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A Poisson mixture model of discrete choice

  • Burda, Martin
  • Harding, Matthew
  • Hausman, Jerry

In this paper, we introduce a new Poisson mixture model for count panel data where the underlying Poisson process intensity is determined endogenously by consumer latent utility maximization over a set of choice alternatives. This formulation accommodates the choice and count in a single random utility framework with desirable theoretical properties. Individual heterogeneity is introduced through a random coefficient scheme with a flexible semiparametric distribution. We deal with the analytical intractability of the resulting mixture by recasting the model as an embedding of infinite sequences of scaled moments of the mixing distribution, and newly derive their cumulant representations along with bounds on their rate of numerical convergence. We further develop an efficient recursive algorithm for fast evaluation of the model likelihood within a Bayesian Gibbs sampling scheme. We apply our model to a recent household panel of supermarket visit counts. We estimate the nonparametric density of three key variables of interest–price, driving distance, and their interaction–while controlling for a range of consumer demographic characteristics. We use this econometric framework to assess the opportunity cost of time and analyze the interaction between store choice, trip frequency, search intensity, and household and store characteristics. We also conduct a counterfactual welfare experiment and compute the compensating variation for a 10%–30% increase in Walmart prices.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 166 (2012)
Issue (Month): 2 ()
Pages: 184-203

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Handle: RePEc:eee:econom:v:166:y:2012:i:2:p:184-203
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Nevo, Aviv, 1998. "Measuring Market Power in the Ready-To-Eat Cereal Industry," Food Marketing Policy Center Research Reports 037, University of Connecticut, Department of Agricultural and Resource Economics, Charles J. Zwick Center for Food and Resource Policy.
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  10. Greene, William, 2007. "Functional Form and Heterogeneity in Models for Count Data," Foundations and Trends(R) in Econometrics, now publishers, vol. 1(2), pages 113-218, August.
  11. Andrés Romeu & Marcos Vera-Hern�ndez, 2005. "Counts with an endogenous binary regressor: A series expansion approach," Econometrics Journal, Royal Economic Society, vol. 8(1), pages 1-22, 03.
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  16. repec:cup:cbooks:9780521844727 is not listed on IDEAS
  17. Munkin, Murat K. & Trivedi, Pravin K., 2003. "Bayesian analysis of a self-selection model with multiple outcomes using simulation-based estimation: an application to the demand for healthcare," Journal of Econometrics, Elsevier, vol. 114(2), pages 197-220, June.
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