Answering Paul Grignon

By Marc Gauvin (c) 21/4/2014

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In 2009 Prof. Sergio Dominguez and I wrote a paper that has had certain circulation  in which we perform a "formal stability analysis on common lending practices",  the purpose of the paper was  to frame monetary analysis in the context of standard stability analysis of discrete LTI systems that to my knowledge at least, has not been forthcoming from financial experts and economists.   The key conclusions were:

  1. Interest (both simple and compound) is indeed the root cause of instability of common lending practices.
  2. That the instability is not identified by the ability or not to pay loans but by the fact that if for whatever reason loans are not paid the debts will continue to grow (or for as long as loans remain unpaid they continue to grow).
  3. That said instability has unavoidable systemic consequences:
    1. Because  P < P+I a minimum constant demand for new money exists in the system.
    2. Because all paid interest is built in as a cost,  prices will absorb the full impact of the instability to be carried into future cycles.
    3. That the absorbed interest charges force the constant demand of new collateral in order to generate the increased amounts of Principal that need to be provided.
    4. That interest not only compounds as a function of time but as a function of passing on interest costs across the value chain thus guaranteeing that even an economy made up of simple interest will generate an exponential aggregate system debt growth output.
    5. The aggregate exponential debt output translates into a requirement for similar growth in future industrial output in order to stave off inflation.
    6. Because such exponential output cannot be sustained it is only a matter of time before inflation sets in and as we all know inflation, as with savings,  is not simple but compound.  
    7. Such a system is doomed to collapse sooner or later.

Now some things worth taking note of:

Implicitly the model assumes the ideal that new principal loans are forth coming for any increment of new collateral in the system.  Which means that even without any shortage of new Principal (i.e. zero re-lending) the system remains unstable.

Because interest increments prices and these are compounded across the value chain and ultimately fed back to everyone, the system, due to interest,  is unstable no matter whether there is failure in payments or not.

The increase in demand for new P,  is not expressed in terms of economic failure but rather in terms of inflation due to interest.

So,  from the above it can be seen that our analysis is not centred on failure to satisfy payments per se,  but on how the instability of interest forces aggregate exponential growth and thus makes failure increasingly more probable and therefore inevitable.

Paul Grignon's Rebuttal:

Following publication of the afore mentioned paper,  Paul Grignon attempted to if not invalidate at least trivialise it on the basis that he believes that for any loan over any period and any term, both interest and principal can hypothetically be paid and therefore, interest, cannot be a root cause of instability.  Having discarded interest as a root cause of instability in this manner,  he proceeded to seek another "root cause" of instability concluding that instability of debt was due to the repeated "re-lending of principal in the system and that that instability is independent of interest i.e. will manifest itself on the basis of re-lending even in an interest free scenario.   

However,  Paul's thesis is anchored in the conceptual error of defining instability as being equal to the inability to pay and since he believes that interest is payable then therefore it cannot be a cause of instability and therefore our thesis is of no importance.    However,  what Paul has failed to see,  is that our thesis for instability is not based on pay-ability of interest but rather on the growth imperative that ensues as inevitably interest as a cost, is absorbed and compounded by the system as interest charges are passed on across the value chain and ultimately feed back in consumer prices.

Paul's claim that 100% of P+I can be satisfied.

It has been very difficult to discuss this issue with him because his theories and arguments are expressed in prose without presenting his "proofs" in any formal fashion as we have.   Yet he has continued to misrepresent both the nature and the scope of our paper and labelled the "interest is not created argument" a "fallacy" as he does here.  He states his belief that potentially both principal and interest of any loan can be fully satisfied without ANY new principal being added,  however so far he has not produced any equation that models what precisely he is talking about,  yet he refuses to acknowledge how the standard linear simple interest debt equation can be used to prove how his statement is categorically wrong as follows:

Proof that 100% of P+I of any loan can never be fully satisfied on its own Principal alone.

P = Outstanding Principal

I  = Total interest over k periods.

i  = interest payment per period

p = principal contributions to payments.

k = remaining periods within the term of the loan.

P also represents all available money in the system, such that all and any payments (p+i) must necessarily come out of outstanding P AT ALL TIMES.

The standard equation for outstanding debt over k periods is:

Debt = P(1+ik)

    1. Because at all times P < P+I and interest sum is always applied to all outstanding balances, then at no period k > 0  can P+I be fully satisfied by P.
    2. Because outstanding P (principal) is also equal to all the money in circulation at any point in time, and all p+i payments necessarily come from P,  then it is clear that on the last payment k,  P = p (now all the remaining Principal in the system)!

Therefore and since on the last payment P = p it follows that not all p+i payments can be satisfied over the term of k payments and therefore not all P+I (sum of all p+i over k payments) can be satisfied over said term. 

End of proof.

Explanatory notes:  While this elementary conclusion does not preclude that recycled interest payments CAN potentially satisfy most payments,  it does nonetheless preclude that ALL 100% of p+i payments will be satisfied unless sufficient new Principal from which to draw on is forthcoming.  The reason is quite clear,  while it is true that interest payments are not cancelled out of existence,  all +ve P payments ARE cancelled against -ve debt balances, such that if no new principal is added to the system at some point P, the remaining money in the system, is equal to p! For which interest is charged in excess of that amount.  It should therefore be clear that when remaining p payments are equal to remaining P in the system then remaining P+I cannot be satisfied and without new P being added from some other loan,  such a situation is inevitable.  Therefore 100% of P+I of any loan can never be fully satisfied on its own Principal alone.

The re-lending of principal = non pay-ability = instability fallacy.

In order to test this thesis we must isolate re-lending i.e. we must test re-lending in an interest free scenario.

It should suffice to say that Paul's argument that re-lending on its own is a "root cause of instability" confuses the notion of instability of debt with un-payability of debt (with money) and without clarifying this confusion, Paul's thesis is at best ambiguous.  

First of all an interest free debt that cannot be satisfied by existing money is still stable in the sense that, because it is interest free, the balance is constant over time and therefore bounded (stable).

Secondly,  Paul's model ignores that the subsequent re-lending of a finite sum of money is by definition between different parties therefore there is no accumulation of debt to the favour of any single party:

A lends to B that lends to C ... and so on.   This means that while debt might be accumulating in the system on an aggregate level it does not accumulate in the favour of any single party. 

Thirdly, nothing in the theory systematically forces any particular debt multiplication versus debt and debt cancellation scenario.  That is the notion that debt will only multiply indefinitely is not without loss of generality.

Fourthly,  assuming that borrowers can spend any such money at the onset those who do so are benefiting so that any interest free demand for equivalent amounts cannot be construed as depriving the borrower and therefore cannot be considered abusive.

From the above and without a clear mathematical model it is very difficult to conclude that re-lending alone constitutes instability.  However, the moment interest is charged, then the borrower is exposed to having to pay ever increasing amounts of value over time and thus the growth of such loans would identify the underlying instability due to interest but not due to re-lending.

It is of utmost priority that whatever theory that is proposed,  can stand up to at least this elementary level of mathematical and logical rigour and analysis.  Without responding in kind,  one may say that one believes otherwise but one cannot say they have proven anything.   So far Paul has not synthesised his theory in a formal proof and no matter how obvious things are to him and others, unless he can express his case in an objective formal common scientific language,  then he cannot expect others to assume that he has proven anything.   Of course nothing can prevent him or anyone from claiming otherwise.   However, the importance of expressing oneself in such rigorous and unambiguous terms cannot be denied and requests to do so should be welcomed as opposed to being shunned.

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