Stochastic prediction in multinomial logit models

It is standard practice to form predictions from multinomial logit models by ignoring the estimation error associated with the parameter estimates and solving for the predicted endogeneous variable (market share) in terms of the exogenous variables and the point estimates of the parameters. It has long been recognized in the econometrics literature that this type of nonstochastic prediction, which ignores the sampling distribution of the parameter estimates, leads to incorrect inferences about the endogenous variable. We offer a simulation-based approach for approximating the exact stochastic prediction. We show that this approach provides very accurate approximations with minimal computation time and would be easy to implement in industrial applications.