IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v111y2002i1p103-133.html
   My bibliography  Save this article

Bayesian analysis of nested logit model by Markov chain Monte Carlo

Author

Listed:
  • 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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Lahiri, Kajal & Gao, Jian, 2002. "Bayesian analysis of nested logit model by Markov chain Monte Carlo," Journal of Econometrics, Elsevier, vol. 111(1), pages 103-133, November.
  • Handle: RePEc:eee:econom:v:111:y:2002:i:1:p:103-133
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(02)00125-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Weiler, William C., 1989. "A flexible approach to modelling enrollment choice behavior," Economics of Education Review, Elsevier, vol. 8(3), pages 277-283, June.
    2. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    3. Geweke, John, 1994. "Priors for Macroeconomic Time Series and Their Application," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 609-632, August.
    4. Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(3), pages 409-431, August.
    5. 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.
    6. 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.
    7. 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 429-443, June.
    8. McFadden, Daniel, 1980. "Econometric Models for Probabilistic Choice among Products," The Journal of Business, University of Chicago Press, vol. 53(3), pages 13-29, July.
    9. Catherine L. Kling & Joseph A. Herriges, 1995. "An Empirical Investigation of the Consistency of Nested Logit Models with Utility Maximization," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 77(4), pages 875-884.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Siddhartha Chib & Edward Greenberg, 1996. "Bayesian Analysis of Multivariate Probit Models," Econometrics 9608002, University Library of Munich, Germany.
    15. K. Bruce Newbold, 1997. "Primary, Return And Onward Migration In The U.S. And Canada: Is There A Difference?," Papers in Regional Science, Wiley Blackwell, vol. 76(2), pages 175-198, April.
    16. 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.
    17. Kenneth Train, 1980. "A Structured Logit Model of Auto Ownership and Mode Choice," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(2), pages 357-370.
    18. Matthews, Peter, 1993. "A slowly mixing Markov chain with implications for Gibbs sampling," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 231-236, June.
    19. Hausman, Jerry A. & Leonard, Gregory K. & McFadden, Daniel, 1995. "A utility-consistent, combined discrete choice and count data model Assessing recreational use losses due to natural resource damage," Journal of Public Economics, Elsevier, vol. 56(1), pages 1-30, January.
    20. 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 657-667, November.
    21. Christopher A. Sims, 1991. "Comment on 'To Criticize the Critics,' by Peter C. B. Phillips," Cowles Foundation Discussion Papers 985, Cowles Foundation for Research in Economics, Yale University.
    22. Berkovec, James & Rust, John, 1985. "A nested logit model of automobile holdings for one vehicle households," Transportation Research Part B: Methodological, Elsevier, vol. 19(4), pages 275-285, August.
    23. John Geweke, 1999. "Using Simulation Methods for Bayesian Econometric Models," Computing in Economics and Finance 1999 832, Society for Computational Economics.
    24. 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.
    25. Siddhartha Chib & Edward Greenberg & Yuxin Chen, 1998. "MCMC Methods for Fitting and Comparing Multinomial Response Models," Econometrics 9802001, University Library of Munich, Germany, revised 06 May 1998.
    26. Sims, Christopher A, 1991. "To Criticize the Critics: Comment," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 423-434, Oct.-Dec..
    27. Poirier, Dale J., 1996. "A Bayesian analysis of nested logit models," Journal of Econometrics, Elsevier, vol. 75(1), pages 163-181, November.
    28. J. C. Naylor & A. F. M. Smith, 1982. "Applications of a Method for the Efficient Computation of Posterior Distributions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(3), pages 214-225, November.
    29. 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.
    30. 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.
    31. 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.
    32. 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 205-211, May.
    33. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Method of the month: custom likelihoods with Stan
      by Sam Watson in The Academic Health Economists' Blog on 2018-05-18 06:00:27

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ricardo A. Daziano & Luis Miranda-Moreno & Shahram Heydari, 2013. "Computational Bayesian Statistics in Transportation Modeling: From Road Safety Analysis to Discrete Choice," Transport Reviews, Taylor & Francis Journals, vol. 33(5), pages 570-592, September.
    2. Gil-Molto, Maria Jose & Hole, Arne Risa, 2004. "Tests for the consistency of three-level nested logit models with utility maximization," Economics Letters, Elsevier, vol. 85(1), pages 133-137, October.
    3. Martin, Gael M. & Frazier, David T. & Maneesoonthorn, Worapree & Loaiza-Maya, Rubén & Huber, Florian & Koop, Gary & Maheu, John & Nibbering, Didier & Panagiotelis, Anastasios, 2024. "Bayesian forecasting in economics and finance: A modern review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 811-839.
    4. Gael M. Martin & David T. Frazier & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2023. "Bayesian Forecasting in the 21st Century: A Modern Review," Monash Econometrics and Business Statistics Working Papers 1/23, Monash University, Department of Econometrics and Business Statistics.
    5. 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, November.
    6. 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.
    7. Rik Pieters & Michel Wedel, 2012. "Ad Gist: Ad Communication in a Single Eye Fixation," Marketing Science, INFORMS, vol. 31(1), pages 59-73, January.
    8. Grzenda Wioletta, 2021. "Modelling the occupational and educational choices of young people in Poland using Bayesian multinomial logit models," Statistics in Transition New Series, Statistics Poland, vol. 22(3), pages 175-191, September.
    9. 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.
    10. Mauricio Sillano & Juan de Dios Ortúzar, 2005. "Willingness-to-Pay Estimation with Mixed Logit Models: Some New Evidence," Environment and Planning A, , vol. 37(3), pages 525-550, March.
    11. Kajal Lahiri & Chuanming Gao & Bernard Wixon, 2020. "Value of Sample Separation Information in a Sequential Probit Model," Arthaniti: Journal of Economic Theory and Practice, , vol. 19(2), pages 151-176, December.
    12. 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 Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    13. 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.
    14. 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.
    15. DeSouza, Sergio Aquino, 2006. "Combining Aggregate and Plant-Level Data to Estimate a Discrete-Choice Demand Model," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 26(2), November.
    16. Wioletta Grzenda, 2021. "Modelling the occupational and educational choices of young people in Poland using Bayesian multinomial logit models," Statistics in Transition New Series, Polish Statistical Association, vol. 22(3), pages 175-191, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kurt Schwabe & Peter Schuhmann & Roy Boyd & Khosrow Doroodian, 2001. "The Value of Changes in Deer Season Length: An Application of the Nested Multinomial Logit Model," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 19(2), pages 131-147, June.
    2. Schwabe, Kurt A. & Schuhmann, Peter W., 1999. "The Value Of Increasing The Length Of Deer Season In Ohio," 1999 Annual meeting, August 8-11, Nashville, TN 21574, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    3. Poirier, Dale J., 1996. "A Bayesian analysis of nested logit models," Journal of Econometrics, Elsevier, vol. 75(1), pages 163-181, November.
    4. Luc Bauwens & Charles S. Bos & Herman K. van Dijk, 1999. "Adaptive Polar Sampling with an Application to a Bayes Measure of Value-at-Risk," Tinbergen Institute Discussion Papers 99-082/4, Tinbergen Institute.
    5. Gil-Molto, Maria Jose & Hole, Arne Risa, 2004. "Tests for the consistency of three-level nested logit models with utility maximization," Economics Letters, Elsevier, vol. 85(1), pages 133-137, October.
    6. Gil-Molto, Maria Jose & Hole, Arne Risa, 2004. "Tests for the consistency of three-level nested logit models with utility maximization," Economics Letters, Elsevier, vol. 85(1), pages 133-137, October.
    7. Hoogerheide, Lennart F. & Kaashoek, Johan F. & van Dijk, Herman K., 2007. "On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: An application of flexible sampling methods using neural networks," Journal of Econometrics, Elsevier, vol. 139(1), pages 154-180, July.
    8. Florian Pelgrin & Stéphane Adjemian, 2008. "Un regard bayésien sur les modèles dynamiques de la macroéconomie," Économie et Prévision, Programme National Persée, vol. 183(2), pages 127-152.
    9. repec:rri:wpaper:200704 is not listed on IDEAS
    10. Christiadi & Brian Cushing, 2007. "Conditional Logit, IIA, and Alternatives for Estimating Models of Interstate Migration," Working Papers Working Paper 2007-04, Regional Research Institute, West Virginia University.
    11. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    12. Arne R. Hole & Felix R. FitzRoy, 2003. "Commuting in small towns in rural areas: the case of St Andrews," Urban/Regional 0312001, University Library of Munich, Germany, revised 12 Apr 2004.
    13. Lennart F. Hoogerheide & Johan F. Kaashoek, 2004. "Functional Approximations to Likelihoods/Posterior Densities: A Neural Network Approach to Efficient Sampling," Computing in Economics and Finance 2004 74, Society for Computational Economics.
    14. Gael M. Martin & David T. Frazier & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2023. "Bayesian Forecasting in the 21st Century: A Modern Review," Monash Econometrics and Business Statistics Working Papers 1/23, Monash University, Department of Econometrics and Business Statistics.
    15. Stafford, Tess M., 2018. "Accounting for outside options in discrete choice models: An application to commercial fishing effort," Journal of Environmental Economics and Management, Elsevier, vol. 88(C), pages 159-179.
    16. Brownstone, David, 2001. "Discrete Choice Modeling for Transportation," University of California Transportation Center, Working Papers qt29v7d1pk, University of California Transportation Center.
    17. Martin, Gael M. & Frazier, David T. & Maneesoonthorn, Worapree & Loaiza-Maya, Rubén & Huber, Florian & Koop, Gary & Maheu, John & Nibbering, Didier & Panagiotelis, Anastasios, 2024. "Bayesian forecasting in economics and finance: A modern review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 811-839.
    18. Phaneuf, Daniel J. & Smith, V. Kerry, 2006. "Recreation Demand Models," Handbook of Environmental Economics, in: K. G. Mäler & J. R. Vincent (ed.), Handbook of Environmental Economics, edition 1, volume 2, chapter 15, pages 671-761, Elsevier.
    19. Tsionas, Mike G., 2019. "Multi-objective optimization using statistical models," European Journal of Operational Research, Elsevier, vol. 276(1), pages 364-378.
    20. John Geweke & Joel Horowitz & M. Hashem Pesaran, 2006. "Econometrics: A Bird’s Eye View," CESifo Working Paper Series 1870, CESifo.
    21. Efthymios G. Tsionas, 2006. "Inference in dynamic stochastic frontier models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(5), pages 669-676, July.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:111:y:2002:i:1:p:103-133. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.