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Bayesian analysis of random coefficient logit models using aggregate data

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  • Jiang, Renna
  • Manchanda, Puneet
  • Rossi, Peter E.

Abstract

We present a Bayesian approach for analyzing aggregate level sales data in a market with differentiated products. We consider the aggregate share model proposed by Berry et al. [Berry, Steven, Levinsohn, James, Pakes, Ariel, 1995. Automobile prices in market equilibrium. Econometrica. 63 (4), 841-890], which introduces a common demand shock into an aggregated random coefficient logit model. A full likelihood approach is possible with a specification of the distribution of the common demand shock. We introduce a reparameterization of the covariance matrix to improve the performance of the random walk Metropolis for covariance parameters. We illustrate the usefulness of our approach with both actual and simulated data. Sampling experiments show that our approach performs well relative to the GMM estimator even in the presence of a mis-specified shock distribution. We view our approach as useful for those who are willing to trade off one additional distributional assumption for increased efficiency in estimation.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 149 (2009)
Issue (Month): 2 (April)
Pages: 136-148

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Handle: RePEc:eee:econom:v:149:y:2009:i:2:p:136-148

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Random coefficient logit Aggregate share models Bayesian analysis;

References

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  1. Steven T. Berry, 1994. "Estimating Discrete-Choice Models of Product Differentiation," RAND Journal of Economics, The RAND Corporation, vol. 25(2), pages 242-262, Summer.
  2. repec:rje:randje:v:37:y:2006:i:4:p:964-982 is not listed on IDEAS
  3. Aviv Nevo, 1998. "Measuring Market Power in the Ready-to-Eat Cereal Industry," NBER Working Papers 6387, National Bureau of Economic Research, Inc.
  4. Avi Goldfarb & Qiang Lu & Sridhar Moorthy, 2009. "Measuring Brand Value in an Equilibrium Framework," Marketing Science, INFORMS, vol. 28(1), pages 69-86, 01-02.
  5. Aviv Nevo, 2000. "Mergers with Differentiated Products: The Case of the Ready-to-Eat Cereal Industry," RAND Journal of Economics, The RAND Corporation, vol. 31(3), pages 395-421, Autumn.
  6. Conley, Timothy G. & Hansen, Christian B. & McCulloch, Robert E. & Rossi, Peter E., 2008. "A semi-parametric Bayesian approach to the instrumental variable problem," Journal of Econometrics, Elsevier, vol. 144(1), pages 276-305, May.
  7. Pradeep Chintagunta & Jean-Pierre Dubé & Vishal Singh, 2003. "Balancing Profitability and Customer Welfare in a Supermarket Chain," Quantitative Marketing and Economics, Springer, vol. 1(1), pages 111-147, March.
  8. Charles Romeo, 2007. "A Gibbs sampler for mixed logit analysis of differentiated product markets using aggregate data," Computational Economics, Society for Computational Economics, vol. 29(1), pages 33-68, February.
  9. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-90, July.
  10. K. Sudhir, 2001. "Competitive Pricing Behavior in the Auto Market: A Structural Analysis," Marketing Science, INFORMS, vol. 20(1), pages 42-60, January.
  11. Goettler, Ronald L & Shachar, Ron, 2001. "Spatial Competition in the Network Television Industry," RAND Journal of Economics, The RAND Corporation, vol. 32(4), pages 624-56, Winter.
  12. 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.
  13. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
  14. K. Sudhir, 2001. "Competitive Pricing Behavior in the US Auto Market: A Structural Analysis," Yale School of Management Working Papers ysm228, Yale School of Management.
  15. Han Hong, 2007. "A Statistical Inquiry into the Plausibility of Recursive Utility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(4), pages 523-559, Fall.
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Citations

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Cited by:
  1. Bart Bronnenberg & Jean Dubé & Carl Mela & Paulo Albuquerque & Tulin Erdem & Brett Gordon & Dominique Hanssens & Guenter Hitsch & Han Hong & Baohong Sun, 2008. "Measuring long-run marketing effects and their implications for long-run marketing decisions," Marketing Letters, Springer, vol. 19(3), pages 367-382, December.
  2. Mathias REYNAERT & Frank VERBOVEN, 2012. "Improving the performance of random coefficients demand models: the role of optimal instruments," Center for Economic Studies - Discussion papers ces12.07, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  3. German Zenetti & Thomas Otter, 2014. "Bayesian estimation of the random coefficients logit from aggregate count data," Quantitative Marketing and Economics, Springer, vol. 12(1), pages 43-84, March.
  4. Abidoye, Babatunde & Herriges, Joseph A. & Tobias, Justin, 2010. "Controlling for Observed and Unobserved Site Characteristics in Rum Models of Recreation Demand," Staff General Research Papers 31559, Iowa State University, Department of Economics.
  5. Benjamin Reed Shiller, 2012. "Digital Distribution and the Prohibition of Resale Markets for Information Goods," Working Papers 59, Brandeis University, Department of Economics and International Businesss School.
  6. Klomp, Jeroen, 2010. "Causes of banking crises revisited," The North American Journal of Economics and Finance, Elsevier, vol. 21(1), pages 72-87, March.
  7. Zenetti, German, 2010. "A Note on 'Bayesian analysis of the random coefficient model using aggregate data', an alternative approach," MPRA Paper 26449, University Library of Munich, Germany.
  8. Zhou, Yiyi, 2012. "Failure to Launch in Two-Sided Markets: A Study of the U.S. Video Game Market," MPRA Paper 42002, University Library of Munich, Germany.
  9. Sugawara, Shinya, 2012. "A nonparametric Bayesian approach for counterfactual prediction with an application to the Japanese private nursing home market," MPRA Paper 42154, University Library of Munich, Germany.

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