网络的引力模型：整合最大熵和计量经济学方法
Gravity models of networks: integrating maximum-entropy and econometric approaches
摘要：
世界贸易网（WTW）是世界各国之间的国际贸易关系网络。通过一个单一的模型来描述WTW的局部链路权重（观察到的交易量）和全局网络结构（大规模拓扑结构）仍然是一个悬而未决的问题。虽然传统的引力模型（GM）通过使用GDP和地理距离等宏观经济属性成功地复制了观察到的贸易量，但不幸的是，它预测了一个完全连接的网络，从而返回了一个完全不现实的WTW拓扑结构。为了克服这个问题，在计量经济学和统计物理学中引入了两类不同的模型。计量经济学方法将传统的GM解释为概率分布的期望值，可以任意选择并与其他分布进行测试。统计物理学方法从一组选定的可测量的结构约束和测试分布产生不同的约束，构建（加权）图的最大熵概率分布。在这里，我们比较和整合这两种方法，考虑一类最大熵模型，可以纳入标准计量经济学模型中使用的宏观经济属性。我们发现，综合的方法比纯粹的计量经济学的一个实现了更好的性能。这些结果表明，最大熵结构可以作为一个可行的计量经济学框架，其中广泛和密集的利润率可以分别控制，通过结合拓扑约束和二元宏观经济变量。
英文摘要：
The World Trade Web (WTW) is the network of international trade relationships among world countries. Characterizing both the local link weights (observed trade volumes) and the global network structure (large-scale topology) of the WTW via a single model is still an open issue. While the traditional Gravity Model (GM) successfully replicates the observed trade volumes by employing macroeconomic properties such as GDP and geographic distance, it, unfortunately, predicts a fully connected network, thus returning a completely unrealistic topology of the WTW. To overcome this problem, two different classes of models have been introduced in econometrics and statistical physics. Econometric approaches interpret the traditional GM as the expected value of a probability distribution that can be chosen arbitrarily and tested against alternative distributions. Statistical physics approaches construct maximum-entropy probability distributions of (weighted) graphs from a chosen set of measurable structural constraints and test distributions resulting from different constraints. Here we compare and integrate the two approaches by considering a class of maximum-entropy models that can incorporate macroeconomic properties used in standard econometric models. We find that the integrated approach achieves a better performance than the purely econometric one. These results suggest that the maximum-entropy construction can serve as a viable econometric framework wherein extensive and intensive margins can be separately controlled for, by combining topological constraints and dyadic macroeconomic variables.
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