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A Mata Geweke–Hajivassiliou–Keane multivariate normal simulator

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  • Richard Gates

    (StataCorp LP)

Abstract

An accurate and efficient numerical approximation of the multivariate normal (MVN) distribution function is necessary for obtaining maximum likeli- hood estimates for models involving the MVN distribution. Numerical integration through simulation (Monte Carlo) or number-theoretic (quasi-Monte Carlo) tech- niques is one way to accomplish this task. One popular simulation technique is the Geweke-Hajivassiliou-Keane MVN simulator. This paper reviews this technique and introduces a Mata function that implements it. It also computes analytical first-order derivatives of the simulated probability with respect to the variables and the variance – covariance parameters. Copyright 2006 by StataCorp LP.

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  • Richard Gates, 2006. "A Mata Geweke–Hajivassiliou–Keane multivariate normal simulator," Stata Journal, StataCorp LP, vol. 6(2), pages 190-213, June.
    • Handle: RePEc:tsj:stataj:v:6:y:2006:i:2:p:190-213
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    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Keane, Michael P, 1994. "A Computationally Practical Simulation Estimator for Panel Data," Econometrica, Econometric Society, vol. 62(1), pages 95-116, January.
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    4. Vassilis A. Hajivassiliou & Daniel L. McFadden, 1998. "The Method of Simulated Scores for the Estimation of LDV Models," Econometrica, Econometric Society, vol. 66(4), pages 863-896, July.
    5. Lorenzo Cappellari & Stephen P. Jenkins, 2003. "Multivariate probit regression using simulated maximum likelihood," Stata Journal, StataCorp LP, vol. 3(3), pages 278-294, September.
    6. Bolduc, Denis, 1999. "A practical technique to estimate multinomial probit models in transportation," Transportation Research Part B: Methodological, Elsevier, vol. 33(1), pages 63-79, February.
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