Connected Substitutes and Invertibility of Demand

30 Pages Posted: 11 Jul 2011  

Steven Berry

Yale University - Department of Economics; National Bureau of Economic Research (NBER); Yale University - Cowles Foundation

Amit Gandhi

University of Wisconsin - Madison

Philip A. Haile

Yale University - Department of Economics; National Bureau of Economic Research (NBER); Yale University - Cowles Foundation

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Date Written: July 2011

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.

Suggested Citation

Berry, Steven and Gandhi, Amit and Haile, Philip A., Connected Substitutes and Invertibility of Demand (July 2011). NBER Working Paper No. w17193. Available at SSRN: https://ssrn.com/abstract=1882161

Steven T. Berry (Contact Author)

Yale University - Department of Economics ( email )

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National Bureau of Economic Research (NBER)

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Yale University - Cowles Foundation

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Amit Gandhi

University of Wisconsin - Madison ( email )

716 Langdon Street
Madison, WI 53706-1481
United States

Philip A. Haile

Yale University - Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8264
United States
203-432-3568 (Phone)
203-432-6323 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Yale University - Cowles Foundation

Box 208281
New Haven, CT 06520-8281
United States

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