, January.
    7. Nikhil Agarwal, 2015. "An Empirical Model of the Medical Match," American Economic Review, American Economic Association, vol. 105(7), pages 1939-1978, July.
    8. Guillermo Gallego & Ruxian Wang, 2014. "Multiproduct Price Optimization and Competition Under the Nested Logit Model with Product-Differentiated Price Sensitivities," Operations Research, INFORMS, vol. 62(2), pages 450-461, April.
    9. Minjae Song, 2007. "Measuring consumerwelfareinthe CPU market: anapplication of the pure-characteristics demand model," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 429-446, June.
    10. Ward Hanson & Kipp Martin, 1996. "Optimizing Multinomial Logit Profit Functions," Management Science, INFORMS, vol. 42(7), pages 992-1003, July.
    11. Lijie Bai & John Mitchell & Jong-Shi Pang, 2013. "On convex quadratic programs with linear complementarity constraints," Computational Optimization and Applications, Springer, vol. 54(3), pages 517-554, April.
    Full references (including those not matched with items on IDEAS)


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:63:y:2015:i:3:p:639-659. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.