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A Gibbs sampler for mixed logit analysis of differentiated product markets using aggregate data

  • Charles Romeo

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    In this paper, we offer the Gibbs sampler as an alternative to the GMM estimator developed by Berry, Levinsohn, and Pakes (Econometrica 63(4), 841–890, 1995) in their equilibrium differentiated product market analysis of the automobile industry. We use the GMM objective as the basis for forming a posterior distribution, thereby making use of certain attributes of the GMM approach that reduce the computational cost of conducting posterior inference. The advantages provided by the our Bayesian GMM approach are that it enables us to conduct inference under the exact posterior distribution for the parameters, to estimate moments of functions of interest that are not readily available using GMM, and to capture non-normalities in the parameter distributions. The cost of posterior inference takes the form of additional distributional assumptions and longer computational time. In an illustration within, we find the random coefficients to be only weakly identified by the data. This results in highly non-normal distributions. The GMM estimates hint at this problem, but it can only be fully characterized by the Gibbs sampler. Copyright Springer Science+Business Media, LLC 2007

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    File URL: http://hdl.handle.net/10.1007/s10614-006-9074-y
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    Article provided by Society for Computational Economics in its journal Computational Economics.

    Volume (Year): 29 (2007)
    Issue (Month): 1 (February)
    Pages: 33-68

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    Handle: RePEc:kap:compec:v:29:y:2007:i:1:p:33-68
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    1. Sha Yang & Yuxin Chen & Greg Allenby, 2003. "Bayesian Analysis of Simultaneous Demand and Supply," Quantitative Marketing and Economics, Springer, vol. 1(3), pages 251-275, September.
    2. Roberts, G. O. & Smith, A. F. M., 1994. "Simple conditions for the convergence of the Gibbs sampler and Metropolis-Hastings algorithms," Stochastic Processes and their Applications, Elsevier, vol. 49(2), pages 207-216, February.
    3. Steven Berry & Oliver Linton & Ariel Pakes, 2002. "Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems," Cowles Foundation Discussion Papers 1372, Cowles Foundation for Research in Economics, Yale University.
    4. Nevo, Aviv, 2001. "Measuring Market Power in the Ready-to-Eat Cereal Industry," Econometrica, Econometric Society, vol. 69(2), pages 307-42, March.
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    7. Aviv Nevo, 1998. "A Research Assistant's Guide to Random Coefficients Discrete Choice Models of Demand," NBER Technical Working Papers 0221, National Bureau of Economic Research, Inc.
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    13. Amil Petrin, 2002. "Quantifying the Benefits of New Products: The Case of the Minivan," Journal of Political Economy, University of Chicago Press, vol. 110(4), pages 705-729, August.
    14. Keane, Michael P, 1994. "A Computationally Practical Simulation Estimator for Panel Data," Econometrica, Econometric Society, vol. 62(1), pages 95-116, January.
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