Sunday, April 1, 2012

The Case of Keen

(Warning: To anyone reading this who's not immersed in the debates of the econo blogosphere, this post will fully live up the blog's subtitle.)

One of the big things this past week was Krugman's criticism of Steve Keen. This was a Big Deal, since it is, sadly, rare for someone of Krugman's stature to engage with anyone in the heterodox world. Unfortunately it wasn't a productive exchange; no real information was exchanged, and neither side, IMveryHO, covered themselves in glory. For anyone interested in what's wrong with Krugman's side, there's a good discussion in the comments to this Nick Rowe post. Here I am going to focus on Keen.

Keen's most recent paper is here; it gives the clearest statement of his view that I've seen. As I see it, there are two parts to it. First, he argues that a tradition running from Minsky back to Keynes and Schumpeter (and, I would add, Wicksell and on back to the "caps" in 17th century Sweden) sees money as endogenously created by the banking system, rather than exogenously set by central banks (or, earlier, by the supply of gold). This means that banks can lend to borrowers without a prior decision by anyone to save, which in turn means that changes in the terms on which banks extend credit are an important source of fluctuations in aggregate demand that drive movements in output and prices. With all this, I am in perfect agreement.

But then he tries to formalize these ideas. And about the best thing you can say about his formalization is that it uses terms in such an idiosyncratic way that communication is all but impossible. I know I'm not the only one who's found Keen's stuff a bit like the novel Untitled in Martin Amis' The Information, which literally cannot be read. But let's make an attempt. Here are what seem to be the two key elements.

Keen repeatedly says that "aggregate demand is income plus change in debt." There are many variations on this through his writing, he evidently regards it as a central contribution. But what does it mean? To a non-economist, it appears to be a challenge to another, presumably orthodox, view that aggregate demand is equal to income. But if you are an economist you know that there is no such view, whether neoclassical, Keynesian or radical.

What economist do believe, across the spectrum, is that total expenditure = total output = total income, or Y = Z = C + I + G + X - M. Given the way our national accounts are set up, this is an identity. The question, as always, is which way causality runs. The term "aggregate demand" is shorthand for the argument that causality runs from aggregate expenditure to aggregate income, whereas pre-Keynesian orthodoxy held that causality ran strictly from income to expenditure. (It's worth noting that in this debate Krugman is solidly with Keen -- and me -- on the Keynesian side.) But there isn't any separate variable called "aggregate demand"; AD is just another name for aggregate expenditure insofar as it determines output. Nobody ever says that AD is equal to income; what they typically say is that AD is a function of income, along with other variables such as interest rates, wealth, and changes in sentiment. (People do say that income is equal to AD, but that is a very different claim, and it's true by definition.)

I can imagine various more or less sensible things Keen might have meant by the statement, but it feels kind of silly to speculate. As written it makes no sense at all.

The second formalism is Keen's equation, which he gives the jawbreaker of a name "the Walras-Schumpeter-Minsky's Law":

Y(t) + dD/dt = GDP(t) + NAT(t).

Y is income, D is debt, and NAT is net asset turnover. This last is defined as "the price index for assets P, times their quantity Q, times the annual turnover T expressed as a fraction of the number of assets, T<1: NAT = P*Q*T."

And now we really run into problems.

First of all, is this an accounting identity, or a behavioral equation? Does it hold exactly by definition, or does it describe an empirical regularity that holds only approximately? This is the most basic thing you need to know about any equation in economics, but Keen, as far as I can tell, doesn't say.

Second, in the national accounts and every economic tradition that I'm aware of, aggregate income Y is identically equal to GDP. They're just two ways of representing the same quantity. So it seems that Keen is using "income" in some idiosyncratic way that he never specifies. Alternatively, and more in the spirit of Minsky and Schumpeter, perhaps he is thinking of Y as anticipated or current-period income, and GDP as realized or next-period income. But again, it's not much use to speculate about what Keen might have meant.

The next problem is units. GDP and presumably Y are flows over a specified period (a year or a quarter); they are in units of dollars. dD/dt is an instantaneous rate of flow; it is in units of dollars per unit time. And NAT, as defined, is the product of two indexes times a fraction, so it is a dimensionless number. Well, you can't add variables with different units. That is just algebra. So again, whatever Keen has in mind, it is something other than what he wrote. And while it's easy enough to replace dD/dt with delta-D over the period that GDP is being measured, I really have no idea what to do with the NAT term.[1]

It doesn't help that at no point in the paper -- or in any of his other stuff that I've seen -- does he give any values for Y or NAT. He has lots of graphs of debt, output, employment, etc., showing -- to the surprise of no one -- that these cyclical variables are correlated. But since Y and NAT don't figure in any of them, it's not clear what work the Walras-Schumpeter-Minsky's Law is supposed to be doing. Again, if his point is that endogenous changes in credit supply are important to business cycles, I'm with him 100%. (Though so are, it's worth noting, some perfectly orthodox New Keynesians.) But if your idea is just that there is some important connection between A and B and C, the equation A = B + C is not a good way of saying it.

Honestly, it sometimes feels as though Steve Keen read a bunch of Minsky and Schumpeter and realized that the pace of credit creation plays a big part in the evolution of GDP. So he decided to theorize that relationship by writing, credit squiggly GDP. And when you try to find out what exactly is meant by squiggly, what you get are speeches about how orthodox economics ignores the role of the banking system.

Keen is taken seriously by serious people. He's presenting this paper at the big INET conference in Berlin next week. It's not OK that he writes in a way that makes it impossible to understand or evaluate his ideas. For better or worse, we in the world of unconventional economics cannot rely on the usual professional gatekeepers. So we have a special duty to police each other's work, not of course for ideology, but for meeting basic standards of logic and evidence. There are very important arguments in Schumpeter, Minsky, etc. about the role of the financial system in capitalism, which mainstream economics has downplayed, just as Keen says. And he may well have something important to add to those arguments. But until he writes in a language spoken by people other than himself, there's no way to know.

[1] Not to mention the odd stipulation that T < 0. Why is it impossible for the average turnover time of assets to be less than a year? Or does he really mean the fraction of assets that change hands at least once? What possible economic meaning could that have?

EDIT: I'm a bit unhappy about this post. It's too harsh on Keen. As Steve Randy Waldman suggests in comments, there probably is a valid insight in there, if one can just get past his opaque terminology. (Altho that's all the more reason for him to stop speaking in idiolect...) More importantly, posting this critique of Keen makes it seem like I am on Krugman's side, when his contributions to the debate have been every bit as bad in their own way -- as lucid as Keen is impenetrable, but also just embarassingly wrong, at least form where I'm sitting. This post by Michael Stephens Randy Wray at the Levy Institute blog does a good job laying out the issues. I agree with everything he says, I think.

EDIT 2:... and now here's Keen saying that
Krugman’s part of the economic establishment, which for thirty or forty years has got away with arguing that you can model a capitalist economy as if it had no banks in it, no money, and no debt… You just don’t have a model of capitalism if you don’t include those components. 
I'm also unhappy with that. Krugman (and New Keynesians/monetarists in general) are very specifically modeling an economy with money, but without banks. I agree with Keen that you do need to think about the financial system to understand macro dynamics, but you can't make the case for that if you can't correctly describe the position you are arguing against. I don't think we will make intellectual progress without being more careful about this stuff.


  1. JW: I couldn't make head nor tail of Steve Keen's equation 1.1 either.

    Maybe, just maybe, somewhere deep down, what he is trying to say is something like the Wicksellian hot potato process. If the central bank cuts the rate of interest, planned expenditure exceeds expected income, and the stock of money exceeds the desired stock of money.

  2. JW — re the mouthful "law", I've not reviewed the most recent, but I've seen this equation in other places, and casually interpreted it. I hope you get a response from Steve Keen. (And I hope it is civil and on-point, rather than polemic in response to a bit of polemic tone here. I'm tired of that, although I am certainly guilty of it too.)

    Anyway, your more detailed criticism has me trying to clarify why I did not, in my casual interpretation, write Keen's equation off as unintelligible. I don't think I can defend the equation as written, but I think I understand what it is trying to do and I'm not sure it's as impenetrable as you think. Here is my quick take (which is probably all wrong, and looks forward to correction by Keen).

    1) This is an equation in continuous time, so units are a bit slippery. Y(t), DP(t), and NAT(t) all represent instantaneous flows, not the output of any period. For example, you'd have to integrate Y(t) from t0 to t1 to get a number whose units was dollars. Everything else, including the dD/dt term has a unit d$/dt.

    2) The equation breaks the identity that Y equals-by-definition GDP, and unconventionally redefines Y. Y refers here to dollar income from selling goods and services or from selling existing assets. dD/dt refers to purchasing power created via new credit extension. New credit extension is not considered an asset sale: that is, when I promise my future labor to the bank in exchange for $100 loan, that engenders production of a new asset and totally new purchasing power. In the future, if that loan is bought or sold, that is just asset turnover, and the income that sale generates falls under Y. The left-hand-side is supposed to represent "instantaneous purchasing power", the right-hand-side represents "instantaneous goods-services-and-assets purchased". (cont'd)

  3. As I said, I can't justify the equation as quite-right as written. I'm okay with the left-hand-side, almost. But the right-hand-side does provoke a bit of unit confusion in my mind. Over all, it is unclear to me whether the d$/dt refers to a change in "real" or "nominal" dollars. If it is nominal dollars, I think that there needs to be a price-level elevator on the GDP term as well as on the asset turnover term. That elevator wouldn't be the same as for the assets: our simplified, aggregated financial asset prices need not rise at the same rate as our simplified, aggregated goods-and-services prices, but goods and services prices do change in terms of nominal dollars.

    If d$/dt refers to real dollars, meaning by definition that the price level of GDP is constant, perhaps everything is okay. But in this case, it's a bit mindbending to understand the quantity that you get when you integrate across time. For example, if you integrate across the left-hand side, you get the purchasing power of the income you would have received over a period of time in "real, constant dollars". I guess that's okay, actually. it's just a bit weird to me, because it represents an aggregation of what i could have bought instantaneously with my dollar income rather than of any kind of money I could actually keep and hold as savings. (Of course i might have bought assets, in which case the notional value, in real terms, of my "savings" over the period would be determined by integrating the fraction of the left-hand side that went into asset purchases over the change in the asset price level. Note that the change in the asset-price level must be interpreted as relative to the change in price of goods and services, which is apparently normalized to 1.)

    The trickiest term is the asset turnover term. I don't think there's a huge unit problem with the price level elevator. P represents an asset inflation rate, and should in general be a function of t, but there's no real problem with holding that constant as a simplification for tractibility's sake. There's also not a huge problem with T, I think. It'd be the instantaneous fraction of assets that turns over, not a per-period turnover rate, and again in general it should be a function but we can hold it constant for tractibility's sake. I'm not sure I agree with Keen that it should necessary be less than one, though — that seems like it would be a function of the units over which time will be integrated. Perhaps we should interpret the less-than-one condition as a suggestion about empirically realistic orders of magnitude if we measure t in terms of years?

    But the big problem, it seems to me, has to do with Q. Q should also be a function of t, and it's no good to hold it constant as a matter of tractibility, because dQ/dt should equal dD/dt. Every increase in debt also increases the quantity of financial assets that might be bought and sold and absorb income. This is the biggest issue I see with the equation. (cont'd)

  4. Over all, the Q issue is the only one that I think is critical. As long as we interpret the units as real dollars, and understand that we can't hold real dollars, so we end up with a measure (on the left-hand side) of how much we might have purchased over a period, not how much we hold at the end of the period, everything else can be defined in a way that hangs together.

    A minor point: Keen must be defining goods and services as fully perishable, and financial assets as the only means of transferring wealth forward in time. Otherwise we'd need another asset term for durable goods turnover, along with a depreciation term (and perhaps a separate price elevator, though we can do without this if we define durable goods inflation to be the same as for perishable goods). But I think omitting durable goods and modeling a perishable goods economy is an okay choice, at least for a first-pass model. Including turnover of durable goods and commodities might be worth exploring as an extension.

    Again, I'm taking liberties here, responding on-the-fly to your post, not reviewing the paper for now. So I can't comment on clarity of exposition, or whether in fact what Keen says is consistent with my interpretation here. I'm taking a lame commenter's prerogative to do a lot less homework that I would for a full post. I agree very much that heterodox economists must help one another ensure that our ideas are coherent and that, as much as humanly possible, our style of communication is intelligible to people with conventional understandings of words and variables. But I do think that there is an insight in Keen's equation that is real and that can be communicated effectively (although I think the issue regarding Q remains to be resolved).

  5. the way, I think the equation should be interpreted as an accounting identity (in a simplified economy without durable goods), not a behavioral equation. It simply states that the purchasing power received (the left-hand side of the equation) is equal to the purchasing power spent (the right-hand side of the equation) in a world in which purchasing power can be "saved" only by explicitly buying financial assets.

  6. Steve,

    Thanks a lot for these comments, which deserve a much fuller response than I can make right now. You're right, the tone of my post was oversnarky. We non-mainstream economists need to hold each other accountable, but we also need to read each other charitably. You did a much better job with that here than I did.

    I was actually thinking, walking home from the subway just now, of an interpretation something like yours, though I hadn't formulated it as clearly. Definitionally, the flow of income from any set of transactions must equal total expenditure in those transactions. In our conventional GDP measure we single out the set of transactions associated with sales of final goods, but there's no reason that that particular identity has to be the most useful one. This is usually discussed in terms of changing the definition of final goods, but in principle there's no reason one couldn't add some set of financial transactions.

    You make it a lot clearer how Keen's equation can be understood in those terms, but I'm not sure your story is his story. For one thing, you suggest that P should be considered constant, but Keen explicitly says, "There will thus be a relationship between change in debt and the level of both economic activity and asset prices." In other words, he seems to be thinking of Q and T constant and P as what is adjusting to maintain the equality.

    Anyway, you are certainly right that I was too dismissive and need to work harder to reframe the argument in a way that makes sense to me.

  7. I think that Steve would agree that GDP = aggregate income for the period passed , but that credit was a component. For modeling purposes for the next period , you start with the previous gdp and combine with the credit contribution. I agree that he's not precise in his descriptions. Mayer et al. may have done better in that regard , here :

    My guess is that Keen's addition of asset values to the model is an attempt to advance the work of Mayer , and that he does intend the equation to be an identity , but one that will only be revealed retrospectively due to behavioral effects , as you noted. I think he's hoping that the asset swings will soak up the residuals in the credit flow data , making the correlations of GDP growth and credit flow tighter. I think that might be a tall order , however , as getting all the necessary asset pricing information right will be tough. Even the credit data seems suspect to me , given the problems with double-counting , handling of financial sector and public sector debts , etc. Still , I give him credit. I think he's on the right track.

  8. "The term "aggregate demand" is shorthand for the argument that causality runs from aggregate expenditure to aggregate income, whereas pre-Keynesian orthodoxy held that causality ran strictly from income to expenditure. "

    This is an ill defined statement without introducing the concept of 'expected' and you would still have to make the case that 'expected spending' is independently flexible but expected income is not. I wonder how you are establishing any such thing.

    It would start to make sense if one were to replace income with supply and expenditure with demand and aggregate demand with output. And the it would be historically incorrect.

    1. I don't understand what you are saying here. Everyone agrees -- I thought? -- that realized income is equal to aggregate expenditure. The difference is that the classical view was that actors knew what their realized income would be (based on endowments, etc.) and made spending plans accordingly, whereas in the Keynesian view changes in desired expenditure could cause realized or ex post income to deviate from expected income. When we speak of expenditure s aggregate demand, we are imagining the second case -- where changes in desired expenditure lead to changes in realized income.

      In any case, I am not trying to "establish" anything. I am just offering what I would have thought was an uncontroversial summary of Keynes. Honestly, I have no idea where you are coming from. Do you think I am mis-stating the Keynesian position, or do you reject the Keynesian position or what?

    2. No I agree with the paradox of thrift etc., planned vs actual, income adjusting etc. Nothing to disagree with Keynes, except for his unfair characterization of Marshall.

      I'm just wondering why the language of unidirectional causality. As in, why does desired expenditure change. Increased liquidity demand, presumably (I subsume money demand under liquidity demand). Which can itself arise from a change in expected income. Perhaps I'm getting confused - the language of aggregate income and aggregate expenditure is not very clear, to me at least.

      The point on history was simply that this planned vs actual difference origin of the business cycle goes back at least to J S Mill. Keynes's great achievement would be integrate this into a price theoretic framework, I think.

    3. I think the heart of the Keynesian idea of aggregate demand is that changes in desired expenditure lead to changes in realized income. Why desired expenditure changes has lots of answers. It might be because of changes in desired liquidity, but it might not be. The NK-monetarist position, as I understand it, is that demand for money is the only factor that can produce variations in desired expenditure -- this is the moral of Krugman's babysitting co-op -- but I think one of the important analytic gains of endogenous money is seeing that desired expenditure can vary independently of money demand.

      I think Keyes himself would agree with your last sentence --Patinkin and Leijonhufvud both quote him to this effect. But I'm not sure most other people would agree.

    4. Thanks.

      Somewhat unrelated, but I hope you take this up at some point of time. One thing which has always bothered me about MMT/Pk versions of the interaction of banks and central bank is - why is the discussion always asymmetric. The point always is - given a fed funds rates, the Fed must step in to fulfill whatever reserves the banking system seeks in aggregate, otherwise it risks its feds funds target being violated/ the payments system being disrupted etc. Point taken.

      But what about the reverse scenario. Somebody pays off a loan and the deposit that goes with it is destroyed. The banking system now has excess reserves. What legal/institutional/operational mechanism necessitates the Fed to now mop off the excess reserves. There is no threat to the payments system - the fed funds rate cannot go arbitrarily low and the rate temporarily breaching the Fed's target on the underside should not be particularly worrisome. So why have these excess reserves been mopped off in the past?

      As a corollary, how did conventional monetary easing proceed when times were more normal?

  9. And yes, I didn't get the T<1 constraint either. IBM stock turnover has sometimes exceeded its market cap within a week of trading. If that's not what Keen means by turnover then I'm not sure what he means.

  10. JW — Don't worry. You weren't that snarky. I'm oversensitive today, actually, because I got annoyed at Keen and at Krugman both. In every relevant policy debate, Keen and Krugman are right now on the same side, and yet we get a high-profile exchange in which Krugman calls Keen a mystic, and Keen calls Krugman Ptolemy. I'm a fan of Krugman and of Keen, though I have my differences with both. But the tone of their conversation rules out genuine communication. It's becomes about grand dramas and wounded egos and point-scoring, rather than finding common ground and working to move policy in a humane direction. Keen and Krugman (and Wray and Rowe and Sumner) will likely always have theoretical differences, and never agree on "optimal" policy, but they might find a lot of overlap in the space of things we might label "better than the status quo". I wish they would find a way to debate that is intellectually vigorous without precluding some leadership in forming coalitions among people who come at things from different perspectives. The forest is being lost in the bickering of all the leaves.

    You're probably much closer to Keen in interpreting asset turnover as adjusting only via price. (Again, I'm unforgivably and lazily not looking at primary sources.) I'm still nervous about leaving out the relationship between debt growth and asset quantity.

    (By the way, you once did a post that was almost psychic in capturing my view of Krugman, simultaneously a national treasure for whom I'm profoundly grateful and extremely frustrating when the topic is economics.)

  11. I will read SRW's comments here and think more carefully about the issue of units. I don't know Keen's work well, but my impression is that the equation is supposed to be an identity, and that the intention is to modify the usual identity between national income and national product. The left-hand side of the equation is the revised income side; the right-hand side is the revised product side. Intuitively, it says that the nation's income at a time plus it's total accumulation of debt liabilities at that time is equal to the nation's real output at that time plus its total "financial asset output".

    So people receive income and borrow money, and they use that income to purchase both real product and financial products. And the total inflow of income plus net borrowings = the total outflow (sales) of real product + financial product. Of course, people might not use all of their income and borrowings to purchase things, but that is reflected in the left hand side by the fact that the derivative is not strictly speaking borrowings, but the change in the stock of debt. So if people save income, that offsets the changes to the stock of debt induced by new borrowings.

    In the statement I just made, "real", means the same thing as "non-financial". But that isn't to be confused with the distinction that can be made between real and nominal. The identity is supposed to hold whether real or nominal values are used.

    All of the terms are flow terms. But only one of them is expressed as a derivative, because the debt function D(t) is a stock, not a flow.

    Does this make sense.

    1. I'm not sure this works.

      Income from production of goods and services == expenditure on new goods and services.

      Increase in credit liabilities == increase in credit assets.

      So where does asset turnover come in?

      Maybe the notion is that every asset transaction is financed by a new debt contract? But if some current consumption is financed by debt, then some current income must be spent on assets. So that won't work.

      Remember, it is always true that income from goods and services = expenditure on goods and services. It has to be, since every expenditure is income for someone. I can't help feeling that Keen is confused about this. He is confusing the link income --> expenditure with the link expenditure --> income.

    2. It's true that income on goods and services must be equal to expenditure on goods and services. But I don't think Keen is confused about this. I think there is something else going on here.

      As I understand it, national income accounting leaves out purchases of financial assets on the understanding that for each financial asset created there is a corresponding liability, so such purchases don't add to the nation's product. I guess we could call this the "neutrality of credit", and it seems to me that Keen is trying to add that aspect of the economy back into macroeconomic modeling.

      If we expand the notion of income beyond the payments that units receive in exchange for real goods and services to include also the units' borrowings, then we have to ask what goes on the other, right-hand side of the equation to balance the expanded left-hand side. We have to include financial assets purchased.

      So you then raise a good question as to why Keen is using asset turnover instead of something like "assets sold". But that looks to be what the extra term in the right hand side of the equation is. Each financial asset has a price in dollars, and the total dollar value of those assets is the price times the quantity (marked to market? marked to value?). But not all assets are actually sold at their price. So we need to reduce that total valuation of the assets by some factor representing the proportion of that value that is actually transacted. The change in debt on the left-hand side corresponds to the transacted asset value on the right-hand side.

      I don't know if this is the right interpretation. But there is enough going on here to make me want to read Keen more carefully.

  12. SRW

    The units are correct. Y(t) etc. don't have to be (or by definition already are)'instantaneous flows' - all you need to do is simply say US GDP is $15 trillion per annum, rather than the conventional formulation where the per annum is excluded.

    Like Dan says, it's just stocks and flows.

  13. Ritwik & Dan — I don't have a problem with the units, as you say, they are all flows, real $ per unit time expressed as infinitessimals. It's just worth understanding that those "real dollars" can't be stored or saved as such (though they can be plowed into financial asset purchases as foreseen in the turnover term).

  14. JW,

    One small correction: the post at the Levy Institute blog is actually by Randy Wray.


  15. I'm still trying to make sense of this. on the one hand, I think the original post was unfair to Keen. But on the other, there's a certain conservation of annoyance principle here, since the more I believe Keen probably has something valuable to say, the more frustrated I am that he writes in a way that makes it so hard to know what it is.

    One variation on SRW's approach is to say:

    (A) income from production of goods and services = (B) expenditure on new goods and services.

    (C) income from sale of financial assets = (D) sales of financial assets.

    (E) income from issuing new credit liabilities = (F) growth in stock of credit assets

    Now let's call the sum of (A) and (C) Y, and we call the sum of (D) and (F) NAT. E is of course the growth in debt. Then since A=B, C=D, and E=F, it follows that Y + E = B + NAT. This will be true as an identity and there's no issue with units, we can do it in either discrete or continuous time. Read this way, it's not nonsense -- it scans -- but I have to admit I don't see what the point of it is. Writing an equation that says, in effect, that the growth of debt plus GDP is equal to GDP plus the growth of debt doesn't really do anything to elucidate the connections between them.

    What am I missing?

    1. Hmmm...I am assuming that the additional term on the left-hand side is not supposed to be capital gains - income from sales of financial assets - but borrowings. For example, the money that comes into my household in any given period consists in both the income received as payment for goods and services, as well as any money my household has borrowed. That's why the additional term on the left is positive if debt increases.

      Now for my household alone, the monetary payments going out might fall short of the monetary payments going out. But (in a one sector model) this cannot be true of the economy as a whole.

      Its supposed to be an identity, so I agree the equation alone doesn't say anything about causation. But it at least then provides a modeling framework in which causal factors related to debt dynamics can be discussed. If you leave the financial asset transactions out of the equations altogether, then there is no framework for analyzing debt dynamics at all within the conceptual bounds of those equations.

    2. From an accounting standpoint , everyone agrees that one person's debt is another's asset. The problem arises when debt is converted into the ability to purchase new goods and services , thereby increasing gdp growth with the attendant expansion of productive capacity and employment , but in a way that doesn't provide the means for the holders of debt to service that debt. The debt goes bad , the corresponding asset goes bad , and the expanded economy that was based on it goes bad.

      Keen starts with a simple proposition - that debt/gdp( or debt/income) , whether for one sector or for the economy as a whole , can't grow without limit. He can point to all of recorded history for evidence.

      The debt = assets identity is used to argue against that proposition , without any empirical data in support.

      By modeling the effects of debt growth on gdp growth , Keen is trying to move towards defining the parameters for sustainable economic growth and avoidance of depressions.

      Empirically it's clear that changes in credit flows correlate strongly with gdp growth , or , roughly , for a given time period the 2nd derivative of debt equals the first derivative of gdp . Keen's equation simply reflects this empirical observation. The NAT variable compensates for the fact that not all of the change in debt flows ends up in a change in gdp for a given period. That "leakage" would show up in NAT.

  16. the dD/dt term is borrowing. But what about the additional income that goes into Y? If we think that all purchases of financial assets are on the right side, then all sales of financial assets are on the left side. Sales of newly issued assets are dD/dt, and sales of existing assets are folded into Y.

    I feel increasingly convinced he must have meant something like this.

  17. By modeling the effects of debt growth on gdp growth , Keen is trying to move towards defining the parameters for sustainable economic growth and avoidance of depressions.


    With due respect, I don't see any modeling.

    I see him pointing to a very real and important phenomenon. But I don't see a model. I don't see anything in his equation, or anywhere else in the paper, that would help us identify "parameters for sustainable growth." Where is it?

    I am certainly happy to read more of his stuff if there are specific papers or posts that clarify these questions.

    (Also, could you use a handle of some kind? We get multiple anons here and it gets confusing.)

    1. In this short video you can see Keen demonstrating what looks like - to my untrained eyes , anyway - a model :

      I believe at one point he made it ( named , appropriately , "Minsky" ) freely available for download , but that may have changed since he got the INET grant.

      In suggesting that the model could help us identify "parameters for sustainable growth" , I didn't mean that it can do so today. I'm just saying that it might , with further development. I think you'd need to incorporate many more variables to get there - things like income distribution , debt/income distribution by income decile or firm size , labor/capital shares , etc. As an example , a household aggregate debt/income ratio of 150% might be sustainable in a society where all income groups were close to that level , but not in one where the ratio was 300% for the middle-class and 0% above and below the middle.

      Clearly this sort of modeling is in its infancy , and Keen won't perfect it by himself. It's analogous to climate modeling in complexity. Hopefully , like climate models , it will yield useful information without the need to input an overwhelming number of variables.

      If you look at the EU Commission "Economic Scoreboard" , you can see that some officials are establishing such sustainability parameters already , based on judgements drawn from historical data. Debt/gdp ratios , rates of credit expansion , etc. , are being determined that are supposed to help detect developing imbalances and allow their correction before they reach critical mass. This surely makes more sense than sticking with Greenspan's doctrine of cleaning up the mess after the bubbles break.

      Sorry about the ID confusion. I'll try to remember to sign off henceforth....

      Anon Y. Mous

  18. (Also, it's a minor point, but WHY write it in continuous time? If you want to confront the equation with data -- it's in a section called "Applying Minsky to Macroeconomic Data," after all -- you are going to have to convert everything to discrete time anyway.)

    1. JW,

      I just saw this Keen quote and it reminded me of your question :

      "if it isn’t disequilbrium, then it isn’t economics…“disequilibrium” is so common in real sciences that they don’t even call it that: they call it dynamics. Any dynamic model of a process must start away from its equilibrium, because if you start it in its equilibrium, NOTHING HAPPENS. It’s about time that economists woke up to the need to model the economy dynamically."

      Anon Y. Mous

  19. JW — I think that what drives the enterprise is the fact that new debt issue is not modeled as the sale of a pre-existing asset (a reasonable modeling choice, since we could never meaningfully inventory or characterize everything that can be lent against). New lending is a de novo stream of purchasing power that might be used to purchase current goods and services as well as financial assets.

    I still call foul on that not translating to an increase in Q of financial assets on the right-hand side. But if Keen were to agree and make my correction, it wouldn't qualitatively change the set-up. As long as T can be a small number, there can still be plenty of purchasing power derived from credit expansion that is matched by the GDP flow term rather than by the asset turnover flow term. And that I think is his point. Holding income growth constant, credit expansion (an increase in the flow of credit) must, as a matter of keeping purchasing power flows in balance, be matched by a high rate of turnover in financial assets, price appreciation of financial assets, or an increase in real GDP. I think that's a real and helpful insight.

    1. SRW

      In this formulation, how is Y different from GDP. It must be because otherwise what's the point?

    2. Y is defined as income from the sale of goods and services and pre-existing financial assets. GDP represents funds spent (and therefore identically income from) sales of goods and services only.

      Obviously, this breaks the conventional accounting identity Y = Z = GDP. Keen uses a different definition of Y to develop a different (but still valid and still tautological) accounting identity.

    3. I was leaning toward the idea that this is what he means too. But this morning I'm less sure, and I'm even less sure that it's what he should have meant. Note the quote from Minsky a bit before he introduces the equation:

      "For real aggregate demand to be increasing, . . . it is necessary that current spending plans, summed over all sectors, be greater than current received income and that some market technique exist by which aggregate spending in excess of aggregate anticipated income can be financed. It follows that over a period during which economic growth takes place, at least some sectors finance a part of their spending by emitting debt or selling assets."

      Here, the role of debt is clearly to allow a departure of realized (expenditure-determined) income from anticipated income. If the equation is intended to formalize the logic of Minsky's argument here, then Y and GDP must refer to the same flow, but ex ante and ex post (or in two different periods.) If your reading is right, it's hard to understand why this quote is there.

  20. In case nobody has seen this - empirically, Keen's accounting identity appears to be correct:

    1. A correctly formulated accounting identity is *always* empirically correct. That's what it means to be an accounting identity. The question is, is it useful?

    2. It was just in case anybody believed it wasn't correctly formulated - I got the feeling some were doubtful. Apologies if that wasn't the case.

      And I think it is pretty useful for understanding bubbles.

    3. Well, its correct as Merijn Knibbe interprets it. But note that his interpretation is rather different from Steve Randy Waldman's. (Or at least I think it is -- maybe if Steve is still reading he can say if I'm mistaken.)

  21. I have to say that I was waiting for this post since I read Krugman's post on Keen.

    Some years ago I read very often Keen's blog. From those readings I would say that:
    a) the formula is supposed to be an accounting identity, but
    b) Keen believes that it is the change in debt that drives the economy, and all the rest "adjusts".

    Note that, from a policy perspective, b) makes some sense, since the growth of debt is the factor that can be influenced most easyly by the government; however, I don't know what policy would be justified by this, since in pratice the government can either stimulate the economy by incresing the rate of growth of debt, but at the same time cause a credit bubble, or either slow or reverse credit growth, but at the same time causing a recession.

    1. I think the policy implications are that debt MUST go into financing investment - at least, for the most part, else the debt will outweigh the productive capacity of the economy. It also implies that low interest rates are desirable to reduce the costs of servicing debt.

      I also believe that, in Keen's models, reducing the wage share of the economy too much causes an implosion, as there is either not enough spending or too much debt to make up the gap.

  22. Here is a more technical outline of professor Keen's simple model of credit money:

    Professor Keen expresses his ideas in terms of a mathematical model of a pure credit economy. Hopefully this will help understanding of his ideas.

    Alex Plante

  23. Credit expansion or contraction defines economic growth or shrinkage in our age of purely debt based money. It is a mistake to focus on bank lending because that is no longer the main source of systematic credit. In aggregate it matters not where the supply of credit, or its demand, comes from.

    While the economic consensus has studiously totally avoided the central role of total systematic credit as a determinant of GDP don't think for a moment that Greenspan nor the new coke fueled Street didn't get it by the late 80s. As banks and bank lending suffered in the late 80's early 90's Greenspan et al understood but never mentioned it that the new source of non bank credit was going to be font of growth. So they encouraged all flavors of ABS and of course the final mother of the credit expansion, MBS particularly by the GSE's.

    Quite simply the Federal Government has had to borrow and spend around 13% of GDP the last 4 years to keep the system intact. Nobody else would or could borrow so much and so keep total systematic credit expanding at the roughly $2 trillion a year level to avoid a debt deflationary collapse.

    Non of which addresses directly this Keen/Krugman thing directly except Keen would recognize my drift and Krugman would? Well who knows.

  24. On household debt and aggregate demand, Keen is a 100% right,and his contribution is a novelty. It is one thing to say wealth and interest rated affect aggregate demand (as in orthodox modelling that I have done for 7 years myself) and it is another thing to say DEBT (in the sense Keen sees it) directly affects total demand. Orthodox models derive household consumption from utility maximization, imports and exports from firm behaviour and impose an ad hoc government spending on top: here you go, you have AD. You might deny it but a large proportion of orthodox models explicitly label the right hand side of the accounting identity you use as AD and make it equal to AS to find the equilibrium. The problem in these models is that Consumption depends on income, interest rates, wealth and utility function parameters, not borrowing or credit from banks! Using a single household who also owns the firm, this leads to utterly useless demand functions that have nothing to do with reality. Or in other words, banks do not lend against collateral (although there is some modelling of secured credit in the literature) or sometimes against nothing but future income (consumer credit for example)
    Here is a good empirical paper that shows why Prof. Keen is making a very important point.

    1. Anon-

      I agree with you on the substantive points, but I don't agree that they are novel. There are a number of papers from 15-20 years ago that made essentially the same points about the role of bank-created credit in aggregate demand. I will do another post on this stuff shortly.

    2. Hi Mason

      Thanks for replying so promptly, I would be very happy to read your new post on that issue as someone who is attempting to build more realistic models of the economy.

  25. "The next problem is units. GDP and presumably Y are flows over a specified period (a year or a quarter); they are in units of dollars. dD/dt is an instantaneous rate of flow; it is in units of dollars per unit time"

    Late comment but good post generally - same as my observation except the above.

    GDP has dimensions of dollars per unit time - it is just that it is suppressed while displaying on reports by national accountants. It looks silly to use dimensions at all places - better to avoid it altogether.

    dD/dt can appear next to GDP in continuous time formulation and this would not be incorrect purely from a dimensional analysis viewpoint.

    1. Should say it better. GDP in continuous time formulation has dimensions of inverse time. Measured GDP over a period is ∫ GDP dt with suitable limits and hence no dimensions.

      But in a continuous time formulation GDP does have the right dimensions Keen assumes.

  26. There are some more recent videos by Keen that explains much of this with the maths included. I would highly recommend the recent 2014 talks in Berlin on YouTube and also the UMKC one where he tries to reconcile MMT with MCT. The significance of his work is not that it is totally unique or novel (like all of us, he stands on the shoulders of giants like Minsky and Godley) and somehow negated by an older academic publication that might say something similar, but that his approach and methodology and assumptions are pretty much contrary to what is taught at most universities or held to be self evident by leading economists like Krugman. Keen knows that Krugman's stance (as a New Keysian) is closer to his own positions (at least in a policy sense) than the more hardline Chicago school neo-classicals but his core point is that the underlying assumptions of neo-classical economics are so fatally flawed that we need to go back to first principles and that the underlying tools and beliefs mainstream economics is incorrigibly wrong and beyond theoretical redemption. Keen's familiarity of neoclassical literature is encyclopedic and he constantly uses it to support his case that the whole neoclassical belief system is built on theoretical sand. It is up to you whether you share this view but Keen is at least putting forward quite a complete alternative view with its own set of analytical tools. He is mathematically rigorous and he is works closely with top mathematicians so it would be a mistake to assume he is making simple definitional errors as he has many detractors go through his work with a tooth comb to try to pick holes in it. He has detractors even from the Post Keysian side. Another mistake is to try to make his definitions fit into the standard neoclassical framework given his overall iconoclastic approach. There is a massive paradigm shift at play here.