Estimation of Multinomial Logit Models with Unobserved Heterogeneity using Maximum Simulated Likelihood

Abstract

In this paper, we suggest a Stata routine for multinomial logit models with unobserved heterogeneity using maximum simulated likelihood based on Halton sequences. The purpose of this paper is twofold. First, we describe the technical implementation of the estimation routine and discuss its properties. Further, we compare our estimation routine with the Stata program gllamm, which solves integration by using Gauss–Hermite quadrature or adaptive quadrature. For the analysis, we draw on multilevel data about schooling. Our empirical findings show that the estimation techniques lead to approximately the same estimation results. The advantage of simulation over Gauss–Hermite quadrature is a marked reduction in computational time for integrals with higher dimensions. Adaptive quadrature leads to more stable results relative to the other integration methods. However, simulation is more time efficient. We find that maximum simulated likelihood leads to estimation results with reasonable accuracy in roughly half the time required when using adaptive quadrature.