CES Transaction Functions in Macroeconomic Rationing Models

In recent years a large number of macroeconomic rationing models with smooth CES transaction functions have been estimated. In this paper we examine the derivation of such aggregate transaction functions from assumptions on the distribution of demand and supply across micro markets. 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. General properties of transaction functions based on "multiplicative distributional assumptions" are analysed. 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 more constructive objective is to show that the CES transaction function with one parameter can be derived on the basis of the Weibull distribution, and that both this function and the more general nested CES transaction function have reasonable properties.