Aggregation in Models with Quantity Constraints. The CES Aggregation Function

This paper is devoted to the problem of aggregation in models with quantity constraints. The focus is on quantity rationing macroeconomic (QRM) models where the micromarket outcome can be written as the minimum of several variables and where the diversity of situations across micromarkets is explicitly recognized. The aggregation result given in this paper generalizes that of Lambert (1988) to employment functions with more than two components, and leads to approximate aggregate functions of the CES variety. The approximation used can accomodate general variance-covariance structures. Simulation experiments show that the approximation error remains within reasonable bounds (1±4%). It thus seems that the CES formulation can accomodate a large variety of situations. It remains in particular valid when the (restrictive) conditions required to obtain the CES function as an exact result (independently and identically distributed Weibull variables) are not satisfied.