Trade Networks
Ch. 2: Trade networks
Important concepts
directed networks
weighted networks
sorts, and their quantitites
time
discover multiplex networks
Towards Clustering
reciprocity
assorativity
- discover hidden structures
The directed network model
Theme: discover non-trivial relationships among countries
look at how they trade and what they trade
Weighted networks
Bipartite networks
The country-to-product network induces country-to-country and product-to-product relationships.
Reconstruction
\[ C = M_{cp}\cdot M_{cp}^T \]
\[ P = M_{cp}^T\cdot M_{cp} \]
Analysis of neighbours
For a node i, let \(k_i\) be its degree.
For directed networks: \(k_i = k_i^{in} + k_i^{out}\).
The distribution of degree \(P(k)\) provides a signature of the network.
The average degree is denoted \(\langle k \rangle.\)
Reciprocity
For a given directed network, reciprocity is the probability that of having links in both directions between two vertices.
R measures how the economies of two countries become interconnected (or interdependent).
\[ r = \frac{L^\leftrightarrow}{L} \]
\(L^\leftrightarrow\): number of reciprocal links
\(L\): total number of links.
Assortativity
Do vertices tend to connect with those with similar/dissimilar degree? Compute
- the avg. degree of node \(i\)’s neighbors:
\[ K_{nn}(i) = \frac{\sum_{\langle ij\rangle} k_j}{k_i} \]
- Next, the avg. \(K_{nn}\) for the \(n_d\) nodes which have degree \(d\)
\[ K_{nn}(d) = \frac{\sum_{i:k_i=d} K_{nn}(i)}{n_d} \]
\[ K_{nn}(d) = \frac{\sum_{i:k_i=d} K_{nn}(i)}{n_d} \]
Are \(d\) and \(K_{nn}(d)\) close?
Does assortativity grow over time?
Balassa’s RCA
The export matrix \(M\) is an adjacency matrix which reprents a bipartite graph.
Each scalar value \(M_{cp}\) corresponds to the aggregated export of product \(p\) by country \(c.\)
We can compute fractional ownership of export, product by product.
Many countries export coffee, so none really controls it.
Italy exports 100% of Bergamot oil (cfr. Prince of Wales tea).
The Revealed Comparative Advantage (RCA) is in controlling a high fraction of some product.
\(\sum_{p^\prime} M_{cp^\prime}\): total value of export by country \(c\).
\(\textrm{RCA}_{cp} = \frac{\frac{M_{cp}}{\sum_{p^\prime} M_{cp^\prime}}}{\frac{\sum_{c^\prime} M_{c^\prime p}}{\sum_{c^\prime} \sum_{p^\prime} M_{c^\prime p^\prime}}}\)