多产品世界贸易网络的Google矩阵分析
Google matrix analysis of the multiproduct world trade network
摘要：
使用联合国COMTRADE数据库\cite{comtrade}，我们构建了谷歌矩阵$G$的联合国国家之间的多产品世界贸易，并分析了该网络上的贸易流量的属性1962 - 2010年。这一结构基于马尔可夫链，在平等的民主基础上对待所有国家，而与其富裕程度无关，同时考虑到贸易产品的贡献与其贸易量成比例。我们考虑了多达227个国家的61种产品的贸易。结果表明，产品的贸易贡献是不对称的：有些产品是出口导向型的，有些产品是进口导向型的，即使在对世界各国进行平均后，它们的贸易额在出口和进口方面是对称的。通过构建谷歌矩阵，可以调查贸易差额对石油和天然气等产品价格变动的敏感性，同时考虑到贸易联系的世界连通性。基于PageRank和CheiRank概率的贸易差额凸显了近年来中国和其他金砖国家在世界贸易中的主导作用。我们还表明，$G$的本征态与大的本征值选择特定的贸易社区。
英文摘要：
Using the United Nations COMTRADE database \cite{comtrade} we construct the Google matrix $G$ of multiproduct world trade between the UN countries and analyze the properties of trade flows on this network for years 1962 - 2010. This construction, based on Markov chains, treats all countries on equal democratic grounds independently of their richness and at the same time it considers the contributions of trade products proportionally to their trade volume. We consider the trade with 61 products for up to 227 countries. The obtained results show that the trade contribution of products is asymmetric: some of them are export oriented while others are import oriented even if the ranking by their trade volume is symmetric in respect to export and import after averaging over all world countries. The construction of the Google matrix allows to investigate the sensitivity of trade balance in respect to price variations of products, e.g. petroleum and gas, taking into account the world connectivity of trade links. The trade balance based on PageRank and CheiRank probabilities highlights the leading role of China and other BRICS countries in the world trade in recent years. We also show that the eigenstates of $G$ with large eigenvalues select specific trade communities.
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