从生产函数到生产Copula的范式转换：企业生产活动的统计描述
A Paradigm Shift from Production Function to Production Copula: Statistical Description of Production Activity of Firms
摘要：
经济主体的异质性是宏观经济学发展的新趋势。因此，新兴学科要求人们用一种能够明确考虑企业生产活动分配的替代方法来取代传统经济学中的关键思想之一--生产函数。在本文中，我们提出了一个新的想法，称为生产copula，copula是一种分析手段建模变量之间的依赖关系。这种生产联结函数以概率的方式预测了给定资本和劳动力的企业所产生的增加值。因此，它与生产函数形成鲜明对比，在生产函数中，企业的产出是完全确定的。我们使用日本上市公司的金融数据实证构建了生产Copula。对数据的分析表明，它们的资本、劳动力和增加值之间存在显著的相关性，并证实增加值过于分散，无法用生产函数来表示。我们采用四种模型的生产Copula，即三变量版本的弗兰克，Gumbel和生存克莱顿和不可交换的三变量Gumbel;最后一个效果最好。
英文摘要：
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 firms with given capital and labor in a probabilistic way. It is thereby in sharp contrast to the production function where the output 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 employ four models for the production copula, that is, trivariate versions of Frank, Gumbel and survival Clayton and non-exchangeable trivariate Gumbel; the last one works best.
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