One big problem in the visualization of bilateral statistics is that maps don’t work very well.
Dendrograms give a very attractive and intuitive solution to the problem by dispensing with geographic information altogether. The dendrogram shows how clusters of countries form along a continuum of closeness. For international trade, I’ve presented below a cluster analysis of the OECD by share of total imports sourced from the partner country. Here, the linkages are bilateral, meaning that if countries A and B source 10% and 20% of their total imports from one another (respectively), the A-B partnership would join the same cluster at a threshold of 10% of imports.
At the top of the screen (0% of imports), all countries belong to a single supercluster. At the bottom of the screen (100%), no country sources 100% of its imports from any trade partner. Moving up the screen from the bottom, countries join the same cluster when the lesser of their mutual import shares falls above the threshold value. Technical notes below.
Tomorrow, I will post dendrograms for unilateral linkages (essentially the same as above, but using the greater of the two numbers). The following day, I will post dendrograms using the raw import flows, rather than the share of total imports. Following that, expect images depicting GDP weighted import flows. Next week, I will post the same series of images for imports.
My dendrograms follow Lee (2004) “Two Maps of the Worlds Trade Integration.” Lee treats trade shares as a direct measure of distance, rather than the basis for euclidean or Hamming distance measurements. This analysis treats trade flows themselves as indicators of proximity in a high-dimensional space.
For technical reasons, I have taken bilateral trade flows reported to the OECD, normalized those by total imports reported among those countries, calculated the reciprocals of the trade measures (to give an inverse distance measure), and then taken the logarithms of the distances in order to compress the scale onto a single graph. The units on the left scale are completely abstract, but they are a monotone transformation of the true trade shares, meaning that the order in which clusters aggregate on the dendrogram is accurately represented.
This analysis completely ignores countries not reporting imports to the OECD. Dendrograms from IMF’s Direction of Trade Statistics will follow by year’s end, if time permits.