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  • 9 - Systemic Risks

  • Hideaki Aoyama, Kyoto University, Japan, Yoshi Fujiwara, Yuichi Ikeda, Hiroshi Iyetomi, Wataru Souma, Nihon University, Tokyo, Hiroshi Yoshikawa, Rissho University, Japan
  • Book:
    Macro-Econophysics
    Print publication:
    27 April 2017, pp 306-336

  • Summary

    Network theory provides a critique of standard wisdom on how to create a stable financial system.

    Joseph E. Stiglitz

    Credit–debt relationships among economic agents comprise large-scale networks of the economic system on national and global scales. There are different layers in such networks even at the core of real economic and financial systems. One layer is the arena of the real economy, namely supplier–customer links among firms as nodes. Firm activities are financed by financial institutions as well as directly by financial markets. The layer of the supplier–customer network is thus linked to another layer of financial networks between firms and banks. Furthermore, banks are also creditors and debtors of themselves comprising another layer of inter-bank networks.

    As a financial system, the inter-bank network resides at the core, which is connected with firms, via bank–firm networks, at the periphery of the system; the periphery is a large network of suppliers and customers comrising the engine of the real economy. These networks are actually further linked to financial markets, but one may depict the basic picture as in Fig. 9.1.

    Systemic risk is a network effect caused by failures or financial deterioration of debtors and creditors through the credit–debt links to other nodes even in a remote part of the network. Systemic risk often has considerable consequences at a nation-wide scale, and sometimes at a world-wide extent, as one experiences today in repeated financial crises.

    While an understanding of the inter-bank network at the core of the financial system is crucial, no less important is the propagation of risk from the core of banks to the periphery of firms, or vice versa, as well as the propagation of risk among firms. Unfortunately, empirical studies based on the real data of bank–firm networks or supplier–customer networks on a large scale is still lacking.

    In this chapter, we shall study how one can quantify the systemic risk by using real data on a nation-wide scale for inter-firm production networks and firm–bank credit networks.

    Nation-wide Production Network

    Supplier–customer relationships among firms in the production network are the arenas where financial distress spreads from distressed debtors of customers to its creditors of suppliers. While the events of bankruptcies can be easily observed, the underlying contagion effect of financial distress can have considerable consequences such as a chain of bankruptcies.

  • Appendix A - Computer Programs for Beginners

  • Hideaki Aoyama, Kyoto University, Japan, Yoshi Fujiwara, Yuichi Ikeda, Hiroshi Iyetomi, Wataru Souma, Nihon University, Tokyo, Hiroshi Yoshikawa, Rissho University, Japan
  • Book:
    Macro-Econophysics
    Print publication:
    27 April 2017, pp 337-346

  • Summary

    People think that computer science is the art of geniuses but the actual reality is the opposite, just many people doing things that build on each other, like a wall of mini stones.

    Donald Knuth

    Mathematica Codes for Finance

    If you want to start the study of macro-econophysics, economics, finance, physics, statistics, and mathematics, through analysis of real data, Mathematica is a useful tool. Mathematica provides data and tools. We list a few useful commands for finance here.

    In[1]:= SetDirectory[NotebookDirectory[]]

    In[2]:= FinancialData[“Classes”]

    In[3]:= FinancialData[“Exchanges”]

    In[4]:= FinancialData[“NYSE*”]

    In[5]:= Take[FinancialData[“NYSE*”], 20]

    In[6]:= Take[FinancialData[“NASDAQ*”], 20]

    In[7]:= Take[FinancialData[“∧*”], 20]

    In[8]:= FinancialData[“NASDAQ:AAPL”, “Properties”]

    In[9]:= FinancialData[“NASDAQ:AAPL”, “Name”]

    In[10]:= FinancialData[“AAPL”, “Exchange”]

    In[11]:= FinancialData[“∧DJI”, “Name”]

    In[12]:= FinancialData[“SP500”, “Name”]

    In[13]:= FinancialData[“∧GSPC”, “Name”]

    In[14]:= FinancialData[“NASDAQ:AAPL”, “OHLCV”]

    In[15]:= Take[FinancialData[“NASDAQ:AAPL”, “OHLCV”,All],20]

    In[16]:= DateListPlot[FinancialData[“NASDAQ:AAPL”, All], PlotRange -> All]

    In[17]:= Export[“Apple.csv”, FinancialData[“NASDAQ:AAPL”, “OHLCV”, All]]

    In[18]:= DateListPlot[FinancialData[“NASDAQ:AAPL”, “Return”, All], PlotRange -> All]

    In[19]:= data = FinancialData[“NASDAQ:AAPL”, “OHLCV”, All]; logret = Table[fdata[[i, 1]], Log[data[[i, 2, 4]]/data[[i, 2, 1]]]g, fi, Length[data]g]; Take[logret, 20] DateListPlot[logret, PlotRange -> All]

    In[20]:= data = FinancialData[“NYSE:*“]; Take[data, 10] n = Length[data]

    In[21]:= For[i = 1, i < 4, i++, Export[StringReplace[data[[i]], “NYSE:” -> ““] <> ”.csv”, FinancialData[data[[i]], “OHLCV”, All]]]

    In[22]:= For[i = 1, i < n + 1, i++, Export[StringReplace[data[[i]], “NYSE:” -> ““] <> ”.csv”, FinancialData[data[[i]], “OHLCV”, All]]]

    Tools for Network Analysis

    Many tools for network analysis and visualization are available today. Readers are able to find them using a web search. Here we list a limited number of them based on a somewhat biased selection.

    Pajek (http://mrvar.fdv.uni-lj.si/pajek)

    Netminer (http://www.netminer.com)

    UCINET (https://sites.google.com/site/ucinetsoftware)

    These three are originally developed in sociology for social network analysis, while recent development enables faster computation for larger networks.

    NetworkX (https://networkx.github.io)

    Python library; network analysis and visualization, exible as a script language; also applicable to small-scale visualization. anaconda, all scientific libraries in a single package, includes this and the required libraries, and is better for easy installation.

    igraph (http://igraph.org)

    R library; network analysis and visualization, exible as a script language with abundant tools of R, statistical computing and graphics; easy to install. Python and C versions are also available.

    Gephi (https://gephi.org)

    Network visualization with basic tools of network analyses included; applicable to relatively large-scale networks.

  • 3 - Income and Firm-size Distributions

  • Hideaki Aoyama, Kyoto University, Japan, Yoshi Fujiwara, Yuichi Ikeda, Hiroshi Iyetomi, Wataru Souma, Nihon University, Tokyo, Hiroshi Yoshikawa, Rissho University, Japan
  • Book:
    Macro-Econophysics
    Print publication:
    27 April 2017, pp 53-96

  • Summary

    Society is not homogeneous, and those who do not deliberately close their eyes have to recognize that men differ greatly from one another from the physical, moral, and intellectual viewpoints.

    Vilfredo Pareto

    Distribution of income is a vital issue in every country. The stability of society crucially depends on it. Piketty (2014) in his worldwide bestseller Capital in the Twenty-First Century once again reminded us of the fact that income and wealth are very unevenly distributed in most advanced countries. In the late 19th century, Pareto (1897) already found that income distribution is so skewed that it is actually what we now call the Pareto distribution. Exploration into the mechanisms generating the observed empirical income distribution was started by Gibrat (1931) and Champernowne (1952, 1973). Following their lead, this chapter presents modern treatments and our own results.

    What is said about wealth can also be said about firms: The size of firms, measured by the profit they make, the number of employees or assets, differ from firm to firm, by much more difference than people's income or wealth. For these reasons, we first present many distribution functions which were proposed to explain the distribution of income, wealth, and firm size (for details, see Kleiber and Kotz, 2003). And then we will study the properties of large values that result from power-law distributions in detail, as powerlaw distributions are the most common class of distributions that we observe in economic systems, both people's income and firm sizes.

    One caution: in summarizing various distribution functions, the reader may be tempted to play the fitting game. One may use all the possible functions in the following section or that he/she can think of to find the best-fit to a given distribution. It is a fruitless effort beyond a certain point. Imagine that a variable xtakes only seven values. Then we have seven data, the number of occurrences at those seven values of x. Anyone clever enough can think of a function with seven parameters, that fits the data perfectly. But it is evidently fruitless. Nothing was revealed by such a fit. Only when it is fitted with a small number of parameters, does it lead to some insight to the deep nature of the data (Aoyama and Constable, 1999).

  • Epilogue

  • Hideaki Aoyama, Kyoto University, Japan, Yoshi Fujiwara, Yuichi Ikeda, Hiroshi Iyetomi, Wataru Souma, Nihon University, Tokyo, Hiroshi Yoshikawa, Rissho University, Japan
  • Book:
    Macro-Econophysics
    Print publication:
    27 April 2017, pp 356-357

  • Summary

    SALVIATI: Yesterday took us into such good digressions on Prof. Feynman's words and his van that I do not know whether I shall be able to go ahead without your assistance in putting me back on the track of macro-econophysics.

    SAGREDO: You do not need to worry, Salviati. Together with Simplicio, I read this book to my pleasure. I found it to contain many beautiful considerations which are novel and impressive. … You shake your head, Simplicio and smile as if I uttered some absurdity.

    SIMP.: I merely smile, but believe me. I have an impression that all matters of economy are not covered and the authors do not have answers on business cycles, not to mention how to predict an economic crisis and how to deal with it.

    SALV.: I may remind you that we do not yet have a basic understanding of the underlying dynamics of anything at the micro-level: Anyone can write out models of interactions between economic agents like firms and financial institutions, and simulate the dynamics on simulated networks. But there are so many parameters and so many artificial networks.

    SAGR.: Ahuh… They have real credit and trade networks, don't they, which can serve as a basis for all the new directions of work?

    SALV.: Doubtless there are. We need all the analytical and mathematical tools and modeling ideas exposed in this book to strive for a real understanding of the nature of economic dynamics.

    SIMP.: You are simply talking about agent modeling and everyone knows that they are so limited.

    SALV.: You may know mathematics well, but you don't know science by just looking at real world. Non-linear equations for macro-variables, exact solutions, stability and chaos may be fun to play with. But they are made-up plays only.

    SAGR.: I agree with Salviati. Think of molecules. They interact with each other, optimizing action, which may be comparable to the notion of utility function in economics. With complete understanding of such interactions at micro-level and introducing concepts of statistical physics on how to handle the large number of such interacting heterogeneous objects comes understanding of the dynamics of macro-matter.

    SALV.: Such was elaborated upon in Chapter 1.

  • Prologue

  • Hideaki Aoyama, Kyoto University, Japan, Yoshi Fujiwara, Yuichi Ikeda, Hiroshi Iyetomi, Wataru Souma, Nihon University, Tokyo, Hiroshi Yoshikawa, Rissho University, Japan
  • Book:
    Macro-Econophysics
    Print publication:
    27 April 2017, pp xxix-xxxii

  • Summary

    All truths are easy to understand once they are discovered; the point is to discover them.

    — Galileo Galilei

    SALVIATI: Greetings, Sagredo, and Simplicio, my good friends. Yesterday, we resolved to meet today and discuss as clearly and in as much detail as possible the character and the efficacy of those laws of macro economics, which up to the present, have been put forth by the books of Aoki and Yoshikawa (2006) and Aoyama et al. (2010a), the very same authors of this book.

    SAGREDO: Indeed, I am truly glad and honored to meet you and Simplicio on this occasion of the completion of this book.

    SIMPLICIO: Indeed, indeed, (with a touch of doubt on his face) what is “macro-econophysics”?

    SALV.: You must be familiar with “econophysics”. It is evidence-based economics as a science. You may recall that it has the word “physics” in it as many physicists have devoted their research to this area, guided by the concepts and ideals of physics in their heart.

    SAGR.: I see that most of the authors are physicists, except for Prof. Yoshikawa, who I heard is a macro-economist.

    SALV.: They both have put forth the same ideals of revolutionizing the way real economy is studied in their respective books before. Now they have joined forces to introduce the term Macro-econophysics.

    SAGR.: I have heard that it shares its ideals with “agent-based modelling”, which is yet another great approach.

    SIMP.: That is good. But isn't this book a mere collection of the respective topics from each of the authors?

    SALV.: Absolutely not. They have been working together for the last few years, combining the best of physics and economics and publishing papers. They have spent many days and nights discussing all things big and small included in this book.

    SAGR.: And look… they have Professor Richard Feynman's very hopeful words on the front cover.

    SALV.: This book is one of the latest efforts to construct a science of economics, which forms a part of the basis of this new development and will be improved and passed on to the next generation of academics.

    SAGR.: And look at this photograph taken by the first author (who, by the way, is the first author because of the names being listed in alphabetical order) on December 1, 1979, at UC Irvine, California. He and his famous van!

  • 6 - Business Cycles

  • Hideaki Aoyama, Kyoto University, Japan, Yoshi Fujiwara, Yuichi Ikeda, Hiroshi Iyetomi, Wataru Souma, Nihon University, Tokyo, Hiroshi Yoshikawa, Rissho University, Japan
  • Book:
    Macro-Econophysics
    Print publication:
    27 April 2017, pp 162-209

  • Summary

    No, no, you're not thinking; you're just being logical.

    Niels Bohr

    What causes business cycles? A look at Haberler (1964) shows that all kinds of theories had already been advanced by the end of the 1950s. In recent years, macroeconomists had been so confident of their skillful policy management as to hail it as the “Great Moderation”. Lucas Jr. (2003), in his presidential address to the meeting of the American Economic Association, declared:

    Macroeconomics was born as a distinct field in the 1940's, as a part of the intellectual response to the Great Depression. The term then referred to the body of knowledge and expertise that we hoped would prevent the recurrence of that economic disaster. My thesis in this lecture is that macroeconomics in this original sense has succeeded: Its central problem of depression prevention has been solved, for all practical purposes, and has in fact been solved for many decades (Lucas Jr., 2003, [p.1]).

    Ironically, when Lucas delivered this address, the American economy had been on a steady road to the worst post-war recession, perhaps even depression. Business cycles are still with us and await further investigation.

    Describing the characteristics of business cycles has been one of the most difficult problems in the study of economies because of the presence of various economic shocks. In this chapter, we analyze the characteristics of business cycles more directly than in the standard approach using a method motivated by physics. First, we identify the causes of business cycles using the random matrix theory and principal component analysis.

    We then identify evidence of synchronization in Japanese business cycles and the international business cycle. Finally, we discuss the mechanism of this synchronization using the coupled limit-cycle oscillator model.

    What Causes Business Cycles

    Business cycles are defined as a type of uctuation in the aggregate economic activity of nations that organize their work mainly around business enterprises. A cycle consists of expansions occurring at roughly the same time in many economic activities, followed by similar general recessions, contractions, and revivals that merge into the expansion phase of the next cycle; it is a sequence of change that is recurrent but not periodic.

  • 1 - Introduction: Reconstructing Macroeconomics

  • Hideaki Aoyama, Kyoto University, Japan, Yoshi Fujiwara, Yuichi Ikeda, Hiroshi Iyetomi, Wataru Souma, Nihon University, Tokyo, Hiroshi Yoshikawa, Rissho University, Japan
  • Book:
    Macro-Econophysics
    Print publication:
    27 April 2017, pp 1-9

  • Summary

    We are no river. But we are not made of clay.

    Miroslav Penkov

    Background and Motivation

    Macroeconomics is aimed at understanding the behavior of the economy as a whole— business cycles, economic growth, employment/unemployment, in ation/de ation, and inequality of income. A macroeconomy, such as that of the U.S. and Japan, consists of more than 100 million consumers and one million firms. Evidently, the behavior of the macroeconomy is the outcome of the aggregation and interactions of a large number of micro units such as consumers and firms. To understand such interactions beneath the surface of the macroeconomy, one must resort to new methods that are different from those of standard microeconomics. We propose that this new method be called Macro-econophysics. It provides one not only with novel theoretical insights but also with new empirical methods. Following the spirit of physics and other natural sciences, macro-econophysics puts equal importance on theory and on empirical findings. This book is concerned with both macroeconomic theory and important findings that advanced the study of macroeconomics.

    Macroeconomics was born in the first half of the 20th century. Above all, it was expected to make a good diagnosis of, and hopefully provide a prescription for depression and high unemployment. Keynes’ General Theory of Employment, Interest, and Money, published in 1936, was a landmark work, and had such a profound impact on the discipline that after the war, macroeconomics became synonymous with Keynesian economics (Keynes, 1936). Paul Samuelson once proposed “the neoclassical synthesis,” wherein it is held that the achievement of full employment requires Keynesian intervention but neoclassical theory is valid and useful for efficient resource allocation when full employment is achieved. To many, it was then obvious that the economy occasionally lapses into a recession where labor and other resources are left unemployed. The usefulness of Keynesian economics was taken for granted. Thus, during the 1950s and 1960s, the profession accepted the neoclassical synthesis, and held that economics stood on two pillars, namely, neoclassical microeconomics and Keynesian macroeconomics.

    However, Arrow (1967), in his review of the Collected Scientific Papers of Paul Samuelson, pointed out that the neoclassical synthesis was actually nothing but a common sense argument and lacked rigor.

  • 2 - Basic Concepts in Statistical Physics and Stochastic Models

  • Hideaki Aoyama, Kyoto University, Japan, Yoshi Fujiwara, Yuichi Ikeda, Hiroshi Iyetomi, Wataru Souma, Nihon University, Tokyo, Hiroshi Yoshikawa, Rissho University, Japan
  • Book:
    Macro-Econophysics
    Print publication:
    27 April 2017, pp 10-52

  • Summary

    The whole is simpler than its parts.

    Josiah Willard Gibbs

    This chapter explains basic concepts and analytical methods extensively used in subsequent chapters. Readers begin with learning fundamental stochastic modeling to reproduce distributions with power-law tails. Such skewed distributions are discussed extensively in Chapter 3, with important examples of income and firm-size distributions. Next, we explain entropy. Readers must have already recognized that the concept of statistical equilibrium and probabilistic description, developed in physics, would be indispensable for understanding complex macroeconomic phenomena. Mechanical equilibrium cannot adequately accommodate the diversity of an economic system. Entropy, which measures the degree of randomness or disorder in a system, is a major player in thermal and statistical physics. The statistical equilibrium of a system is regarded as a manifestation of the maximum entropy principle. We first reiterate the basics of entropy especially for readers who have no physics background; this serves as a prelude to Chapter 4 that deals with the distribution of labor productivity. Finally, we provide a brief account of the stochastic modelling of stationary and non-stationary time series with a avor of nonlinear physics. This part is expanded in Chapters 5, 6, 7, and 8 on multivariate time series analysis, business cycles, collective motion of prices, and correlation and synchronizing networks, respectively.

    Stochastic Models and Fat Tails

    Many phenomena in socio and economic systems exhibit fat-tailed and skewed distributions. We have observed and will observe this fact for personal income, firm-size, productivity dispersion, economic networks, and so forth in this book. It is often called “A few giants and many dwarfs”. Presence of a few giants and comovement of many dwarfs has important consequences to a macroeconomic system as we shall explain at places in this book.

    Natural science has also witnessed many phenomena, notably in the study of fractals and scaling, and attracted many researchers who found models and scenarios specific to each domain, and even speculated “universal” explanations for the origin of such distributions, especially of power-laws that possess mathematical properties of scale-free.

    In fact, one of the oldest and most widely known models is the so-called Yule's model to explain distribution of biological species.

  • 8 - Complex Networks, Community Analysis, Visualization

  • Hideaki Aoyama, Kyoto University, Japan, Yoshi Fujiwara, Yuichi Ikeda, Hiroshi Iyetomi, Wataru Souma, Nihon University, Tokyo, Hiroshi Yoshikawa, Rissho University, Japan
  • Book:
    Macro-Econophysics
    Print publication:
    27 April 2017, pp 225-305

  • Summary

    I read somewhere that everybody on this planet is separated by only six other people. Six degrees of separation. Between us and everybody else on this planet.

    In a play written by John Guare

    As pointed out in the Introduction, a macro economy consists of many micro agents. These agents are not independent of each other, but form networks, i.e., they have relationships among each other. An understanding of their interactions is crucial for an understanding of a macro economy.

    This chapter explains the basic concepts and techniques for understanding the structure of economic networks, and then applies them to economic networks. Economic networks are not random nor regular, but exhibit fat-tailed distributions for the numbers and weights of relationships. They also form densely knit groups that are only loosely connected with each other, called clusters or communities.

    Basic tools cover

  • • fundamental graph search algorithms that are applied to identify upstream and downstream in networks and also to model financial distress propagation

  • • a class of random networks used as a null model, namely a configuration model

  • • the concept of modularity derived from assortative mixing and the configuration model

  • • detection of communities by modularity and its extension

  • • visualization of large-scale networks by physical simulations in addition to other graph-theoretical tools. Applications include

  • • a nationwide production network comprising of a million firms and millions of supplier–customer relationships

  • • a community structure in correlation with the stock market found by the RMT and its extension

  • • a globally-coupled network of equities and currencies in the world found by the CHPCA method

  • • a world input–output database for countries and industrial sectors

  • • global production data for G7 countries

    • We will show that one can retrieve interesting information and implications by applying network analyses to these applications.

    Basic Tools

    Graph search and simple applications

    Computational algorithms for simulation on a network are often based on graph-search algorithms and their modifications. Graph search refers to a way of visiting nodes and/or edges exhaustively by putting “marks” on them in a systematic manner. It is analogous to the well-known Greek tale about the hero, Theseus, who successfully escaped from a labyrinth of Minotaur by following Ariadne's thread, but is far more elaborate.

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