The robustest clusters in the input–output networks: global $$\hbox {CO}_2$$ CO 2 emission clusters

Abstract

Graph partitioning methods or clustering methods in general have been widely used for understanding and visualizing fundamental features of social and economic network complexity, e.g., Newman and Girvan (2004), Kagawa et al. (2013a, b), Liang et al. (2015). A striking environmental study has been provided by Kagawa et al. (2015); the authors identified CO 2 emission clusters within global supply-chain networks formed by the final demand impulse of a specific final product and argued how the identified emission clusters have contributed to increasing CO 2 emission transfers and have grown over time [see also Davis et al. (2011) andPeters et al. (2011) for the analysis of CO 2 emission transfers]. The authors applied the nonnegative matrix factorization (NMF) approach (Lee and Seung 1999) and obtained certain clusters whose normalized cut value (Ncut value) is minimized, which implies that the obtained clusters could best explain the environmentally important supply chains (Kagawa et al. 2015).Although Kagawa et al. (2015) provided important emission clusters for climate change mitigation, there is a crucial problem that the obtained results highly depend on the employed algorithms and parameters. To see the problem, we show an example: Suppose that we apply a typical clustering algorithm such as the K-means method (MacQueen et al. 1967) for the analysis. By setting the parameter K = 10, we can obtain a set of 10 clusters, but if we instead set the parameter K = 11, the obtained 11 clusters could include very different sectors from the ones of K = 10. In such a situation, which AbstractFinding environmentally significant clusters in global supply-chain networks of goods and services has been investigated by Kagawa et al. (Soc Netw 35(3):423-438, 2013a; Econ Syst Res 25(3):265-286, 2013b; Glob Environ Chang, 2015), using the popular clustering method of nonnegative matrix factorization, which actually yields sensitive cluster assignments. Due to this sensitivity issue, there is a danger of overfitting of the results. In order to confirm the robustness of the obtained clusters, which in fact have strong implications for international climate change mitigation, especially for the USinduced Chinese clusters, we design a simulation-based experiment. Empirical findings of the proposed approach are compared with those of Kagawa et al. (Glob Environ Chang, 2015). The environmental implications are reported as well.