吸收马尔科夫链在全球价值链位置测度中的应用

Application of Absorbing Markov Chain in Global Value Chain Measurement

研究目标:在全球价值链测度框架中引入吸收马尔科夫链方法,拓宽其研究路径和内容。研究方法:通过比较全球价值链位置测度和吸收马尔科夫链理论,构建基于吸收马尔科夫链视角的全球价值链测度框架,并在全球投入产出表中进行应用。研究发现:本文讨论并拓展了Kostoska等(2020)的吸收马尔科夫链研究框架,发现特定吸收马尔科夫链路径与全球价值链中的生产路径具有一一对应关系,增加值分解与吸收概率、生产步长与条件平均吸收时间、非等间距价值链测度与马尔科夫奖励过程具有对应关系,且Ghosh逆矩阵和Leontief逆矩阵对应的吸收马尔科夫链在全球增加值分布和最终产品分布下互为可逆吸收马尔科夫链,表明全球范围内的价值链测度在Ghosh逆矩阵和Leontief逆矩阵测度下等价。研究创新:揭示了吸收马尔科夫链与全球价值链位置测度的形式一致性,提供了将吸收马尔科夫结论引入全球价值链测度的理论基础,并基于马尔科夫链中经历不同暂态比例、暂留时间、访问状态空间子集次数和条件首达时间等概念扩充了全球价值链测度内容。研究价值:在一定程度上拓展了全球价值链测度研究方法和内容,揭示了部分价值链测度指标和方法的数学本质,为进一步研究全球价值链测度体系提供了新方法和新途径。

Research Objectives:To introduce the absorbing Markov chain method into the global value chain measurement framework and broaden its research path and content.Research Methods:By comparing the global value chain measurements and absorbing Markov chain theory,a global value chain measurement framework based on the absorbing Markov chain theory is constructed and applied in the world input output table.Research Findings:This paper discusses and expands the absorption Markov chain research framework of Kostoska et al.(2020),and finds that the specific absorption Markov chain path has a one to one correspondence with the production chain in the global value chain measurements theory,the value added share(VB)matrix has a correspondence with the absorbing probabilities,the production length has a correspondence with the conditional mean absorption time,and the non equidistant value chain measure has a correspondence with the Markov reward process,The absorbing Markov chains corresponding to Ghosh inverse matrix and Leontief inverse matrix are reversed absorbing Markov chains when their initial distribution is global value added distribution and final goods distribution respectively and vice versa,indicating that the global value chain measures are equivalent under Ghosh inverse matrix and Leontief inverse matrix worldwide.Research Innovations:This paper reveals the formal similarity of absorbing Markov chain and GVC measurements.It provides the theoretical basis for introducing the absorbing Markov chain’s conclusions into GVC measurements and expands the content of global value chain measurement based on the concepts of transient probabilities,sojourn time,number of visits to subsets of state space and conditional mean first passage time.Research Value:To a certain extent,it expands the research methods and contents of global value chain measurement,reveals the mathematical essence of some value chain measurement indicators and methods,and provides new methods and ways for further study of global value chain measurements.