Financial crisis, Omori's law, and negative entropy flow

The 2008 global financial crisis has revived great interest in early warning system (EWS) models for reducing the risks of future crises. Existing EWS models employ aggregated variables that cannot examine the nonlinear dynamics of participating players on scales smaller than a country in unstable, non-equilibrium economies. To help understand the mechanism of financial crises and identify new robust indicators for financial crises and economic recessions, in this work, we take an “anatomical” approach, i.e., to examine the income structures of different sectors of an economy separately, as well as to analyze the exposure networks associated with Fannie Mae/Freddie Mac, Lehman Brothers, and American International Group. We show that the losses in exposure networks can be modeled by a two-parameter Omori-law-like distribution for earthquake aftershocks. Such a distribution suggests that losses will be widespread around crises or recessions. Indeed, around crises or recessions, the heavy-tailed distributions for the negative income cluster are even heavier than those for the positive income cluster. Consequently, the entropies associated with the distribution of the negative income cluster exceed that of the positive income cluster. Moreover, instability propagates from the crisis initiating sector to other sectors. Therefore, the anatomical approach developed here can indeed shed some light on the detailed dynamics of financial crises and economic recessions, and the distribution and entropy approaches can help predict economic downturns.