A Trick of the (Pareto) Tail

Several economic phenomena are found to follow an approximate Pareto distribution, at least in the upper tail. The debate is well established for the distribution of wealth and business firms, and has recently been particularly animated with respect to city sizes. In this paper we contribute to this stream of the literature by showing that the power-law tail emerges upon aggregation, and this holds true across three different domains: cities, firms and trade flows. We explore different mechanisms that could give rise to this effect, from mere sample size to correlation among the number of constituent parts of aggregate entities and their size, to the aggregation rule, and discuss their impact on the Pareto tail. Our results suggest that the debate on the shape of the distribution of city size is not yet closed and deserves further scrutiny. Using multiple statistical tests we find that the existence of a Pareto tail for the city size distribution is questionable due to sample size issues. Furthermore, the presence of a positive correlation between the number of elementary units (products) comprised in each aggregate level (firm) and their average size is key to explain why the size distribution of business firms displays a significant power-law tail. Conversely, we do not find any Pareto tail for trade flows. The paper casts new light on the mechanisms through which idiosyncratic shocks do not average out upon aggregation, so that id- iosyncratic shocks to individual units are not washed away in economic aggregates (as the central limit theorem would predict), but can even be magnified.