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Shape Invariant Demand Functions


  • Arthur Lewbel

    () (Boston College)


Shape invariance is a property of demand functions that is convenient for semiparametric demand modelling. All known shape invariant demands are 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, which are widely used in welfare calculations. This paper provides a counterexample, i.e., a shape invariant demand system that is not derived from a transform of IB/ESE utility. A general theorem is then provided that characterizes all shape invariant demand systems. The usual practice of equating shape invariance with the IB/ESE utility class is shown to be not quite right, but it can be made valid by testing for the small class of exceptions noted here. In particular, all the exceptions have rank two, so any rank three or higher shape invariant system must be derived from transforms of IB/ESE utility.

Suggested Citation

  • Arthur Lewbel, 2007. "Shape Invariant Demand Functions," Boston College Working Papers in Economics 669, Boston College Department of Economics, revised 26 Nov 2008.
  • Handle: RePEc:boc:bocoec:669

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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 M. & 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


    Shape Invariance; Equivalence Scales; Engel curves; Consumer demand; Demand Systems; Utility; Cost Functions.;

    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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