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Calculation of Multivariate Normal Probabilities by Simulation, with Applications to Maximum Simulated Likelihood Estimation
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Calculation of Multivariate Normal Probabilities by Simulation, with Applications to Maximum Simulated Likelihood Estimation

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  • Lorenzo Cappellari
  • Stephen P. Jenkins

Abstract

We discuss methods for calculating multivariate normal probabilities by simulation and two new Stata programs for this purpose: mvdraws for deriving draws from the standard uniform density using either Halton or pseudo-random sequences, and an egen function mvnp() for calculating the probabilities themselves. Several illustrations show how the programs may be used for maximum simulated likelihood estimation.

Suggested Citation

  • Lorenzo Cappellari & Stephen P. Jenkins, 2006. "Calculation of Multivariate Normal Probabilities by Simulation, with Applications to Maximum Simulated Likelihood Estimation," Discussion Papers of DIW Berlin 584, DIW Berlin, German Institute for Economic Research.
    • Handle: RePEc:diw:diwwpp:dp584
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    References listed on IDEAS

    as
    1. Lorenzo Cappellari & Stephen P. Jenkins, 2004. "Modelling low income transitions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(5), pages 593-610.
    2. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, September.
    3. Stephane Hess & John Polak, 2003. "An alternative method to the scrambled Halton sequence for removing correlation between standard Halton sequences in high dimensions," ERSA conference papers ersa03p406, European Regional Science Association.
    4. William W. Gould & Jeffrey Pitblado & Brian Poi, 2010. "Maximum Likelihood Estimation with Stata," Stata Press books, StataCorp LP, edition 4, number ml4, March.
    5. Steven Stern, 1997. "Simulation-Based Estimation," Journal of Economic Literature, American Economic Association, vol. 35(4), pages 2006-2039, December.
    6. Peter Haan & Arne Uhlendorff, 2006. "Estimation of multinomial logit models with unobserved heterogeneity using maximum simulated likelihood," Stata Journal, StataCorp LP, vol. 6(2), pages 229-245, June.
    7. Stephen P. Jenkins & Lorenzo Cappellari & Peter Lynn & Annette Jäckle & Emanuela Sala, 2006. "Patterns of consent: evidence from a general household survey," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(4), pages 701-722, October.
    8. 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.
    9. Lorenzo Cappellari & Stephen P. Jenkins, 2003. "Multivariate probit regression using simulated maximum likelihood," Stata Journal, StataCorp LP, vol. 3(3), pages 278-294, September.
    10. Mark Stewart, 2006. "Maximum simulated likelihood estimation of random-effects dynamic probit models with autocorrelated errors," Stata Journal, StataCorp LP, vol. 6(2), pages 256-272, June.
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    More about this item

    Keywords

    Simulation estimation; maximum simulated likelihood; multivariate probit; Halton sequences; pseudo-random sequences; multivariate normal; GHK simulator;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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