Identifying Demand with Multidimensional Unobservables: A Random Functions Approach

22 Pages Posted: 4 Nov 2011 Last revised: 8 Nov 2011

See all articles by Jeremy T. Fox

Jeremy T. Fox

University of Michigan at Ann Arbor

Amit Gandhi

University of Wisconsin - Madison

Date Written: November 2011

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.

Suggested Citation

Fox, Jeremy T. and Gandhi, Amit, Identifying Demand with Multidimensional Unobservables: A Random Functions Approach (November 2011). NBER Working Paper No. w17557. Available at SSRN: https://ssrn.com/abstract=1954484

Jeremy T. Fox (Contact Author)

University of Michigan at Ann Arbor ( email )

500 S. State Street
Ann Arbor, MI 48109
United States

Amit Gandhi

University of Wisconsin - Madison ( email )

716 Langdon Street
Madison, WI 53706-1481
United States

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
10
Abstract Views
346
PlumX Metrics