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Designed quadrature to approximate integrals in maximum simulated likelihood estimation
[Evaluating simulation-based approaches and multivariate quadrature on sparse grids in estimating multivariate binary probit models]

Author

Listed:
  • Prateek Bansal
  • Vahid Keshavarzzadeh
  • Angelo Guevara
  • Shanjun Li
  • Ricardo A Daziano

Abstract

SummaryMaximum simulated likelihood estimation of mixed multinomial logit models requires evaluation of a multidimensional integral. Quasi-Monte Carlo (QMC) methods such as Halton sequences and modified Latin hypercube sampling are workhorse methods for integral approximation. Earlier studies explored the potential of sparse grid quadrature (SGQ), but SGQ suffers from negative weights. As an alternative to QMC and SGQ, we looked into the recently developed designed quadrature (DQ) method. DQ requires fewer nodes to get the same level of accuracy as QMC and SGQ, is as easy to implement, ensures positivity of weights, and can be created on any general polynomial space. We benchmarked DQ against QMC in a Monte Carlo and an empirical study. DQ outperformed QMC in all considered scenarios, is practice ready, and has potential to become the workhorse method for integral approximation.

Suggested Citation

  • Prateek Bansal & Vahid Keshavarzzadeh & Angelo Guevara & Shanjun Li & Ricardo A Daziano, 2022. "Designed quadrature to approximate integrals in maximum simulated likelihood estimation [Evaluating simulation-based approaches and multivariate quadrature on sparse grids in estimating multivariat," The Econometrics Journal, Royal Economic Society, vol. 25(2), pages 301-321.
    • Handle: RePEc:oup:emjrnl:v:25:y:2022:i:2:p:301-321.
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    References listed on IDEAS

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