Zipf's Law for Integrated Economies

We first demonstrate that, within a fully integrated economy (FIE) in which there is free mobility of goods and factors, each FIE member's share of total FIE output will equal its shares of the total FIE stock of each productive factor. This equal-share property implies that, if economic policies are also largely harmonized across FIE members, the growth in any member's output and factor shares can be viewed as a random event. This then implies that the limit distribution of output and factor shares across FIE members will conform to a rank-share distribution that exhibits Zipf's law. This result means that growth models of FIE members must embody the assumption of homogeneity of random growth processes across members. Given its importance for our understanding of underlying growth mechanisms for such members, we empirically examine for evidence of Zipf's law for the distribution of output and factor shares of two (presumably) integrated economies: the 51 US states and 14 countries of the European Union (EU). Our findings support Zipf's law for US states and indicate convergence towards this law among EU countries.