On the estimation of multinomial logit models from relative frequency data

Standard estimators for the binomial logit model and for the multinomial logit model allow for an error arising from the use of relative frequencies instead of the true probabilities as the dependent variable. Recently Amemiya and Nold (1975) have considered the effect of the presence of an additional specification error in the binomial logit model and have proposed a modified logit estimation scheme to take the additional error variance into account. This paper extends their idea to the multinomial logit model and proposes an estimator that is consistent and asymptotically more efficient than the standard multinomial logit estimator. The paper presents a comparison of the results of applying the new estimator and existing estimators to a logit model for the choice of automobile ownership in the United States.