Working Paper: NBER ID: w17557
Authors: Jeremy T. Fox; Amit Gandhi
Abstract: We explore the identification of nonseparable models without relying on the property that the model can be inverted in the econometric unobservables. In particular, we allow for infinite dimensional unobservables. In the context of a demand system, this allows each product to have multiple unobservables. We identify the distribution of demand both unconditional and conditional on market observables, which allows us to identify several quantities of economic interest such as the (conditional and unconditional) distributions of elasticities and the distribution of price effects following a merger. Our approach is based on a significant generalization of the linear in random coefficients model that only restricts the random functions to be analytic in the endogenous variables, which is satisfied by several standard demand models used in practice. We assume an (unknown) countable support for the the distribution of the infinite dimensional unobservables.
Keywords: demand systems; nonseparable models; infinite dimensional unobservables; elasticities; price effects
JEL Codes: C01; L00
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| identification strategy (F55) | identification of the distribution of demand functions (D39) |
| joint distribution of market observables (D39) | identification of the distribution of demand functions (D39) |
| demand function is a real analytic function of prices (C69) | identification of the distribution of demand functions (D39) |
| identification of demand functions (D12) | estimation of various economic quantities (C13) |
| distribution of demand unobservables (D39) | unique identification from the reduced form of the model (C29) |
| generalization of the linear random coefficients model (C51) | identification of demand functions (D12) |
| identification of demand functions (D12) | insights into price elasticities and effects of mergers (D43) |