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Connected Substitutes and Invertibility of Demand

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  • Steven 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.
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Suggested Citation

  • Steven Berry & Amit Gandhi & Philip Haile, 2013. "Connected Substitutes and Invertibility of Demand," Econometrica, Econometric Society, vol. 81(5), pages 2087-2111, September.
    • Handle: RePEc:ecm:emetrp:v:81:y:2013:i:5:p:2087-2111
    DOI: ECTA10135
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    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles

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