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

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). We find that the shape of the GPF is determined by all the relations among technological innovations and output and the way they are combined.