# Some notes on Pontus Rendahl’s review of ‘Keensian Economics’

In a short presentation at a seminar at Cambridge England last week Pontus Rendahl responded to a presentation by Steve Keen outlining his theories (or rather a subset of them in time constraints).

This is interesting as it is the first serious (as opposed to a sly remark in a blog Krugman style) review of Keen’s ideas by a noted neoclassical economist.

Pontus’s remarks in part result from not knowing the full corpus of Keen’s work (such as on bank’s power to lend) and as Keen acknowledges ‘talking past each other’ on occasion. But what is interesting is that Pontus’s main thrust is not utterly dismissive of Keen but are implied in general equilibrium models dating back 30 or 40 years. Of course the mainstream reaction to any heterodox idea is at first dismiss it and then to acknowledge we have known this all along.

Keen’s analysis starts from a very neoclassical observation … In the macroeconomy everything comes from somewhere and goes somewhere …The rest of us call this General equilibrium”

No the sectoral balances approach – though implicit in and predating Keynes – was neglected by neoclassical economics and only taken up interdependently by Wyne Godley and Hyman Minsky. An economy modeled as ‘everything comes from somewhere and goes somewhere’ is the classical circular flow paradigm, not the neoclassical snapshot of an instantaneous equilibrium of prices with no retention of ‘stocks’ such as capital accumulation through time. *Note the key driver of the Classical adjustment process was switches in equity funding, this is not yet modelelled though by Keen.*

Keen is of course not modelling a snapshot of equilibrium but the process of change between one set of prices and another and how and why that changes. The Walrasian approach has nothing to say about how and why economic actors move prices towards or away from equilibrium. The simultaneous equation approach is simply one (like the neo-ricardian project) a modelling of possible sets of prices not of price formation, profits and loss. Keen’s systems dynamics approach can models dynamics of prices moving towards equilibrium – but also potentially overshooting it and building up pressures which can result in disequilibrium and breakdown – financial crisis. The GE approach cannot do that.

Also of course GE not a stock – flow consistent approach, Pontus rather puzzlingly claims

All GE models (including DSGE) are stock flow consistent

Well only if SFC is redefined to include abolishing stocks and cash accumulation, we only have flow (period 1) flow (period 2) consistency in DGSE.

Pontus also says Says Law holds in Keen model. Keen of course claims that monetary injections (credit) invalidate Says Law. There is an important insight here though – that the law of markets (Says Law) does hold if you add two qualifiers:

1) You include credit advanced for investment; and

2) The prices planned at the point of investment are realised (markets clear and their is no inventory remaining)

Of course the view of the business cycle as a credit cycle – which Keen has revived – shows circumstances where entrepreneurship overestimate sale prices, because they have speculated on goods prices, and / or by the time the consumption good is ready demand is depressed by debt repayments and deliveraging forcing sale of inventory at market clearing prices of a new (lower price point) equilibrium. Perhaps one way of looking at the Circuitist tradition to which Keen belongs is explaining when and when not the ‘law of markets’ works and why (and why not).

I should note though that although Keens models currently include modelling of ‘inventory’ in labour markets it is not yet modeled in goods markets. However of course if these is insufficient demand in one market Walras’s law dictates there must be excess demand in another so it is no great fault, it is implied.

Pontus claims Keen’s model lacks any ‘forward looking’ behavior Code for rational expectations and microfoundations. Keen’s approach though is based on Keynes’s insight on radical uncertainty in fluctuating markets – economic actors carrying on doing what they have been doing. His aggregative approach assume firms invest if their are profits and hire workers as a result these incomes and profits being reinvestment etc. There is as yet no sophisticated modelling of investment functions (even in Kaleckian form). or modelling of portfolio preferences. Though there are others modelling in the Stock Flow Consistent tradition that do include portfolio – optimising behavior (such as for example the NEF model). The key point where is whether an approach founded on Keens approach can be modified to include these. It shows important results without them suggesting that the Keynes insight that the key driver of the economy is demand is correct and the claims for microfoundations somewhat overblown, macrofoundations are more important than microfoundations.

Pontus states that Keen’s insight that effective (aggregate) demand must exceed (exante) income is – ‘nice but not novel’ and is implied in Lucas’s cash in advance model from 1982. Keen claims the concept of ‘cash in advance comes from a Minsky paper in 1963 (claims about priority seem to go nowhere as Clower, Simonsen and Minsky all seem to have discovered the concept in 1963 in response to the Patinken controversy).

*Note The ‘Cash in Advance’ concept seems to me weak as the decision to spend against a liquidity constraint is always made simultaneous with a decision to not spend to maintain liquidity for future spending – which also undermines the pure Keynsian concept of ‘liquidity preference’ as idle balances can accumulate or without concious decision to vary them, automatically running up with wages and investment returns, running down faster than anticipated as interest rates and prices rise etc. The Randall Wray’s concept of a demand for money depending on current balance sheet levels and investment plans (which can translate into a demand for credit) seems much superior. *

But the Lucas approach, though endlessly cited (my theory is that papers that use hard but not excessively difficult in obfusicating, dry, none real world way are cited so much to make the author look clever to their PHD and Journal referees) is based on a world with no debt or cash /capital accumulation. However the insight that even with a single ‘Representative consumer’ that they require an injection of money is important. Of course in Lucas’s world that injection is from exogenous money from a monetary authority that mysitcially anticipates the investment and monetary requirements of banks. One might ask that if Lucas had seen this why he did not map out the dynamic implications for business cycles it implies and predict the GFC, when instead in his address to the AEF in the mid 1990s he suggested an eternity of stability.

Pontus accuses Keen of implying that

banks [mindlessly and recklessly] extend credit

But this is a caricature as Keen (though not in the Cambridge Presentation) – has modelled explicitly the balance sheet constraints on the creation of endogenous money – such as in his INET paper of earlier this year for example. If Keen is to be criticsed is that this modelled does not yet (at least in published form) include the sources of investment to create this lending power – such as from equity or retained profits (Keyne’s revolving fund of credit) and how this lending power transmits through and across banks through excess reserves – which my own modelling has attempted to fill.

Pontus also states that Keens graph of discontinuous demand from an injection of credit was generated in a drawing prtogramme and not a maths one, im sure this is right but very quickly im sure the Fields Institute will send one generated in Mathematica slam dunking the point. His point about infinate integrals is not relevent to Lebesgue integration used by Keen where integrals are calculated horizontally as follows where the top is conventional Reimann integration and the bottom is Lebesgue integration.

Also if Pontus doubts this how does he square this with the assertion that discountinous injections are implied in the Lucas Cash in Advance model – either Keen is right or the Lucas Model is mathematically flawed, which is it to be?

Posted on December 6, 2012, in urban planning. Bookmark the permalink. 29 Comments.

“This is interesting as it is the first serious (as opposed to a sly remark in a blog Krugman style) review of Keen’s ideas by a noted neoclassical economist.”

I’m not really a “noted” neoclassical economist. But on another of Steve Keen’s works:

http://worthwhile.typepad.com/worthwhile_canadian_initi/2012/12/a-post-for-steve-keen.html

And Chris Auld’s more thorough review:

http://chrisauld.com/2012/12/06/steve-keen-still-butchering-basic-microeconomics/

We all get stuff wrong, of course. And maybe there’s some good ideas in there too (actually, I think there maybe is). But, aside from neoclassical economists, I am really wondering if any of those who follow Steve have really worked through his models, and thought about what he is saying.

Chris Aulds work was so full of errors it was hardly worth commenting on.

I did not know of your post – though of course you are quite prolific.

Of course so is steve, their is his critique of macroeconomics and their is his attempt to reformulate macroeconomics. Perhaps because of the micro bias of the majority of the way the profession is taught the former attracts more attention that the latter, I perhaps should have qualified that this was the first serious attempt to deal with his macroeconomics.

This Rendal is obvouisly a troll,very unpolite and inmature in extreme.It seems very strange Cambridge hire such a second rate apologist for a reductionistic neoclassical approach.Just look at this stupidities he posted recently at Lars Syll.

http://larspsyll.wordpress.com/2013/11/11/market-failures-and-rational-expectations/#comment-7654

Andrew,

I can only assume that you were not present at the seminar as none of these points were raised during the Q&A session. Anyway, let me address your criticism.

1, If stock flow consistency is neoclassical, classical or whatnot; I do not care. This whole game of attaching labels to ideas is just silly, and our effort should be directed to trying to understand the economy instead of who-said-what, or what X-really-meant, type of gimmickry.

2, DSGE model are stock-flow consistent. If you want to claim something else – which Keen does not, by the way – why don’t you at least provide a reference to a paper which is not? I brought up a very simple model (or at least the budget constraints of it) from 1982 which virtually nests everything Keen says, but does so in a more straightforward and elegant way. It include both stocks (bonds, debt, money), and flows (consumption, saving, income), and everything “comes from somewhere, and goes somewhere”. But yes, for simplicity I ignored capital formation. But only as it is normally the most vanilla ingredient in any DSGE model, such as the Solow growth model or the Ramsey growth model (which form the main building blocks of any DSGE model … and, oh, they happen to be SFC too!). So writing that “not the neoclassical snapshot of an instantaneous equilibrium of prices with no retention of ‘stocks’ such as capital accumulation through time.” is just a red herring.

3, Say’s law holds in the model Keen presented. That’s just a fact once you write stuff like: Y=K/eta — i.e. supply creates its own demand. In fact, the model Keen had in his paper didn’t even have a demand component as Say’s law is implicitly assumed to do that job. Silly? Yes. But it’s not my model.

4, I’m well aware of Clower’s contributions to the cash in advance hypothesis. But time limitations forced me to focus on Lucas’ work, which I think provides the most lucid discussion.

5, “His point about infinate integrals is not relevent to Lebesgue integration”. Oh god. First of all, I didn’t even mention anything about “infinite integrals”, nor is Lebesgue integration or measure theory even relevant here. Keen says that debt, D(t), takes discrete jumps in time (and on finitely many occasions). That means — by definition — that D(t) is discontinuous with respect to time, t. So any differential equation with including the time derivative d D(t)/d t is either undefined or equal to infinity. So I’m eagerly waiting for the “Fields Institute [to] send one generated in Mathematica” to me! Perhaps you can call them up?*

I should also be noted that Keen had no problem granting me this point.

Lastly, “Also if Pontus doubts this how does he square this with the assertion that discountinous injections are implied in the Lucas Cash in Advance model – either Keen is right or the Lucas Model is mathematically flawed, which is it to be?”

Neither, and this point really shows how mathematically illiterate you are. A short answer: Keen is wrong and Lucas’ model is right and mathematically sounds. Why? Lucas’ model is set in discrete time, while Keen’s is in continuous time. Lucas’ model does not use differential equations, but difference equations, and those are well defined for any discrete changes (in fact, all changes must be discrete for a solution to be non-trivial).

*This may sounds like mathematical knit-picking, and maybe it is. But Keen has made a career on mathematical knit-picking so I think this is fair game — something Keen agreed with.

I heard the podcast and there were only a few questions that did not address these points, but of course they may have been raised in general chit chat and I was not there.

My response

1. Ok so lets get on with true SFC modelling not faux SFX modelling

2. No they are not, flogging a dead horse here. There is no accumulation in the Lucasian model so no stocks! I could have brought up pages and pages of papers knocking DGSE (I wont stoop to quoting my own paper) and advocating SFC modelling making the same point but of course Godley and Lavoie ‘Monetary Economics’ is the classic reference attacking the RBC models which Lucas himself recently admits are are of the same class as DGSE models. A stock is not just money but money accumulated by an economic agent – not a mythical representative agent. The Solow model includes a mysterious ‘Solow residual’ which work on SFC models fully explains and solves the mystery of total factor productivity (see my papers on the profits puzzle). The Ramsey model is SFC inconstant without stock of agents accumulating savings which others invest. If you dont have accumulation you arnt dynamically modelling rates of saving (or financing as Keynsians would call it). The red herring point is just handwaving.

3. Well Keen would say the Says-Schumpter (whatever) law, not a big point as it amends the key variable that neoclassicals make when discussing Says Law (That debt doesn’t matter). I was stressing a point of potential agreement here that if we can model Says Law we can finally empirically test it.

4. Fair point, that was actually a small criticism of Keen’s Economic History. Arguments over priority is always weak way to argue.

5. Keen originally wrote his paper with reference to Reimann integration and has not amended it in terms of notation to refer to Lebesque integration – as this is a pretty new insight from the Fields Insitute (who know their maths better than you or I). Really this is not a big deal as if corrected there is no mathematical contradiction. Your argument relies on the former. Im sure a calculation using Lebesque integration is winging its way to you then I think you will be fair minded enough to accept this point.

A key problem with the Lucas model is the use of discrete time, the real world does not operate in discrete time but continuous time with discontinuous monetary events. Bernard Schmitt made this point in the 60s and the circuitist project in the form continued by Keen advances it. Answer a simple point then, how can a discontinous injection of money from credit (which your rearrangement of Lucas’s equations implies) be discrete and differentiable? You agree it cant so we must abandon discrete time and adopt Lebesgue calculus. Simples. The maths works much better and can be much more easily simulated, so why stick to methods of the 70s and hope to stay relevant? Kipper Tie Economics.

Allright, here we go again.

1, Ok.

2, So you can give me “pages and pages of papers knocking DGSE” but refuse to give me one which shows that GE models are stock-flow inconsistent? You’re losing credibility here. Lucas’ model contains the stock of bonds (private sector), the stock of debt (government sector), and the stock of money (normally called “the money stock”). The Solow model and the Ramsey model both contain the capital stock. Look, in the economy variables are either stocks or flows. There is nothing else. So if the capital stock is not a stock according to you, is it a flow then? Good luck pushing that argument. The TFP discussion is beside the point. And the Ramsey growth model does contain agents that accumulate savings that others invest. So yeah, it’s stock-flow consistent. Keen did not dispute this, nor did anyone else in the audience. This is your own battle.

3, Ok, not a “big point” is a completely different argument. Stick to your original statements instead of changing them as soon as you’re challenged and proven wrong. Say’s law holds, end of story. Keen did not dispute this either, and nor did anyone else in the audience.

4, Fine I guess. But it was a cheap shot to begin with.

5, What is it you don’t understand here? Measure theory (under which Lebesque integration falls) is over 100 years old . It’s not “a pretty new insight from the Fields Insitute” (and if they think it is, their knowledge of mathematics really leaves something to be desired … but I rather suspect it’s you that is making stuff up as you go). And yes, Lebesque integration allows for integration even if the underlying function is discontinuous (as long as the discontinuities is of measure zero). But the differential equations cannot be solved, and there is simply no mathematical program in the world that can do anything about that. So there is nothing to integrate!

As I said, I dare you to set up and solve a differential equation where the time-derivative does not exist. Please, please, accept my challenge!

“the real world does not operate in discrete time but continuous time with discontinuous monetary events” So how can output grow continuously when spending occurs discretely? It can’t. This is just a logical flaw. And it is completely beside the point anyway; yet again you’re changing your arguments on the fly.

Next.

“Answer a simple point then, how can a discontinous injection of money from credit (which your rearrangement of Lucas’s equations implies) be discrete and differentiable?”

Sure. It cannot. The difference is that Lucas’ model (which I have NOT rearranged) does not require differentiability, but Keen’s does. And as a “discontinous injection of money from credit” leads to non-differentiabilities, Keen’s model is wrong. It can be rescued, but as it stands right now, it’s just wrong.

Pontus lets stick to 2 for the next 5 minutes because the internet cant really understand your brazen gall here.

One of the Golden rules of systems dynamics is a stock flows to another stock. If a stock flows back to itself then its not a stock its just a flow of no value in modelling reality. There is no capital stock in the lucas model because it is not a factor return to holders of capital there is no M-C-M’. Its just money its not capital. There is no accumulation in the DGSE model so to adopt a Ramsey model is inconsistent – that was the point I was making not knocking the Ramsey model.

On SFc consistency of DGSE see

http://andrewlainton.wordpress.com/2012/04/21/why-dgse-is-so-hard-to-displace-and-a-programme-for-its-displacement/

Varoufakis, Y. (2012) A Most Peculiar Failure On the dynamic mechanism by which the inescapable theoretical failures of neoclassical economics reinforce its dominance.

Schlefer, J., The Assumptions Economists Make. 2012, Harvard: Harvard University Press.

Buiter, W., The unfortunate uselessness of most ‘state of the art’ academic monetary economics”, in ft.com/maverecon. 2009, Financial Times.

Godley, W. and M. Lavoie, Monetary economics: an integrated approach to credit, money, income, production and wealth. 2007: Palgrave Macmillan.

Kinsella, S., Words to the Wise: Stock Flow Consistent Modeling of Financial Instability. SSRN eLibrary, 2011.

3. Any economist that holds that Says Law (by which I think you mean Says Identity) always and everywhere holds should be sent back to the 18th C. Explain the GFC then (and dont say everyone went on holiday at once).

On 5 though check the vast literature on Lebesque integration in engineering control systems – which uses difference equations not ODES – and includes many many diagrams of the form you are seeking – see for example Utkin, V. I. (1987): “Discontinuous control systems: State of the art in theory and applications.” In simulations the equations are easily solvable. In Preprints 10th IFAC World Congress. Munich, Germany. Then you might have to admit on this point we are

bothout of our mathematical depth. At this point I expect the mathematicians, physicists and engineers to pile in.Well, cooking up your own definitions of stocks and flows just won’t make the cut. I don’t think you’ll manage to convince anyone else apart from yourself of this.

There was nothing in your reference that showed that DSGE models are stock flow inconsistent. But that’s not a surprise: In fact I have never seen anyone successfully defending — or even making — this erroneous point.

“On 5 though check the vast literature on Lebesque integration in engineering control systems – which uses difference equations not ODES – and includes many many diagrams of the form you are seeking”

Oops, so we’re leaving the realm of differential equations now and turning attention to difference equation!? Quelle surprise! I previously wrote

“Lucas’ model is set in discrete time, while Keen’s is in continuous time. Lucas’ model does not use differential equations, but difference equations, and those are well defined for any discrete changes (in fact, all changes must be discrete for a solution to be non-trivial).”

So it looks like I’ve been right all along.

But as you refuse to respond to my initial challenge; here is a much easier one: Suppose that the solution to a differential equation is given by

X(t) = 5 if t>=1, and X(t) = 0 if 1>t>=0

What is the ode corresponding to this solution? Guess what, you won’t find it! And neither will Keen.

Try any textbook of systems dynamics pontus – its you are trying to handwave away SFC.

Definition from Systems Dynamics Society

So you have read 6 books in 5 minutes – I believe you thousends wouldnt.

Granted on 5. The confusion on 5 arose because Keen wrote a paper using reimann and presnted a slide using Lebesque – so his system is not yet squared. However if we set a system using Diff Eqs and continuous time I suspect we shall see there is a deep common foundation to dynamic and equilibrium/disequilibrium theory and most of the maths issues will go away.

Neither of us is talking about ODES! We both agree their is an issue to be fixed here, but fixed it can be. So why not look as well at fixing it.

On the point you made in the podcast that economist believe that you need a path between multiple equilibrium any physicis or engineer would say that the answer lies in the principle of least action – but thats an aside and a thouight for future investigation.

Oh, and please point out to me where I’ve even claimed that “a discontinous injection of money from credit [...] be discrete and differentiable?”

Or explain why you keep on putting words in my mouth.

You state that the Keen demand function is implied in Lucas and then say that the Keen function is mathematically nonsense – so logically that implies…..All together now.

“You state that the Keen demand function is implied in Lucas”

Really? Where? I don’t even know what “the Keen demand function” is.

Lucas used the idea that nominal income becomes disposable with a lag (which can be arbitrarily small), which implies that there must be an increase in money (or the velocity) for nominal GDP to grow. But this does not violate the idea that contemporaneous output must equal to contemporaneous income — which is what Keen is struggling with.

You have no idea what you’re talking about.

You spent a lot of time both knocking the keen demand function Demand =income +change in debt +NAT , whilst also saying its nothing new, so dont play the innocent.

Keen is not struggling with that issue he has solved the (supposed) ex ante ex poste discrepancy. As many other noted economists such as Scott Fullweiller and Stephanie Kelton now accept.

You are saying at the same time that there is not a discrepancy and it is mathematically impossible – you believe 2 impossible things before breakfast.

I take from your Lucas reconstruction is that any monetary system that exists in time must imply as you say – ‘there must be an increase in money (or the velocity) for nominal GDP to grow.’ which of course is precisely the key nostrom of classical economicsas stated many times by figures such as Torrens and Tooke (or even back to Cantillon) – because between commencing production and sale we must have an addition of value backed by money – so for all your heat their is a surprising amount of agreement. It is simply you do not understand other economic traditions and ways of arguing and from this position accuse falsely others of ignorance.

“You are saying at the same time that there is not a discrepancy and it is mathematically impossible”

Wow, you must be completely incapable of having two thoughts in mind at the same time! I’m really wasting my time here. Last response then I’m out. Life is too short.

Keen’s point (which is neither his — and he wouldn’t claim so — nor unique) is valid in a different setting. Part of my discussion boiled down to exactly this. But it is an inconsistent point within his own setting, as it relies on differential and not difference equations; a point that you yourself just confirmed.

And for the record, I did not know that the equation you are referring to is called the “Keen demand function”. And it’s one equation with four unknowns! (and by the way, it’s Demand =income +change in debt – NAT, not +NAT)

Actually Pontus I have been critical of Keens treatment of asset incomes. He has recently produced a different formulation with different formulas for effective demand and aggregate supply with net changes to assets on the supply side, which I think is better. The reason of course being that in most cases asset transactions across the economy as a whole will cancel. It may be appropriate in some cases however to include net income from assets in a demand function, such as when calculating export and imports from a country, when looking at income from financial as opposed to real assets (as the transaction occurs across time and so their is an expectation of value released which may not happen), when looking at sales from excessive inventory and when the focus is on an individual economic unit or sector rather than the economy as a whole. All of this of course requires calculation of accumulation of stock assets, which if your economic model has no concept of accumulated stocks you cannot calculate or predict, so you cant predict booms or busts.

On the issue of Stock and flows it is useful if you dont trust the definitions used in systems dynamics to go back to definitions used in economic literature – which of course date back to Simon Newcombe who used them to derive mathematically the modern form of the Quantity Identity (as well as to debunk the wages fund concept) and which directly led to Fishers concept of the discount rate. Newcomb, Simon (1886) Principles of Political Economy. Harper & Bros. Reprint A.M.Kelly. http://archive.org/details/principlesofpoli00newcuoft

So the key is that stock and flows have different dimensions and if you mix them up you get dimensionless and meaningless outputs. So measure theory (of which Lebesque calculus is a branch) is critical to eco0nomically meaningful models.

For a good modern treatment of the relationship between measure theory and stock flow modelling in economics see Nakaji 2006 http://www1.tcue.ac.jp/home1/k-gakkai/ronsyuu/ronsyuukeisai/48_3/nakaji3.pdf

He debunks IS-LM for example as follows

If you substitute DGSE for IS-LM in the above quote you have exactly the same argument made by the whole SFC modelling community. In dealing solely with flow equilibrium and having no conception of accumulation of stock its results are dimensionally meaningless, and of course why it cannot predict a global financial crisis.

DGSE simply cannot handle balance sheets and thus financial asset-liability pairs and hence any formulation including the fundamental equation of accounting (and of course double entry bookkeeping is dimensionally consistent), and any conception of debt, profit or loss, liquidity or solvency, its a dead useless dodo.

Tobin 1980 ‘Money and Macroeconomic Processes’

Now I doubt you are read in the whole issue of stock flow consistency or you offer no references or proofs for your axiomatic assumption that DGSE is SFC. If you were you would have offered Foleys’ (1975) ‘proof’ that under perfect foresight of rational expectations there is no stock flow distinction. I don’t think this holds up to a measure theory critique but even if you set this aside, and how under perfect foresight any firm would ever make a profit, if for a moment you have less than perfect foresight you have unsold stocks of goods (excess inventory) and accumulations of unspent money. With excess/insufficient demand you by definition slip out of walrasian equilibrium and because DGSE has no conception of stocks and accumulation it has no way of determining the path the economy will take. Therefore DGSE requires perfect foresight (impossible) and is not simply based on it.

A postscript Carethedory wrote a book in 1918 reconstructing the whole of calculus in Lebesque intregral form including a proof whereby any ODE can be rewritten to as a lebesque integral (with certain conditions ). A consequence of this is that an ODE can be rewritten as the sum of an ODE over the continuous part of the function plus a difference equation over the discontinuous part. As a consequence there is no need to rewrite models that use ODEs, they can easily be rewritten to be fully differentiable over the discontinuous part of the function if mathematical pedants such as Pontus insist. See Chapter II of Scwabeck’s textbook

“There was nothing in your reference that showed that DSGE models are stock flow inconsistent.”

Why not actually read the references?

“For a good modern treatment of the relationship between measure theory and stock flow modelling in economics see Nakaji 2006 http://www1.tcue.ac.jp/home1/k-gakkai/ronsyuu/ronsyuukeisai/48_3/nakaji3.pdf”

You have to be joking! That article contains nothing on measure theory what so ever! And it contains several high-school level errors. For instance, equation 2.2.5 does not follow from 2.2.4. What is even worse is that equation 2.2.5 is obviously wrong. The direction of change of a stock is not related to the direction of change of a flow! Instead, the correct equation would be dS/dt = I-O, which is an ODE. The author fails to take into account that flows shrink as time intervals goes to zero, and therefore arrives at the wrong conclusion. Clearly, for any non-zero value of I or O, I/dt or O/dt approach |infinity| as dt approaches zero. Is this a Sokal style hoax? How did this pass the refereeing process!?

The fact that you consider this “a good modern treatment of measure theory” when it contains no such thing, and is additonally erroneous and false, and the fact that you seem to believe that lebesgue integration is “a pretty new insight from the Fields Insitute” just reveals your striking ignorance of mathematics. Why don’t you stick to things you know? Like “town planning”.

And no, I didn’t read your 5 books. Did you seriously expect me to do that? But I did read your older blog post, which, yet again was filled with either trivialities or nonsense. I’m soliciting a one page proof where it is shown that the stocks and flows in a standard dsge model does not add up. Apparently you can’t provide that.

And FYI, the Lucas model satisfies your view of stocks and flows. Private savings follow b_{t+1}=b_t+s_t, where b_t is the stock of wealth in period t, and s_t is saving (a flow). Debt follows an analogous law of motion, and so does money. They’re all stocks linked over time through flows. And the stocks and the flows add up. In the Solow or Ramsey model, the capital stock follows k_{t+1}=k_t-delta k_t+i_t, where k_t is the capital stock in period t, delta is the rate of depreciation (so delta k_t is an outflow), and i_t is investment (flow). In continuous time these relations are d b_t/dt = s_t, and d k_t/dt = i_t-delta k_t. That’s pretty simple stuff.

So far you haven’t answered a single question of mine. Perhaps you can answer one? I’ll state it again: How can income/GDP grow continuously with time, when spending only enters on discrete time intervals? What is it that makes income grow if it’s not spending or demand?

You claimed you had read all 5 books and they did not contain any reference to why DGSE was not SFC, now you state you have not read them, pretty damning.

My claim was the new insight was that Lebesque integration solves the expost exante debate was solvable, not that LB Int was new! The fact that you missed that shows you have not been following the debate on this over the last couple of years – also telling.

BTW the rate of saving is a flow the amount of savings is a Stock. The two are of course related. The DGSE model does not relate the stock and flow aspects of savings, only deals in flows and therefore is not SFC. In fact you don’t address ANY of my issues over SFC at all. Such as why for example I have now 3000 shilling in my pocket? (a stock).

Ill let Nakaj answer the points in my paper I added him to simply state that precise definitions of stocks and flows are current in modern economics, why do you persist in claiming they are the same and accumulation doesn’t matter – are you claiming that wealth effects don’t exist?

You don’t answer my point at all that ODES can be represented in LB INT form and so your mathematical critique has no legs, and this has been known for over a century.

The rate of depreciation in the lucas model depends on the opportunity price of the stock of similar goods, as the stock is not modelled only the flow the interest rate is indeterminate (as it depends on an unmodelled stock only a rate of flow which does not and cannot accumulate) and so succumbs to a crusonia tree like capital fallacy . There is no depreciation in value terms. It simply doesn’t work.

You ask a new question, or you radically rephrase a question you have previously asked

‘How can income/GDP grow continuously with time, when spending only enters on discrete time intervals? What is it that makes income grow if it’s not spending or demand?’

Well it doesn’t we don’t spend in discrete time interval rather we spend discontinuous amounts in continuous time at specific points in that time. So for example I spend 2000 shillings at a specific instantaneous point in time Tx or whatever, at that instant the money enters a balance sheet or is cash on hand. What are you claiming that money is spent in units of 1 infinitesimal of a shilling between period To and T1? If you are you would lose a fortune at high frequency trading. Sidelining the real issues I think.

More specifically on your point PKs would argue that the spending becomes income which finances investment which increase the stock of real wealth via the law of reflux. This increase in the stock of real goods is matched by the stock of new money creation to finance the investment.

Of course it is not the demand that creates the income rather demand create the investment opportunity to invest in value creating productive processes that are more productive than previous processes. If that is malinvested it destroys value it does not create it.

This is of course very similar to the law of markets. The key difference, from Minksy, Hoyt, Bentham, Kindleberger and Fisher, is that the whole process can go horribly wrong if the new money is used to boost prices beyond their real (non speculative) rates of return.

“You claimed you had read all 5 books”

No I did not. I wrote “There was nothing in your reference that showed that DSGE models are stock flow inconsistent.” Reference. Singular. Stop lying.

“My claim was the new insight was that Lebesque integration solves the expost exante debate was solvable [sic]”

So when you wrote that “[...] and has not amended it in terms of notation to refer to Lebesque integration – as this is a pretty new insight from the Fields Insitute [sic]“, you really claimed that the Fields Institute has been involved in the post-Keynesian “expost exante debate”? Well, I think you’re full of sh*t and is making up new arguments as you go. Can you give any reference to precisely where the “Fields Institute” has been involved in this debate? And what is the Fields Institute anyway? It looks to me as a part of the university of toronto established as recently as 1992. Why do you keep talking about this place?

“You don’t answer my point at all that ODES can be represented in LB INT form and so your mathematical critique has no legs, and this has been known for over a century.”

You’re getting the order wrong. A function which is discontinuous wrt to time cannot be represented as an ODE. So once you write down an ODE you assume that the variable of interest is differentiable, and therefore also continuous, with respect to time. And once you say that the variable is discontinuous, and therefore also non-differentiable, it cannot be described by an ODE. This is where Keen makes a mistake. So no, you’re still wrong.

“The rate of depreciation in the lucas model depends on the opportunity price of the stock of similar goods, as the stock is not modelled only the flow the interest rate is indeterminate (as it depends on an unmodelled stock only a rate of flow which does not and cannot accumulate) and so succumbs to a crusonia tree like capital fallacy.”

Lol, this is complete gibberish!

“why do you persist in claiming they are the same and accumulation doesn’t matter”

I’ve never done that. Do you hear voices?

“Well it doesn’t we don’t spend in discrete time interval rather we spend discontinuous amounts in continuous time at specific points in that time.”

Oh dear god. What is a “discontinuous amount”!!?? How can an amount be continuous or discontinuous? Continuity is a property of functions, not of elements in some space. This is nonsense.

“What are you claiming that money is spent in units of 1 infinitesimal of a shilling between period To and T1?”

Well, if you model the economy in continuous time this is pretty much what you have to assume. And this is also what Keen also assumes in his “demand function”.

I presumed as I quoted 5 references and you used ‘reference’ the lack of an s was a spelling error – sigh. You still dont refer to which reference you actually read or more importantly the 4 you didnt.

This is the link to the joint MMF – MCT seminar which involved the Fields inistitute http://www.youtube.com/watch?v=pOxZixjorho&list=PLE08CAD5D63F36D49&index=2 There are lots of other links to the outcomes to the joint work, and background to it on Steve’s blog. Sorry you havnt heard of them. Your loss.

If you claim accumulation matters why dont you model it in a model that includes monetary stocks? If you dont model monetary stocks or its holders its mot a modetary model.

No a stock is a level of some amount in space, this goes right to the mathematical definition of systems dynamics, the modelling of changes to stocks in space over time, if a function doesn’t enable the spatialisation of the level of a stock it cannot be used in SFC modelling. Space matters. The level of a stock can be discontiousos in time in a monetary sense but changes in stocks of real (information carrying) objects can never be discontinuous in space, they don’t teleport. I think your lack of familiarilarity with this field leads you to think perfectly reasonable and well unsterstood statements from well developed fields are gibberish. Only leads me and others to confirm what an unreal ivory tower most economist today live it.

No money is not like water, it exists in quantums of the unit of account which often has a minimum amount for exchanage purposes. Go out and try and buy 1 billionetnth of a penny of chewing gum. As I suggested going out and brushing up on some Bernard Schmitt would fill out the large gaps in your knowledge.

Thye logic of your argument is

‘I dont know this field, I wont read up on it, it is gibberish, utter gibberish’

Cost accounting enforces a scarcity of total individual incomes in comparison to prices, and the nature of a profit making economic system is to inflate prices over time. By directly supplementing individual incomes with a periodic dividend/monetary gift you approximately eliminate the deficit of adequate income keeping the micro economy free flowing. Keep both micro and macro economy balanced and inflation virtually eliminated with a generalized discount on prices to consumers the totals of such discounts compensated back to participating retailers to make them whole on their margins.

The velocity of money is a fallacious THEORY because (at least under the current system) money does not just fall from the sky nor is the money merchants receive from customers just willy nilly their 100% purchasing power. In other words the utterly embedded REALITY of the cost accounting discipline that effects every dollar that ACTUALLY enters or re-enters the economy, as stated at the beginning of this post, ENFORCES the scarcity of total individual incomes in comparison to total prices. Here is a basic stock/flow inconsistency which is being missed by virtually ALL economists, and thus it IS the most basic unacknowledged instability factor effecting the system(s).

Changing the consumer financial paradigm from loan ONLY to Dividend and loan if desired and creditable, and utilizing a general discount to consumers changes EVERYTHING in economics. From monetary scarcity to adequacy, from individually oppressive to individually free, from systemically sticky and bogging to free flowing, from a paradigm of only this for that to one that also includes and incorporates an individual monetary policy of Grace, the free monetary gift. Economic reform is inadequate. Transformation is what is needed and required. Neither capitalism nor socialism are adequately humane or wise economic theories. To have an economy that comes up to the standard of Man’s accurate species designation, homo sapiens, wise and discerning man, wisdom actually has to integrated into it. The ultimate condensations of human wisdom can be summed in the four ideas, values, purposes and experiences of Faith as in Confidence, Hope, Love and a sense of Grace. And that is exactly what the policies I have just enumerated accurately reflect. Alignment of thought and action. Ain’t it nice?

When Social Creditors start understanding value added in cost accounting there will be less mistakes on this issue.

Oh but they do understand it. That’s why they have the other mechanism of Social Credit, the compensated retail discount. Retail sale is the end of the micro-economic cycle and hence the RETAIL discount catches and reduces any and all additional cost push or demand pull price added.

pontus you really need to show some more civility in your blog comments.

Anyway, 2 things strike me here. Whether or not pontus is right doesn’t really matter, because either:

(1) We are talking about semantic difference (are DSGE models SFC)

(2) We are talking about things that can easily be fixed (Say’s Law, Keen using a discrete time interval when he should be using a continuous one).

Great to see mainstream attention to “Keenonomics”! I hope this doesn’t put Pontus off it forever. Interesting exchange. It is amazing mainstream economists just can’t seem to get their heads around why private debt matters etc

I am trying to synthesize (not formally) some of these ideas, partly to help explain them to the general public, here http://open.salon.com/blog/clintballinger/2012/12/17/post_keynesianism_mmt_100_reserves_project_question_1

Anyway – great work Andrew, sometimes technical stuff is all the mainstream can hear, so it is good to see someone answering them on that level. I still think the basic reasoning of Keen is sound and provable just from simpler descriptive stats on debt etc, but mainstream economists are so used to hand waving that they can’t see anything less rococo than their own deluded arguments as insightful.

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