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Bayesian Analysis of Nested Logit Model by Markov Chain Monte Carlo

  • Kajal Lahiri
  • Jian Gao

We develop a Markov Chain Monte Carlo (MCMC) algorithm for estimating nested logit models in a Bayesian framework. Appropriate "heating target" and reparameterization techniques are adopted for fast mixing. For illustrative purposes, we have implemented the algorithm on two real-life examples involving 3-level structures. The first example involves Social Security's disability determination process, Lahiri et al. (1995). The second one is taken from Amemiya and Shimono's (1989) model of labor supply behavior of the aged. We applied a combination of various convergence criteria to ensure that the chain has converged to its target distribution.

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File URL: http://www.albany.edu/economics/research/workingp/2001/isba5.pdf
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Paper provided by University at Albany, SUNY, Department of Economics in its series Discussion Papers with number 01-14.

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Date of creation: 2001
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Handle: RePEc:nya:albaec:01-14
Contact details of provider: Postal: Department of Economics, BA 110 University at Albany State University of New York Albany, NY 12222 U.S.A.
Phone: (518) 442-4735
Fax: (518) 442-4736

Order Information: Postal: Department of Economics, BA 110 University at Albany State University of New York Albany, NY 12222 U.S.A.
Web: http://www.albany.edu/economics/research/workingp/index.shtml Email:


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  1. Herriges, Joseph A. & Kling, Catherine L., 1996. "Testing the Consistency of Nested Logit Models with Utility Maximization," Staff General Research Papers 1500, Iowa State University, Department of Economics.
  2. Cameron, Trudy Ann, 1985. "A Nested Logit Model of Energy Conservation Activity by Owners of Existing Single Family Dwellings," The Review of Economics and Statistics, MIT Press, vol. 67(2), pages 205-11, May.
  3. John Geweke, 1999. "Using simulation methods for bayesian econometric models: inference, development,and communication," Econometric Reviews, Taylor & Francis Journals, vol. 18(1), pages 1-73.
  4. Hensher, David A, 1986. "Sequential and Full Information Maximum Likelihood Estimation of a Nested Logit Model," The Review of Economics and Statistics, MIT Press, vol. 68(4), pages 657-67, November.
  5. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  6. Kling, Catherine L. & Herriges, Joseph A., 1995. "Empirical Investigation of the Consistency of Nested Logit Models with Utility Maximization (An)," Staff General Research Papers 1499, Iowa State University, Department of Economics.
  7. Jianting Hu & Kajal Lahiri & Denton R. Vaughan & Bernard Wixon, 2001. "A Structural Model Of Social Security'S Disability Determination Process," The Review of Economics and Statistics, MIT Press, vol. 83(2), pages 348-361, May.
  8. Catherine L. Kling & Cynthia J. Thomson, 1996. "The Implications of Model Specification for Welfare Estimation in Nested Logit Models," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 78(1), pages 103-114.
  9. Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(03), pages 409-431, August.
  10. Siddhartha Chib & Edward Greenberg & Yuxin Chen, 1998. "MCMC Methods for Fitting and Comparing Multinomial Response Models," Econometrics 9802001, EconWPA, revised 06 May 1998.
  11. Train, Kenneth, 1980. "A Structured Logit Model of Auto Ownership and Mode Choice," Review of Economic Studies, Wiley Blackwell, vol. 47(2), pages 357-70, January.
  12. John Geweke, 1992. "Priors for macroeconomic time series and their application," Discussion Paper / Institute for Empirical Macroeconomics 64, Federal Reserve Bank of Minneapolis.
  13. Train, Kenneth E & Ben-Akiva, Moshe & Atherton, Terry, 1989. "Consumption Patterns and Self-selecting Tariffs," The Review of Economics and Statistics, MIT Press, vol. 71(1), pages 62-73, February.
  14. Matthews, Peter, 1993. "A slowly mixing Markov chain with implications for Gibbs sampling," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 231-236, June.
  15. Koop, Gary & Poirier, Dale J., 1993. "Bayesian analysis of logit models using natural conjugate priors," Journal of Econometrics, Elsevier, vol. 56(3), pages 323-340, April.
  16. Paulo Guimaraes & Robert J. Rolfe & Douglas P. Woodward, 1998. "Regional Incentives and Industrial Location in Puerto Rico," International Regional Science Review, , vol. 21(2), pages 119-138, August.
  17. 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.
  18. Daniel McFadden, 1977. "Quantitative Methods for Analyzing Travel Behaviour of Individuals: Some Recent Developments," Cowles Foundation Discussion Papers 474, Cowles Foundation for Research in Economics, Yale University.
  19. Kling, Catherine L. & Thomson, Cynthia J., 1996. "Implications of Model Specification for Welfare Estimation in Nested Logit Models (The)," Staff General Research Papers 1599, Iowa State University, Department of Economics.
  20. Koning, Ruud H. & Ridder, Geert, 1994. "On the compatibility of nested logit models with utility maximization : A comment," Journal of Econometrics, Elsevier, vol. 63(2), pages 389-396, August.
  21. Poirier, Dale J., 1996. "A Bayesian analysis of nested logit models," Journal of Econometrics, Elsevier, vol. 75(1), pages 163-181, November.
  22. Borsch-Supan, Axel, 1990. "On the compatibility of nested logit models with utility maximization," Journal of Econometrics, Elsevier, vol. 43(3), pages 373-388, March.
  23. McFadden, Daniel, 1980. "Econometric Models for Probabilistic Choice among Products," The Journal of Business, University of Chicago Press, vol. 53(3), pages S13-29, July.
  24. Falaris, Evangelos M, 1987. "A Nested Logit Migration Model with Selectivity," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(2), pages 429-43, June.
  25. Brownstone, David & Small, Kenneth A, 1989. "Efficient Estimation of Nested Logit Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(1), pages 67-74, January.
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