A Poisson mixture model of discrete choice
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Hausman_A Poisson.pdf
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Author(s)
Burda, Martin
Harding, Matthew
Hausman, Jerry A.
Date Issued
September 2011
Journal
Journal of Econometrics
Publisher
Elsevier
Citation
Burda, Martin, Matthew Harding, and Jerry Hausman. “A Poisson Mixture Model of Discrete Choice.” Journal of Econometrics 166, no. 2 (February 2012): 184–203.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Economics
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Creative Commons Attribution-Noncommercial-NoDerivatives
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DOI of Published Version
https://doi.org/10.1016/j.jeconom.2011.09.001
