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CES Transaction Functions in Macroeconomic Rationing Models

Published online by Cambridge University Press:  17 August 2016

Eskil Heinesen
Eskil Heinesen*
Affiliation:
Institute of Economics, University of Copenhagen
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Summary

In recent years a large number of macroeconomic rationing models with smooth CES transaction functions have been estimated. The widely used CES transaction functions with three arguments are often claimed to be derivable (as approximate relationships) from an assumption of lognormally distributed demands and supplies. One objective of this paper is to point out that the reasoning offered in the literature for this claim is not very clear or rigorous. Another, and more constructive, objective is to analyse and discuss in detail the derivation and properties of the CES transaction functions. Basic assumptions underlying the CES transaction functions are illuminated on the basis of a rather general description of the aggregation problem in models with both goods and labour markets, and general properties of transaction functions based on “multiplicative distributional assumptions” are analysed. Several new results concerning the exact derivation of the CES transaction functions on the basis of the Weibull distribution are shown. The quality of the CES transaction functions as approximate relationships given lognormally distributed demands and supplies is discussed. Finally it is shown that the CES transaction functions have reasonable properties.

Résumé

Résumé

Ces dernières années un grand nombre de modèles macro-économiques de rationnement avec fonctions de transaction CES ont été estimés. Les fonctions de transaction CES avec trois arguments, qui sont largement utilisées, sont prétendues dérivables (comme relations approchées) grâce à l’hypothèse de distribution log-normale des offres et demandes. Un des objectifs de cet article est de montrer que le raisonnement fourni dans la litérature pour justifier cette approximation n’est ni très clair ni rigoureux. Un autre objectif, plus constructif, est d’analyser et de discuter en détail la dérivation et les propriétés des fonctions de transaction CES. Des hypothèses de base sous-jacentes aux fonctions de transaction CES sont mises en lumière grâce à une description assez générate du problème d’agrégation dans des modèles avec à la fois un marché des biens et un marché du travail. Les propriétés générates des fonctions de transaction basées sur «l’hypothése de distribution multiplicative» sont analysées. On démontre plusieurs nouveaux résultats concernant la dérivation exacte des fonctions de transaction CES basées sur la distribution de Weibull. On discute la qualité de l’approximation par des fonctions de transaction CES lorsque les demandes et les offres sont distributées log-normalement. Enfin, on montre que les fonctions de transaction CES ont des propriétés raisonnables.

Keywords

C51E12C51E12
Type
Research Article
Information
Recherches Économiques de Louvain/ Louvain Economic Review , Volume 60 , Issue 3 , September 1994 , pp. 301 - 331
Copyright
Copyright © Université catholique de Louvain, Institut de recherches économiques et sociales 1994 

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Footnotes

(*)

An earlier version of this paper (which is partly based on my Ph.D. thesis, Heinesen [1992a]) has been presented at the European Meeting of the Econometric Society in Brussels, august 1992. I am grateful to Ellen Andersen, Horst Entorf, Christian Hjorth-Andersen, Søren Johansen, Guy Laroque, Esfandiar Maasoumi, Michael Osterwald-Lenum, Christian Schultz, Bent Sørensen, Karl Vind and two anonymous referees for very helpful comments.

References

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