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. 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 under- lying 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.