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A Multinomial Probit Model with Latent Factors: Identification and Interpretation without a Measurement System

Author

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  • Piatek, Rémi

    (University of Copenhagen)

  • Gensowski, Miriam

    (Rockwool Foundation Research Unit)

Abstract

We develop a parametrization of the multinomial probit model that yields greater insight into the underlying decision-making process, by decomposing the error terms of the utilities into latent factors and noise. The latent factors are identified without a measurement system, and they can be meaningfully linked to an economic model. We provide sufficient conditions that make this structure identified and interpretable. For inference, we design a Markov chain Monte Carlo sampler based on marginal data augmentation. A simulation exercise shows the good numerical performance of our sampler and reveals the practical importance of alternative identification restrictions. Our approach can generally be applied to any setting where researchers can specify an a priori structure on a few drivers of unobserved heterogeneity. One such example is the choice of combinations of two options, which we explore with real data on education and occupation pairs.

Suggested Citation

  • Piatek, Rémi & Gensowski, Miriam, 2017. "A Multinomial Probit Model with Latent Factors: Identification and Interpretation without a Measurement System," IZA Discussion Papers 11042, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp11042
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    References listed on IDEAS

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    1. Axel Borsch-Supan & Vassilis Hajivassiliou & Laurence J. Kotlikoff, 1992. "Health, Children, and Elderly Living Arrangements: A Multiperiod-Multinomial Probit Model with Unobserved Heterogeneity and Autocorrelated Errors," NBER Chapters, in: Topics in the Economics of Aging, pages 79-108, National Bureau of Economic Research, Inc.
    2. Geweke, John & Keane, Michael P & Runkle, David, 1994. "Alternative Computational Approaches to Inference in the Multinomial Probit Model," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 609-632, November.
    3. McCulloch, Robert E. & Polson, Nicholas G. & Rossi, Peter E., 2000. "A Bayesian analysis of the multinomial probit model with fully identified parameters," Journal of Econometrics, Elsevier, vol. 99(1), pages 173-193, November.
    4. Donghoon Lee, 2005. "An Estimable Dynamic General Equilibrium Model Of Work, Schooling, And Occupational Choice," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(1), pages 1-34, February.
    5. 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.
    6. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, September.
    7. McCulloch, Robert & Rossi, Peter E., 1994. "An exact likelihood analysis of the multinomial probit model," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 207-240.
    8. Xuemei Fu & Zhicai Juan, 2017. "Estimation of multinomial probit-kernel integrated choice and latent variable model: comparison on one sequential and two simultaneous approaches," Transportation, Springer, vol. 44(1), pages 91-116, January.
    9. Lane F. Burgette & Erik V. Nordheim, 2012. "The Trace Restriction: An Alternative Identification Strategy for the Bayesian Multinomial Probit Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 404-410, February.
    10. Keane, Michael P, 1992. "A Note on Identification in the Multinomial Probit Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 193-200, April.
    11. Elrod, Terry & Keane, Michael, 1995. "A Factor-Analytic Probit Model for Representing the Market Structure in Panel Data," MPRA Paper 52434, University Library of Munich, Germany.
    12. Bhat, Chandra R. & Dubey, Subodh K., 2014. "A new estimation approach to integrate latent psychological constructs in choice modeling," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 68-85.
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    Cited by:

    1. Dubey, Subodh & Bansal, Prateek & Daziano, Ricardo A. & Guerra, Erick, 2020. "A Generalized Continuous-Multinomial Response Model with a t-distributed Error Kernel," Transportation Research Part B: Methodological, Elsevier, vol. 133(C), pages 114-141.
    2. Ruben Loaiza-Maya & Didier Nibbering, 2020. "Scalable Bayesian Estimation in the Multinomial Probit Model," Monash Econometrics and Business Statistics Working Papers 25/20, Monash University, Department of Econometrics and Business Statistics.
    3. Regina Akello & Alice Turinawe & Pieter Wauters & Diego Naziri, 2022. "Factors Influencing the Choice of Storage Technologies by Smallholder Potato Farmers in Eastern and Southwestern Uganda," Agriculture, MDPI, vol. 12(2), pages 1-16, February.
    4. Subodh Dubey & Prateek Bansal & Ricardo A. Daziano & Erick Guerra, 2019. "A Generalized Continuous-Multinomial Response Model with a t-distributed Error Kernel," Papers 1904.08332, arXiv.org, revised Jan 2020.

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    More about this item

    Keywords

    multinomial probit; latent factors; Bayesian analysis; marginal data augmentation; educational choice; occupational choice;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

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