An instrument-free approach for estimating multinomial logit models with endogenous variables

An approach is developed for estimating multinomial logit models with endogenous explanatory variables that dispenses with the need for instrumental variables, a significant advantage given that good quality exogenous instruments are often not available. The proposed instrument-free method extends and adapts that of Breitung et al. (2024), which was developed specifically for multiple linear regression models. Simulations were conducted to make comparisons with control functions, which do require instruments, and the classic maximum likelihood technique, which does not correct for endogeneity, under different levels of correlation between the endogenous variable and the error term. The results showed that the proposed approach performed very satisfactorily. To supplement the simulations, the instrument-free method was applied to a case with real-world data, once again obtaining good results compared to control functions. The proposed method is easily implemented and can be used with models containing multiple exogenous and endogenous variables, as well as with the multinomial probit model. It should prove very useful for researchers and other professionals estimating models for public policy evaluation, transport planning and consumer behaviour analyses. • A new method (IFCF) is developed for estimating MNL models with endogenous variables. • Our approach dispenses with the need for instrumental variables. • With simulations we compare IFCF with the classic method of control functions (CF). • Our results showed that both IFCF and CF generated consistent estimates. • Also, we present an exogeneity test for explanatory variables.