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.
Highlights
If we take the Forbes Global 2000 list as a snapshot of the global economy, we find that financial firms dominate the top tail of the distribution of firms by asset size: the highest placed firm classified as non-financial is General Electric, which ranks 44th in the 2013 Forbes Global 2000 (FG2000) list
Proportional Random Growth Model The observed Paretian distribution has generally been related to a mechanism of proportional random growth (PRG) which assumes that firms grow proportionally to their size
A key empirical testable hypothesis of PRG models is that the rate of return on assets is independent of the level of assets, as it should be for industries with constant returns to scale
Summary
If we take the Forbes Global 2000 list as a snapshot of the global economy (see Materials and Methods), we find that financial firms dominate the top tail of the distribution of firms by asset size: the highest placed firm classified as non-financial is General Electric, which ranks 44th in the 2013 Forbes Global 2000 (FG2000) list. Its size is not much smaller than the largest firm in the list, Fannie Mae, which has assets worth $3.2 trillion This observation contrasts with the common view in the literature documented across countries and over time (see [1,2,3]) that firm sizes S follow a Paretian distribution as ProbfS§xg^cx{c, ð1Þ with c,cw0. If Zipf’s law were to hold for the top 20 companies, we would expect Fannie Mae to be ten times as large as the Royal Bank of Scotland ($21.3 instead of $3.2 trillion) This anomaly in the shape of the top tail of the assets distribution is the starting point of our analysis. We discuss a simple generalization of the model proposed in Ref. [5], which allows a first investigation of the determinants of the observed anomaly
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