The Interrupted Power Law and the Size of Shadow Banking

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.

Identifying central bank liquidity super-spreaders in interbank funds networks

“…Figure 7 exhibits the double logarithmic scale plot for Colombian financial institutions' assets value, in which the horizontal axis corresponds to the logarithm of assets value, the vertical axis to the logarithm of the cumulative frequency for each asset value, and each circle represents a single local financial institution. As also reported by Fiaschi et al (2013) for the U.S. financial market, such double logarithmic plot exhibits an interesting feature: it is an "interrupted" plot (León, 2014). Such interruption, which yields two different size regimes with two different distributional forms, verifies that in the Colombian financial market there are large (i.e.…”

“…The size of institutions in financial markets is known to be inhomogeneous, with a few that may be regarded as "too-large" and many "too-small", presumably approximating a powerlaw distribution (Gabaix et al, 2003;Fiaschi et al, 2013), even for the Colombian case (León, 2014). By means of an econometric model Craig and von Peter (2010) verify that there is a significant relation between financial institutions' size and their position in the interbank funds' hierarchy, in which large banks tend to be in the core, whereas small banks are found in the periphery.…”

Scale-free tails in colombian financial indexes : a primer

“…human vocabulary) in several languages, the size of avalanches, highway traffic and the water level of rivers (as reported in Bak, 1996;Simon, 1955;Mandelbrot and Hudson, 2004). Regarding the size of financial institutions, Fiaschi et al (2013) find that the assets of financial firms in the United States also comply with Zipf's law; in the Colombian case, however, despite the fit is -again-fairly good (i.e. and for the slope), Zipf's law does not hold according to Figure 2b…”

“…Fiaschi et al (2013) document a similar "interruption" for United States' financial institutions as well.…”

Shadow banking: a geographical interpretation

“…An estimate for the phenomenon at world scale for the period 2003-2012 provides these figures: $61 trillion in 2007 and 64 in 2010 . Taking for granted that SB is a set of businesses concerning the entire banking system, a further estimate, probably in excess, based on peculiar mathematical models, peaks at more than $101 in 2003 and 61 in 2012 (Fiaschi et al, 2013).…”