Summary: Determining the causes of instability and contagion in financial networks is necessary to inform policy and avoid future financial collapse.
In [“Financial networks and contagion”, Am. Econ. Rev. 104, No. 10, 3115–3153 (2014; doi:10.1257/aer.104.10.3115)] M. Elliott, B. Golub and M. O. Jackson proposed a simple model for capturing the dynamics of complex financial networks. In Elliott, Golub and Jackson’s model, the institutions in the network are connected by linear dependencies (cross-holdings) and if any institution’s value drops below a critical threshold, its value suffers an additional failure cost. This work shows that even in this simple model there are fundamental barriers to understanding the risks that are inherent in a network.
First, if institutions are not required to maintain a minimum amount of self-holdings, any change in investments by a single institution can have an arbitrarily magnified influence on the net worth of the institutions in the system. This implies that if institutions have small self-holdings, then estimating the market value of an institution requires almost perfect information about every cross-holding in the system.
Second, even if a regulator has complete information about all cross-holdings in the system, it may be computationally intractable to estimate the number of failures that could be caused by a small shock to the system.