Aggregation with Multinomial Probit and Estimation of Disaggregate Models with Aggregate Data: A New Methodological Approach

This paper describes an analytic aggregation procedure for disaggregate demand models similar to the one proposed in earlier publications by Westin (1974) and McFadden and Reid (1975). The technique, which uses a multivariate normal approximation for the distribution of the vector of attributes, is based on the multinomial profit algorithm proposed by Daganzo, Bouthelier and Sheffi (1977) and can be applied to an arbitrary number of alternatives. The procedure is computationally so efficient that it enables us to calibrate disaggregate models with aggregate data by maximum likelihood using the same or slightly modified codes developed for disaggregated data. The paper also contains a small scale numerical example intended to illustrate the important highlights of the aggregation-estimation problem.