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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.

Suggested Citation

  • Arthur Lewbel, 2000. "A Rational Rank Four Demand System," Boston College Working Papers in Economics 463, Boston College Department of Economics, revised 04 Apr 2003.
  • Handle: RePEc:boc:bocoec:463
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    References listed on IDEAS

    as
    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.
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    3. Lewbel, Arthur, 1989. "A Demand System Rank Theorem," Econometrica, Econometric Society, vol. 57(3), pages 701-705, May.
    4. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-730, 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. 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.
    7. 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 1231-1247, September.
    8. Blundell, Richard & Pashardes, Panos & Weber, Guglielmo, 1993. "What Do We Learn About Consumer Demand Patterns from Micro Data?," American Economic Review, American Economic Association, pages 570-597.
    9. 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.
    10. 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 248-252, April.
    11. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, pages 312-326.
    12. HÄRDLE, Wolfgang & JERISON, Michael, "undated". "Cross section Engel curves over time," CORE Discussion Papers RP 991, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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