Shape-Invariant Demand Functions
AbstractShape 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.
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Bibliographic InfoArticle provided by MIT Press in its journal The Review of Economics and Statistics.
Volume (Year): 92 (2010)
Issue (Month): 3 (August)
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Other versions of this item:
- Arthur Lewbel, 2007. "Shape Invariant Demand Functions," Boston College Working Papers in Economics, Boston College Department of Economics 669, Boston College Department of Economics, revised 26 Nov 2008.
- 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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