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A Rational Rank Four Demand System

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Author Info
Arthur Lewbel () (Boston College)

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Abstract

Past parametric tests of demand system rank employed polynomial Engel curve systems. However, by Gorman's (1981) theorem, the maximum possible rank of a utility derived polynomial demand system is three. The present paper proposes a class of demand systems that are utility derived, are close to polynomial, and have rank four. These systems nest rational polynomial demands, and so can be used to test ranks up to four. These systems are suitable for applications where high rank is likely, such as demand systems involving a large number of goods. A test of rank using this new class of systems is applied to UK consumer demand data.

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File URL: http://fmwww.bc.edu/EC-P/WP463.pdf
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Publisher Info
Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 463.

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Length: 13 pages
Date of creation: 31 May 2000
Date of revision: 04 Apr 2003
Handle: RePEc:boc:bocoec:463

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Related research
Keywords: demand systems; rank; utility functions; Engel curves;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Lwebel Arthur & Perraudin William, 1995. "A Theorem on Portfolio Separation with General Preferences," Journal of Economic Theory, Elsevier, vol. 65(2), pages 624-626, April. [Downloadable!] (restricted)
  2. Bierens, H.J. & Pott-Buter, H.A., 1987. "Specification of household expenditure functions and equivalence scales by nonparametric regression," Serie Research Memoranda 0044, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics. [Downloadable!]
  3. Lewbel, Arthur, 1989. "A Demand System Rank Theorem," Econometrica, Econometric Society, vol. 57(3), pages 701-05, May. [Downloadable!] (restricted)
  4. Howe, Howard & Pollak, Robert A & Wales, Terence J, 1979. "Theory and Time Series Estimation of the Quadratic Expenditure System," Econometrica, Econometric Society, vol. 47(5), pages 1231-47, September. [Downloadable!] (restricted)
  5. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May. [Downloadable!] (restricted)
  6. Blundell, Richard & Pashardes, Panos & Weber, Guglielmo, 1993. "What Do We Learn About Consumer Demand Patterns from Micro Data?," American Economic Review, American Economic Association, vol. 83(3), pages 570-97, June. [Downloadable!] (restricted)
  7. Stephen G. Donald, 1997. "Inference Concerning the Number of Factors in a Multivariate Nonparametric Relationship," Econometrica, Econometric Society, vol. 65(1), pages 103-132, January.
  8. Hausman, J. A. & Newey, W. K. & Powell, J. L., 1995. "Nonlinear errors in variables Estimation of some Engel curves," Journal of Econometrics, Elsevier, vol. 65(1), pages 205-233, January. [Downloadable!] (restricted)
  9. Lyssiotou, Panayiota & Pashardes, Panos & Stengos, Thanasis, 1999. "Preference Heterogeneity and the Rank of Demand Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(2), pages 248-52, April.
  10. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-26, June. [Downloadable!] (restricted)
  11. James Banks & Richard Blundell & Arthur Lewbel, 1997. "Quadratic Engel Curves And Consumer Demand," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 527-539, November. [Downloadable!] (restricted)
  12. Hardle, W. & Jerison, M., 1990. "Cross section Engel curves over time," CORE Discussion Papers 1990016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Xavier Labandeira & José M. Labeaga & Miguel Rodríguez, 2005. "A Residential Energy Demand System for Spain," Econometrics 0503005, EconWPA. [Downloadable!]
    Other versions:
  2. Thomas F. Crossley & Hamish W. Low, 2005. "Unexploited Connections Between Intra- and Inter-temporal Allocation," Quantitative Studies in Economics and Population Research Reports 395, McMaster University. [Downloadable!]
    Other versions:
  3. Andrés Carvajal & Alvaro Riascos, 2004. "Global identification from the equilibrium manifold under incomplete markets," Royal Holloway, University of London: Discussion Papers in Economics 04/30, Department of Economics, Royal Holloway University of London, revised Nov 2004. [Downloadable!]
    Other versions:
  4. Veeramani, Venkat & Maynard, Leigh, 2004. "Testing For The Existence Of Price Points In Retail Milk Scanner Data Using Microeconomic Theory," 2004 Annual meeting, August 1-4, Denver, CO 20378, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association). [Downloadable!]
  5. Panayiota Lyssiotou & Panos Pashardes & Thanasis Stengos, 2001. "Nesting Quadratic Logarithmic Demand Systems," University of Cyprus Working Papers in Economics 0201, University of Cyprus Department of Economics. [Downloadable!]
    Other versions:
  6. Cranfield, J.A.L. & Preckel, Paul V. & Hertel, Thomas W., 2005. "A Modified, Implicit, Directly Additive Demand System," Working Papers 34145, University of Guelph, Department of Food, Agricultural and Resource Economics. [Downloadable!]
  7. Amelia Bilbao & Celia Bilbao & José M. Labeaga, . "The excess burden associated to characteristics of the goods: Application to housing demand," Working Papers 2005-09, FEDEA. [Downloadable!]
  8. Silvia Tiezzi & Fabrizio balli, 2008. "Households Consumption Patterns and Equivalence Scales in Italy: 1997-2004," Department of Economics University of Siena 535, Department of Economics, University of Siena. [Downloadable!]
  9. Cranfield, J.A.L., 2005. "Demands for Food Products Across the Development Spectrum: Application of a Rank Four Demand System," Working Papers 34111, University of Guelph, Department of Food, Agricultural and Resource Economics. [Downloadable!]
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