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Integrability of Demand Accounting for Unobservable Heterogeneity: A Test on Panel Data

  • Mette Christensen

In recent years it has become apparent that we must take unobservable heterogeneity into account when conducting empirical consumer demand analysis. This paper is concerned with integrability (that is, whether demand is consistent with utility maximization) of the conditional mean demand (that is, the estimated demand) when allowing for unobservable heterogeneity. Integrability is important because it is necessary in order for the demand system estimates to be used for welfare analysis. Conditions for conditional mean demand to be integrable in the presence of unobservable heterogeneity are developed in the literature. There is, however, little empirical evidence suggesting whether these conditions for integrability are likely to be met in the data or not. In this paper we exploit the fact that the integrability conditions have testable implications for panel data and use a unique long panel data set to test them. Because of the sizeable longitudinal length of the panel, we are able to identify a very flexible specification of unobservable heterogeneity: We model individual demands as an Almost Ideal Demand system and allow for unobservable heterogeneity by allowing all intercept and slope parameters of the demand system to be individual-specific. We test the conditions for integrability of the conditional mean demand of this demand system. We do not reject them. This means that the conditional mean demand generated by a population of consumers with different preferences described by different Almost Ideal Demand systems is consistent with utility maximization. Given that integrability is not rejected, we conclude by an comparing the estimated demand system elasticties and welfare effects from a model with no heterogeneity (which is the model that would usually be estimated from cross sectional data) to those obtained from our heterogeneous model. We find that the homogeneous model severely overestimates income elasticities for luxury goods and that the welfare

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Paper provided by Economics, The University of Manchester in its series The School of Economics Discussion Paper Series with number 0713.

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Date of creation: 2007
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Handle: RePEc:man:sespap:0713
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  1. Haerdle,Wolfgang Jerison,Michael, 1988. "Cross section Engel curves over time," Discussion Paper Serie A 160, University of Bonn, Germany.
  2. Arthur Lewbel, 2001. "Demand Systems with and without Errors," American Economic Review, American Economic Association, vol. 91(3), pages 611-618, June.
  3. Pesaran, M.H. & Smith, R., 1992. "Estimating Long-Run Relationships From Dynamic Heterogeneous Panels," Cambridge Working Papers in Economics 9215, Faculty of Economics, University of Cambridge.
  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. Laurent E. Calvet & Etienne Comon, 2000. "Behavioral Heterogeneity and The Income Effect," Harvard Institute of Economic Research Working Papers 1892, Harvard - Institute of Economic Research.
  6. Martin Browning & Thomas F. Crossley & Guglielmo Weber, 2002. "Asking Consumption Questions in General Purpose Surveys," Social and Economic Dimensions of an Aging Population Research Papers 77, McMaster University.
  7. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-26, June.
  8. Richard Blundell & Alan Duncan & Krishna Pendakur, 1998. "Semiparametric estimation and consumer demand," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(5), pages 435-461.
  9. Muellbauer, John, 1975. "Aggregation, Income Distribution and Consumer Demand," Review of Economic Studies, Wiley Blackwell, vol. 42(4), pages 525-43, October.
  10. Collado, M Dolores, 1998. "Separability and Aggregate Shocks in the Life-Cycle Model of Consumption: Evidence from Spain," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 60(2), pages 227-47, May.
  11. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
  12. Browning, Martin & Meghir, Costas, 1991. "The Effects of Male and Female Labor Supply on Commodity Demands," Econometrica, Econometric Society, vol. 59(4), pages 925-51, July.
  13. Heckman, James & Singer, Burton, 1984. "A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data," Econometrica, Econometric Society, vol. 52(2), pages 271-320, March.
  14. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
  15. Brown, Bryan W & Walker, Mary Beth, 1989. "The Random Utility Hypothesis and Inference in Demand Systems," Econometrica, Econometric Society, vol. 57(4), pages 815-29, July.
  16. Walter Beckert, 2005. "Estimation of Heterogeneous Preferences, with an Application to Demand for Internet Services," The Review of Economics and Statistics, MIT Press, vol. 87(3), pages 495-502, August.
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