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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 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, 2018. "Semiparametric estimation under shape constraints," Econometrics and Statistics, Elsevier, vol. 6(C), pages 74-89.
    2. Bargain, Olivier B. & 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).
    3. 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.
    4. 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).
    5. 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.
    6. 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.
    7. 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.
    8. Olivier Bargain, 2022. "Income Sources, Intra-Household Allocation And Individual Poverty," Commitment to Equity (CEQ) Working Paper Series 121, Tulane University, Department of Economics.
    9. 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.
    10. Thibault Fally, 2018. "Integrability and Generalized Separability," NBER Working Papers 25025, National Bureau of Economic Research, Inc.
    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

    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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