1: ‘Estimation of the Mixed Multinomial Logit model using permuted antithetic draws’

Estimation of the mixed multinomial logit (MMNL) model requires the use of maximum simulated likelihood (MSL) to locate the parameters of interest. The simulation of the random parameter distributions is typically done using quasi Monte Carlo (QMC) techniques. In this paper, we demonstrate that the econometric structure of the MMNL model will result in multiple MSL solutions given a finite number of QMC draws when the most predominate type of simulated draws currently employed within the literature are used. We then demonstrate how the use of full factorial antithetic draws can be used to provide a single unique solution.

2: ‘Can we scale and coefficient heterogeneity in random coefficients models?’

There is growing interest in the notion that a significant component of the heterogeneity retrieved in random coefficients models may actually relate to variations in absolute sensitivities, i.e. scale heterogeneity, rather than variations in relative sensitivities. This has in part motivated the development of specialised modelling tools such as the G-MNL model. While not disagreeing with the notion that scale heterogeneity across respondents exists, this paper argues that attempts in the literature to disentangle scale from preference heterogeneity are not possible given that the two effects are perfectly confounded. In particular, we show how the various model specifications can in fact simply be seen as different parameterisations, and that any gains in fit are the results of using more flexible distributions, rather than an ability to capture scale heterogeneity. We illustrate our arguments through an empirical example and show how the conclusions from past work are based on misinterpretations of model results.