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What can we learn about correlations from multinomial probit estimates?

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  • C. Monfardini
  • J.M.C. Santos Silva

Abstract

It is well known that, in a multinomial probit, only the covariance matrix of the location and scale normalized utilities are identified. In this study, we explore the relation between these identifiable parameters and the original elements of the covariance matrix, to find out what can be learnt about the correlations between the stochastic components of the non-normalized utilities. We show that, in certain circumstances, it is possible to obtain information on these behavioural parameters and define appropriate tools for inference. We illustrate the usefulness of our results in applied settings using an example.

Suggested Citation

  • C. Monfardini & J.M.C. Santos Silva, 2006. "What can we learn about correlations from multinomial probit estimates?," Working Papers 558, Dipartimento Scienze Economiche, Universita' di Bologna.
  • Handle: RePEc:bol:bodewp:558
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    References listed on IDEAS

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    1. Dansie, B. R., 1985. "Parameter estimability in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 19(6), pages 526-528, December.
    2. Monfardini, Chiara, 2003. "An illustration of Cox's non-nested testing procedure for logit and probit models," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 425-444, March.
    3. 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.
    4. Andrew Chesher & J. M. C. Santos Silva, 2002. "Taste Variation in Discrete Choice Models," Review of Economic Studies, Oxford University Press, vol. 69(1), pages 147-168.
    5. Wolak, Frank A., 1989. "Local and Global Testing of Linear and Nonlinear Inequality Constraints in Nonlinear Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(01), pages 1-35, April.
    6. Joseph A. Herriges & Catherine L. Kling, 1999. "Nonlinear Income Effects in Random Utility Models," The Review of Economics and Statistics, MIT Press, vol. 81(1), pages 62-72, February.
    7. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
    8. Bunch, David S., 1991. "Estimability in the Multinomial Probit Model," University of California Transportation Center, Working Papers qt1gf1t128, University of California Transportation Center.
    9. Bunch, David S., 1991. "Estimability in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 25(1), pages 1-12, February.
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    Cited by:

    1. W. Kuiper & Anton Cozijnsen, 2011. "The Performance of German Firms in the Business-Related Service Sectors Revisited: Differential Evolution Markov Chain Estimation of the Multinomial Probit Model," Computational Economics, Springer;Society for Computational Economics, vol. 37(4), pages 331-362, April.

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    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables

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