Proposed new metric: the Perpetual Debt Level

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Please cite the paper as:
“Paul Grignon, (2013), Proposed new metric: the Perpetual Debt Level, World Economics Association (WEA) Conferences, No. 1 2013, The political economy of economic metrics, 28th January to 14th March, 2013”



A critical metric in economics is missing: the Perpetual Debt Level. This is the amount of bank credit money in circulation that is not available on time nor free of any other debt, to extinguish the debt to a bank that created it. This creates a borrow from Peter to pay Paul and vice versa Perpetual Debt situation in which the amount of the principal involved can never shrink, and the timing of its delivery can never slow down without causing mathematically inevitable defaults. Therefore, to avoid such defaults, it is, in practice, necessary to maintain growth of the money supply at all times. (1) I further claim that there is no escape from this destructive arithmetic problem within the concept of money as a quantity of a thing-in-itself, and especially within the current practice of money created as a debt-of-itself. The only remedy is radical, a total transformation of our concept of money.

20 responses

  • Peter Baril says:

    A fresh and provocative new frame for monetary theory and policy.

    I would be interested in Paul’s further thought on a by product of ‘default’, one that seems to obtain regardless of whether Perpetual Debt or Impossible Interest are used to map the process which culminates in default: the by-product being collateralization and/or contractualization of obligation as a lien or legal transfer of ownership of some real property.

    It is not this remorseless, nearly automatic eventual TRANSFER-OF-TITLE-UPON-DEFAULT from borrower, back through the chain of debt to the root or initial lender, on which lay society has recently focused and which argument will increasingly be used to justify tactical default?

    Whether sovereign, corporate, or individual debt, the implicit message of the various ‘Occupy’ and ‘1%’ movements seems to be that debt, as currently implemented is tantamount to fraud, violates natural law, and, therefore, justifies mistrust, even revolt.

    • Peter Baril says:

      Erratum: Third paragraph should begin. “Is it not …?”

      Txs… pb

    • Paul Grignon says:

      NOTE: twice-lent Principal defines BOTH perpetual principal debt (even in a hypothetical interest-free situation) and compound interest growing to infinity. Both are the same principal lent more than once.

      To quote myself from another essay:

      “Note please that the banker is still a PARASITE if his services are not worth the value he reaps for running a money system.

      The banker is still a FRAUDSTER if people are duped into thinking the bank is lending its own or other peoples’ money when it is in fact underwriting the issuer’s own credit.

      The bank and the borrower BOTH commit a logical fraud when new money is created on the basis of collateral neither the bank nor the nominal borrower owns at the time it is pledged.

      The system itself is FRAUD because it is designed for extortion, political control, mathematical failure on command and the theft of real property from the nominal borrowers.

      Banks are like insurance companies, they are not supposed to take risks they can’t afford. That was their semi-valid social role, the evaluation, distribution and enforcement of credit at their own RISK. But with taxpayer bailouts of supposedly too-big-to-fail banks, theft has replaced service, the legitimate role has been abandoned, and absent these services…


  • Marc Gauvin says:

    First where the paper IS correct:

    Indeed, money as a thing is a conceptual error. This error of treating the representation of value as the value being represented, is what creates the underlying fallacy of the money PSYOP, leading to the false notion that money can “circulate” be lent and borrowed and rented (interest). All of these notions, are logically incoherent and constitute the current false money paradigm.

    This idea has been treated extensively in literature published prior to the current paper under discussion and from the same source ( that the author uses for his 3rd reference.


    Chapter 5 “ The Money in Cult” from “BIBOCURRENCY The Science of Stability as Applied to Money Systems” Marc Gauvin Feb. 2011, the “ …underlying double think of money as both a unit of measure and a scarce commodity “, is fully explored. This book has been freely available on line for two years at:

    On June 2012 the following paper was published at the same site and distributed on line:
    Most recently, a new book titled “The Money PSYOP” Nov. 2012 soon to be published and that has been circulated in draft form for pre-press review, the fallacy of money as an object of intrinsic value, thoroughly analyses the logical definition of money as both a unit of measure and a scarce commodity of variable value. A summary of the book can be found here:

    Where the paper is NOT correct:

    1) Interest and Stability

    In control systems engineering and stability theory, the requirement for instability is NOT that growth reach infinity but that it approach infinity. To prove instability, it is sufficient that function lack its own inherent limit. That is any function whose output is not bounded by the function itself is unstable. This is exactly what is meant by the difference between bounded and unbounded according to BIBO stability theory here:

    Applied to Discrete LTI systems (all money systems are discrete LTI)here:

    Therefore the author’s statement:

    ” …so often cited as the root cause of system instability and the growth imperative, is that if a debt is left unpaid, the interest compounds and the debt can grow to infinity, P (P+I). Therefore it is NOT a fallacy to claim that interest generates a deficit over the terms of all outstanding P loans.

    Furthermore, the claim that the sum of remaining P ALWAYS exceeds the sum of payments required in ANY period, is false for all cases where principal payments extinguish portions of principal in circulation and all periodic payments accrue interest. Since by definition (equations above), interest accrues at the end of the periods/term, then in the last period of the last loan remaining, P < P+I. Hence P cannot satisfy 100% of (P+I) over the term. At best and to the degree that an inconclusive circulation of money permits, it can only be said that recirculation of P MAY cancel an amount that approaches total (P+I) for the term, but since interest always accrues at the end of the period, it never reaches 100% of P+I.

    Therefore, the theory that the indisputable deficit (over the term) created by interest, is eliminated by re-circulating existing P within the term, is a false.

    What is more, the exact % of (P+I) that hypothetically at best MAY be satisfied cannot be determined and therefore neither can the real ability to pay P+I in any period. This further debilitates the thesis put forward.

    The indeterminate nature of the required circulation is documented in the paper where the author himself writes:

    "…Economists refer to the ‘velocity’ of money, a term imperfectly borrowed from physics. In physics, velocity includes both speed and a specified direction. But no direction is specified to the movements of bank credit money in the current money system…"

    The statement that the velocity of money is not a vector has been explained by me since before Sept 2011 as shown here:

    In any event and given the importance of the money issue we must concentrate on defining as a stable unit of measure and no longer as a scarce commodity of variable value the Stability Science for this is taking place at

    • Paul Grignon says:

      The reader should note that I have responded to Marc with the same arguments for over 3 years at this point. Marc wrote:

      QUOTE: At best and to the degree that an inconclusive circulation of money permits, it can only be said that recirculation of P MAY cancel an amount that approaches total (P+I) for the term, but since interest always accrues at the end of the period, it never reaches 100% of P+I. ENDQUOTE

      Marc’s claim here is that instability results from there being an interest component in the final payment. On a $1000 loan, the interest on the final payment might be $1. This dollar, once spent by the lender, remains in circulation as a SURPLUS for a following loan. Thus this “shortage” is created by Marc taking one loan out of what is, in reality a continuum. In the continuum, a “delay” of $1 exists and has to be dealt with, but a “shortage” does not exist. The minor math problem could be remedied by making the last payment 100% principal.

      As for the “inconclusive circulation of money”, Marc does not believe in the idea that interest is spent and available to be earned by borrowers. He concludes from this that interest is the root problem. But the same uncertainty applies to ALL PRINCIPAL, not just that part paid as interest. This is the whole point of my “twice-lent money” theorem. It’s not the interest. It’s the principal that is inconclusively circulated.

      ONE dollar can extinguish an INDEFINITE number of dollars in interest debt because it is NOT extinguished when paid to the lender.

      ONE dollar can only extinguish ONE dollar of Principal Debt.

      Equal uncertainty applies to both.

      So why the obsession with interest?

      Marc has never accepted the idea of “twice-lent money” despite my explaining how it is the design of the banking system itself.

  • Marc Gauvin says:

    Some how the equations of my previous post were truncated

    2) Interest deficit or no deficit?
    Considering the following standard interest growth equations:
    Debt = P(1 +ik) (simple interest)

    where “P” is the Principal, “i” is the interest charged in any period and “k” is any period in the term

    Debt = P(1+(r/n))^nt (compound interest)

    where “P” is the Principal, “r” is the interest rate, “n” is the number of compounds per t and “t” is years.

    It is irrefutable that in both cases (simple and compound) at ALL points of time, ALL available P in the system is ALWAYS insufficient to cancel ALL outstanding P + interest in the system. There is no point of time where P > (P+I).

    Therefore it is NOT a fallacy to claim that interest generates a deficit over the terms of all outstanding P loans.

  • Marc Gauvin says:

    Also truncated from the orginal post:


    Therefore the author’s statement:

    ” …so often cited as the root cause of system instability and the growth imperative, is that if a debt is left unpaid, the interest compounds and the debt can grow to infinity, P < (P + ∞)."

    Is incorrect, as the claim for instability is NOT that interest "can grow to infinity" but rather that it grows TOWARDS infinity as opposed to growing towards a fixed limit determined by the function itself.

    As long as debt growth is a function of time without any inherent fixed limit defined by the growth function, then it is unstable and so will be any system that is made up of such functions.

    The fact that such unstable growth can be arrested or contained by actions that are external to the growth does not render the system stable. But rather, the fact that such external measures are required to arrest the growth i.e it does not arrest itself, is proof of instability!!!

    • Dave says:

      “As long as debt growth is a function of time without any inherent fixed limit”

      This hypothetical is addressed by 2 components in the real world
      1)loan documents usually contain a clause defining the duration of the loan
      2)In the case of a natural person the loan is terminated after a finite amount of time upon death of the natural person.
      Hence, only a hypothetical situation could be seen to exhibit the instability due to infinite interest.

      • Marc Gauvin says:

        These limits you mention are external to the growth function, I was referring to a fixed limit inherent to the function itself as required for stability.

    • Paul Grignon says:
      Marc’s paper spend 22 pages of analysis, calculus and real evidence to produce this conclusion:
      (emphasis added)

      “Therefore, to the extent to which the loan models herein have been analyzed, instability is identified for any of the cases where either part of the principal loan or the interest on that amount CANNOT BE PAID whatever the reason, in which case the debt will continue to grow towards infinity.”

      Formal Stability Analysis of Common Lending Practices and Consequences of Chronic Currency Devaluation Sergio Dominguez and Marc Gauvin 21/05/200

      I have always agreed with this honest conclusion. It’s a truism that didn’t really need to be proved in my opinion. We learned about interest growing towards infinity when we took exponential functions in grade school. I think the authors were looking for more and failed to find it. That is because, like so many others they are fixated on interest rather than multiple debts of the same principal.

      I claim, in my paper that there is a root cause of instability, multiple debts of the same principal that arises independent of interest and when all debts are PAID. (until a downturn in new bank credit creation causes mathematically induced defaults.)

      P money 1

      Pretty simple.

      • Marc Gauvin says:

        No Paul,

        The purpose was to show, through technically indisputable methods, that an interest based system is inherently unstable. As having proven such, it is trivial to realise that it remains so whether or not there is second hand lending.

        The prime dispute I have with your claim is your choice of the term “root”. That second hand lending will potentially multiply debt is a trivial conclusion, but that it is a root cause is questionable because if any other aspect of the design is the cause of that second hand lending, then it ceases to be a “root” cause.

        Where your analysis breaks down is when you resort to claiming that P+I does not create a deficit by virtue of the potential of circulation of money. However and as I show over the term P+I does create a deficit and so called “velocity of money” can only approach satisfying P+I but because interest by definition accrues at that end of the term (every instalment including the last has an interest component), then the math of interest unequivocally tells us that at the very least there will be a deficit of the interest in the last installment.

        But such is not representative of reality, because it assumes that so called velocity of money has a direction, namely to satisfy loan payments in perfect synchronicity. I have long debunked that notion for the reasons you yourself admit too. So, if the statistical hypothesis of circulation of money to cancel all debt cannot be upheld, then we must assume that circulation of money does not and cannot compensate 100% of the indisputable term deficit of I. In which case your argument that interest does not generate a deficit fails.

        Now the question is if interest is a root cause of scarcity, the way to test that hypothesis is to ask if there exists a practical means by which the deficit caused by interest can be consistently compensated for. We have just shown that it cannot, because:

        a) So called velocity of money has no direction.

        b) If direction were to be bestowed on the speed of money it could only approach satisfying 100% of P+I but never quite get there.

        So interest does cause a deficit over the term and over a minimum of one installment and given that so called velocity of money is a fallacy, statistically over many more than one installment.

        But where we agree, is that the real problem is people’s perception of money as a scarce thing of value. So the next question is whether twice lent is at the root of this perception, we have just shown that interest certainly helps fulfill this prophecy by at the very least increasing demand for money. Or is it something else? Is it the cultural baggage of associating a primitive measure of value with precious metals? Does it matter?

        What we say at BIBO Currency is that it does not matter. In my book BIBOCURRENCY the Science of Stability as Applied to Money Systems, I make it clear that the definition of money as both a unit of measure and a scarce commodity of variable value is simply nonsense. Whatever the reason we believe it to be so, it simply will not stand up to logic and science. Anyone who has studied first year science will remember the calculation of error in measurements, an impossible task to achieve if you have not defined your standard unit within fixed bounds.

        This then leads us to having to decide if we throw out both measure and scarce commodity or if we keep one of the two. If we opt for scarce commodity then we have no measure, but if we opt for measure, how then do we maintain its stability?

        It is in answering this question where our apparently trivial formal analysis becomes instrumentally necessary as it leads us to the “Stable Currency Unit Theorem” see (, as stability analysis and control engineering clearly shows that the only sine qua non requirements for unit stability are that:

        a) All recorded units are products of transactions
        b) All transacations are Passive BIBO Stable (i.e. positive and negative account entries < or = to transaction input "price".

        Therefore we can have unlimited access to units if and only if all units are measures of the value of wealth (price) and the debt and current account balances (system output) never exceeds price.

        This is very simple but subtle and it is by no means a trivial result.

      • Marc Gauvin says:

        I wrote a response to this comment and it was not posted. Can someone tell me why?

  • The first sentence of this paper contains so much nonsense that I cannot summon up the will to read further. The first sentence reads:
    “Imagine that money-as-a-thing-in-itself in any form, say a gold coin, enters circulation….”
    The phrase “as-a-thing-in-itself” is a very unusual phrase. Grignon really needs to tell readers what he means by the phrase: certainly it’s go me baffled.
    Next, if money takes the form of gold, that’s not a debt-based form of money. Of course in a gold based money system, people can borrow and lend, but the money itself does not, as Grignon suggests, “enter circulation” initially as a form of debt. What happens is someone just digs up the gold and spends it, or gives it to someone else in exchange for whatever the latter person has to offer.

    • Paul Grignon says:

      Ralph wrote
      “people can borrow and lend, but the money itself does not, as Grignon suggests, “enter circulation” initially as a form of debt.

      Who said “initially”? Once it is lent ONCE it is “money-as-debt”. It doesn’t matter one whit whether the debt is of a gold coin, a legal tender note, or bank credit, it is payable ONLY in the money-as-a-thing-in-itself. After it gets lent TWICE there are now two debts of the same principal. P < 2P. Gold had to concentrate into few hands to make that happen. Banking as practiced today creates money ONLY as debt and it is twice-lent as soon as the "borrowed" funds get lent back to the banking system as someone else's deposit.

      Money as a thing-in-itself, the value of which is determined by its scarcity, is the opposite concept of money as a promise of something specific from someone specific, the value of which is defined by its promised redemption in some real good or service.

      These are the two fundamental concepts of money, as I see it.

      One depends on the relative volume of the exchange media to determine the value of the medium. The other is independent of the quantity of the exchange media.

      The former creates the insoluble arithmetic problem described in my paper. The latter does not.

      Yes gold coins are not debt in themselves. But when income disparity concentrates their ownership into few hands, most gold coins will enter circulation as debt. You think this has never happened in history?

      Thus, I claim that the root problem is money-as-a-thing-in-itself which is incompatible with an advanced credit-based economy. A credit economy should run on credit for real things at a 1:1 ratio, not as debts-of-money which can easily become more debt than there is money by means of the multiple lending of the SAME principal. P 1.

  • merijnknibbe says:

    Ireland might well be a perfect example of the ideas of Paul. The Bad Bank Anglo Irish still was a bank – or to be more precise: an MFI, a Monetary Financial Institution. Which as I understand it means that the 3,1 billion the Irish government had to pay every year would disappear into nothingness, causing a further decline in the already dwindling amount of money in Ireland. But Anglo Irish has by now been liquidated. This can has been kicked a long way down the road which means that at least in the coming years there is not additional strain on government cash flow on one side and on the amount of money on the other side. And if they did things right, the bonds which took the place of the debt to Anglo Irish are structured in a way which will not lead to money destruction, but I’m at the moment not sure about that. As far as I understand Paul, these are the kinds of problems he writes about. Let’s translate it in economese. Take the MV = PT equation, assume (which is surely right in an accounting sense) that paying back a debt is a part of PT, too. But in the case of paying back a debt to an MFI a very special kind of transaction – i.e. one which also diminishes M.

    • Paul Grignon says:

      Why are the comment getting cut off?

    • Paul Grignon says:

      Was the 3.1 billion the Irish gov’t paid all principal? Interest doesn’t cease to exist. It can move offshore however.

      Anyway, let me try to keep this as simple as possible.

      We’re all familiar with the idea of having to borrow from Peter to pay Paul and vice versa.

      This is the only scenario in which we can perpetuate two debts 2M of the same money, M.

      As long as Peter and Paul will allow the borrower to re-borrow the full amount of M on time to satisfy the other debt of M, the borrower need not default. We can imagine the borrower pays interest to both lenders in the form of services rendered, not money.

      Imagine Peter is the banking system that CREATES MONEY ON DEMAND. Paul is the depositors with money in the bank and professional lenders of existing money. Society at large is the borrower caught between them. Any time DEMAND FOR NEW BANK CREDIT slows down, for any reason, M shrinks to m, and ALL of the loans dependent on M will be in inevitable mathematically-induced default because m < M.

      This is my animated visual explanation: