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

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  • Mette Christensen

Abstract

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 effe
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  • Mette Christensen, 2007. "Integrability of Demand Accounting for Unobservable Heterogeneity: A Test on Panel Data," Economics Discussion Paper Series 0713, Economics, The University of Manchester.
    • Handle: RePEc:man:sespap:0713
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    1. Laura Blow & Valérie Lechene & Peter Levell, 2014. "Using the CE to Model Household Demand," NBER Chapters, in: Improving the Measurement of Consumer Expenditures, pages 141-178, National Bureau of Economic Research, Inc.
    2. Cherchye, Laurens & De Rock, Bram & Sabbe, Jeroen & Vermeulen, Frederic, 2008. "Nonparametric tests of collectively rational consumption behavior: An integer programming procedure," Journal of Econometrics, Elsevier, vol. 147(2), pages 258-265, December.
    3. Fabrice Talla Nobibon & Laurens Cherchye & Bram De Rock & Jeroen Sabbe & Frits Spieksma, 2011. "Heuristics for Deciding Collectively Rational Consumption Behavior," Computational Economics, Springer;Society for Computational Economics, vol. 38(2), pages 173-204, August.
    4. Andreas Chai & Nicholas Rohde & Jacques Silber, 2015. "Measuring The Diversity Of Household Spending Patterns," Journal of Economic Surveys, Wiley Blackwell, vol. 29(3), pages 423-440, July.
    5. Tony Lawson, 2016. "How the Ageing Population Contributes to UK Economic Activity: A Microsimulation Analysis," Scottish Journal of Political Economy, Scottish Economic Society, vol. 63(5), pages 497-518, November.

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