Zipf's Law for International Currencies

Zipf's Law for International Currencies

Ethan Ilzetzki (LSE)

Abstract

Using detailed transaction data from SWIFT, the world's largest financial messaging service, we document a power law distribution of currency denomination. Zipf's law, an inverse relationship between (log) rank and size, with a roughly unitary slope, has been documented in a multitude of settings in social and natural sciences, and random growth theories have been proposed to explain this empirical regularity. We show that currency usage shows an even more skewed distribution than suggested by Zipf's law, which we name ``Hyper-Zipf''. The US dollar and Euro are both used even more than would be predicted by this skewed distribution, suggesting strong ``winner-takes-all'' dynamics. Looking at transactions at a country by currency-pair level, we show that the US is unique in that nearly all in- and out-bound transactions with the US are in US dollars. We then show that dollar usage percolates through US trading partners into the international monetary system. We provide an augmented random-growth network theory to rationalize these findings.