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A Rational Rank Four Demand System

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  • Arthur Lewbel

    ()
    (Boston College)

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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Bibliographic 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

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  1. Wolfgang HÄRDLE & Michael JERISON, 1991. "Cross section Engel Curves over Time," Discussion Papers (REL - Recherches Economiques de Louvain) 1991045, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  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.
  3. 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.
  4. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
  5. 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.
  6. Lewbel, Arthur, 1989. "A Demand System Rank Theorem," Econometrica, Econometric Society, vol. 57(3), pages 701-05, May.
  7. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-26, June.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
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Citations

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Cited by:
  1. Veeramani, Venkat N. & Maynard, Leigh J., 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).
  2. Lyssiotou, Panayiota, 2012. "Demographics and demand: Evaluation of alternative functional forms," Economics Letters, Elsevier, vol. 117(3), pages 627-631.
  3. Celia Bilbao & Amelia Bilbao & José Labeaga, 2010. "The welfare loss associated to characteristics of the goods: application to housing policy," Empirical Economics, Springer, vol. 38(2), pages 305-323, April.
  4. Paul Preckel & J. A. L. Cranfield & Thomas Hertel, 2010. "A modified, implicit, directly additive demand system," Applied Economics, Taylor & Francis Journals, vol. 42(2), pages 143-155.
  5. Xavier Labandeira & José M. Labeaga & Miguel Rodríguez, . "A Residential Energy Demand System for Spain," Working Papers 2005-04, FEDEA.
  6. LaFrance, Jeffrey T., 2008. "The structure of US food demand," Journal of Econometrics, Elsevier, vol. 147(2), pages 336-349, December.
  7. Thomas Crossley & Hamish Low, 2005. "Is the elasticity of intertemporal substitution constant?," IFS Working Papers W05/25, Institute for Fiscal Studies.
  8. Cranfield, John 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.
  9. Crossley, T.F. & Low, H.W., 2005. "Unexploited Connections Between Intra- and Inter-temporal Allocation," Cambridge Working Papers in Economics 0537, Faculty of Economics, University of Cambridge.
  10. Fabrizio Balli & Silvia Tiezzi, 2011. "Equivalence Scales Declining with Expenditure: Evidence and Implications for Income Distribution," Department of Economics University of Siena 611, Department of Economics, University of Siena.
  11. Song, Ze & Li, Lianyou & Ma, Chao, 2013. "The EASI Demand System : Evidence from China Household," MPRA Paper 48435, University Library of Munich, Germany.
  12. Fabrizio balli & Silvia Tiezzi, 2008. "Households Consumption Patterns and Equivalence Scales in Italy: 1997-2004," Department of Economics University of Siena 535, Department of Economics, University of Siena.
  13. 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.
  14. Fabrizio Balli, 2012. "Are Traditional Equivalence Scales Still Useful? A Review and A Possible Answer," Department of Economics University of Siena 656, Department of Economics, University of Siena.
  15. 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.

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