Evaluating simulation-based approaches and multivariate quadrature on sparse grids in estimating multivariate binary probit models

This paper evaluates the performance of a recently emerging multivariate quadrature-based Sparse Grids Integration (SGI) and the well-known Geweke–Hajivassiliou–Keane (GHK) simulator in estimating multivariate binary probit models. Monte Carlo exercises demonstrate that in lower dimension multivariate binary probit models, the multivariate quadrature-based SGI estimator with few quadrature points performs very well and comparable with the GHK simulator. But as the dimension of integration or dependence (error correlation) among equations increases, the GHK simulator outshines the SGI estimator. This indicates that for integration problems involving higher dimension multivariate probit models, and those with strong dependence among variables, the GHK simulator remains to be a more efficient approach.