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A Structured Covariance Probit Demand Model


  • Michael Cohen

    () (New York University)


This paper introduces a heterogeneous agent discrete choice probit demand model with a structural interpretation of product choice covariance designed to overcome two hurdles in discrete choice demand modeling. One hurdle is the curse of dimensionality implicit in covariance probit demand models and the other hurdle is the independence of irrelevant alternatives (IIA) implicit in logit demand models. The structured covariance probit exploits the fact that choice models rely on utility di erences to achieve identi cation. The utility di erence structure implied by the additive random utility model is imposed on the covariance matrix and requires just one parameter in addition to those speci ed in the deterministic component of consumer utility. As an additional advantage the structured covariance probit is a better out-of-sample predictor because it allows covariance to change according to characteristics of the market. To estimate the model the paper develops a Bayesian estimation approach. The model also incorporates a Dirichlet process prior over normally distributed consumer segment clusters to exibly model demand heterogeneity. The new model is evaluated relative to the widely used heterogeneous consumer logit demand model. Sampling experiments con rm that the model performs well under misspeci cation. An empirical analysis demonstrates that the new probit model captures realistic unrestricted switching behavior whereas its logit counterpart exhibits restrictiveness inconsistent with the utility theory on which the model is based.

Suggested Citation

  • Michael Cohen, 2009. "A Structured Covariance Probit Demand Model," Food Marketing Policy Center Research Reports 123, University of Connecticut, Department of Agricultural and Resource Economics, Charles J. Zwick Center for Food and Resource Policy.
  • Handle: RePEc:zwi:fpcrep:123

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    References listed on IDEAS

    1. Botond Kőszegi & Matthew Rabin, 2006. "A Model of Reference-Dependent Preferences," The Quarterly Journal of Economics, Oxford University Press, vol. 121(4), pages 1133-1165.
    2. Jay Bhattacharya & Neeraj Sood, 2005. "Health Insurance and the Obesity Externality," NBER Working Papers 11529, National Bureau of Economic Research, Inc.
    3. Bowman, David & Minehart, Deborah & Rabin, Matthew, 1999. "Loss aversion in a consumption-savings model," Journal of Economic Behavior & Organization, Elsevier, vol. 38(2), pages 155-178, February.
    4. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    5. Botond Koszegi & Matthew Rabin, 2007. "Reference-Dependent Risk Attitudes," American Economic Review, American Economic Association, vol. 97(4), pages 1047-1073, September.
    6. Botond Koszegi & Matthew Rabin, 2009. "Reference-Dependent Consumption Plans," American Economic Review, American Economic Association, vol. 99(3), pages 909-936, June.
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    More about this item


    Probit demand system; Structured covariance; Bayesian MCMC;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation


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