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An efficient decomposition of the expectation of the maximum for the multivariate normal and related distributions

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  • Eggleston, Jonathan

Abstract

In structural dynamic discrete choice models, Monte Carlo integration has been the only way to evaluate the expectation of the maximum when errors are normally distributed. In this paper, however, I show that the expectation of the maximum can be decomposed as a linear combination of multivariate normal CDFs. For related distributions, such as the multivariate t-distribution, this expectation has a similar decomposition. My computational results show speed benefits of my proposed method for models with a low number of choices, although the speed gains are contingent on the use of analytical derivatives as opposed to numerical derivatives.

Suggested Citation

  • Eggleston, Jonathan, 2016. "An efficient decomposition of the expectation of the maximum for the multivariate normal and related distributions," Journal of Econometrics, Elsevier, vol. 195(1), pages 120-133.
    • Handle: RePEc:eee:econom:v:195:y:2016:i:1:p:120-133
    DOI: 10.1016/j.jeconom.2016.07.003
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    More about this item

    Keywords

    Expectation of the maximum; Emax; Multivariate normal; Monte Carlo integration; Dynamic structural models;
    All these keywords.

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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