Circuit Theory and the state of Post Keynesian Economics

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I gave the following presentation at the 4th Dijon Money conference (December 10-12 2009):

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Briefly, my paper explained how various conundrums that have stymied the development of Circuit Theory for 20 years were in fact the result of confusing a stock (an initial loan) with a flow (the economic transactions that loan could initiate over a year). With a proper dynamic approach, using the “tabular” method that I outlined here in “The Roving Cavaliers of Credit“, the conundrums are easily solved–watch the presentation to see how (click here for my Powerpoint presentation, and the two Vissim files that I ran are linked here and here (you will need to “right click” to download them, otherwise you’ll just get a text file). If you don’t have the free Vissim Viewer,  it is downloadable from here. This is one of the Mathcad files that I showed (use a right-click for this one too; it’s poorly structured–written for my use rather than public consumption–but if you have Mathcadyou’ll be able to follow your way around it).

I presented in a parallel session, the morning after the conference dinner, and had a predictably small audience. However that disadvantage had a fortunate side, because that tiny audience included the two conference organisers Louis-Philippe Rochonand Claude Gnos, as well as Basil Moore and Allin Cottrell. Basil is the venerable father of the proposition that the money supply is endogenously determined, rather than set exogenously by the Central Bank, as is still taught (in wild conflict with both the empirical data and actual Central Bank knowledge and practice) in almost all macroeconomics courses; Louis-Philippe and Claude are well-known and respected Post Keynesian monetary economists; Allin is a very capable exponent of Marxian economics, who unlike most Marxists uses computer modelling extensively in his analysis (I just wish he’d update his webpage, which doesn’t appear to have changed since 1997!).

The discussion was therefore possibly better than it would have been, had I presented in a plenary:

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However though I was pleased with the way my paper was received by those present, I was very disappointed with most of the presentations at the conference. Though there were some notable exceptions–one of which I’ll comment on below–the papers were either non-analytic (“What Keynes said was…”, “Economists must take uncertainty seriously…”), bombastic (“The fatal flaw in the capitalist system is …”), or used graphical analytic methods that could not easily be distinguished from the content of an ordinary macroeconomic textbook. There were one or two block diagram expositions, but they too were graphical only–mere drawings, not influence diagrams, and certainly not systems dynamics models.

There are many leading Post Keynesians who weren’t at this conference–including quite a few who attended the Australian Society of Heterodox Economists conference that Peter Kriesler organises at much the same time every year–so I’m not claiming that the papers here are utterly representative of the general state of Post Keynesian economics today. Nevertheless, if they were even mildly representative of the work that Post Keynesian economists are doing in the midst of the biggest crisis that capitalism has faced in seventy years–and one which is causing a crisis in neoclassical economics as well–then they will fail to shift economic theory at all. After ten or fifteen years of economic pain, the neoclassical orthodoxy will be reassembled–since it will be true that “there is no alternative”–and Post Keynesians will remain a noisy and largely ignored minority.

Papers like these, though they are intended to criticise the unreality of neoclassical economics, or to point out issues (uncertainty, bounded rationality, open systems, non-ergodicity, whatever) that should be taken seriously in economics, actually strengthen the resolve of neoclassical economists to do nothing of the sort, since they lack any coherent alternative analytic approach.

Neoclassicals who attend such presentations–which almost always include disparaging remarks about the absurd assumptions neoclassical economists make–walk away quite justifiably thinking that “if that’s the best you can do with realism, then I’ll stick to my ‘absurd assumptions’!”

We can and must do better than that. But to do so, non-orthodox economists have to find tools that can express their vision of the economy analytically, either as mathematical or computer models. If we don’t, then whatever might be said by “Critical Realists” about the inappropriateness of mathematical analysis in economics, or how one can’t model open systems mathematically, the critics will be sidelined in a not too distant future by those who do use such models–and who care a good deal less about realism than the critics do. Yet again, the critics may win the philosophical battle, only to lose the methodological war.

That’s why I’ve put in the effort to learn the methods of dynamical analysis in mathematics (systems of differential equations), engineering (systems dynamics), and computing (multi-agent models), and it’s why I’m trying to develop alternatives to those which make sense in the context of economic modelling–notably my tabular method to develop systems models.

These dynamic models enable us to put our thought processes into a systematic framework, and to explore relations that are simply too complex to follow verbally. This is a major benefit to mathematical analysis that is lost in the critiques non-orthodox economists tend to make of how neoclassicals abuse mathematics: when we outline a causal mechanism verbally, we are in fact stating a differential equation verbally. If we say that “Factor X causes changes in variable Y”, we are actually saying “the rate of change of Y is a function of (amongst other things) Factor X”. In mathematical notation, this is d/dt (Y) = F(X).

The advantage of expressing these concepts mathematically, as well as verbally, is that the mathematical rendition keeps track of all the feedbacks and complex interactions that simply overwhelm our capacity to follow a complex causal process verbally, and they give us a means to provide a rough quantification of how strong those feedback effects are.

The failure to do this within Circuit Theory is why a simple confusion of stocks with flows–mistaking the stock of money for the flows that are initiated by a given stock of money over a year–has stymied for twenty years the development of Graziani’s brilliant insights into a workable theory. As I show in the talk above, the simple expression of the flows initiated by a loan are sufficient to solve all the “conundrums” of Circuit Theory. The conundrums were simply the product of applying the wrong type of analysis–simultaneous equations, “period analysis” with its implicit difference equation form, or worse still mere words–to the issue. A simple application of flow analysis in continuous time shows up all those conundrums for what they really are: confusions resulting from bad analysis and inappropriate analytic methods.

Now I also have to exhort my fellow Post Keynesians to learn at least some of the appropriate methods. Get out of the comfort zone of verbal exposition, historiography, simultaneous equations and graphical analysis–and even the much more sophisticated stock-flow consistent framework of Godley and Lavoie (While this method is certainly a major step in the right direction, using it to try to explain where profit comes from was rather like trying to understand how a horse runs, using photographs of a running horse taken at one hour intervals)–and learn differential equations, or systems dynamics, or computer programming. It’s hard, but the effort is worth it. And if you don’t do it, then prepare to once again be dominated by neoclassical economists once the Global Financial Crisis has passed.

I’ll end on one very positive note: there was one exceptional piece of work done by a PhD student (who is also a full-time school teacher) Pascal Seppecher. He has developed a multi-agent model in Java that also simulates the monetary circuit, and reaches much the same result as I do from a differential equations perspective. His model is called Jamel: Java Agent-based MacroEconomic Laboratory. It’s a brilliant piece of work and I do recommend exploring it.

If a full-time school-teacher with a family can nonetheless acquire the skills and find the time needed to do quality work like this, then it’s high time academic Post Keynesians did the same. Sticking with what you are used to, when what you are used to merely lets you point out what “should be” done rather than actually doing it, is no longer good enough.

About Steve Keen

I am Professor of Economics and Head of Economics, History and Politics at Kingston University London, and a long time critic of conventional economic thought. As well as attacking mainstream thought in Debunking Economics, I am also developing an alternative dynamic approach to economic modelling. The key issue I am tackling here is the prospect for a debt-deflation on the back of the enormous private debts accumulated globally, and our very low rate of inflation.
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121 Responses to Circuit Theory and the state of Post Keynesian Economics

  1. Ramanan/superpoincare says:


    Thanks for your reply.

    I know dimensional analysis, differential equations very well 😉

    I will come back to you once you are relatively free. Gives me time to “Texify” what I have to say as well. For now I have to say a few things:

    1. Even without timelags your equations should be having wF_D AND gammaF_D. Though you can “absorb” it as one, you may not be able to absorb them everywhere into a redefinition.

    2. I have some issues with time-lags. And for time lags I would have expected terms like f(t-tau). Reference:Gandolfo
    Quantities such as 1/tau just introduce a time-scale in the problem not a time-lag.

    3. Stock flow consistency requires you be double-entry book keeping consistent. This is an absolute must. Flows such as interest income do not become an asset for a bank but a means of extinguishing its liability. Interest payments increases liabilities and deposits are bank liabilities too for the bank!

    Will ping you next month.


  2. Steve Keen says:

    Good Ramanan,

    In that case I can address your points more fully.

    1. If I remember you argued for the second term because I should have spending out of wealth as well as out of wages. The W_D account is the recipient of wages, so I have that already: the inputs to W_D are wages and interest income, the output is consumption.

    At a later stage, I would want to have purchases of financial assets by workers and spending based both on their level and income from them, but the model isn’t yet complex enough for that.

    2. f(t-tau) is what systems engineers call a time delay, not a time lag. For a more complete model they would be necessary (to proprely model government policy for example, which will always occur using dated data); again as a first pass I haven’t used them because they dramatically complicate the model. And my systems engineers describe equations using terms like those I have used as “first order time lags”; for general readers they are similar to the functions used to describe radioactive decay.

    3. I am stock-flow consistent–that’s one of the beauties of the system I’ve devised for developing coupled ODE models of the financial system. I do not have interest payments becoming an asset for the bank–they turn up on the liabilities side of the ledger. I do treat them as liabilities for a banking system, but ones that in an intersectoral sense sum to zero with an aggregated banking sector, and generate no interest payment obligations, but are in the aggregate a source of income to the banking sector. In a more complete multi-bank system, they would have intra-sectoral interest payment obligations, but this would still sum to zero at the aggregate level.

  3. vk says:

    > And my systems engineers describe equations using terms like
    > those I have used as “first order time lags”; for general
    > readers they are similar to the functions used to
    > describe radioactive decay.


    I believe the correct term is “time constant”:

    and yes, it is related to the radioactive half life.

    Please do not use time lag or time delay to describe a time constant. These terms do have a valid literal use as the time difference between 2 events’ timestamps – for example the lag between the moment a worker receives his wage and the moment he spends it.

    My memory is a bit rusty on that but if I recall correctly time delays always add instability to a system, i.e. a stable system can be made unstable by introducing delays here and there. In other words a system with in-build delays always needs to be “extra-stable” in order to remain stable after the delays are introduced.

  4. Steve Keen says:

    Thanks vk,

    My systems engineering colleague uses “time lag”, but I take the point from the Wiki entry that “time constant” is probably a better way to describe it. I’ll modify a current paper to suit.

  5. Ramanan/superpoincare says:


    Time lag or time constant – that is not really important. The fact is that every differential equation automatically has parameters which become the “Scale” in the problem. It is no different in difference equations – appearance are deceptive! Appendix 3.3 in Godley-Lavoie is called the mean-lag theorem. The parameter alpha_3 is like a scale in the problem.

  6. frashe says:


    I’ve been working through your algebra and I can’t see how you can make one of your statements – that firms can repay their debt.

    In your description, the debt can be repaid from the proportion of surplus that is retained by the firm. But this is a flow of the physical commodity. It can be given a dollar equivalent value by using the price, but is not available to the firm as a dollar amount. The dollar amounts come to the firm from consumption by both the household and the banker – the producer surplus is consumed in your model.

    If you play around with your equations, what you find is that as the proportion of surplus retained by the firm increases, the price of the commodity increases and the number of units purchased by the household and bank decrease. More units of production are kept off the market by the producer and consumed (or stored or thrown away). The higher price ensures that the firm has enough money to pay the worker and the net interest bill.

    I’m not sure that you’d want to call that profit in the usual sense of the word. Though it does fit into the Marxist analysis – raise prices to send the worker to the survival level and expropriate the benefit of labour to yourself.

  7. Steve Keen says:

    Re #106 Circuit theory,

    Welcome aboard Frank.

    The price system converts the entire amount sold into a monetary sum, part of which is easily capable of repaying the debt. I’m not sure which equations you’re looking at here, but if you download this paper and check pages 13-16 on which I model the standard proposition in Post Keynesian economics (with which I disagree) that debt repayment destroys money, the debt is nonetheless repaid. When I model the situation that I think is more realistic–that debt is paid down and money therefore taken out of circulation and credited to the bank’s capital (or equity) and later relent, debt is never eliminated completely. But that’s because if it were, money in circulation would drop to zero (since lending to firms is the only lending in that simple “toy” model), not because it isn’t feasible for debt to be repaid.

  8. Ramanan/superpoincare says:


    This comment caught my attention. Would put it differently. A payment of principal does not go into the bank’s capital. Consider a simple bank which lends and takes deposits. Whenever a loan is repaid, the deposits go down. I think you will agree with that. The (loan) interest payment part goes into the capital. Dividend payments and payment of interest on deposits by a bank reduce capital – so it is simpler to think of retained earnings (undistributed profits) adding to a bank’s capital. This is because according to Basel 2, rules banks can lend upto Capital/(Adequacy Ratio) and a “rule of thumb” is that they can lend 12 times – though the details are more complicated because of risk weights.

    If a bank lends L, it neither adds to the capital nor destroys it. Retained earnings add to capital and nonperforming loans reduce capital, in case you want to include the latter. When banks raise more equity (say, in a public offering), that adds to capital as well.

    You may include “Capital” in the definition of money supply, if you wish to define it that way. At any rate I would imagine, you will end up either supporting horizontalism or taking a “structuralist” position and not differing from PKists.

  9. Ramanan/superpoincare says:

    No “this is because” in my first para in #108

  10. Steve Keen says:

    Re #108 Ramanan,

    I don’t have time to consider this issue in detail now, though I do want to do so before embarking on further modelling. However the reason I treat interest payments differently to loan repayments is to prevent the “seignorage” effect of a bank then being able to base its own spending directly on the money it creates. At some stage I should produce a simulation to show the outcome of this; I think that might make the case clearer than verbal discussion.

  11. frashe says:


    I’d reproduced all the equations for your model from the description in your slides. Your paper, apart from the section in p13-16 doesn’t add much i.e. the slides were a good summary.

    My point is, who buys the extra goods that I’ve produced so that I have the cash to repay some of the debt? In your simple model all goods are bought to be consumed and you’ve included the consumption of the bankers and households. There is no other cash flowing around the system. If the bank requires dollars as a repayment of a loan and this is coming out of the profit, then who supplies the dollars?

    If you look at the flow of commodities in your model you’ll find that the surplus of the firm is in the form of the commodity produced, to which we can nominally calculate a value using the price. But this calculation is only a nominal one, it is not a conversion of the commodity to a dollar amount. Dollars in this model can only be created by the bank. All the bank cashflows are stated by your model and none of them give dollars to the firm with which it can repay the loan.

    I have a simple spreadsheet which shows all this.

  12. ak says:


    I totally agree with you. Debt money exists only as long as the debt is not repaid, therefore if we don’t want to see a collapse in the simple model:

    1. firms cannot repay its debt or
    2. another class of agents needs to be indebted to create credit money elsewhere in the system (e.g. households) or
    3. fiat money has to be introduced

    In reality we can observe what happens when M3 collapses and debt is repaid. This is consistent with this very simple model.

  13. Steve Keen says:

    Re #111 Frashe,

    Adam is spot on. This model implements the Circuitist endogenous money perspective that “loans create deposits” in a simple “pure credit economy”–ie one in which there is no central bank or government (that itself causes some fraction with Chartalists, but let’s ignore that for once -:) ).

    If loans are repaid, then–whether I then implement my perspective that loan repayment does not destroy money but does take it out of circulation (consistent with Keynes’s “revolving fund of credit” vision in his 1937 paper “The rate of interest”) or the standard Circuitist perspective that the money is actually destroyed when debt is repaid–the money in circulation drops and over time economic activity will cease because there is no money in the economy.

    One way to answer your question is that the bank supplies the dollars with which its debt is repaid: repayment is simply returning to the bank the money it created endogenously in the first place when it issued the loan. While the debt continues to exist, it finances a turnover of economic activity equivalent to F_D/tau_S — the money in the firm’s deposit account divided by the turnover period (the time between M and M+ in Marx’s terminology)–which can be several times the size of the loan per year. If the debt falls to zero, then so does the money in F_D and all the other bank accounts, and economic activity ceases.

    By the way, would you mind sharing your spreadsheet with the blog? There are several people here working on different computing technologies to implement the model (Warren Raftshol, who’s done some brilliant work to extend the model in Scilab, began with a spreadsheet version from memory, while AK is working on a Scilab front-end to my tabular system, and my off-list collaborator Cyril Wilkinson is developing a standalone interface in the Lua language), and every bit of cross-fertilisation helps.

  14. frashe says:


    I’m not so much worried about paying back the loan, as your comment that it can be done with the profit. The “profit” in your model doesn’t seem to be monetary, it is physical. I’ve attached the spreadsheet, which I hope is self-explanatory. The two rightmost columns show the production consumed by the household and the banker. There is a surplus of production kept by the capitalist but unless someone buys it off him (and we’re assuming this doesn’t happen becasue we haven’t specified that cash flow) then there is no cash with which to repay the loan. Or almost no cash – there is some in the firm’s working (variable) capital and we can use this cash to reduce the debt.

    To keep the bank’s assets and liabilities in balance the repayment from reducing the working capital (FD in your work) of course exactly matches the reduction in the loan (FL).

    The slide bars allow the user to easily change any of the variables and see what happens to the output in real time. (Warning, may not work on Mac.) I find this a useful tool to get a feel for these things, and an invaluable teaching tool.


  15. frashe says:

    What’s the best way of sharing the spreadsheet. The little “Browse” box only seems to allow a jpg to be added.


  16. Steve Keen says:

    The capitalist spending is implicit in this sectoral model Frank, since I can’t show purchases of goods by capitalists from other capitalists in an inter-sectoral account–it sums to apparently zero. This is why I deliberately split all sectors in two in the larger multi-sectoral model so that I could explicitly show intra-sectoral purchases as requiring cash.

    However in the single sectoral model, this intra-sectoral expenditure by capitalists on the output of other capitalists appears as a zero, but it is still there in the actual dynamics of the model.

    Total spending is F_D/tau_S per annum: this reflects workers spending of (1-s)*F_D/tau_S (from their wages) and implicitly s*F_D/tau_S expenditure by capitalists (bank expenditure from its net income is a zero-sum transfer and therefore doesn’t contribute to aggregate spending).

    When I first wrote the model I used a “supply and demand” price-setting equation where supply was the output and demand was the monetary sum of worker plus capitalist expenditure, which is F_D/tau_S. This returned exactly the same values in equilibrium as using the price setting equation I use in the paper.

    I know it looks strange at first, but it is an artefact of the intersectoral nature of the model.

    I’m busy writing a paper with a 5pm today deadline, so I’ll have to leave a more detailed exposition to later. I’ll see if I can post an earlier version of the paper that will make this point clearer.

  17. frashe says:


    Thanks for responding so quickly.

    I’ve taken all the points you make into account in my thinking. For instance, if the capitalists are buying from each other then where is their cash held when we take a snapshot? It’s either held in an account X that is not currently included in the model, or, without loss of generality, we can assume it’s the deposit at the bank FD.

    In equilibrium we would have X constant. From a modelling point of view this is equivalent to FD constant.

    If loans are repaid from X then this will decrease the value of X until it disappears.

    X can’t be an asset or liability of the bank, otherwise we’d have to put it into the bank’s balance sheet. In a Circuitist approach it can be the credit of the capitalists circulating between themselves. If so, then how does the bank allow it to reduce a bank debt? The bank needs to monetise the debt by lending against the capitalist credit or by consuming additional commodities. This would require a reduction in their savings (effectively the bank’s capital).

    If X is in the form of a stock of bank notes then there should be a liability of the bank reflecting this.

    What this gets down to is essentially what you have in your model on p14 – FD and FL are reduced in equal amounts.

    BTW, I can’t understand the model on p14. When a bank reduces the loans and deposits in equal amount then there is no change in the level of reserves. The cashflow to the bank is positive from the reduction in the loan, and negative in the reduction of the deposit. As these amounts are identical in size they cancel each other out, leaving no excess amount to flow into reserves. By adding this “reserve” term into the model you have upset all your carefully balanced stocks and flows.

    Frank Ashe

  18. Steve Keen says:

    Its possible to “cut and paste” a link statement from a html page into the window Frank, if you can post the file to a website (I’d like to provide more than that, but the last time I installed a plugin that gave additional facilities to posting, it caused chaos with the blog–this was just 2 weeks ago).

    Alternately, send the file to me via email (debunking at gmail dot com) and I’ll post it to my FTP site and thence to here.

  19. frashe says:

    Steve, I’ve sent the spreadsheet. Frank

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