In the study of economic networks, econometric approaches interpret the traditional Gravity Model specification as the expected link weight coming from a probability distribution whose functional form can be chosen arbitrarily, while statistical-physics approaches construct maximum-entropy distributions of weighted graphs, constrained to satisfy a given set of measurable network properties. In a recent, companion paper, we integrated the two approaches and applied them to the World Trade Web, i.e. the network of international trade among world countries. While the companion paper dealt only with discrete-valued link weights, the present paper extends the theoretical framework to continuous-valued link weights. In particular, we construct two broad classes of maximum-entropy models, namely the integrated and the conditional ones, defined by different criteria to derive and combine the probabilistic rules for placing links and loading them with weights. In the integrated models, both rules follow from a single, constrained optimization of the continuous Kullback-Leibler divergence; in the conditional models, the two rules are disentangled and the functional form of the weight distribution follows from a conditional, optimization procedure. After deriving the general functional form of the two classes, we turn each of them into a proper family of econometric models via a suitable identification of the econometric function relating the corresponding, expected link weights to macroeconomic factors. After testing the two classes of models on World Trade Web data, we discuss their strengths and weaknesses.
翻译:在对经济网络的研究中,计量经济学方法将传统的重力模型规格解释为:从概率分布得出的预期联系权重,其功能形式可以任意选择,而统计-物理方法则建立加权图表的最大湿度分布,但限于满足一套特定可测量的网络属性。在最近的一份配套文件中,我们综合了这两种方法并将其应用于世界贸易网,即世界各国之间的国际贸易网络。虽然配套文件只涉及离散的有价值联系权重,但本文件将理论框架扩大到持续估值的联系权重。特别是,我们构建了两大类最丰富模型,即综合模型和有条件模型,这些模型由不同标准界定,用以得出并结合连接和加载其重量的概率性规则。在综合模型中,这两种规则都来自对不断的Kullback-Lebeller差异的单一、有限的优化;在有条件模型中,两种规则是分解的,而加权分配的功能形式则是从一个有条件的、优化的链接程序。在通过不同的标准来制定和综合的、有条件的、有条件的、有条件的、有条件的、有条件的、有条件的、有条件的、有条件的、有条件的模型的模型之后的两种模式,我们通过不同的标准界定的、我们通过两种计量的宏观经济的宏观经济的宏观经济的模型之后,然后将每个的宏观经济的宏观经济的等级的模型的宏观经济的等级的等级的模型的、我们通过两个等级的宏观经济的宏观经济的等级的等级的等级的等级的等级的等级的宏观经济的等级的等级的等级的宏观经济的等级的等级的模型。