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Alternative computational approaches to inference in the multinomial probit model

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  • John Geweke
  • Michael Keane
  • David Runkle

Abstract

This research compares several approaches to inference in the multinomial probit model, based on Monte-Carlo results for a seven choice model. The experiment compares the simulated maximum likelihood estimator using the GHK recursive probability simulator, the method of simulated moments estimator using the GHK recursive simulator and kernel-smoothed frequency simulators, and posterior means using a Gibbs sampling-data augmentation algorithm. Each estimator is applied in nine different models, which have from 1 to 40 free parameters. The performance of all estimators is found to be satisfactory. However, the results indicate that the method of simulated moments estimator with the kernel-smoothed frequency simulator does not perform quite as well as the other three methods. Among those three, the Gibbs sampling-data augmentation algorithm appears to have a slight overall edge, with the relative performance of MSM and SML based on the GHK simulator difficult to determine.

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Bibliographic Info

Paper provided by Federal Reserve Bank of Minneapolis in its series Staff Report with number 170.

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Date of creation: 1994
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Handle: RePEc:fip:fedmsr:170

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Keywords: Econometric models;

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  1. Vassilis A. Hajivassiliou & Axel Borsch-Supan, 1990. "Smooth Unbiased Multivariate Probability Simulators for Maximum Likelihood Estimation of Limited Dependent Variable Models," Cowles Foundation Discussion Papers 960, Cowles Foundation for Research in Economics, Yale University.
  2. Vassilis A. Hajivassiliou, 1993. "Simulating Normal Rectangle Probabilities and Their Derivatives: The Effects of Vectorization," Cowles Foundation Discussion Papers 1049, Cowles Foundation for Research in Economics, Yale University.
  3. Geweke, John, 1988. "Antithetic acceleration of Monte Carlo integration in Bayesian inference," Journal of Econometrics, Elsevier, vol. 38(1-2), pages 73-89.
  4. McFadden, Daniel & Ruud, Paul A, 1994. "Estimation by Simulation," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 591-608, November.
  5. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  6. John F. Geweke & Michael P. Keane & David E. Runkle, 1994. "Statistical inference in the multinomial multiperiod probit model," Staff Report 177, Federal Reserve Bank of Minneapolis.
  7. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S19-40, Suppl. De.
  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. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
  10. Geweke, John, 1986. "Exact Inference in the Inequality Constrained Normal Linear Regression Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 1(2), pages 127-41, April.
  11. Dansie, B. R., 1985. "Parameter estimability in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 19(6), pages 526-528, December.
  12. Bunch, David S., 1991. "Estimability in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 25(1), pages 1-12, February.
  13. 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.
  14. Lee, L.F., 1992. "Asymptotic Bias in Maximum Simulated Likelihood Estimation of Discrete Choice Models," Papers 93-03, Michigan - Center for Research on Economic & Social Theory.
  15. 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.
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