COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1806 Connected Substitutes and Invertibility of Demand Steven Berry, Amit Gandhi, and Philip Haile June 2011 We consider the invertibility of a nonparametric nonseparable demand
system. Invertibility of demand is important in several contexts, including identification
of demand, estimation of demand, testing of revealed preference, and economic theory
requiring uniqueness of market clearing prices. We introduce the notion of "connected
substitutes" and show that this structure is sufficient for invertibility. The
connected substitutes conditions require weak substitution between all goods and
sufficient strict substitution to necessitate treating them in a single demand system.
These conditions are satisfied in many standard models, have transparent economic
interpretation, and allow us to show invertibility without functional form restrictions,
smoothness assumptions, or strong domain restrictions. |
