Wednesday, August 28, 2013

Accounting identities for the Keen model

This is long overdue, but now that Steve Keen is visiting the Fields Institute again I thought I should revisit the topic of aggregate demand, income, and debt in his models. Loyal readers will recall that this was the subject of a somewhat heated exchange on this and other blogs last year. 

So here is the full balance sheet/transaction/flow of funds table for one of Keen's models, together with the implied accounting relationships, as well as my take on the "demand = income + change in debt" statement and its variants. 

As I had mentioned in one of the old posts, the point it to disaggregate the firms and households from the banking sector, so that endogenous money creation can play a significant role in the story. 

In my view, accounting identities that put the entire private sector together (i.e firms + houses + banks) somehow obfuscate the role of endogenous money and end up putting undue emphasis in the only other relevant observation, namely that private sector surplus should equal government deficit. 

31 comments:

  1. Looks good. Income=Expenditure! I think this framework will allow you to model debt-financed expenditure and its impact of GDP correctly.

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    1. Thanks! I thought you would enjoy.

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    2. Never read about keen model.What's that?

      Thanks
      Sanola Jerry

      Accounting Software

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    3. Check here:

      http://ms.mcmaster.ca/~grasselli/GrasselliCostaLima_MAFE_published.pdf

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    4. The keen model seems very interesting after reading.The link provided by you has helped me to understand the facts about keen model.Thanks for sharing.

      Regards
      Sanola Jerry

      Accounting Software

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  2. Nice improvement.

    So does that mean aggregate demand is no longer GDP plus change in debt?

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    1. I think so, at least the way I understand the model. But you have to ask Steve to get his take.

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  3. Shouln't the last line in your link be aggregate expenditure = aggregate income rahter aggregate demand?

    As far as I'm concerned, you're free to define aggregate demand as you like but defining it as equal to current income doesn't make much sense to me. If demand cause prices to change, it needs to be there before the transaction is recorded. I tought Keen always refered to aggregate demand in the sense of "current spending plans" as per Minsky.

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    1. Throughout the whole document "demand" is used as synonymous of "expenditure" (e.g items like PC_h for household consumption are part of expenditure, and therefore demand), whereas "income" refer to payments received, like wages, profits, interest on debt, etc.

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  4. Reading your piece more carefully, there's something I can't manage to understand. Looking at line 7, I read :

    The flow of wages plus the flow of interest on households deposits minus the flow of households consumption equals the rate of change of households deposits.

    Then,at line 12 you come up with:

    Household demand = households income + the change in debt of households to banks

    This would imply that the change in households deposits necessarily equal the change in debt of households to banks? I guess I don't get that at all.

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    1. Households don't make loans in this model, so their only relationship with the banking sector is through deposits. So H_D (deposits of households) is really the debt of banks to households (the bank owe the households an amount equal to H_D) and its negative (i.e -H_D) is the debt of households to banks.

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    2. Well, I guess you will be alone on that one. In that model, debt is FL and households doesn't have any debt. It refers to debt of non-bank to banks, which expands/contract banks balance sheet. You really have to rethink the whole thing more carefully.

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    3. Well, I'm afraid you are wrong: F_L are loans from banks to firms, whereas F_D are firm deposits, so the net debt of firms to banks is (F_L-F_D). Similarly, households don't take out loans, so all they have are deposits H_D, which is debt of banks to households. So naturally -H_D is debt of households to banks.

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    4. I don't mean to bother you but I'm afraid you're using a disingenius definition of debt here. According to your definition, in the aggragate net debt is always zero by identity (FL = FD + HD + Vb), so in the aggregate there can't be any change in debt.

      I don't mean to say that income doesn't equal expenditure and if you define demand as a synonym of expenditure it's also equal to income. Since every flow comes from somewhere and goes somewhere, it's impossible for "the model" to violate this identity. However, it does not mean that the change in debt can't add to both income and expenditure over time.

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    5. Disingenuous or not, this is the definition of net debt. It's a closed model, so evidently the aggregate net debt is always zero. However, the net debt of one sector (households + firms) to another (banks) does change, and its change is the difference between expenditure and income for that sector. I really don't know what part of the piece that I wrote you are objecting to. In any event, it's all there, and I don't think I can be any more clear.

      Moreover, there's a limit to the amount of anonymous communication that I'm prepared to entertain.

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  5. This seems right to me, with the problem being Keen's repeated use of gross debt in the aggregate, rather than net (external) debt.

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  6. Two points.

    Your table is quite like Godley/Lavoie's approach.

    You - at least Keen has presented it as something revolutionary as if nobody before you - not even G&L implicitly - understood what you are trying to say.

    So what's new?

    Second - I agree generally with Anonymous here.

    I will try to say it in somewhat different words:

    Your usage of debt is for all kinds of debts including deposits. So consider your statement in the pdf:

    "bank demand = bank income + change in debt of banks to firms and households"

    So suppose a bank makes a loan and deposits rise as a result.

    The debt of banks to firms and households increases because of the rise in deposits.

    (Of course net debt doesn't rise because it is cancelled by increase in indebtedness of firms and households to the bank).

    So your statement

    "bank demand = bank income + change in debt of banks to firms and households"

    would imply something else has to change as well. Bank income cannot change because the interest on this loan and others aren't paid at this moment of time (the time the loan is made) and bank demand for goods and services has to rise which is silly.

    (That is not to say banks do not have expenditure on goods and services but your definition would imply that it is so even in the above case when the bank simply makes a loan)

    So you have to use net debt instead of saying debt.

    Not that this is a pedantic issue because when Keen starts going "aggregate demand = GDP plus change in debt", the change in debt is taken by people as gross debt and they complain. If it is net debt it gets cancelled out in the aggregate (such as the case for a closed economy), so why the need?

    In short, care is needed to say if it is gross debt or net debt.

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    1. For the first point, as I said, I can't speak for Steve, so I make no claims about what's new and what isn't. I'm just presenting it the way I understand it. From here I'll go on analyzing the mathematical properties of the dynamical systems that arise as a result of the model, which might or might not be new, who knows. But all I was trying to do with the pdf was to explain my current understanding of the issue - and if that conforms with G&L, well, all the better.

      For the second point, it's net debt all along, as it should be clear from the pdf.

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    2. Well, I haven't been looking recently, but previously Keen has most certainly used change in gross debt when adding to GDP.

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    3. And again, I can't speak for Steve. All I can do is write down my own understanding of the issues. The table corresponds to the accounts and transactions as presented in his JEBO 2011 paper (in a slightly simplified version without things like bank vault, etc), and as I said, I wrote it down as a starting point for my own work on the subject.

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  7. You may not be the one to do it, but I think it would reflect favorably on your enterprise if somebody were to give some recognition to Godley and Lavoie 2006.

    Whatever it is you’re trying to do, they came before you, like Keynes came before almost everybody, if not everybody.

    The two of them jointly (GL) were experts on the accounting and the accounting logic – without comparison in the economic profession, in my opinion. And they understood the central importance of accounting coherence to economics. The word they used to describe it is “watertight”. You guys seem to be struggling with this.

    That said, it took them a long time to it together, understandably. And maybe you are attempting to take it in a new direction. Nevertheless, a similar accounting foundation is required, and more acknowledgement of predecessor efforts would be nice to see – because some of us are in a position to compare the two, and are doing some head scratching about it.

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    1. Thank you for the advice, but you don't really need to worry. The pdf is just a "note-to-self" type of document: a skeleton to build-up on. It has no references (not even to Keen), and no text either, just a table and some equations that follow from it.

      However, in both my research papers and grant proposals, you can find proper references to GL and others in the SFC camp. As a matter of fact, I communicate with Marc regularly for discussion and advice, and one of his messages read: "I gave a very quick look to the proposal. It seems that you have fully comprehended the framework of Godley-Lavoie!"

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    2. That’s very good for you - you understand and acknowledge (here) the foundation then. But my observation was about the finished product of the joint enterprise. And I’m also wondering its going that’s different than what’s been done. But it’s probably not your role to speak to that.

      Good luck in any event. Nothing ventured, nothing gained.

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  8. Matheus,

    There are a few more things I don't feel are right but unable to translate into words but for now this one:

    Sometimes when you generalize a model, some relationships do not survive.

    So while the equations seem okay, the statements following the equations seem odd.

    So consider the statement:

    "firm demand = firm income + change in debt of firms to banks. "

    That would be taken to mean firms borrowing from households (or even non-bank financials) and subsequently spending it say as capital expenditure does not add to aggregate demand. However this is not the case. It as much affects aggregate demand as borrowing from the bank and spending it the same way.

    (Of course that doesn't mean a model with firms borrowing from households compared to the simpler one has the same path of output and there can be differences but the differences are different from the way you emphasize).

    I know you have mentioned in the comments that it is perhaps best to ask some things to Steve Keen and I think he himself misreads some of the results as my reading of his comments on Nick Rowe's blog leads me to conclude. So someone else may even misinterpret it more inaccurately.


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    1. Ramanan,

      It's certainly true that relationships that hold in a model don't necessarily survive when you generalize it. For example, in the Goodwin model, which is a special case of the Keen model without any banks whatsoever, it holds that "all profits are reinvested, all wages are consumed", but this is clearly not the case in the general model.

      So for sure when we include household lending to firms (say by equity purchase), the statement will have to be revised. Similarly when we include non-bank financials.

      In general, it's logically impossible to know in advance which statements will survive when one generalizes a model, since any result that holds in a particular model might depend on an assumption that is subsequently dropped in the course of the generalization. So one has to wait and see what the generalized model looks like

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  9. Matheus,

    First up, I think this is a huge improvement on Steve Keen's attempts to explain his thoughts. I'm a big fan of this type of framework. If Steve is persuaded by this approach, it should go a long way to clarifying some of the confusion that has arisen from his way of presentation.

    I also liked the comment in your final paragraph to the effect that over-aggregation means we risk losing sight of what is going on. The dynamics of a monetary economy are all about the relationship between creditors and debtors. If we aggregate too much, we have to cancel these out and then we can't see what is going on. Nick Rowe made a comment on your analysis that it had "too many sectors". I'm not sure if he was joking - to me, three is pretty much the minimum for looking at this sort of thing.

    I would be interested to see what you conclude on the impact of non-bank lending. Steve seems to be pretty fixed on the idea that only bank lending matters, because of its link to money creation. I think he is quite wrong on this and I think that the framework you are using is the best way to bring that out.

    Also, I would agree with other commentators that, because Steve has appeared to talk about gross debt, it would be useful to make clear that the quantity in your formula is net debt.

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    1. Thanks Nick,

      I was not aware of the discussion going on at Nick Rowe's blog, but found it interesting, although I of course disagree with him about having "too many sectors" in the model. If anything it still has too few sectors, since I still need to add both the government and the RoW (not to mention non-bank financials, etc).

      I also think it's important to distinguish net and gross debt, but I thought it was clear from the formulas (e.g I call the difference F_L-F_D "firm debt", so it's clear that this is net). But I'll make sure to have the distinction clear in future writing (and modelling).

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  10. Matheus,

    Have you seen this BoE paper:

    Growing Fragilities? Balance Sheets in the Great Moderation by Richard Barwell and Oliver Burrows

    http://www.bankofengland.co.uk/publications/Pages/fsr/fs_paper10.aspx

    it has tables which are like yours but has a lot of details and its intentions are similar to yours - studying stocks and flows and trying to detect fragilities in the system.

    It also has some nice tricks to consider both gross and net debt - such as by using net accumulation of financial assets and net incurrence of liabilities.

    On your point about bank lending versus non-bank lending/borrowing - at this moment all I can say it that there is overemphasis on bank lending. You can for example tinker with G&L models to see firms borrowing from banks against the case of firms borrowing both from banks and households and compare the output behaviour. The thing that is important is the act of expenditure itself. That is not to say debt is unimportant because it may require going into debt and so on and debts can become unsustainable.

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    1. Thanks Ramanan,

      I actually discussed that paper with Oliver when he presented a preliminary version of it in Waterloo last year, but I see that it's a lot more developed now. I plan to incorporate their main empirical findings in some of the extensions of the basic model that I'm currently working on, especially household borrowing for purchase of existing assets (e.g houses). Another important aspect of the Barwell/Burrows paper is the detailed treatment of the RoW (rest-of-the-world) sector, which is admittedly a blind spot for me and something I really want to learn about.

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  11. Of course that paper is more empirical but still nice. On the modeling side, I'd say James Tobin's work will be highly relevant - he will be your good friend - supreme genius.

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    1. Thanks again,

      What I'm doing right now with one of my co-authors (Adrien Nguyen) uses some of Tobin's work on portfolio selection. Any particular readings you recommend?

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