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Long-Run Patterns of Demand: The Expenditure System of the CDES Indirect Utility Function - Theory and Applications


  • Bjarne S. Jensen
  • Paul de Boer


In this paper, we unify and extend the analytical and empirical application of the ”indirect addilog” expenditure system, introduced by Leser (1941), Somermeyer- Wit (1956) and Houthakker (1960). Using the Box-Cox transform, we present a parametric analysis of the Houthakker specification of the fundamental indirect utility function - called the CDES specification (constant differences of Allen elasticities of substitution) by Hanoch (1975). It is shown that the CDES demand system is less restrictive than implied by standard parameter restrictions in the literature, Hanoch (1975), Deaton & Muellbauer (1980), or else neither adequately indicated, Houthakker (1960), Silberberg & Suen (2001). Our parametric examination implies that Marshallian own-price elasticities are no longer restricted to being all larger than one in absolute value; hence CDES can now naturally exhibit both the inelastic and elastic own price elasticities of observable (Marshallian) demands. Furthermore, we argue that in computable general equilibrium models (CGE), the CDES compares favorably with other expenditure systems, e.g. the linear expenditure system (LES), since CDES and LES need the same outside information for calibration of the parameters, but CDES is not confined to constancy of marginal budget shares (linear Engel curves). Moreover, we show that the non-homothetic CDES preferences are a simple and natural extension of the homothetic CES (constant elasticities of substitution) preferences, and, accordingly, CDES can more realistically be used in specifying CGE models with a demand side of non-unitary income elasticities. A succint theoretical briefing of the CDES history with general and concise formulas is offered. We illustrate CDES estimation and the calculation of a comprehensive set of income and price elasticities by applying CDES to Danish budget survey data. With a large number budget items included, coherent numerical values for the income, own, and cross price elasticities, as shown here, seem nowhere calculated and available in the voluminous literature.

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  • Bjarne S. Jensen & Paul de Boer, 2006. "Long-Run Patterns of Demand: The Expenditure System of the CDES Indirect Utility Function - Theory and Applications," DEGIT Conference Papers c011_056, DEGIT, Dynamics, Economic Growth, and International Trade.
  • Handle: RePEc:deg:conpap:c011_056

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    References listed on IDEAS

    1. Barten, A. P., 1969. "Maximum likelihood estimation of a complete system of demand equations," European Economic Review, Elsevier, vol. 1(1), pages 7-73.
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    4. William A. Barnett, 1979. "Theoretical Foundations for the Rotterdam Model," Review of Economic Studies, Oxford University Press, vol. 46(1), pages 109-130.
    5. de Boer, P.M.C. & Missaglia, M., 2005. "Introducing the indirect addilog system in a computable general equilibrium model: a case study for Palestine," Econometric Institute Research Papers EI 2005-25, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. Cramer, J. S., 1970. "Interaction of price and income in consumer demand," European Economic Review, Elsevier, vol. 1(3), pages 428-436.
    7. 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. Martin O'Brien & Raymond Markey & Eduardo Pol, 2018. "The Short Run Impact of Penalty Rate Cuts on Employment Outcomes in Retail and Hospitality Sectors in Australia," Economic Papers, The Economic Society of Australia, vol. 37(3), pages 270-286, September.
    2. Paul De Boer & Richard Paap, 2009. "Testing non‐nested demand relations: linear expenditure system versus indirect addilog," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(3), pages 368-384, August.
    3. Phil Lewis, 2014. "Paying the Penalty? The High Price of Penalty Rates in Australian Restaurants," Agenda - A Journal of Policy Analysis and Reform, Australian National University, College of Business and Economics, School of Economics, vol. 21(1), pages 5-26.

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    CDES demand systems; non-homothetic preferences; general price elasticities; CGE modeling; budget data implementation;
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