Production Copula

Heterogeneity of economic agents is emphasized in a new trend of macroeconomics. Accordingly the new emerging discipline requires one to replace the production function, one of key ideas in the conventional economics, by an alternative which can take an explicit account of distribution of firms’ production activities. In this paper we propose a new idea referred to as production copula; a copula is an analytic means for modeling dependence among variables. Such a production copula predicts value added yielded by a firm with given capital and labor in a probabilistic way. It is thereby in sharp contrast to the production function where the productivity of firms is completely deterministic. We demonstrate empirical construction of a production copula using financial data of listed firms in Japan. Analysis of the data shows that there are significant correlations among their capital, labor and value added and confirms that the values added are too widely scattered to be represented by a production function. We study four models including the variants of Frank, Gumbel, Clayton copulas and find that the non-exchangeable Gumbel copula describes the data distribution and the correlations very accurately.