We present an analysis of the credit market of Japan. The analysis is performed by investigating the bipartite network of banks and firms which is obtained by setting a link between a bank and a firm when a credit relationship is present in a given t
ime window. In our investigation we focus on a community detection algorithm which is identifying communities composed by both banks and firms. We show that the clusters obtained by directly working on the bipartite network carry information about the networked nature of the Japanese credit market. Our analysis is performed for each calendar year during the time period from 1980 to 2011. Specifically, we obtain communities of banks and networks for each of the 32 investigated years, and we introduce a method to track the time evolution of these communities on a statistical basis. We then characterize communities by detecting the simultaneous over-expression of attributes of firms and banks. Specifically, we consider as attributes the economic sector and the geographical location of firms and the type of banks. In our 32 year long analysis we detect a persistence of the over-expression of attributes of clusters of banks and firms together with a slow dynamics of changes from some specific attributes to new ones. Our empirical observations show that the credit market in Japan is a networked market where the type of banks, geographical location of firms and banks and economic sector of the firm play a role in shaping the credit relationships between banks and firms.
Production in an economy is a set of firms activities as suppliers and customers; a firm buys goods from other firms, puts value added and sells products to others in a giant network of production. Empirical study is lacking despite the fact that the
structure of the production network is important to understand and make models for many aspects of dynamics in economy. We study a nation-wide production network comprising a million firms and millions of supplier-customer links by using recent statistical methods developed in physics. We show in the empirical analysis scale-free degree distribution, disassortativity, correlation of degree to firm-size, and community structure having sectoral and regional modules. Since suppliers usually provide credit to their customers, who supply it to theirs in turn, each link is actually a creditor-debtor relationship. We also study chains of failures or bankruptcies that take place along those links in the network, and corresponding avalanche-size distribution.
Research activities of Kyoto Econophysics Group is reviewed. Strong emphasis has been placed on real economy. While the initial stage of research was a first high-definition data analysis on personal income, it soon progressed to firm dynamics, growt
h rate distribution and establishment of Paretos law and Gibrats law. It then led to analysis and simulation of firm dynamics on economic network. Currently it covers a wide rage of dynamics of firms and financial institutions on complex network, using Japanese large-scale network data, some of which are not available in other countries. Activities of this group for publicising and promoting understanding of econophysics is also reviewed.
We show that an economic system populated by multiple agents generates an equilibrium distribution in the form of multiple scaling laws of conditional PDFs, which are sufficient for characterizing the probability distribution. The existence of the do
uble scaling law is demonstrated empirically for the sales and the labor of one million Japanese firms. Theoretical study of the scaling laws suggests lognormal joint distributions of sales and labor and a scaling law for labor productivity, both of which are confirmed empirically. This framework offers characterization of the equilibrium distribution with a small number of scaling indices, which determine macroscopic quantities, thus setting the stage for an equivalence with statistical physics, bridging micro- and macro-economics.
Our recent study of a nation-wide production network uncovered a community structure, namely how firms are connected by supplier-customer links into tightly-knit groups with high density in intra-groups and with lower connectivity in inter-groups. He
re we propose a method to visualize the community structure by a graph layout based on a physical analogy. The layout can be calculated in a practical computation-time and is possible to be accelerated by a special-purpose device of GRAPE (gravity pipeline) developed for astrophysical N-body simulation. We show that the method successfully identifies the communities in a hierarchical way by applying it to the manufacturing sector comprising tenth million nodes and a half million edges. In addition, we discuss several limitations of this method, and propose a possible way to avoid all those problems.
We present a new approach to understanding credit relationships between commercial banks and quoted firms, and with this approach, examine the temporal change in the structure of the Japanese credit network from 1980 to 2005. At each year, the credit
network is regarded as a weighted bipartite graph where edges correspond to the relationships and weights refer to the amounts of loans. Reduction in the supply of credit affects firms as debtor, and failure of a firm influences banks as creditor. To quantify the dependency and influence between banks and firms, we propose a set of scores of banks and firms, which can be calculated by solving an eigenvalue problem determined by the weight of the credit network. We found that a few largest eigenvalues and corresponding eigenvectors are significant by using a null hypothesis of random bipartite graphs, and that the scores can quantitatively describe the stability or fragility of the credit network during the 25 years.
An agent-based model for firms dynamics is developed. The model consists of firm agents with identical characteristic parameters and a bank agent. Dynamics of those agents is described by their balance sheets. Each firm tries to maximize its expected
profit with possible risks in market. Infinite growth of a firm directed by the profit maximization principle is suppressed by a concept of going concern. Possibility of bankruptcy of firms is also introduced by incorporating a retardation effect of information on firms decision. The firms, mutually interacting through the monopolistic bank, become heterogeneous in the course of temporal evolution. Statistical properties of firms dynamics obtained by simulations based on the model are discussed in light of observations in the real economy.
Labour productivity distribution (dispersion) is studied both theoretically and empirically. Superstatistics is presented as a natural theoretical framework for productivity. The demand index $kappa$ is proposed within this framework as a new busines
s index. Japanese productivity data covering small-to-medium to large firms from 1996 to 2006 is analyzed and the power-law for both firms and workers is established. The demand index $kappa$ is evaluated in the manufacturing sector. A new discovery is reported for the nonmanufacturing (service) sector, which calls for expansion of the superstatistics framework to negative temperature range.
We have conducted an agent-based simulation of chain bankruptcy. The propagation of credit risk on a network, i.e., chain bankruptcy, is the key to nderstanding largesized bankruptcies. In our model, decrease of revenue by the loss of accounts payabl
e is modeled by an interaction term, and bankruptcy is defined as a capital deficit. Model parameters were estimated using financial data for 1,077 listed Japanese firms. Simulations of chain bankruptcy on the real transaction network consisting of those 1,077 firms were made with the estimated model parameters. Given an initial bankrupt firm, a list of chain bankrupt firms was obtained. This model can be used to detect high-risk links in a transaction network, for the management of chain bankruptcy.
