Hi Yoshinori,

I don't think you can work out much just from the network being scale free - you'd need some assumptions about the dynamics of transactions. For example, if these were independent random walkers that had reached a stationary state, and the network were undirected (symmetric), then the expected value of the flow of walkers along any link would be the same as along any other, irrespectively of degrees.

Sam

Sam,

Thank you for your comment. I am working on monetary economics and want to know what determines the demand for money. Imagine a network of all economic transactions. They are done by individuals and firms. They are nodes of transaction network. Some nodes have enormous number of clients or supplies. Some others have rather few of them. It seems this network forms a scale free network. But it is quite difficult what kind of distribution the links have. I want to know any previous research made over these questions.

Sorry, I hadn't seen this when I posted the other reply. I'm afraid I don't know of any empirical results for that kind of network. However, it seems to me that, in the scenario you describe, either all inflows and outflows will indeed be equal for any node, or some nodes will be running up debts that add up to others' surpluses. Unless, of course, some of your nodes are banks and are thus allowed to create more money. In this case, as M Rowbotham nicely sketches out in The Grip of Death, http://www.goodreads.com/book/show/1033699.The_Grip_of_Death , you could get a positive feedback mechanism exploding your money supply (and total debt) in the following way:

- Both firms and consumers have to pay back previous debts plus interests, meaning purchasing power is constrained (Say's law is violated);

- People must borrow to buy, and firms to survive and sell;

- Banks re-lend at least part of the money returned to them (augmented by the money multiplier);

- Purchasing power is constrained even more; go to top.

This would seem to explain why debt of all kinds (private, public, industrial...) always increases inexorably. However, I don't know if it will be of any use for your model...

Thanks a lot. While I am writing an answer for your request, you have written me a long comment. I will read The Grip of Death.

I have ordered the book. But as the copy comes from U.S., it may take more than two weeks.

Good idea - I'm actually still reading it myself, but I can certainly attest the quality of the first half :)

I really like the unscaled network idea.

The money demand generated by the process Samuel described is just one process that may increase money demand, from many many others. Interest it's just the cost of lending services, and just a fraction of -it.

Your approach to monetary and financial problems seems very interesting and promising. Your papers BANCRUPCY-RECOVERY DECISION IN A SYSTEMIC VIEW and APPROACHAING ECONOMIC ISSUES THROUGH EPISTMOLOGY were most interesting.

Your research is based on complex systems theory and I am also in the same tradition, although I worked mainly in the domain of international trade theory and evolutionary analysis of human economic behaviors. I am now interesting to the financial asset market and in monetary questions in particular. Scale free network may give a good parable not only for the functioning of the monetary economy, but also some inspirations for a new view of economic development, including new product introductions.

The epidemiological research on economy, my favorite topic, is highly related to the networked economy functioning. However, i found little data to support the contagion in micro-systems. I need the network map and mathematics to prove my concept, so i am really interested in any progress regarding the scale free networks in economics.

Hi Yoshinori,

I'm also looking at the monetary system from a network perspective. imho - the problem essentially has to be divided into two separate aspects, the flow of money around the system establishing price levels - which is essentially a closed-flow network (instantaneously - there are complications with the behaviour of the money supply over long periods) and debt - which is a contractually agreed asymmetric flow of money over time. I think a network approach to analysing debt has a lot of potential - but be warned to do this properly requires a very detailed understanding of the banking system, and the different kind of debt it generates.

As far the scale free stuff is concerned, certainly the debt networks created by banks are anything but random, and I would predict, highly structured, but there are probably some quite interesting differences between countries with large numbers of small banks, and those with small numbers of large banks.

Jacky,

Thank you for your advice. I am interested in monetary theory, because monetary and financial economy became too important that I cannot escape from thinking about it. I studied major textbooks and papers in monetary theory. But I am not satisfied with most of the monetary theory based on equilibrium framework. Circuit theory attempt seems challenging but I want to know more about how the money (its distribution and movements) affects the production. If you know any paper of this kind please let me know with a brief introduction.

Yoshinori

Bradut,

A friend of mine has suggested that a book "Connected!" by Nicholas A. Christakis and James H. Fowler may be interesting for us. You may have read this book but I did not even know this book. It seems this book became a giant seller.

Christakis is a political scientist who specializes in Health Care Policy, Sociology, and Medicine. He was selected as one of 100 most influential people in the world in 2009 by the TIME magazine. Chapter 4 of this book treats the contagion of diseases.

Seems interesting, and it's going to appear in our bookshops soon. I have found some speeches of James Fowler on the topic. Not sure it will help us as method, but may suggest something we should take into account. What if we should reduce the matter to individuals and consider companies just as groups of individuals managing capitals?

Of course, it will be a popularization of the idea of scale free network and others. I am asking my friend (another one than the friend who taught me Connected. ) to give me some references. He is studying pandemic expansion by an agent based simulation.

Maybe we can write a short paper on this.

Bradut,

Do you have any concrete idea?

Jacky Mallett,

I received your e-mail requesting my old paper. I am thinking to send you an offprint by postal mail. Would you teach me your address?

Is this sufficient?

Jacky Mallett

Icelandic institute of intelligent machines

Reykjavík University

Iceland

Bradut Bolos,

You probably know these papers, but these are two of papers that my friend working on epidemics model taught me:

http://eaton.math.rpi.edu/csums/papers/ScaleFree/Scale-Free%20Networks.pdf

http://fisica.cab.cnea.gov.ar/estadistica/abramson/notes/Epidemics-Lectures-PANDA.pdf

Unfortunately, it seems my friend has not written any English papers on scale-free network and epidemics.

Dear Yoshinory Shiozawa

Thanks, actually those two articles were not on my list. Actually your comment here have made me search for scale free networks related articles for the first time.

Best regards

Bradut Bolos

Hi Yoshinory,

Monetary theories describe the relationship between money and output of the economy. Look up any intermediate textbook and read on neoclassical/monetarist as well as Keynesian theory of money and you'll see the relationship.

Hi Jacky,

I believe developing a network of flow of funds is an interesting idea. However, I fail to see why the type of loans would make a difference in the network. Could you expand on it a bit?

Sure, sorry I should have been a bit clearer.

There are essentially 2 types of loan in modern economies. One is when I have money, I lend it to you, and you then repay me over time. Corporate bonds, government treasuries are these types of loan. The other are the loans which are made by banks, which essentially involve the continuous creation and then destruction as the loan is repaid (i really don't like the money out of free air description at all for this btw.) of bank deposit money (which is money to all intents and purposes today.)

Although in many respects the operations of these two types of loans are the same, they are not identical, and in particular there can be side effects (money creation or destruction) with bank loans that don't happen with other types of loans.

This is why I think it was such a big mistake to allow banks to securitize their lending btw., it led to a rapid increase in the ratio of debt : money in the banking systems that allowed it, and much of the instabilities that we're currently seeing today.

Jacky,

Loans are loans. There is only one kind of money transaction: lending and receiving funds. Your statement tells me that you differentiate between loanable funds (loans based on the existing liquidity in the banking system) and loans based on increased liquidity to the banking system, that is, increased supply of money.

In the final analysis, in a network analysis of flow of funds, it does not matter which source the funds are coming from.

I beg to differ - just as a point of scientific practice, if you can make the same operation on two things and have different results, then they are not the same. Loan default handling is a useful example of this.

But let me also make the observation that a key property of any real time network, and one of the determinants of its information space, is its topology. Which in a loan network would be the map of the relationships between borrowers and lenders.

Jacky,

I have published an article on modeling technological systems of economies using social network analysis. Please see my publication list for the reference. So, I am pretty much familiar with network analysis and the statistical properties of the network topology. Even though I have yet to learn how the dynamics of the network change its topology. So, I completely understand and agree with the content of your second paragraph.

Nonetheless, I still fail to see why the sources of loanable funds, whether it is coming from the existing liquidity or from newly created money supply, would matter in a network of loan transactions. I am hoping that you could clarify this for me.

Just as a side-note - the overloading of the term "liquidity" wrt to banking system operations is very confusing when attempting analysis - I'll assume you're referring to lending capacity (in terms of liability deposits), rather than inter-bank clearing liquidity.

Let's take loan default as an example, it's easier. If we have a transfer loan (between two individuals), then if you default, I don't get my money back, but there are no larger implications beyond that, in particular there are no money supply implications. The money is still in the system somewhere. With a bank loan on the other hand, there is a small buffer provided by profits and loss provisions against which a loan default can be written off, but beyond that there is a leveraged impact on the money supply, as the bank reduces its capital holdings, and lending contracts, and a very real (and repeatedly seen historically) risk of cascade failure across the network.

As to how large scale networks change their topology - typically by growing, otherwise slowly if at all. It's extremely hard for a large scale communicating network to effect topology changes since any attempt to do so requires more information space than the network has. The analogy from data communication networks that may be helpful is "Broadcast Storm".

Dear Abdol,

this is another question I asked in this ReearchGate Question page in the beginning of this year:

I am interested in monetary theory. But I am not satisfied with most of the monetary theory based on equilibrium framework. Circuitist attempt seems challenging but I want to know more about how the money (its distribution and movements) affects the production. If you know any paper of this kind please let me know with a brief introduction.

There were no answers to this question. So I changed my question to a more concrete one.

Dear Yoshinori,

I believe you have interesting ideas. However, you do not explain why you are not interested in the traditional monetary theories (as you put it in equilibrium framework), which deal with the effect of money on output, price level, employment, exchange rate, interest rate, etc.

You have not articulated the argument that the traditional theories do not explain how the macroeconomic system goes into disequilibrium, but I have a feeling that this is why the traditional models do not satisfy you. Is my assessment correct?

I would very much like to learn about "circuitist" model. Moreover, at least Keynesian and post-Keynesian monetary models exactly specify that transaction demand and precautionary demand for money affect output and production.

Am I missing your point altogether?

Jacky,

By liquidity I mean the supply of money to the economy. As I am sure you are aware, the central bank injects high -powered money (monetary base) into the banking system. The reserve to the banking system through the money multiplier creates the aggregate supply of money in the economy. Hence, lending and borrowing between individuals does enter into the picture of how money supply is created. That type of transaction falls into demand for money analysis in an inter-temporal framework.

Note that even the interbank lending/borrowing does not create additional liquidity to the banking system. When the overnight interbank lending rate LOBOR or Fed Funds rate increase disproportionately, the monetary authorities see that as a sign of shortage of liquidity in the banking system, and usually but not always, increase reserve to the banking system.

As an example of a situation when the Fed did not peg the interest rate by increasing the reserve to the banking system, we can think of early 1980s when the Fed allowed the discount rate, and by implication the Fed Fund rate, to increase to a double digit figure.

This brings us back to the original discussion of your differentiation between lending/borrowing"old" money and "new" money in a network analytic framework. My position is that, first it is impossible to differentiate between the types of transactions, and secondly, even if one could do it, one could gain no additional insights.

Abdol,

There are two types of "liquidity" in that definition. One is the bank's asset money, central bank's liability - which is then statistically multiplexed against the liability (bank deposit money) of the commercial banks. In most banking systems today, the two can be regarded as effectively separate circulating systems, with the central bank money playing a small regulatory role, as well as providing the "liquidity" for inter-bank clearing operations.

It then depends under what regulatory framework the banking system is running. In modern banking systems, the basel capital requirements dominate, so the money multiplier theory is at best partially valid. What happened in the 1980's is in the gray zone between Basel and Bretton Woods of course. (The text book model, as I imagine you're aware, has a number of flaws, but wrt to the money multiplier in particular, once loan repayments are included the situation becomes rather more complex, as they also act to throttle the expansion factor.) Not that that particularly matters, since no modern banking system that I'm aware of has reserve requirements that cover all its liability accounts. It is possible to differentiate the different types of transactions, and it is extremely useful in understanding the operational characteristics of the system, but that is a larger discussion than is really practical here.

Wrt. general equilibrium theory - perhaps we can turn the question round a little. Obviously I can't speak for Yoshinori, but I believe he like me comes from a field where damped recursive feedback systems (which is the classification the banking system falls under), are certainly not known for their stability. What would perhaps be helpful to both of us, would be your opinion on the form a disproof of general equilibrium theory would have to take to be accepted by the Economic Academy?

Jacky,

What do you mean by general equilibrium(GE) theory? Do you mean GE in Walarsian framework, or in Hick's GE of money and product markets, that is, IS and LM analysis?

Abdol,

Most simple criticism against monetary theory based on equilibrium is the same as what Frank Hahn once asserted. In almost all general equilibrium theories or models, there is a good named money but it is only (n+1) st good among many other goods and there is no essential difference between money and ordinary goods. Hahn himself tried to make a real monetary theory but I cannot say that he has succeeded.

There are many other "monetary" theories constructed on partial equilibrium framework and still I am dissatisfied with them. Take the strongest case for the proponents of monetary theory in the equilibrium framework, that of Keynes's General Theory. In the process of writing the draft of this book, Keynes named his theory "monetary theory of production." But the result was not so successful. One of the novelties of that work was liquidity preference theory. That is one of precursors of present-day portfolio theories, but those portfolio theories and finance engineering theories paved the way to financial crisis symbolized by the Lehman shock. Liquidity preference may be useful concept for some situation but we should think that it is quite weak theory by which to analyze monetary shocks and crisis.

Another symptom of Keynes's failure is his formulation of the "effective demand." He defined it as a cross point of two aggregate curves. The failure is most easily demonstrated by the fact that the concept of effective demand is now wiped out from the university level textbooks on Macroeconomics. The concept of aggregate demand remained but the concept of effective demand and the principle of effective demand vanished from the new Keynesian terminology. But I am thinking that the concept and the law of effective demand were the keystone of Keynes’s monetary theory of production. In order that formulate this principle properly, it is necessary to go out of equilibrium and observe what kind of process will happen in ever changing economies.

Don Patinkin once pointed out after an old Jewish saying that money buys goods but goods do not buy money. Clower objected this saying but I think Clower was wrong and the popular saying is much more realistic than any other economic theory based on equilibrium, be it partial or general.

Yoshinori,

Are you familiar with Hyman Minisky's financial fragility theory of capitalist financial crisis? If not I recommend you take a look at his analysis, which is squarely based on a fundamental idea that was developed by Keynes, that is, finance plays the central role in capitalist development. Minisky showed that financial fragility is endogenously developed by operations of the markets.

On capitalist crises and stagnation in general emerging from inadequate ( "vanished") effective demand (of course vanished from textbooks authored by neo-liberal ideologues), please read on under consumption theories of Alvin Hansen, Paul Sweezy, and Josef Steindl, and find out what has been ailing Japan over the last 30 years and what is ailing Europe and America over the last 50 years. We certainly don't need to reinvent the wheel so far as the crisis theory is concerned.

Abdol,

thank you for your information. Yes, I am interested in Hyman Minsky. Last term, I read his "Stabilizing Unstable Economy " with my graduate students. I think he is among the best economists in financial and monetary economics.

For example, he write as follows:

A basic characteristic of capitalist economy, then, is the existence of two set of prices: one set for current output, the other set for capital assets. The prices of current output and of capital assets depend upon different variables and are determined different markets. The prices however are linked, for investment out put is part of current output. (Minsky, 2008, pp.195-196 )

This is a very important remark and a person like me, who approached from the real economy side to the financial economy side, feels that Minsky is focusing too much on capital asset markets. He does not distinguish two kinds of investment: investment on production capacities and investment on financial assets. The first kind of investment, as opposed to the second kind, is not sensitive to the small change of interest rates. His observations on investment are sometimes erroneous if we think it is investment of the first kind.

I believe a kind of synthesis is requested.. But, of course, one single person cannot do every thing. So, a collaboration of different orientations is required.

Abdol,

this is a second and more positive answer to your question about equilibrium framework.

You and probably your students work to detect non-linearity in the various monetary time series. Those are fine works and I highly appreciate them. My question is if the generation of these time series can be explained by a mechanism which is usually understood as an equilibrium or shifting of equilibrium?

Of course, a spot price or exchange rate, concluded at a point of time, is determined by a value point where demand and offer are balanced. So, we can say that any spot price is determined by an equilibrium. But how about the movement or the fluctuation of these prices? You have detected a non-linearity in various time series. Don't you think that there are some mechanisms which work behind the apparent fluctuation? A kind of positive feedback and others? You observe clustering of high volatility moment. Are these all results of purely circumstantial random noises?

Suppose we are physicists. You have detected that a time series does not obey classical random walking (or normal or log normal distribution). Then, you or some others start to try finding a mechanism behind the observed facts. Major parts of fluctuations may be random. But some parts of fluctuations may be governed by an undetected mechanism. The influence of these mechanism can be neglected in normal times. But in some rare cases, this mechanism starts to generate a dominant role in the time series. We may interpret this phenomenon a financial crisis. I am probably searching these behind the scene mechanism and I don't think that equilibrium framework gives good hints in this investigation.

Hi Yoshinori,

Thank you for your thoughtful comments. I comment on both posting below.

First, on capitalist financial crisis. I am very happy that you are familiar with Minisky's financial fragility theory. However, the passage you quote from Minisky does not reflect the core of his financial fragility hypothesis. The core of Minisky's financial fragility hypothesis can be summarized as follows: Exogenous shocks, speculative mania empowered with unrestricted bank credit, assets price bubble, insider dealing and other capitalist swindling, debt-deflation, bursting of bubble and asset price plummeting. One can show this pattern of events time and again simply by historical observations of financial crises (please see Kindleberger's Manias, panics and crashes: A history of financial crises). As, I am sure you have surmised by now, there is nothing here that deals with neoclassical fairy tale of general equilibrium.

Note that by its "normal' operations markets create crisis and the key element in creation of such crisis is the banking sector, not only the banks regulated by the government, but also the "shadow banking system", which operate under the radar of the regulators (the financial sector) play the pivotal role in creating conditions that inevitable leads to financial collapse.(Please read Paul Krugman's entertaining little book: The Return of Depression Economics and the crisis of 2008.

Second, on your comments and question that appeared in your second posting.

I start with thanking you for your nice comment and appreciation of my work on applications of nonlinear dynamical system methods and algorithms in economics and finance. I also agree with you and appreciate your position that general equilibrium analysis is incapable of providing a reasonable explanation for the dynamics of the financial and goods markets. That is exactly the reason that I have shifted my attention to use of nonlinear dynamical systems theory in unraveling the nature of the financial data generating processes. I have given up the idea of using economic (mathematical) modeling in explaining the dynamics of the markets. I may be overly pessimistic, but I believe it is impossible to fit the data to the molds (models?) of economic theoretician's mental edifices and come up with rational and realistic conclusion about what is going on and what has transpired . Hence, the only viable alternative I see is to have the data tell us what is going on, rather than use data to confirm our ideas are correct!

I should point out that my and my co-researchers' works on this topic are not confined to detection of non-linearity in the observed financial time series. Showing that the series are generated by nonlinear data generating process (DGP) is only the first step in unraveling the true nature of dynamical systems from which we have only one set of observations. The truly challenging task after establishing that non-linearity is present in the data is determining the type of nonlinear dynamics that generated the data. The dynamics could be deterministic (chaotic), stochastic or pure white noise or random.

In my mind, given the tools of analysis at this historical epoch, determining the data is based on which of these dynamics is the best we can do. However, there are people who have given up already and believe that it is impossible to determine the dynamics of the financial or economic systems.

Again, one can find no trace of neoclassical fairy tale of general equilibrium in the financial data according to the methods of nonlinear dynamical systems..

That is all for now.

Look forward to comments from you and other readers.

Abdol,

thank you for your detailed explanations. I now understand that we are thinking economics and viewing economy in a quite similar way.

Thank you again for the reading point of Minsky. Yes, you are right on pointing that the core of Minsky's financial fragility lies on the mechanism or series of events which leads to a bubble and to a crush. What I am wondering is whether his framework of explanation is good enough one.

The confusion made between real investment (investment of entrepreneurs) and financial investment (investment on securities) exits also in Keynes's General Theory. As you know well, anti-Keynesian counter revolution occurred since around 1970's and it led to now dominant New Classical Macroeconomics including Rational Expectations and Real Business Cycle. We may criticize their theoretical flaws but what is more important is to doubt more deeply the foundation of Keynes's economics on which Minsky's work lies its base. We have to admit that there are some serious defects in the Keynes's construction of his monetary theory of production and that this led inevitably to the anti-Keynesian counter revolution. The confusion I pointed concerning Minsky is just one of such defects we can find in General Theory.

I may propose a new question on this theme but probably next week. As for non-linearity of financial time-series, let me give a bit of time. I think this will be a very interesting theme of discussion.

Dear Samuel Johnson, Bradut Bolos, Jacky Mallet, and Abdol Soofi,

I found an interesting paper which may be interesting for all contributors in this question page. It is the paper by Hideaki Aoyama entitled "Systemic Risk in a Japanese Financial Network"

http://c-faculty.chuo-u.ac.jp/~jafee/papers/Aoyama_Hideaki2.pdf

Abstract reads

We study Japanese bank-firm bipartite network, whose links are bank's lending to each firm. By assigning 'distress variable' to each agent in this work and studying spread of distress from a bank to the whole network, we evaluate the bank’s importance with respect to the systemic risk of this financial network.

In the Introduction Aoyama writes

"there are basically two ways to approach [the systemic risk] problem.

-Realistic, but complex approach: One may set up some numbers of equations for dynamic interactions between agents, whose variables are entries in financial statements, like saving, borrowing, sales, profit and what not.

-Abstract, but simple approach: One may define some abstract quantities that reflect the most important characterization of each agent and define interactions among them.”

Aoyama adopts the second approach. Of course, one may blame his analysis to be too abstract and it is only a parable. Even if it is a parable, systemic risk is the most important question which the finance engineering ignored systematically. Therefore, I think Aoyama's attempt shows us a new possible approach from which we can start thinking on systemic risk further and more deeply.