Zambrano Eduardo, Hernando Alberto, Fernández Bariviera Aurelio, Hernando Ricardo, Plastino Angelo
Social Thermodynamics Applied Research (SThAR), EPFL Innovation Park, Bâtiment C, 1015 Lausanne, Switzerland
Department of Business, Universitat Rovira i Virgili, Av. Universitat 1, 43204 Reus, Spain.
J R Soc Interface. 2015 Nov 6;12(112). doi: 10.1098/rsif.2015.0789.
The distribution of firms' growth and firms' sizes is a topic under intense scrutiny. In this paper, we show that a thermodynamic model based on the maximum entropy principle, with dynamical prior information, can be constructed that adequately describes the dynamics and distribution of firms' growth. Our theoretical framework is tested against a comprehensive database of Spanish firms, which covers, to a very large extent, Spain's economic activity, with a total of 1,155,142 firms evolving along a full decade. We show that the empirical exponent of Pareto's law, a rule often observed in the rank distribution of large-size firms, is explained by the capacity of economic system for creating/destroying firms, and that can be used to measure the health of a capitalist-based economy. Indeed, our model predicts that when the exponent is larger than 1, creation of firms is favoured; when it is smaller than 1, destruction of firms is favoured instead; and when it equals 1 (matching Zipf's law), the system is in a full macroeconomic equilibrium, entailing 'free' creation and/or destruction of firms. For medium and smaller firm sizes, the dynamical regime changes, the whole distribution can no longer be fitted to a single simple analytical form and numerical prediction is required. Our model constitutes the basis for a full predictive framework regarding the economic evolution of an ensemble of firms. Such a structure can be potentially used to develop simulations and test hypothetical scenarios, such as economic crisis or the response to specific policy measures.
企业增长与企业规模的分布是一个受到密切关注的话题。在本文中，我们表明，可以构建一个基于最大熵原理并带有动态先验信息的热力学模型，该模型能够充分描述企业增长的动态过程和分布情况。我们的理论框架通过一个涵盖西班牙企业的综合数据库进行检验，该数据库在很大程度上涵盖了西班牙的经济活动，共有1,155,142家企业在整整十年间不断发展。我们表明，帕累托法则的经验指数（这一规律常在大型企业的排名分布中被观察到）可以由经济系统创建/摧毁企业的能力来解释，并且该指数可用于衡量以资本主义为基础的经济体的健康状况。实际上，我们的模型预测，当指数大于1时，企业创建受到青睐；当指数小于1时，企业摧毁则更受青睐；而当指数等于1（符合齐普夫定律）时，系统处于完全宏观经济均衡状态，意味着企业可以“自由”创建和/或摧毁。对于中型和小型企业规模而言，动态机制会发生变化，整个分布无法再拟合为单一的简单解析形式，需要进行数值预测。我们的模型构成了一个关于企业群体经济演变的完整预测框架的基础。这样的结构有可能用于开展模拟并测试假设情景，例如经济危机或对特定政策措施的反应。
