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Aggregation Theory for Incomplete Systems

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  • LaFrance, Jeffrey T.
  • Beatty, Timothy K.M.
  • Pope, Rulon D.

Abstract

Gorman's theory of demand is extended comprehensively to incomplete systems. The incomplete systems approach dramatically increases this class of models. The separate roles of symmetry and adding up are identified in the rank and the functional form of this class of models. We show that symmetry determines rank and the maximum rank is three. We show that adding up and 0o homogeneity determines the functional form and there is no functional form restriction for an incomplete system. We prove that every full rank system and reduced rank systems with a minimal level of degeneracy can be written as a polynomial in a single function of income. A complete set of closed form solutions for the indirect objective functions of this class of models is derived. A simple method to nest rank and functional form for incomplete systems is presented.

Suggested Citation

  • LaFrance, Jeffrey T. & Beatty, Timothy K.M. & Pope, Rulon D., 2005. "Aggregation Theory for Incomplete Systems," CUDARE Working Papers 25033, University of California, Berkeley, Department of Agricultural and Resource Economics.
    • Handle: RePEc:ags:ucbecw:25033
    DOI: 10.22004/ag.econ.25033
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    References listed on IDEAS

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    1. Jerison, Michael, 1993. "Russell on Gorman's Engel curves : A correction," Economics Letters, Elsevier, vol. 43(2), pages 171-175.
    2. Cicchetti, Charles J & Fisher, Anthony C & Smith, V Kerry, 1976. "An Econometric Evaluation of a Generalized Consumer Surplus Measure: The Mineral King Controversy," Econometrica, Econometric Society, vol. 44(6), pages 1259-1276, November.
    3. Russell, Thomas, 1983. "On a theorem of Gorman," Economics Letters, Elsevier, vol. 11(3), pages 223-224.
    4. LaFrance, J. T. & Beatty, T. K. M. & Pope, R. D. & Agnew, G. K., 2002. "Information theoretic measures of the income distribution in food demand," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 235-257, March.
    5. Browning, Martin & Deaton, Angus & Irish, Margaret, 1985. "A Profitable Approach to Labor Supply and Commodity Demands over the Life-Cycle," Econometrica, Econometric Society, vol. 53(3), pages 503-543, May.
    6. Jeffrey T. LaFrance & W. Michael Hanemann, 1989. "The Dual Structure of Incomplete Demand Systems," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 71(2), pages 262-274.
    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. Russell, Thomas, 1996. "Gorman demand systems and lie transformation groups: A reply," Economics Letters, Elsevier, vol. 51(2), pages 201-204, May.
    9. John Muellbauer, 1975. "Aggregation, Income Distribution and Consumer Demand," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(4), pages 525-543.
    10. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-326, June.
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    Cited by:

    1. Kenneth A. Baerenklau, 2010. "A Latent Class Approach to Modeling Endogenous Spatial Sorting in Zonal Recreation Demand Models," Land Economics, University of Wisconsin Press, vol. 86(4), pages 800-816.
    2. LaFrance, Jeffrey T., 2005. "Energy efficiency and appliance replacement," CUDARE Working Papers 120462, University of California, Berkeley, Department of Agricultural and Resource Economics.

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