Evidence and Implications of Zipf's Law for Integrated Economies

This paper considers the distribution of output and productive factors among members of a fully integrated economy (FIE) in which there is free mobility of goods and factors among members and whose members share the same technology. We first demonstrate that, within an FIE, each member’s share of total FIE output and its shares of total FIE stocks of productive factors will be equal. If economic policies are largely harmonized across FIE members then this “equal-share” property implies that the growth in any member’s shares of FIE output and factor stocks can be taken to be a random outcome. Building on Gabaix’s (1999) result for the distribution of city sizes we argue that, if output and factor shares among FIE members evolve as geometric Brownian motion with a lower bound, then the limiting distribution of these shares will exhibit Zipf’s law. We empirically examine for Zipf’s law for the distribution of output and factor shares across two (presumably) integrated economies: the 51 U.S. states and 14 European Union (E.U.) countries. Our empirical findings strongly support Zipf’s law with respect to the distribution of output, physical capital and human capital among U.S. states and among E.U. countries. These findings imply that models used to characterize the growth of members within an FIE should embody a key assumption: that the underlying growth process of shares is random and homogeneous across FIE members.