On Speci ̄cation and Identi ̄cation of Stochastic Demand Models

This paper is concerned with stochastic demand systems that arise from structural random utility models for J continuous choice variables. It examines under which conditions on the structural preference speci ̄cation the implied reduced form model is invertible. And it investigates the conditions under which the structural model can be locally identi ̄ed from the reduced form under moment assumptions on the stochastic components in the structural preference model. The paper shows that analogues to conventional assumptions on preferences, together with some further conditions which are easily veri ̄able in practice, provide enough structure for local identi ̄cation through conditional moments, which can be derived from either the reduced form or, if analytically intractable, ̄rst-order conditions. ¤I thank Chunrong Ai, Hide Ichimura, Daniel McFadden, Lea Popovic, Paul Ruud and Chris Shannon for helpful comments and discussions. All errors are mine.