Large-scale structure of a nation-wide production network

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.Comment: 17 pages with 8 figures; revised section VI and references adde

Time and frequency structure of causal correlation networks in the China bond market

There are more than eight hundred interest rates published in China bond market every day. Which are the benchmark interest rates that have broad influences on most interest rates is a major concern for economists. In this paper, multi-variable Granger causality test is developed and applied to construct a directed network of interest rates, whose important nodes, regarded as key interest rates, are evaluated with inverse Page Rank scores. The results indicate that some short-term interest rates have larger influences on the most key interest rates, while repo rates are the benchmark of short-term rates. It is also found that central bank bills'rates are in the core position of mid-term interest rates'network, and treasury bond rates are leading the long-term bonds rates. The evolution of benchmark interest rates is also studied from 2008 to 2014, and it's found that SHIBOR has generally become the benchmark interest rate in China. In the frequency domain we detect the properties of information flows between interest rates and the result confirms the existence of market segmentation in China bond market.Comment: 9 pages, 7 figure