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Individual versus Aggregate Income Elasticities for Heterogeneous Populations

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  • Michal Paluch
  • Alois Kneip
  • Werner Hildenbrand

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    Abstract

    This paper deals with different concepts of income elasticities of demand for a heterogenous population and the relationship between individual and aggregate elasticities is analyzed. In general, the aggregate elasticity is not equal to the mean of individual elasticities. The difference depends on the heterogeneity of the population and is quantified by a covariance term. Sign and magnitude of this term are determined by an empirical analysis based on the U.K. Family Expenditure Survey. It is shown that the relevant quantities can be identified from cross-section data and, without imposing restrictive structural assumptions, can be estimated by nonparametric techniques. It turns out that the aggregate elasticity significantly overestimates the mean of individual elasticities for many commodity groups.

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    File URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonedp/bgse13_2007.pdf
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    Bibliographic Info

    Paper provided by University of Bonn, Germany in its series Bonn Econ Discussion Papers with number bgse13_2007.

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    Length: 34
    Date of creation: Aug 2007
    Date of revision:
    Handle: RePEc:bon:bonedp:bgse13_2007

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    Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
    Fax: +49 228 73 6884
    Web page: http://www.bgse.uni-bonn.de

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    Keywords: household demand; aggregation; heterogeneity; nonparametric methods;

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    1. Rosa L. Matzkin, 1999. "Nonparametric Estimation of Nonadditive Random Functions," Working Papers 38, Universidad de San Andres, Departamento de Economia, revised Sep 2001.
    2. J├╝rgen Arns & Kaushik Bhattacharya, 2005. "Modelling Aggregate Consumption Growth with Time-Varying Parameters," Bonn Econ Discussion Papers bgse15_2005, University of Bonn, Germany.
    3. Davidson, James E H, et al, 1978. "Econometric Modelling of the Aggregate Time-Series Relationship between Consumers' Expenditure and Income in the United Kingdom," Economic Journal, Royal Economic Society, vol. 88(352), pages 661-92, December.
    4. Campbell, John Y. & Mankiw, N. Gregory, 1990. "Permanent Income, Current Income, and Consumption," Scholarly Articles 3353762, Harvard University Department of Economics.
    5. Stefan Hoderlein & Enno Mammen, 2007. "Identification of Marginal Effects in Nonseparable Models Without Monotonicity," Econometrica, Econometric Society, vol. 75(5), pages 1513-1518, 09.
    6. Lewbel, Arthur, 1992. "Aggregation with Log-Linear Models," Review of Economic Studies, Wiley Blackwell, vol. 59(3), pages 635-42, July.
    7. Lewbel, Arthur, 1990. "Income distribution movements and aggregate money illusion," Journal of Econometrics, Elsevier, vol. 43(1-2), pages 35-42.
    8. Manisha Chakrabarty & Anke Schmalenbach & Jeffrey Racine, 2004. "On the Distributional Effects of Income in an Aggregate Consumption Relation," Keele Economics Research Papers KERP 2004/09, Centre for Economic Research, Keele University.
    9. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    10. 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.
    11. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
    12. Hildenbrand, Werner & Kneip, Alois, 2005. "Aggregate behavior and microdata," Games and Economic Behavior, Elsevier, vol. 50(1), pages 3-27, January.
    13. Li, Qi & Racine, Jeffrey S, 2008. "Nonparametric Estimation of Conditional CDF and Quantile Functions With Mixed Categorical and Continuous Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 423-434.
    14. Lewbel, Arthur, 1989. "Nesting the AIDS and Translog Demand System," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(2), pages 349-56, May.
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