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Estimation of multivariate probit models by exact maximum likelihood

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  • Jacques Huguenin
  • Florian Pelgrin
  • Alberto Holly

Abstract

In this paper, we develop a new numerical method to estimate a multivariate probit model. To this end, we derive a new decomposition of normal multivariate integrals that has two appealing properties. First, the decomposition may be written as the sum of normal multivariate integrals, in which the highest dimension of the integrands is reduced relative to the initial problem. Second, the domains of integration are bounded and delimited by the correlation coefficients. Application of a Gauss-Legendre quadrature rule to the exact likelihood function of lower dimension allows for a major reduction of computing time while simultaneously obtaining consistent and efficient estimates for both the slope and the scale parameters. A Monte Carlo study shows that the finite sample and asymptotic properties of our method compare extremely favorably to the maximum simulated likelihood estimator in terms of both bias and root mean squared error.

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Bibliographic Info

Paper provided by University of Lausanne, Institute of Health Economics and Management (IEMS) in its series Working Papers with number 0902.

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Length: 49 pages
Date of creation: Feb 2009
Date of revision:
Handle: RePEc:hem:wpaper:0902

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Related research

Keywords: Multivariate Probit Model; Simulated and Full Information Maximum Likelihood; Multivariate Normal Distribution; Simulations;

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References

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  1. Keane, Michael P, 1994. "A Computationally Practical Simulation Estimator for Panel Data," Econometrica, Econometric Society, vol. 62(1), pages 95-116, January.
  2. Lee, Lung-Fei, 1995. "Asymptotic Bias in Simulated Maximum Likelihood Estimation of Discrete Choice Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 437-483, June.
  3. Lee, L.F., 1994. "Simulated Maximum Likelihood Estimation of Dynamic Discrete Choice Statistical Models--Some Monte Carlo Results," Papers 94-06, Michigan - Center for Research on Economic & Social Theory.
  4. V A Hajivassiliou & DL McFadden, 1997. "The Method of Simulated Scores for the Estimation of LDV Models," STICERD - Econometrics Paper Series /1997/328, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  5. J. A. Hausman & D. A. Wise, 1976. "A Conditional Profit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Working papers 173, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. Lorenzo Cappellari & Stephen P. Jenkins, 2003. "Multivariate probit regression using simulated maximum likelihood," United Kingdom Stata Users' Group Meetings 2003 10, Stata Users Group.
  7. Daniel McFadden, 1987. "A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration," Working papers 464, Massachusetts Institute of Technology (MIT), Department of Economics.
  8. Tetsuhisa Miwa & A. J. Hayter & Satoshi Kuriki, 2003. "The evaluation of general non-centred orthant probabilities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 223-234.
  9. Bertschek, Irene & Lechner, Michael, 1998. "Convenient estimators for the panel probit model," Journal of Econometrics, Elsevier, vol. 87(2), pages 329-371, September.
  10. Robin C. Sickles & Paul J. Taubman, 1984. "An Analysis of the Health and Retirement Status of the Elderly," NBER Working Papers 1459, National Bureau of Economic Research, Inc.
  11. Peter Craig, 2008. "A new reconstruction of multivariate normal orthant probabilities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 227-243.
  12. Sandor, Zsolt & Andras, P.Peter, 2004. "Alternative sampling methods for estimating multivariate normal probabilities," Journal of Econometrics, Elsevier, vol. 120(2), pages 207-234, June.
  13. Breslaw, Jon A, 1994. "Evaluation of Multivariate Normal Probability Integrals Using a Low Variance Simulator," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 673-82, November.
  14. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  15. Lee, Lung-fei, 1999. "Statistical Inference With Simulated Likelihood Functions," Econometric Theory, Cambridge University Press, vol. 15(03), pages 337-360, June.
  16. V A Hajivassiliou, 1997. "Some Practical Issues in Maximum Simulated Likelihood," STICERD - Econometrics Paper Series /1997/340, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  17. Butler, J S & Moffitt, Robert, 1982. "A Computationally Efficient Quadrature Procedure for the One-Factor Multinomial Probit Model," Econometrica, Econometric Society, vol. 50(3), pages 761-64, May.
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Cited by:
  1. Paleti, Rajesh & Bhat, Chandra R., 2013. "The composite marginal likelihood (CML) estimation of panel ordered-response models," Journal of choice modelling, Elsevier, vol. 7(C), pages 24-43.
  2. Bhat, Chandra R., 2011. "The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 923-939, August.

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