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Bayesian analysis of nested logit model by Markov chain Monte Carlo

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  • Lahiri, Kajal
  • Gao, Jian

Abstract

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 111 (2002)
Issue (Month): 1 (November)
Pages: 103-133

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Handle: RePEc:eee:econom:v:111:y:2002:i:1:p:103-133

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

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  1. 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.
  2. Geweke, John, 1994. "Priors for Macroeconomic Time Series and Their Application," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 609-632, August.
  3. Matthews, Peter, 1993. "A slowly mixing Markov chain with implications for Gibbs sampling," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 231-236, June.
  4. 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.
  5. Herriges, Joseph A. & Kling, Catherine L., 1996. "Testing the consistency of nested logit models with utility maximization," Economics Letters, Elsevier, vol. 50(1), pages 33-39, January.
  6. 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.
  7. Siddhartha Chib & Edward Greenberg & Yuxin Chen, 1998. "MCMC Methods for Fitting and Comparing Multinomial Response Models," Econometrics 9802001, EconWPA, revised 06 May 1998.
  8. 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.
  9. 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.
  10. Poirier, Dale J., 1996. "A Bayesian analysis of nested logit models," Journal of Econometrics, Elsevier, vol. 75(1), pages 163-181, November.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  20. 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.
  21. 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.
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Citations

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Cited by:
  1. Verlinda, Jeremy A., 2005. "A Bayesian analysis of tree structure specification in nested logit models," Economics Letters, Elsevier, vol. 87(1), pages 67-73, April.
  2. Gary Koop, 2004. "Modelling the evolution of distributions: an application to Major League baseball," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 167(4), pages 639-655.
  3. Sergio Aquino de Souza, 2011. "A Simplified Mixed Logit Demand Model with an Application to the Simulation of Entry," Working Papers 04-2011, Universidade de São Paulo, Faculdade de Economia, Administração e Contabilidade de Ribeirão Preto.
  4. María José Gil-Moltó & Arne Risa Hole, 2003. "Tests for the consistency of three-level nested logit models with utility maximization," Econometrics 0312001, EconWPA, revised 08 Jan 2004.
  5. Haijime Katayama & Shihua Lu & James Tybout, 2003. "Why Plant-Level Productivity Studies are Often Misleading, and an Alternative Approach to Interference," NBER Working Papers 9617, National Bureau of Economic Research, Inc.
  6. Sergio Aquino de Souza, 2008. "Combining Prior Information and Data to Uncover the Parameters from the Random Coefficient Discrete? Choice Demand Model," Anais do XXXVI Encontro Nacional de Economia [Proceedings of the 36th Brazilian Economics Meeting] 200807211342080, ANPEC - Associação Nacional dos Centros de Pósgraduação em Economia [Brazilian Association of Graduate Programs in Economics].
  7. Katayama, Hajime & Lu, Shihua & Tybout, James R., 2009. "Firm-level productivity studies: Illusions and a solution," International Journal of Industrial Organization, Elsevier, vol. 27(3), pages 403-413, May.

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