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Shape Invariant Demand Functions

Author

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  • Arthur Lewbel

    (Boston College)

Abstract

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, 2018. "Semiparametric estimation under shape constraints," Econometrics and Statistics, Elsevier, vol. 6(C), pages 74-89.
    2. Kesternich, Iris & Siflinger, Bettina M. & Smith, James P. & Winter, Joachim, 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 of Labor Economics (IZA).
    3. Ligon, Ethan, 2023. "Risk sharing tests and covariate shocks," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt2zr503fq, Department of Agricultural & Resource Economics, UC Berkeley.
    4. De Nadai, Michele & Lewbel, Arthur, 2016. "Nonparametric errors in variables models with measurement errors on both sides of the equation," Journal of Econometrics, Elsevier, vol. 191(1), pages 19-32.
    5. Bargain, Olivier & Lacroix, Guy & Tiberti, Luca, 2021. "Intrahousehold Resource Allocation and Individual Poverty: Assessing Collective Model Predictions against Direct Evidence on Sharing," IZA Discussion Papers 14406, Institute of Labor Economics (IZA).
    6. Olivier Bargain, 2022. "Income Sources, Intra-Household Allocation And Individual Poverty," Commitment to Equity (CEQ) Working Paper Series 121, Tulane University, Department of Economics.
    7. Christian Dudel & Jan Marvin Garbuszus & Julian Schmied, 2021. "Assessing differences in household needs: a comparison of approaches for the estimation of equivalence scales using German expenditure data," Empirical Economics, Springer, vol. 60(4), pages 1629-1659, April.
    8. Thibault Fally, 2018. "Integrability and Generalized Separability," NBER Working Papers 25025, National Bureau of Economic Research, Inc.
    9. Ulugbek Aminjonov & Olivier Bargain & Maira Colacce & Luca Tiberti, 2022. "Culture, Intra-household Distribution and Individual Poverty," Working Papers - Economics wp2022_21.rdf, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    10. Brown, Caitlin & Calvi, Rossella & Penglase, Jacob, 2021. "Sharing the pie: An analysis of undernutrition and individual consumption in Bangladesh," Journal of Public Economics, Elsevier, vol. 200(C).
    11. Lyssiotou, Panayiota, 2012. "Demographics and demand: Evaluation of alternative functional forms," Economics Letters, Elsevier, vol. 117(3), pages 627-631.
    12. Syed Abul Hasan, 2016. "Engel curves and equivalence scales for Bangladesh," Journal of the Asia Pacific Economy, Taylor & Francis Journals, vol. 21(2), pages 301-315, April.

    More about this item

    Keywords

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

    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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