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

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  • Charles Romeo

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    Abstract

    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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    Bibliographic Info

    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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    Web page: http://www.springerlink.com/link.asp?id=100248
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    Related research

    Keywords: Gibbs sampler; Mixed logit; Differentiated product markets; L1; C11; C15; C33;

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    1. Amil Petrin & Kenneth Train, 2003. "Omitted Product Attributes in Discrete Choice Models," NBER Working Papers 9452, National Bureau of Economic Research, Inc.
    2. Nevo, Aviv, 2001. "Measuring Market Power in the Ready-to-Eat Cereal Industry," Econometrica, Econometric Society, vol. 69(2), pages 307-42, March.
    3. John Geweke, 1995. "Monte Carlo simulation and numerical integration," Staff Report 192, Federal Reserve Bank of Minneapolis.
    4. Steve Berry & Oliver B. Linton & Ariel Pakes, 2004. "Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems," Review of Economic Studies, Wiley Blackwell, vol. 71, pages 613-654, 07.
    5. Sofia Berto Villas-Boas, 2007. "Vertical Relationships between Manufacturers and Retailers: Inference with Limited Data," Review of Economic Studies, Oxford University Press, vol. 74(2), pages 625-652.
    6. Peter Davis, 2006. "Spatial competition in retail markets: movie theaters," RAND Journal of Economics, RAND Corporation, vol. 37(4), pages 964-982, December.
    7. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-90, July.
    8. Vassilis A. Hajivassiliou & Axel Borsch-Supan, 1990. "Smooth Unbiased Multivariate Probability Simulators for Maximum Likelihood Estimation of Limited Dependent Variable Models," Cowles Foundation Discussion Papers 960, Cowles Foundation for Research in Economics, Yale University.
    9. 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.
    10. Steven Berry & James Levinsohn & Ariel Pakes, 2001. "Differentiated Products Demand Systems from a Combination of Micro and Macro Data: The New Car Market," Cowles Foundation Discussion Papers 1337, Cowles Foundation for Research in Economics, Yale University.
    11. 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.
    12. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1, January.
    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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    Cited by:
    1. Jiang, Renna & Manchanda, Puneet & Rossi, Peter E., 2009. "Bayesian analysis of random coefficient logit models using aggregate data," Journal of Econometrics, Elsevier, vol. 149(2), pages 136-148, April.

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