一个马尔可夫模型的演变世界投入产出网络
A Markovian Model of the Evolving World Input-Output Network
AI总结：
本文利用马尔可夫链方法分析1995-2011年世界经济网络演变，通过混合时间、Kemeny常数等指标评估全球化程度和系统风险，揭示了经济节点活动变化对整体货币流动的影响。
摘要：
本文回顾了Leontief投入产出模型与马尔可夫链之间的理论联系，指出尽管马尔可夫链具有多样的数学性质，但尚未有全面利用马尔可夫链方法研究演化的世界经济网络。利用最近可用的世界投入产出数据库，我们通过分析一系列有限马尔可夫链，建模了1995至2011年间世界经济网络的演变。我们通过马尔可夫链的不同属性，如混合时间、Kemeny常数、稳态概率和转移矩阵的扰动分析，评估了该演化的系统。首先，我们展示了混合时间和Kemeny常数的时间序列如何作为全球化的综合指标。接着，我们聚焦于稳态概率作为衡量经济节点结构权力的指标，与传统以GDP份额衡量的经济指标相比较。进一步，我们引入了两个系统性风险的度量，称为系统性影响和系统性脆弱性，前者是由于节点活动变化导致的受影响节点数与总节点数的比率，后者则基于特定经济节点被其他节点活动变化影响的次数。最后，聚焦于Kemeny常数作为全球货币流动的指标，我们展示了经济节点活动水平的变化对整体网络货币流动的悖论效应。尽管多数高结构权力节点的经济放缓导致网络平均货币流动减慢，但某些节点的放缓却提升了网络在连接性和平均货币流动方面的质量。
英文摘要：
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, there has not been a full investigation of evolving world economic networks with Markov chain formalism. Using the recently available world input-output database, we modeled the evolution of the world economic network from 1995 to 2011 through analysis of a series of finite Markov chains. We assessed different aspects of this evolving system via different 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. 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 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 monetary flow.
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