TY - JOUR
AU - Fox,Jeremy T.
AU - Gandhi,Amit
TI - Identifying Demand with Multidimensional Unobservables: A Random Functions Approach
JF - National Bureau of Economic Research Working Paper Series
VL - No. 17557
PY - 2011
Y2 - November 2011
UR - http://www.nber.org/papers/w17557
L1 - http://www.nber.org/papers/w17557.pdf
N1 - Author contact info:
Jeremy T. Fox
Economics Department
University of Michigan
238 Lorch Hall
611 Tappan Ave
Ann Arbor, MI 48109
Tel: 734-330-2854
Fax: 734-274-2331
E-Mail: jeremyfox@gmail.com
Amit Gandhi
University of Wisconsin
1180 Observatory Drive
Madison, WI 53706-1393
E-Mail: agandhi@ssc.wisc.edu
AB - 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.
ER -