It is good to see that we haven’t committed any errors because otherwise I am sure you would have pointed them out by now 😉

Neither have you proven that our model is insufficient to draw the conclusions we do. Your comment basically reduces to the assumption that we have not explored sufficiently the real model, but that remains to be proven to be the case.

Basically you have proposed only two things that you suspect could come to bear on the question of stability. These are foreclosure and write offs. However, both of these are handled either directly or implicitly in our paper as follows:

A) The first is the question of foreclosure. Foreclosure is what we refer to as failure in our model, this is one of the two outcomes we predict. Foreclosure on the aggregate level means total system collapse. Foreclosure cannot ever be considered as negative feedback as it represents simply the cessation of the underlying growth and once the function ceases there is nothing to feedback to.

B) The second is the question of debt write offs. Here the banks assume the loss themselves against their limited capital guaranty. Granted no current account entries are erased at the time of the write off, but the compensatory effect is necessarily very limited and by no means approaches any level that would significantly impact the underlying debt dynamics and certainly not of other loans. Also, technically it does not imply the debt is erased. The write off is just an internal bank accounting mechanism to handle the imminent loss of asset. This is why it is a marginal measure compared to foreclosure which, as stated above does not compensate the instability but rather just stops the function. In reality, if write offs were to be used to any significant level, then the system would collapse because the banks would go broke, very quickly.
Finally, write offs at the aggregate system level don’t make much sense and essentially mean that the system has failed.

Therefore, neither of your suggested mechanisms can effectively act to compensate the identified instability to alter the conclusion we arrived at. I presume that you read the reasoning that follows the greater system diagram that concludes that there can only be two possible outcomes given the identified underlying instability of the loan models that is not in dispute:

1: Either the system stops or collapses or
2: It produces exponential output

Can you think of any other existing compensatory mechanisms other than Foreclosure and Write offs? I certainly cannot except for the obvious one of killing the root instability that again is not in dispute?

Also for the record, I don’t agree that my question regarding an arbitrary limit to the term of a growth function affecting its instability is at all ambiguous. The term either is relevant or it is not. We have given ample mathematical proof that it isn’t relevant.

Best wishes,

Marc

I have asked Marc to produce just THREE professors of Control Systems Engineering who would unanimously agree with him that in the formula Yk = P(1+kr1), when the input, k, is limited in duration (as it always is in the REAL world), the output, Yk MUST be unbounded. (By “limited” I mean, of course, “always comes to an end”.)

MG: We have already given ample rebuttals to this inane statement of Ardeshir.

AM: “Marc has not been able to produce them, which seems to indicate that professors of Control Systems Engineering would NOT agree with him.”

First of all I produced Sergio and Sergio produced several citations of the world’s foremost experts in the field to completely put to rest Ardeshir’s absurd statement:

AM: “Because the term of the interest debt function is finite, then the output is bounded and therefore the it is not unstable.”

In any event, the proposal is completely fallacious as Roberto pointed out, the number of references or not says nothing about the truth of the statement.

But the content of the references that we gave tells and Ardeshir’s total inability to respond to them, tells volumes about Ardeshir’s sincerity and integrity.

When you are in a ditch and want to get out, stop digging!!!

Marc

Have you asked yourself why we expressly modeled the growth without any payments of Principal?

We all know that by paying the principal and interest the debt is eliminated. But that does not mean that the initial loan proposition is stable. Why? Because and as stated in our paper “If for whatever reason either principal or interest is not paid, then the debt will grow towards (not to) infinity”.

For this last statement to be true the stability analysis must consider the case we model. In other words we need to establish formally the underlying instability in the extreme case (no principal payments) to be able to PROVE make the statement:

“If for whatever reason either principal or interest is not paid, then the debt will grow towards (not to) infinity”.

Marc

On page 3 of the paper we see the following, expressed in table form:

[QUOTE]

?Model Variables:

P Principal of the loan??Y Total debt in each period

I Cumulative regular interests produced by the loan

X Total funds paid to cancel I

R1 Total regular interest not covered by X

D Cumulative penalty interests produced by R1

W Total funds paid to cancel D

R2 Total penalty interest not covered by W

[END QUOTE]

The paper also says that k denotes “the period for which the variables take their present value” (see page 3), and clarifies it further as follows:

“The parameter k is an integer, indicating the k-th period of the loan, whatever the period a week, month etc. This means that wherever the k subscript appears it indicates that the variable takes on its value for the k?th period portion of the loan’s life” (see page 4).

The paper then goes on to say (at page 4):

[QUOTE]

Evolution of total debt

Yk = Pk + R1k + R2k = Pk + (Ik – Xk) + (Dk – Wk)

[END QUOTE]

Up to this point I have only quoted the paper. Now comes my critique thereof.

To anyone familiar with common lending practices, what stands out immediately from the paper is the LACK of any variable representing the total funds paid to cancel the Principal P.

Let us call such a variable F, and define it as:

F Total funds paid to cancel P

Given that k denotes “the period for which the variables take their present value” (as it is defined on page 3 of the paper), the evolution of the total debt generated by a loan in the REAL world would ACTUALLY be as follows:

Yk = Pk + R1k + R2k = (P – Fk) + (Ik – Xk) + (Dk – Wk)

… where P (without a k) denotes the INITIAL Principal of the loan. (Thus Pk = P – Fk).

In other words, the total debt at the k-th period would be equal to the amount of the initial principal of the loan at the k-th period, plus the cumulative amount of interest – of every kind – at the k-th period, from which sum must be subtracted the total funds paid up to the k-th period to cancel the initial Principal as well as the total funds paid to cancel all the interest due up to the k-th period.

This is the common lending practice, as may be confirmed by examining any detailed loan schedule.

If, therefore, the loan is for a term of j periods, and all the required payments to repay the loan have been made, then at the j-th period, that is, when k = j,

Yk = (P – Fk) + (Ik – Xk) + (Dk – Wk) = 0

… which is to say, the total debt Yk when k = j will be zero.

This also is the common lending practice, as may also be confirmed by examining any detailed loan schedule.

The diagrams illustrated in Figures 1, 2, 3 and 4 of the paper are clearly, therefore, rendered invalid by this calculation and conclusion.

Best wishes.

Yes, I should have said “a flow diagram with a one-page description of the diagram”, to be exact. But this does not change a bit the problem with your paper: it had no mathematical model or systems of equations to formalize the flow diagram (Fig. 6). No formal stability analysis of this flow diagram was done. I will leave it to others to conclude whether your one-page description is a “very extensive analysis”.

You used heavy mathematical artillery to analyze a very simple open-loop model (whose solution could have been easily derived with using standard differential/difference equation methods). Laplace and z-transforms are precisely used best for models of complex systems with many interconnected components and subsystems, whose simultaneous differential/difference equations would be very difficult to solve directly (though computers can now do so numerically).

But instead, you skipped the use of these transforms and associated pole-zero analysis where they would have been most useful — in analyzing the *full model* (Fig. 6), not just one simple component of the model.

Your defense is that “the [full] system is dead simple so there is no need for more convoluted analysis”. I don’t consider the financial system (or even your simplified model of it in Fig. 6) “dead simple” at all. The open-loop loan model you analyzed with the transform method is so much simpler, yet you subjected the latter to transform analysis. Why not do formal analysis of the full system, if it is also simple? Why denigrate as “convoluted” the use of method where it will be most useful?

Your defense seems to be that, having shown one component (your variations of linear, quadratic and exponential loan models with positive slopes and non-negative second derivatives) of the system to be unbounded, then the whole system is therefore unbounded.

This is plain wrong. The way components and subsystems are interconnected is critical in determining if the overall system is bounded or not, is stable or not. (By the way, there’s a difference between bounded and stable: oscillatory behavior is unstable but may be bounded.) Foreclosure of collaterals and/or writing off a bad debt are part of what you call “common lending practices”. They create a negative feedback loop in the loan model. If you don’t include such feedback loop in your formal stability analysis, your conclusions cannot apply to systems (theoretical or real-world) which contain such feedback loops.

I earlier surmised that the output of a closed-loop loan model might be a triangular pulse. You have misinterpreted this as total breakdown of the economy, which is not correct. It means that a particular instance of debt is extinguished, the money supply shrinks slightly. You have not shown at all thru formal stability analysis the effect of such a triangular pulse (or a succession of them) on the larger financial system.

The financial system might indeed be inherently unstable (as many of us believe), but because of your paper’s defects, it unfortunately fails to show that this is so.

You can improve your paper significantly if you: 1) replace your open-loop loan model with a more realistic one that takes into account foreclosure of collaterals and/or the writing off of bad debts then do formal stability analysis of this more realistic closed-loop model, 2) use this closed-loop loan model, not the open-loop one, as your component for your larger financial system model, and 3) do a proper mathematical model of your flow diagram of the simple financial system in Fig. 6 and subject this model to formal stability analysis.

Your question whether “the term of an unstable growth is finite” is too ambiguous. Give the equation of growth, and point out which term in the equation you are referring to.

Let me finally point out that you have, as some mainstream economists often do, 1) misused maths to bludgeon those like Ardeshir who are less familiar with its more advanced methods but are critical of an approach because they intuitively sense something wrong with it, and 2) made simplifying but unrealistic assumptions based on open-loop models leading to conclusions which cannot be applied to more complex closed-loop models (theoretical or real-world).

To Ardeshir: I disagree with you about the three professors. Invoking titles (or math skills) might win an argument, but does not help establish the truth.

Greetings to all,

Roberto

I have asked Marc to produce just THREE professors of Control Systems Engineering who would unanimously agree with him that in the formula Yk = P(1+kr1), when the input, k, is limited in duration (as it always is in the REAL world), the output, Yk MUST be unbounded. (By “limited” I mean, of course, “always comes to an end”.)

I asked for professors, so that their academic reputations would be on the line if they were to say something utterly absurd. Marc has not been able to produce them, which seems to indicate that professors of Control Systems Engineering would NOT agree with him.

Cheers.

Since the hypotheses used for simulating the models in the paper “Formal Stability Analysis of Common Lending Practices and Consequences of Chronic Currency Devaluation” by Sergio Dominguez and Marc Gauvin do NOT fit the ACTUAL common lending practices, it is clear that the conclusions drawn by these simulations are not valid in the REAL world.

MG: Of course we need to simulate the full extent of growth to fully and rigorously analyse the phenomenon. But that by no means should imply that we assume for a moment that in the real world partial loan payments are not made. The point is to show the inherent instability of the phenomenon.

Again Ardeshir confuses the definition and hence the identification of instability with the result or practices to somehow contain that instability. This is an elementary error that further evidences his complete lack of knowledge and experience in control systems engineering.

The key points of our paper can be summarised as follows:

1) The interest growth is inherently unstable
2) If for whatever reason either part of the interest or principal is not paid the debt will continue to grow
3) Because of 1) and 2) inevitably a minimum residual debt will be produced at some point in time.
4) When refinancing takes place the linear growth becomes exponential planting a minimum debt seed in the economy.
5) With respect to a fixed collateral the refinancing of debt will lead to the system breaking down or to inflation.
6) Increasing collateral will stave off the breakdown and/or inflation but that has physical limits that will always be reached in the real world.

A far cry from Ardeshir’s superficial reading of our paper. But what can we expect from someone who ventures to attempt to debunk the work of others in a discipline where he has no knowledge or experience and where he doesn’t understand the language.

As pointed out by Sergio, Ardeshir has revealed that he takes this as some sort of competition. I have before and now Sergio has also, made it clear that our motive is to analyse the system as rigorously as possible because of the dire consequences it has on the future for everyone particularly children.

I don’t have a problem with his lack of knowledge but I do have a problem with his complete lack of integrity made abundantly obvious by such brazenly clumsy comments.

So with no restraint and to make it absolutely clear to everyone, how absurd his proposition is, I will spell it out in the simplest terms:

Ardeshir’s statement that:

“because the term of a function is finite the output is bounded and therefore not unstable”

Is absolutely inane, because it therefore implies that nothing can be unstable ever BECAUSE EVERYTHING HAS A FINITE TERM IN REAL LIFE.

To assume that the standard Stability Analysis does not fully address this elementary observation and to have not looked it up, further attests to the stupidity of the assertion.

But what is even more extraordinary is that he expects to apply such a statement to the isolated case of Y = P(1+r1k) without realising that in doing so he is implying that instability can never ever exist for any case ever. But then turns around to say that he believes the system is unstable just not for the reasons we give. Of course he is completely unable to provide the formal stability analysis to support his claim, but to the like of Ardershir that isn’t necessary, because all that matters is that he berates other people’s work while seemingly not losing his composure, before what he hopes are people unable to assess his deeply flawed logic.

All this without realising that no one has denied that a growth function with a finite term will produce a finite output. Just that unbounded is not the same as infinite.

We then both in different posts proceeded to explain that a finite term is irrelevant to the question of stability, that unbounded does not mean infinite but does mean persistent growth towards infinity which is another way of saying will grow as long as you don’t stop it. Which is exactly what the interest function does it keeps growing until you stop it.

We then explained that alternatively stability can be determined just by observing the behaviour around the point of equilibrium that wrt to interest growth necessarily is zero debt, by pointing out that the derivative or rate of change of the function is what determines stability, if, as long as the function exist (when it stops there is no function nor ouput) the derivative is positive then the function is unstable.

So Ardeshir has no legs to stand on. We all know and always knew that things are finite or never infinite, and all of us except Ardeshir also know by now that that observation proves nothing wrt to the stability or instability of a system.

When you are in a ditch and realise you can’t get out very easily it is wise to stop digging 😉

Marc

I relayed Ardeshir’s comments to Sergio and here is his response. I think it is in order to take special notice of Sergio’s response to Ardeshir’s carelessly and profoundly offensive remark:

[Comment by Ardeshir]:

“Please note that Dr Dominguez is co-author with Marc of the paper I am critiquing, so his testimony is hardly unbiased.”

Sergio: Your answer could have hardly started worse. This assertion is deeply offensive. No bias is reasonable, just for two reasons:

First, this is not a competition, I’m not trying to win anything or to simply ‘be right’. we’re trying to disclose whether the financial system as it is designed so far is jeopardizing our future and our children’s by leading us to another financial breakdown, throwing them to unemployment, misery and starvation. I really don’t want to be right, I’m really longing to receive a clear proof that everything is OK as it is right now, and that our present crisis is just an accident. But in achieving this goal you’re definitely not on the right track.

Second, these are mathematical arguments, not subject to opinion or bias. If you happen to find a flaw, express it in the same (mathematical) language, not in a pseudo-logical blah, blah, blah, based exclusively in your (limited) view of reality.

If you want to be the winner of something, the alpha male of some herd or whatever, just do yourself up, go to your local disco bar and best of luck to you!

………..

[Comment by Ardeshir]:

“Although I do not deny that the economic system is unstable, I say the REASONS given in Marc’s and Dr Dominguez’s paper are not the reasons for its instability. Dr Dominguez has not proven here that those reasons are valid, except as a THEORETIC possibility.”

Sergio: Have you any such theoretic refutation? You don’t. So don’t bother us with OPINIONS and please contribute something SOUND.

…………

[Comment by Ardeshir]:

“Again, all this is THEORETICAL only. I don’t see how Dr Dominguez has shown above how, if k, the period of a loan, is of finite duration (as it always is in the real world), Yk, the debt that comes into existence as a result of the loan, can be unbounded.”

[Dr Sergio Dominguez wrote]:

Some final remarks: this proof shows that the systems represented by these equations are globally unstable, which means that show this behavior for any value of debt (from one cent to trillions). If you happen to find a refutation of this, or Mr. Mehta find some flaw on the proof, please let me know.

[Comment by Ardeshir]:

I shall be pointing out further errors in the paper shortly, quoting the words of the paper itself, and irrefutably proving that the paper itself is unsound as a description of the REAL world.

Sergio: I’ll override this whole bunch of absurdities, lack of knowledge and/or understanding, contradictions and naive opinions that you have used to annoy us with, and will focus only on your last and unbelievable attempt to put Lyapunov’s theorem down. The only thing you have proven with this last (specially this last, but also all the rest of your arguments) is your IGNORANCE. Sadly, you have tried to cover it up with your BOLDNESS; these two qualities (ignorance and boldness) become very dangerous when put together, because they always lead to the RIDICULOUS, exactly where you are now.

Please, learn maths, I have no time to teach you, nor have I committed to doing so.

Have a nice, long life full of happiness .

Bye forever.

Sergio

“Although I do not deny that the economic system is unstable, I say the REASONS given in Marc’s and Dr Dominguez’s paper are not the reasons for its instability.”

Sure, sure where is your mathematical model of the economic instability? I have asked for it before and you have come up with nothing. If you don’t have any how can you make such a statement?

Why don’t you just admit that:

1) You haven’t a clue about Control Systems Engineering as applied to stability and instability.
2) Have never studied the subject.
3) Know nothing about when it is relevant to reality or just theoretical
4) Lack the math to follow other people’s work on the subject
5) Lack the integrity to admit your ignorance in the subject.

All the above is amply exhibited by your own comment:

“(Some of the mathematical terms do not seem to have been reproduced properly here.)”

This statement proves all I say above because if you had the acumen to follow Dr. Dominguez’s discourse you would not have made that comment without first checking the ample on-line resources to bring you up to speed on the seminal theoretical framework on stability and instability by Lyapunov and other experts with respect to the engineering of real life systems.

But since you don’t have sufficient acumen AT ALL you resort to the very cheap and ungentlemanly tactic of sewing doubt over the math you CLEARLY don’t understand because if you did understand, you could never have made that comment. YOU would have either corrected it or made no comment at all. Hence, such a clumsy comment on your part only reveals your complete incompetence in math and hence in the subject matter!

All, of Ardeshir’s comments on all his posts are riddled with this level of reasoning.

Of course I do not concede a word but I have better things to do than to respond to such rubbish.

Marc

Ardeshir,

You are correct my calculation is incorrect. I should have divided by 6, why I subtracted 600% from the 1400% increase in debt(which is correct see below) I don’t know.

But your reading of nominal debt growth is not correct. In the graph of household debt at:

http://www.businessinsider.com/charts-debt-unemployment–2011-2?slop=1#ixzz1ECYXRViM

the vertical axis has increments of 2 Trillion the value for 1970 indicates a value of around half way between 0 and 2 trillion i.e. about 1 trillion so the increase is 14 times not 10 times.

Therefore, the nominal increase of debt is around 1400% which is sufficient to show that the output of the system is exponential and therefore undoubtedly unstable.

Comment by Ardeshir:

But there is nothing in the data to connect this with interest. There is no evidence to show that if interest were abolished, debt would not grow just as fast if not even faster.

Cheers.