The Interrupted Power Law and The Size of Shadow Banking

TL;DR

This paper reveals an interrupted Pareto distribution in the sizes of the largest firms, with a sharp cut-off in the upper tail caused by shadow banking activities, and introduces a model to estimate shadow banking size.

Contribution

It identifies an interrupted Pareto distribution in firm sizes and links the upper tail cut-off to shadow banking, proposing a new index to estimate shadow banking activity.

Findings

The largest firms follow an interrupted Pareto distribution.

Shadow banking activity causes a sharp cut-off in the upper tail.

The proposed model estimates shadow banking size consistent with prior estimates.

Abstract

Using public data (Forbes Global 2000) we show that the asset sizes for the largest global firms follow a Pareto distribution in an intermediate range, that is ``interrupted'' by a sharp cut-off in its upper tail, where it is totally dominated by financial firms. This flattening of the distribution contrasts with a large body of empirical literature which finds a Pareto distribution for firm sizes both across countries and over time. Pareto distributions are generally traced back to a mechanism of proportional random growth, based on a regime of constant returns to scale. This makes our findings of an ``interrupted'' Pareto distribution all the more puzzling, because we provide evidence that financial firms in our sample should operate in such a regime. We claim that the missing mass from the upper tail of the asset size distribution is a consequence of shadow banking activity and that it provides an (upper) estimate of the size of the shadow banking system. This estimate -- which we propose as a shadow banking index -- compares well with estimates of the Financial Stability Board until 2009, but it shows a sharper rise in shadow banking activity after 2010. Finally, we propose a proportional random growth model that reproduces the observed distribution, thereby providing a quantitative estimate of the intensity of shadow banking activity.