Estimating multinomial logit models with endogenous variables: Control function versus two adapted approaches

Abstract

It is shown that the control function (CF) method’s estimates of the modal constants in a multinomial logit model (MNL) with endogenous explanatory variables are biased. This has not previously been reported in the literature, and has consequences in demand analysis, transportation policy design and project evaluation. Two adaptations of existing approaches are proposed as alternatives to CF for deriving estimators of parameters in MNL models with endogenous explanatory variables that evidence good consistency properties. The first approach is based on moment conditions while the second one combines parameters obtained in two consecutive estimation stages. Both approaches employ instrumental variables. These two adapted approaches are implemented using simulated data from a transport mode choice problem. The results are compared with those obtained using the classic control-function method, typically used by practitioners for estimating transport demand models with endogenous variables and making quantitative evaluations of transport policies and projects. All three approaches generate similar estimates for the parameters of the explanatory variables, but the two proposed adaptations produce considerably more accurate estimates of the modal constants. This greater accuracy has potentially significant consequences for multinomial logit models’ predictive ability and estimates of marginal effects, elasticities and the social benefits of projects based on consumer surplus calculations.