Bridging nestedness and economic complexity in multilayer world trade networks

International trade is a complex system whose understanding is crucial for various economic issues. Previous models, such as monopartite product space networks and bipartite country-product networks, have simplified the system by using single-layer network representations to capture economic complexity. This simplification overlooks important dynamics. This paper proposes a more detailed approach using multilayer networks, with each layer representing the trading relations of a specific product. This framework directly reveals the nested structure within each layer, offering a more nuanced view of economic complexity and providing a new metric for measuring product complexity. The nested structure is observed across a range of economic systems and has links to ecological systems as well. The paper investigates the function of nested structures in economic systems, exploring their nature and predicting the evolution of industrial ecosystems. This work differs from previous approaches by explicitly using multilayer networks to capture the more intricate dynamics of international trade. The research also explores the relationship between nestedness, technological barriers, and the asymmetry of trade networks, aiming to provide a more complete picture of how the global economy functions.

Existing research on international trade often utilizes complex network analysis to represent trade flows, capturing interactions between economic agents and assisting in observation, modeling, and prediction. Studies in economic complexity analyze the structural characteristics of world trade data, linking them to economic development. Previous work modeled data using country-product bipartite networks, revealing a hierarchical nested structure similar to those seen in ecological systems. The nestedness pattern in ecological systems has been linked to biodiversity and stability, while its function in economic systems is less understood. Research has explored the nested nature of observed networks and aimed to predict the evolution of industrial ecosystems. However, the representation of international trade using country-product bipartite networks is considered an oversimplification, ignoring where products are shipped to. Some attempts to use multilayer networks to model international trade have been made, but none have focused on within-layer nestedness in the way this paper does.

The research employs world trade datasets from publicly available databases (Data source is seen in section Data Availability), including data on 261 countries and 786 products from 1976 to 2014. A multilayer network is constructed, where each layer is a directed network representing the export and import relations of a specific product. Each layer is represented by a matrix, M^P_cd = {v^p_cd}, where v^p_cd is the dollar volume of product p exported from country c to country d. A z-score is used to convert the volume data into a binary matrix, with 1 indicating a significant trade flow and 0 otherwise. The Nested Overlap and Decreasing Fill (NODF) metric (Almeida-Neto et al., 2008) is used to quantify the nestedness (η) of each layer, ranging from 0 (no nestedness) to 1 (perfect nestedness). The authors analyze the relationship between product nestedness and product complexity, using the Technology Achievement Index (TAI) to measure the technological capabilities of countries. Asymmetry in the network is quantified using Asy = (k_in - k_out)/N, where k_in and k_out are in-degree and out-degree, and N is the number of nodes. The evolution of product complexity is studied by tracking the nestedness of the highest-nested product types over time. Trade competitiveness is measured by the number of countries a country exports a specific product to (κ(c, p) = ΣM_c(p)). The global trade competitiveness (GTC) is defined as a weighted sum of κ(c, p) by the nestedness of the product p. Finally, the correlation between GTC and various economic indicators (GDP, GDP per capita, GDP PPP, GDP PPP per capita) is analyzed to assess the predictive power of GTC.

The study's key findings are as follows: 1. **Nestedness as a Measure of Product Complexity:** The paper demonstrates that the nestedness of a product's trading network layer is a good indicator of its complexity. Products with high nestedness tend to be exported by countries with advanced technologies to other countries lacking that technology, indicating a technology barrier to entry. This contrasts with low-complexity products which are more widely produced and exported, displaying low nestedness. 2. **Relationship between Nestedness and Asymmetry:** A positive correlation exists between product nestedness and the asymmetry of the corresponding trading network. High nestedness products show greater asymmetry in trade, consistent with the technology barrier hypothesis. 3. **Evolution of Product Complexity:** Analysis shows that product nestedness has increased at a faster rate than relevance decay. This is observed at various levels of product aggregation, indicating that the complexity of high-nested products tends to persist over time, although the overall trend may be towards less nestedness. 4. **Trade Competitiveness of China and the US:** The US maintains high trade competitiveness across the spectrum of product nestedness (from raw materials to sophisticated products). In contrast, China's competitiveness has been growing, particularly after 1990, showing rapid improvement in high nestedness products. 5. **Predictive Power of Global Trade Competitiveness (GTC):** The GTC, calculated by weighting product trade competitiveness by nestedness, is highly correlated with various economic indicators (GDP, GDP (PPP)), particularly after a delay of approximately 10 years. This correlation suggests that GTC can be used to predict a nation's future economic growth, though variations might exist between fast and slow-growing economies.

The study's findings contribute significantly to our understanding of economic complexity by introducing a novel approach using multilayer networks and the nestedness metric. The results confirm that nestedness effectively characterizes product complexity, aligning better with intuitive expectations than previous metrics. The strong correlation between nestedness, technological barriers, and trade asymmetry provides valuable insights into the structural dynamics of international trade. The predictive power of GTC suggests its utility in forecasting economic growth, even if variations in prediction accuracy exist across different development stages. While the paper successfully introduces a novel framework, further research should examine its implications across different economic contexts and time scales. A more in-depth exploration of the mechanisms leading to the observed nested structure is needed.

This research offers a novel approach to modeling international trade using multilayer networks and the nestedness metric, providing a more refined measure of product complexity than previous methods. The strong correlation between nestedness and various economic indicators suggests the potential of this framework for forecasting economic growth. Future research should delve deeper into the underlying mechanisms of nestedness formation and explore the generalizability of the GTC index across diverse economic systems and time periods.

The study's reliance on publicly available data may limit the precision and granularity of the analysis. The NODF metric, although commonly used, might not fully capture all aspects of nestedness in complex systems. The predictive model based on GTC might require refinements to better account for factors beyond trade structure in forecasting economic growth. The analysis is focused on aggregate measures and does not delve into the micro-level interactions that determine trade patterns.