Modeling Global Trade
Complex network theory as a tool to study and model international trade comes originally from analyzing trading communities in the global oil trade. Complex network methods can analyze the world-wide trade system to discover new insights topologically and dynamically. Networks are quite intuitive in the way they model and abstract global trading relations. Originally, complex networks come from analyzing social groups, which can make some algorithm or established indices from the main discipline hard to carry over into global trade network analysis.
Network Construction and Capabilities
In order to analyze and visualize the political economy of the rare earth trade, I break up the collected data into distinct trade networks corresponding to capabilities or steps along the supply chain. \( \textit{TradeNetwork}_c \) is built as a directed and weighted network corresponding to the Capability \( c \in (1,2,3) \):
A \( TradeNetwork^{t}_c = (V^{t}, E^{t}, \boldsymbol{W}^{t}) \) where:
- \( V^{t} \) represents the set of countries participating in the network in year \( t \), serving as the network's nodes.
- \( E^{t} = \{ e^{t}_{ij}: i,j \in V^{t} \} \) denotes the set of directed trade links (or edges) between countries in year \( t \). Each edge \( e^{t}_{ij} \) signifies a trade relationship where trade flows from country \( i \) to country \( j \).
- \( \boldsymbol{W}^{t} = \{ w^{t}_{ij}: i,j \in V^{t} \} \) is the set of edge weights for year \( t \). Each weight \( w^{t}_{ij} \) quantifies the trade value that country \( i \) sends to country \( j \) in year \( t \).
Trade links are constructed using both reported exports and imports by the trading partners to mitigate reporting bias. The final edge weight \( W_{ij} \) is calculated as the average of reported exports from country \( i \) to country \( j \) and reported imports by country \( j \) from country \( i \). In the future I plan to implement something along the lines of a trust index to weigh the reports of different countries differently based on their historical reliability. \[ W_{ij} = \frac{w^{\text{export}}_{ij} + w^{\text{import}}_{ji}}{2} \]
HS Codes & Data Sources
The analysis of Rare Earth Networks uses UN Comtrade data (1989–2020) and the HS codes HS253090, HS280530, HS284610, HS284690, and HS850511. These codes represent various rare earth minerals, compounds, and products.
- HS253090: Mineral substances n.e.c.
- HS280530: Rare-earth metals, scandium and yttrium
- HS284610: Cerium compounds
- HS284690: Compounds of rare-earth metals, excluding cerium
- HS850511: Permanent magnets of metal
Inconsistencies
Inconsistencies in the trade data are measured by the absolute difference between reported exports and imports for each trade link: \[ \Delta_{ij} = \left| w^{\text{export}}_{ij} - w^{\text{import}}_{ji} \right| \] Normalized inconsistencies are calculated to allow for comparison across different years and capabilities: \[ \Delta^{\text{Normalized}}_{ij} = \frac{\Delta_{ij} - \min \Delta_c}{\max \Delta_c - \min \Delta_c} \]
Node Size
Node Size is determined by a measure of centrality, e.g. PageRank, which reflects the influence of a country within the trade network. The PageRank score \( r_i \) for each node \( i \) is calculated using the following formula: PageRank centrality is calculated using the following formula: \[ r_i = \alpha \sum_{j=1}^N \frac{W_{ji}}{\sum_{k=1}^N W_{jk}} r_j + (1 - \alpha)\frac{1}{N} \] where:
- \( r_i \) is the PageRank score of node \( i \),
- \( \alpha \) is the damping factor (\( \alpha = 0.85 \)),
- \( W_{ij} \) is the weight of the edge from node \( i \) to node \( j \),
- \( \sum_{k=1}^N W_{kj} \) is the total outgoing weight from node \( j \),
- \( N \) is the total number of nodes in the network.
For more detail on the used method to calculate the PageRank refer here.