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A Bayesian mixed logit-probit model for multinomial choice

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Author Info

  • Martin Burda
  • Matthew Harding

    (Institute for Fiscal Studies and Stanford University)

  • Jerry Hausman

    () (Institute for Fiscal Studies and Massachusetts Institute of Technology)

Abstract

In this paper we introduce a new flexible mixed model for multinomial discrete choice where the key individual- and alternative-specific parameters of interest are allowed to follow an assumption-free nonparametric density specification while other alternative-specific coefficients are assumed to be drawn from a multivariate normal distribution which eliminates the independence of irrelevant alternatives assumption at the individual level. A hierarchical specification of our model allows us to break down a complex data structure into a set of submodels with the desired features that are naturally assembled in the original system. We estimate the model using a Bayesian Markov Chain Monte Carlo technique with a multivariate Dirichlet Process (DP) prior on the coefficients with nonparametrically estimated density. We employ a "latent class" sampling algorithm which is applicable to a general class of models including non-conjugate DP base priors. The model is applied to supermarket choices of a panel of Houston households whose shopping behavior was observed over a 24-month period in years 2004-2005. We estimate the nonparametric density of two key variables of interest: the price of a basket of goods based on scanner data, and driving distance to the supermarket based on their respective locations. Our semi-parametric approach allows us to identify a complex multi-modal preference distribution which distinguishes between inframarginal consumers and consumers who strongly value either lower prices or shopping convenience.

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File URL: http://cemmap.ifs.org.uk/wps/cwp2308.pdf
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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP23/08.

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Date of creation: Aug 2008
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Handle: RePEc:ifs:cemmap:23/08

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References

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  1. Dunson, David B., 2005. "Bayesian Semiparametric Isotonic Regression for Count Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 618-627, June.
  2. Markus Jochmann & Roberto Leon-Gonzalez, 2003. "Estimating the Demand for Health Care with Panel Data: A Semiparametric Bayesian Approach," Working Papers 2003005, The University of Sheffield, Department of Economics, revised Oct 2003.
  3. Peter J. Green, 2001. "Modelling Heterogeneity With and Without the Dirichlet Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 28(2), pages 355-375.
  4. Jensen, Mark J. & Maheu, John M., 2010. "Bayesian semiparametric stochastic volatility modeling," Journal of Econometrics, Elsevier, vol. 157(2), pages 306-316, August.
  5. Susan Athey & Guido Imbens, 2006. "Discrete Choice Models with Multiple Unobserved Choice Characteristics," Levine's Bibliography 122247000000001040, UCLA Department of Economics.
  6. Keisuke Hirano, 2002. "Semiparametric Bayesian Inference in Autoregressive Panel Data Models," Econometrica, Econometric Society, vol. 70(2), pages 781-799, March.
  7. Imai, Kosuke & van Dyk, David A., 2005. "A Bayesian analysis of the multinomial probit model using marginal data augmentation," Journal of Econometrics, Elsevier, vol. 124(2), pages 311-334, February.
  8. 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.
  9. Beggs, S. & Cardell, S. & Hausman, J., 1981. "Assessing the potential demand for electric cars," Journal of Econometrics, Elsevier, vol. 17(1), pages 1-19, September.
  10. Matthew C. Harding & Jerry Hausman, 2007. "Using A Laplace Approximation To Estimate The Random Coefficients Logit Model By Nonlinear Least Squares," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1311-1328, November.
  11. Chib, Siddhartha & Hamilton, Barton H., 2002. "Semiparametric Bayes analysis of longitudinal data treatment models," Journal of Econometrics, Elsevier, vol. 110(1), pages 67-89, September.
  12. Austan Goolsbee & Amil Petrin, 2004. "The Consumer Gains from Direct Broadcast Satellites and the Competition with Cable TV," Econometrica, Econometric Society, vol. 72(2), pages 351-381, 03.
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Citations

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Cited by:
  1. Martin Burda & Artem Prokhorov, 2012. "Copula Based Factorization in Bayesian Multivariate Infinite Mixture Models," Working Papers 12012, Concordia University, Department of Economics.
  2. Steven T. Berry & Philip A. Haile, 2009. "Nonparametric Identification of Multinomial Choice Demand Models with Heterogeneous Consumers," Cowles Foundation Discussion Papers 1718, Cowles Foundation for Research in Economics, Yale University, revised Mar 2010.
  3. Griffith, Rachel & Miller, Helen & O'Connell, Martin, 2011. "Corporate taxes and the location of intellectual property," CEPR Discussion Papers 8424, C.E.P.R. Discussion Papers.
  4. Igor Prünster & Matteo Ruggiero, 2011. "A Bayesian nonparametric approach to modeling market share dynamics," Carlo Alberto Notebooks 217, Collegio Carlo Alberto.
  5. Patrick Bajari & Jeremy T. Fox & Kyoo il Kim & Stephen P. Ryan, 2009. "A Simple Nonparametric Estimator for the Distribution of Random Coefficients," NBER Working Papers 15210, National Bureau of Economic Research, Inc.
  6. Kenneth L. Judd & Ben Skrainka, 2011. "High performance quadrature rules: how numerical integration affects a popular model of product differentiation," CeMMAP working papers CWP03/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  7. Patricia Apps & Jan Kabátek & Ray Rees & Arthur van Soest, 2012. "Labor Supply Heterogeneity and Demand for Child Care of Mothers with Young Children," CEPR Discussion Papers 677, Centre for Economic Policy Research, Research School of Economics, Australian National University.
  8. Apps, Patricia & Kabatek, Jan & Rees, Ray & van Soest, Arthur, 2012. "Labor Supply Heterogeneity and Demand for Child Care of Mothers with Young Children," IZA Discussion Papers 7007, Institute for the Study of Labor (IZA).

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