China’s Belt and Road Initiative is a significant regional economic cooperation. This paper uses the Belt and Road Initiative (BRI) as a quasi-natural experiment to investigate the impact of regional economic cooperation on environmental quality. Using difference-in-differences (DID) and a series of robustness checks, we find that regional economic cooperation like BRI deteriorates environmental quality in countries along the Belt and Road. The main reason is that the improving effects on environmental quality in the BRI countries are smaller than in the non-BRI countries after the BRI. The ecological impacts of the BRI exist differences in different countries. The results show that the BRI improves environmental quality in South Asia, and Europe and Central Asia. However, the BRI negatively affects environmental quality in East Asia and Pacific, developing and non-OECD countries. We found that, unlike the BRI, the Green BRI improves environmental quality in countries along the Belt and Road. We also discuss the mechanism of the BRI on environmental quality from foreign direct investment (FDI).

Since the financial crisis, especially after the outbreak of COVID-19, the global trade division of labor has been changing rapidly. The global value chain (GVC) keeps shrinking while the domestic value chain (DVC) continues to develop. Therefore, it is important to re-examine the impact of different modes of value chain division of labor on China’s energy efficiency. In this study, we first constructed an input-output model of provinces embedded in the world to measure the dual embedding of domestic and global value chains. Then we used a three-dimensional fixed-effect model to study the impact and mechanism of dual value chain embedding on energy efficiency. We found that domestic value chain embedding inhibits energy efficiency improvement and global value chain embedding promotes energy efficiency improvement. A series of robustness and endogeneity tests support these findings. The heterogeneity tests revealed that the effects of dual value chain embedding on energy efficiency are more pronounced in low-polluting industries, high-tech industries, years before 2008, and coastal regions. The mechanism test revealed that DVC embedding inhibits energy efficiency by exacerbating the low-end lock-in effect, reducing environmental regulation and scale efficiency, and it increases energy efficiency by increasing technological progress efficiency. GVC embedding improves energy efficiency by weakening the low-end lock-in effect and increasing technical efficiency and scale efficiency, and it inhibits energy efficiency improvement by reducing environmental regulation and technological progress efficiency.

Graph Neural Networks (GNNs) have been intensively studied in recent years because of their promising performance over graph-structural data and have provided assistance in many fields. Recalling recent works on graph neural networks, we found that imposing graph smoothing via Frobenius norm was proven to be effective in the architecture of graph neural networks from the standpoint of the graph signal processing. In this paper, we aim to model the graph smoothness of graph neural networks using a Schatten $p$ -norm with $p$ in the interval $[1,2$ ) to characterize smoothness and propose a novel architecture called Schatten graph neural networks. This architecture stems from a primal-dual solution scheme for a graph signal denoising problem. There is difficulty in solving subproblems with respect to the Schatten $p$ -norm. We propose a fixed point iteration scheme and prove that it tracks with the linear convergence rate with solid mathematical analysis. Extensive experiments demonstrate the effectiveness of the proposed architecture of graph neural networks and their robustness to the graph adversarial attacks.

Graph neural networks (GNNs) have developed rapidly in recent years because they can work over non-Euclidean data and possess promising prediction power in many real-word applications. The graph classification problem is one of the central problems in graph neural networks, and aims to predict the label of a graph with the help of training graph neural networks over graph-structural datasets. The graph pooling scheme is an important part of graph neural networks for the graph classification objective. Previous works typically focus on using the graph pooling scheme in a linear manner. In this paper, we propose the real quadratic-form-based graph pooling framework for graph neural networks in graph classification. The quadratic form can capture a pairwise relationship, which brings a stronger expressive power than existing linear forms. Experiments on benchmarks verify the effectiveness of the proposed graph pooling scheme based on the quadratic form in graph classification tasks.