Uncovering the Link Between the Theoretical and Probabilistic Models of the Global Production Function: A Copula Approach

Abstract

We provide micro foundations for the global production function (GPF) based on the standard microeconomic model, and we develop a parallel probabilistic model with similar properties. The theoretical and probabilistic models of the GPF are integrated in the context of a technology choice problem. We construct a primitive, named the augmented transformation function, to obtain a GPF and its associated joint distribution that includes the output and labor-saving and capital-saving technological innovations. This type of primitive allows us not only to derive the theoretical GPF but also to consistently build a link between the substitutability microparameters (elasticities) and the probabilistic parameters (correlations).