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Departures from Slutsky Symmetry in Household Demand Models

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  • Ian Preston

    (University College London)

Abstract

Maximisation of utility by a single consumer subject to a linear budget constraint is well known to imply strong restrictions on the properties of demand functions. Empirical applications to data on households however frequently reject these restrictions. In particular such data frequently show a failure of Slutsky symmetry - the restriction of symmetry on the matrix of compensated price responses. Browning and Chiappori (1998) show that under assumptions of efficient within-household decision making, the counterpart to the Slutsky matrix for demands from a k member household will be the sum of a symmetric matrix and a matrix of rank k-1. We establish the rank of the departure from Slutsky symmetry for couples under the assumption of Nash equilibrium in individual demands. We show that the Slutsky matrix is the sum of a symmetric matrix and another of rank at most 2. This result implies not only that the Browning-Chiappori assumption of efficiency can be tested against other models within the class of those based on individual optimisation, but also that the hypothesis of Nash equilibrium in demands has testable content against a general alternative.

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  • Ian Preston, 2000. "Departures from Slutsky Symmetry in Household Demand Models," Econometric Society World Congress 2000 Contributed Papers 1809, Econometric Society.
  • Handle: RePEc:ecm:wc2000:1809
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    1. Deaton, Angus, 1990. "Price elasticities from survey data : Extensions and Indonesian results," Journal of Econometrics, Elsevier, vol. 44(3), pages 281-309, June.
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    3. M. Browning & P. A. Chiappori, 1998. "Efficient Intra-Household Allocations: A General Characterization and Empirical Tests," Econometrica, Econometric Society, vol. 66(6), pages 1241-1278, November.
    4. 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.
    5. Browning, Martin & Francois Bourguignon & Pierre-Andre Chiappori & Valerie Lechene, 1994. "Income and Outcomes: A Structural Model of Intrahousehold Allocation," Journal of Political Economy, University of Chicago Press, vol. 102(6), pages 1067-1096, December.
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    8. Browning, Martin & Meghir, Costas, 1991. "The Effects of Male and Female Labor Supply on Commodity Demands," Econometrica, Econometric Society, vol. 59(4), pages 925-951, July.
    9. Manser, Marilyn & Brown, Murray, 1980. "Marriage and Household Decision-Making: A Bargaining Analysis," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 31-44, February.
    10. Bergstrom, Theodore & Blume, Lawrence & Varian, Hal, 1986. "On the private provision of public goods," Journal of Public Economics, Elsevier, vol. 29(1), pages 25-49, February.
    11. McElroy, Marjorie B & Horney, Mary Jean, 1981. "Nash-Bargained Household Decisions: Toward a Generalization of the Theory of Demand," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(2), pages 333-349, June.
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