Functional Form and Shape Restrictions in Discrete Choice Models

Discrete choice demand models are commonly used to answer various economic questions. This paper develops a representation theorem that establishes the necessary and sufficient functional form and shape restrictions characterizing a large family of discrete choice demand models extending beyond the traditional additive random utility framework. The representation theorem yields three significant empirical implications. First, it provides economic intuition for (parameter) restrictions commonly imposed on some popular discrete choice models. Second, it offers a specification toolfor building demand models that satisfy mild and easily verifiable properties while being consistent with utility maximization and accommodating rich substitution patterns, including complementarity in demand. Third, it provides an efficient numerical algorithm for demand inversion, a crucial step in the demand estimation procedure.