Rapid Growth and the Emergence of Pareto Tails

Many models have been proposed to explain the Pareto-tailed behavior observed in the upper tails of firm-size and individual-income distributions. However, recent studies have pointed out that these models imply unrealistically long periods for firms or individuals to reach the upper tail, that is, to become very large firms or high-income earners. Moreover, while existing models typically predict that Pareto tails are primarily generated by older firms or individuals, empirical evidence shows that Pareto tails already emerge within the distributions of relatively young firms and individuals. This paper develops an alternative explanation for the emergence of Pareto tails that resolves these empirical inconsistencies. Focusing on the heavy-tailed nature of growth rate distributions, we show that firm growth and income growth are characterized by short episodes of exceptionally high growth. We demonstrate that such rapid-growth events give rise to a Pareto tail.

* We revised this discussion paper with the new title in April 2026. This paper was previously circulated under the title "Explaining Zipf's Law by Rapid Growth."