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Shape-Invariant Demand Functions


  • Arthur Lewbel

    (Boston College)


Shape invariance is a property of demand functions that is widely used for parametric and semiparametric modeling and is associated with a commonly employed class of equivalence scale models used for welfare calculations. This paper derives the set of all shape-invariant demand functions and associated preferences. All previously known shape-invariant demands were derived from utility functions that, up to monotonic transformation, are called IB/ESE (independent of base-equivalence scale exact) utility functions, because they yield IB/ESE equivalence scales. This paper shows that there exist exceptional shape-invariant demands that are not derived from a transform of IB/ESE utility and provides some simple tests for these exceptions. In particular, all the exceptions have rank 2, so any rank 3 or higher demand system is shape invariant if and only if it is derived from a transform of IB/ESE utility. © 2010 The President and Fellows of Harvard College and the Massachusetts Institute of Technology.

Suggested Citation

  • Arthur Lewbel, 2010. "Shape-Invariant Demand Functions," The Review of Economics and Statistics, MIT Press, vol. 92(3), pages 549-556, August.
  • Handle: RePEc:tpr:restat:v:92:y:2010:i:3:p:549-556

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    Cited by:

    1. Wu, Ximing & Sickles, Robin, 2014. "Semiparametric Estimation under Shape Constraints," Working Papers 15-021, Rice University, Department of Economics.
    2. Iris Kesternich & Bettina Siflinger & James P. Smith & Joachim K. Winter, 2013. "Individual Behavior as a Pathway Between Early-Life Shocks and Adult Health Evidence from Hunger Episodes in Post-War Germany," Working Papers WR-1015, RAND Corporation.
    3. Kesternich, Iris & Siflinger, Bettina & Smith, James P. & Winter, Joachim K., 2013. "Individual Behavior as a Pathway between Early-Life Shocks and Adult Health: Evidence from Hunger Episodes in Post-War Germany," IZA Discussion Papers 7713, Institute for the Study of Labor (IZA).
    4. Lyssiotou, Panayiota, 2012. "Demographics and demand: Evaluation of alternative functional forms," Economics Letters, Elsevier, vol. 117(3), pages 627-631.
    5. Syed Abul Hasan, 2012. "Engel Curves and Equivalence Scales for Bangladesh," ASARC Working Papers 2012-15, The Australian National University, Australia South Asia Research Centre.

    More about this item

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation


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