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

Prateek Bansal, Vahid Keshavarzzadeh, Cristian Guevara, Shanjun Li and Ricardo A Daziano

The Econometrics Journal, 2022, vol. 25, issue 2, 301-321

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.

Keywords: Designed quadrature; mixed logit; Monte Carlo integration; quasi-Monte Carlo; sparse grid quadrature (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:oup:emjrnl:v:25:y:2022:i:2:p:301-321.

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