Stationarity, non-stationarity and early warning signals in economic networks

Economic integration, globalization and financial crises represent examples of processes whose understanding requires the analysis of the underlying network structure. Of particular interest is establishing whether a real economic network is in a state of (quasi) stationary equilibrium, i.e. characterized by smooth structural changes rather than abrupt transitions. While in the former case the behaviour of the system can be reasonably controlled and predicted, in the latter case this is generally impossible. Here we propose a method to assess whether a real economic network is in a quasi-stationary state by checking the consistency of its structural evolution with appropriate quasi-equilibrium maximum-entropy ensembles of graphs. As illustrative examples, we consider the International Trade Network (ITN) and the Dutch Interbank Network (DIN). We find that the ITN is an almost perfect example of quasi-equilibrium network, while the DIN is clearly out-of-equilibrium. In the latter, the entity of the deviation from quasi-stationarity contains precious information that allows us to identify remarkable early-warning signals of the interbank crisis of 2008. These earlywarning signals involve certain dyadic and triadic topological properties, including dangerous ‘debt loops’ with different levels of interbank reciprocity.