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A rational rank four demand system

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  • Arthur Lewbel

    (Department of Economics, Boston College, 140 Commonwealth Avenue, Chestnut Hill, MA 02467, USA)

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. Copyright © 2002 John Wiley & Sons, Ltd.

Suggested Citation

  • Arthur Lewbel, 2003. "A rational rank four demand system," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(2), pages 127-135.
  • Handle: RePEc:jae:japmet:v:18:y:2003:i:2:p:127-135
    DOI: 10.1002/jae.677
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    References listed on IDEAS

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    Cited by:

    1. Thomas F. Crossley & Hamish W. Low, 2011. "Is The Elasticity Of Intertemporal Substitution Constant?," Journal of the European Economic Association, European Economic Association, vol. 9(1), pages 87-105, February.
    2. 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.
    3. Andrés Carvajal & Alvaro Riascos, 2005. "The Identification Of Preferences From Market Data Under Uncertainty," DOCUMENTOS CEDE 003599, UNIVERSIDAD DE LOS ANDES-CEDE.
    4. de Ree, Joppe & Alessie, Rob & Pradhan, Menno, 2013. "The price and utility dependence of equivalence scales: Evidence from Indonesia," Journal of Public Economics, Elsevier, vol. 97(C), pages 272-281.
    5. Matteo Barigozzi & Alessio Moneta, 2016. "Identifying the Independent Sources of Consumption Variation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(2), pages 420-449, March.
    6. Amelia Bilbao & Celia Bilbao & José M. Labeaga, "undated". "The excess burden associated to characteristics of the goods: Application to housing demand," Working Papers 2005-09, FEDEA.
    7. Donaldson, David & Pendakur, Krishna, 2015. "Applications of Population Principles: A Note," Economics working papers david_donaldson-2015-22, Vancouver School of Economics, revised 03 Sep 2015.
    8. 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.
    9. Keith R. McLaren & Ou Yang, 2016. "A class of demand systems satisfying global regularity and having complete rank flexibility," Empirical Economics, Springer, vol. 51(1), pages 315-337, August.
    10. Xavier Labandeira & José M. Labeaga & Miguel Rodríguez, 2006. "A Residential Energy Demand System for Spain," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2), pages 87-112.
    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, 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.
    13. Frank T. Denton & Dean C. Mountain, 2016. "Biases in consumer elasticities based on micro and aggregate data: an integrated framework and empirical evaluation," Empirical Economics, Springer, vol. 50(2), pages 531-560, March.
    14. 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.
    15. 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.
    16. LaFrance, Jeffrey T., 2008. "The structure of US food demand," Journal of Econometrics, Elsevier, vol. 147(2), pages 336-349, December.
    17. Lyssiotou, Panayiota & Pashardes, Panos & Stengos, Thanasis, 2002. "Nesting quadratic logarithmic demand systems," Economics Letters, Elsevier, vol. 76(3), pages 369-374, August.
    18. Chen, Shu-Ling & Chern, Wen S. & Lin, Yi-Ru & Liu, Kang Ernest, 2015. "Effects of food safety and health risk information on demand for food in Taiwan," 2015 AAEA & WAEA Joint Annual Meeting, July 26-28, San Francisco, California 205452, Agricultural and Applied Economics Association;Western Agricultural Economics Association.
    19. 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.
    20. Geoffrey R. Dunbar & Arthur Lewbel & Krishna Pendakur, 2017. "Identification of Random Resource Shares in Collective Households Without Preference Similarity Restrictions," Staff Working Papers 17-45, Bank of Canada.
    21. Frank Denton & Dean Mountain, 2014. "The implications of mean scaling for the calculation of aggregate consumer elasticities," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 12(3), pages 297-314, September.
    22. Lyssiotou, Panayiota, 2012. "Demographics and demand: Evaluation of alternative functional forms," Economics Letters, Elsevier, vol. 117(3), pages 627-631.
    23. Cash, Sean B. & Goddard, Ellen W., 2006. "New Directions in Consumer Behaviour Research," CAFRI: Current Agriculture, Food and Resource Issues, Canadian Agricultural Economics Society, issue 07.
    24. 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.
    25. 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).

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