Moosavi Vahid, Isacchini Giulio
Chair for Computer Aided Architectural Design, Department of Architecture, ETH Zurich, Zurich, Switzerland.
Department of Physics, ETH Zurich, Zurich, Switzerland.
PLoS One. 2017 Oct 24;12(10):e0186746. doi: 10.1371/journal.pone.0186746. eCollection 2017.
The initial theoretical connections between Leontief input-output models and Markov chains were established back in 1950s. However, considering the wide variety of mathematical properties of Markov chains, so far there has not been a full investigation of evolving world economic networks with Markov chain formalism. In this work, using the recently available world input-output database, we investigated the evolution of the world economic network from 1995 to 2011 through analysis of a time series of finite Markov chains. We assessed different aspects of this evolving system via different known properties of the Markov chains such as mixing time, Kemeny constant, steady state probabilities and perturbation analysis of the transition matrices. First, we showed how the time series of mixing times and Kemeny constants could be used as an aggregate index of globalization. Next, we focused on the steady state probabilities as a measure of structural power of the economies that are comparable to GDP shares of economies as the traditional index of economies welfare. Further, we introduced two measures of systemic risk, called systemic influence and systemic fragility, where the former is the ratio of number of influenced nodes to the total number of nodes, caused by a shock in the activity of a node, and the latter is based on the number of times a specific economic node is affected by a shock in the activity of any of the other nodes. Finally, focusing on Kemeny constant as a global indicator of monetary flow across the network, we showed that there is a paradoxical effect of a change in activity levels of economic nodes on the overall flow of the world economic network. While the economic slowdown of the majority of nodes with high structural power results to a slower average monetary flow over the network, there are some nodes, where their slowdowns improve the overall quality of the network in terms of connectivity and the average flow of the money.
早在20世纪50年代就建立了列昂惕夫投入产出模型与马尔可夫链之间最初的理论联系。然而，鉴于马尔可夫链具有各种各样的数学性质，迄今为止，尚未对采用马尔可夫链形式主义的世界经济网络演变进行全面研究。在这项工作中，我们利用最近可得的世界投入产出数据库，通过分析有限马尔可夫链的时间序列，研究了1995年至2011年世界经济网络的演变。我们通过马尔可夫链的不同已知性质，如混合时间、凯梅尼常数、稳态概率以及转移矩阵的扰动分析，评估了这个不断演变系统的不同方面。首先，我们展示了混合时间和凯梅尼常数的时间序列如何用作全球化的综合指标。接下来，我们将重点放在稳态概率上，将其作为衡量经济体结构权力的一种度量，这与作为经济体福利传统指标的经济体GDP份额具有可比性。此外，我们引入了两种系统性风险度量，分别称为系统影响力和系统脆弱性，前者是指一个节点活动受到冲击时，受影响节点数量与节点总数的比率，后者则基于特定经济节点受到其他任何节点活动冲击的次数。最后，以凯梅尼常数作为全球网络货币流动的指标，我们表明经济节点活动水平的变化对世界经济网络的整体流动存在一种矛盾效应。虽然大多数具有高结构权力的节点经济放缓导致网络上的平均货币流动变慢，但也有一些节点，它们的放缓在连通性和货币平均流动方面提高了网络的整体质量。
