Working Paper: NBER ID: w17193
Authors: Steven T. Berry; Amit Gandhi; Philip Haile
Abstract: 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.
Keywords: invertibility; demand systems; connected substitutes; nonparametric; nonseparable
JEL Codes: C3; D01
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| connected substitutes conditions (C62) | invertibility (C26) |
| weak substitutes (D10) | demand identification (J23) |
| sufficient strict substitution (D10) | demand identification (J23) |
| invertibility (C26) | unique identification of demand (R22) |
| weak substitutes and sufficient strict substitution (D10) | demand can be uniquely identified (R22) |