Demand systems for market shares

We formulate a family of direct utility functions for the consumption of a differentiated good. This is used to generate a family of demand systems with flexible substitution patterns. Demand models for market shares can be estimated by regression enabling the use of instrumental variables. Models for microdata can be estimated with maximum likelihood. Our direct utility functions are based on a generalization of the Shannon entropy. They include dual representations of all additive random utility discrete choice models and more.