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Heterogeneity of economic agents is emphasized in a new trend ofmacroeconomics. Accordingly the new emerging discipline requires one to replacethe production function, one of key ideas in the conventional economics, by analternative which can take an explicit account of distribution of firms'production activities. In this paper we propose a new idea referred to asproduction copula; a copula is an analytic means for modeling dependence amongvariables. Such a production copula predicts value added yielded by firms withgiven capital and labor in a probabilistic way. It is thereby in sharp contrastto the production function where the output of firms is completelydeterministic. We demonstrate empirical construction of a production copulausing financial data of listed firms in Japan. Analysis of the data shows thatthere are significant correlations among their capital, labor and value addedand confirms that the values added are too widely scattered to be representedby a production function. We employ four models for the production copula, thatis, trivariate versions of Frank, Gumbel and survival Clayton andnon-exchangeable trivariate Gumbel; the last one works best.

A Paradigm Shift from Production Function to Production Copula: Statistical Description of Production Activity of Firms