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Estimation of multivariate probit models by exact maximum likelihood

  • Jacques Huguenin
  • Florian Pelgrin
  • Alberto Holly

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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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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  1. 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.
  2. 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.
  3. Lee, Lung-fei, 1999. "Statistical Inference With Simulated Likelihood Functions," Econometric Theory, Cambridge University Press, vol. 15(03), pages 337-360, June.
  4. 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.
  5. Keane, Michael P, 1994. "A Computationally Practical Simulation Estimator for Panel Data," Econometrica, Econometric Society, vol. 62(1), pages 95-116, January.
  6. 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.
  7. 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.
  8. V A Hajivassiliou & DL McFadden, 1997. "The Method of Simulated Scores for the Estimation of LDV Models," STICERD - Econometrics Paper Series 328, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  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. 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.
  11. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  12. Lorenzo Cappellari & Stephen P. Jenkins, 2003. "Multivariate probit regression using simulated maximum likelihood," Stata Journal, StataCorp LP, vol. 3(3), pages 278-294, September.
  13. repec:cep:stiecm:/1997/340 is not listed on IDEAS
  14. 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.
  15. 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.
  16. 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.
  17. 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.
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