Evidence and Implications of Zipf's Law for Integrated Economies

Abstract

This paper considers the distribution of output and productive factors among members of a fully integrated economy (FIE). We demonstrate that each member's shares of total output and of total factors will be equal. This implies that growth in shares is random. If output and factor shares evolve as reflective geometric Brownian motion, then limiting distribution of these shares will exhibit Zipf's law. Our empirics support Zipf's law for U.S. states and for E.U. countries. These findings imply that models characterizing growth of members within an FIE should embody a key assumption: growth process of shares is random and homogeneous.