We study analytically and numerically Minsky instability as a combination of top-down, bottom-up and peer-to-peer positive feedback loops. The peer-to-peer interactions are represented by the links of a network formed by the connections between firms; contagion leading to avalanches and percolation phase transitions propagating across these links. The global parameter in the top-bottom -bottom-up feedback loop is the interest rate. Before the Minsky Moment, in the 'Minsky loans accelerator' stage the relevant "bottom" parameter representing the individual firms' micro-states, is the quantity of loans. After the Minsky Moment, in the 'Minsky crisis accelerator' stage, the relevant 'bottom' parameters are the number of ponzi units / quantity of failures / defaults. We represent the top-bottom, bottom-up interactions on a plot similar to the Marshall-Walras diagram for quantity-price market equilibrium (where the interest rate is the analog of the price). The Minsky instability is then simply emerging as a consequence of the fixed point (the intersection of the supply and demand curves) being unstable (repulsive). In the presence of network effects, one obtains more than one fixed point and a few dynamic regimes (phases). We describe them and their implications for understanding, predicting and steering economic instability.
It is generally accepted that neighboring nodes in financial networks are negatively assorted with respect to the correlation between their degrees. This feature would play an important 'damping' role in the market during downturns (periods of distress) since this connectivity pattern between firms lowers the chances of auto-amplifying (the propagation of) distress. In this paper we explore a trade-network of industrial firms where the nodes are suppliers or buyers, and the links are those invoices that the suppliers send out to their buyers and then go on to present to their bank for discounting. The network was collected by a large Italian bank in 2007, from their intermediation of the sales on credit made by their clients. The network also shows dissortative behavior as seen in other studies on financial networks. However, when looking at the credit rating of the firms, an important attribute internal to each node, we find that firms that trade with one another share overwhelming similarity.We know that much data is missing from our data set. However, we can quantify the amount of missing data using information exposure, a variable that connects social structure and behavior. This variable is a ratio of the sales invoices that a supplier presents to their bank over their total sales.Results reveal a non-trivial and robust relationship between the information exposure and credit rating of a firm, indicating the influence of the neighbors on a firm's rating. This methodology provides a new insight into how to reconstruct a network suffering from incomplete information. I. INTRODUCTIONThe topology of a network is the visible result of integrative processes in the underlying system. It may be possible to deduce the dynamics of the underlying system from such a network. However, the mechanism so deduced will be extremely sensitive to any data that is missing from the network. If the information on the system is incomplete the rendered network may provide a misleading picture of the system and impact our understanding of the mechanisms that created it.Financial networks are known for being negatively assorted, i.e. neighbouring nodes in the network are dissimilar, in particular as regards the degree of their in-and out-links. Among practitioners and economists this property is desired because it renders the financial network robust to percolation (propagation of distress or growth). The knowledge that contagion rarely happens may catch us by surprise when financial shocks do indeed propagate from the local level to the national/international level. In the events preceding the 2008 financial crisis, small systemic shocks affected large proportions of the industrial and financial networks. The usual response of firms to market downturns was then amplified and the response swept across the network using the monetary (communication) channels. One reason for our lack of control over this incident was that a proportion of the communication channels that link peers were not known to the banking system: the high risk mortga...
Solomon and Golo [1] have recently proposed an autocatalytic (self-reinforcing) feedback model which couples a macroscopic system parameter (the interest rate), a microscopic parameter that measures the distribution of the states of the individual agents (the number of firms in financial difficulty) and a peer-to-peer network effect (contagion across supply chain financing). In this model, each financial agent is characterized by its resilience to the interest rate. Above a certain rate the interest due on the firm's financial costs exceeds its earnings and the firm becomes susceptible to failure (ponzi). For the interest rate levels under a certain threshold level, the firm loans are smaller then its earnings and the firm becomes 'hedge.' In this paper, we fit the historical data (2002-2009) on interest rate data into our model, in order to predict the number of the ponzi firms. We compare the prediction with the data taken from a large panel of Italian firms over a period of 9 years. We then use trade credit linkages to discuss the connection between the ponzi density and the network percolation.We find that the 'top-down'-'bottom-up' positive feedback loop accounts for most of the Minsky crisis accelerator dynamics. The peer-to-peer ponzi companies contagion becomes significant only in the last stage of the crisis when the ponzi density is above a critical value. Moreover the ponzi contagion is limited only to the companies that were not dynamic enough to substitute their distressed clients with new ones. In this respect the data support a view in which the success of the economy depends on substituting the static 'supply-network' picture with an interacting dynamic agents one.
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