Reconciling econometrics with continuous maximum-entropy network models
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连接计量经济学与连续最大熵网络模型
- 研究问题
- 如何将经济网络的引力模型与最大熵加权图框架结合，并从离散连边权重推广到连续权重，同时区分连边形成与权重赋值？
- 方法与思路
- 作者构造整合式与条件式两类最大熵模型，分别通过统一或条件优化推导连边及权重规则，再将预期权重与宏观经济因素关联。
- 材料陈述的贡献
- 摘要称，论文将既有离散框架扩展至连续权重，推导两类模型的一般形式，并在世界贸易网络数据中检验和讨论各自优缺点。
- 阅读关注点
- 应核对两类优化的约束及权重分布、引力函数如何嵌入期望权重、模型参数的识别与估计，以及贸易网络比较的评价标准。
- 阅读边界
- 依据的是 arXiv 预印本摘要，同行评审及期刊接收未核实；摘要未提供具体分布、检验结果或优劣结论，涉及宏观因素并不意味着使用宏观面板。
原文摘要
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.