  In this paper the properties of the maximum approximate composite marginal
likelihood (MaCML) approach to the estimation of multinomial probit models
(MNP) proposed by Chandra Bhat and coworkers is investigated in finite samples
as well as with respect to asymptotic properties. Using a small illustration
example it is proven that the approach does not necessarily lead to consistent
estimators for four different types of approximation of the Gaussian cumulative
distribution function (including the Solow-Joe approach proposed by Bhat). It
is shown that the bias of parameter estimates can be substantial (while
typically it is small) and the bias in the corresponding implied probabilities
is small but non-negligible. Furthermore in finite sample it is demonstrated by
simulation that between two versions of the Solow-Joe method and two versions
of the Mendell-Elston approximation no method dominates the others in terms of
accuracy and numerical speed. Moreover the system to be estimated, the ordering
of the components in the approximation method and even the tolerance used for
stopping the numerical optimization routine all have an influence on the
relative performance of the procedures corresponding to the various
approximation methods. Jointly the paper thus points towards eminent research
needs in order to decide on the method to use for a particular estimation
problem at hand.
