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Tuesday, November 1, 2016

Fun With Accounting Identities

An article with the flamboyant title "The final implosion of MMT" by  Egmont Kakarot-Handtke caught my eye. As I observed at Mike Norman Economics, this was probably just an attempt to troll people. That said, I think it provides another useful example of national accounting works (or does not work...).

The Premise

His incorrect argument may be summarised as:
In order to see this one has to go back to the most elementary configuration, that is, the pure consumption economy which consists only of the household and business sector.**
In this elementary economy three configurations are logically possible: (i) consumption expenditures are equal to wage income C=Yw, (ii) C is less than Yw, (iii) C is greater than Yw.
In case (ii) monetary saving Sm is positive and the business sector makes a loss, i.e. Qm is negative.
The root of the problem is that he has confused cash flow for profits. In a two sector economy, if one sector has a financial surplus, the other sector has to have a corresponding deficit, since the sum of financial flows has to equal zero. (In published economic data, there can be measurement errors that create residuals.)

However, a financial flow is not the same thing as profits. For an economy divided between a household sector and a business sector (that is, the external and governmental sectors are assumed out of existence), there are two main cash flows out of businesses that are not expenses, and which create a wedge between cash flow and profits.
  1. Dividend payments are flows to the household sector (which allows for the purchase of business output) that are emphatically not expenses.
  2. Capital expenditures by businesses are a outward cash flow by businesses that do not immediately give rise to an expense. (Depreciation expenses will arise in the future, however.)
For example, a business can pay a $1000 dividend to its owner, and the dividend is saved in the bank. The household sector has $1000 in savings, and there is no effect on business sector profits.

These two exceptions are not minor; they drive a lot of the action in the national accounts, and in the possibilities for outcomes in model economies. Dividends in particular pose a lot of potential theoretical difficulties. If we have a model in which all transactions in a period settle simultaneously, and all entities are purely forward-looking, there is little to stop dividends from becoming arbitrarily large -- since all output can be immediately purchased with dividends.*

Concluding Remarks

This is a rather silly example, but it underlines why we always have to keep the cases of dividend and fixed investment flows in our minds when discussing the national accounts.

* Anyone with a background in control systems engineering will recognise this as being the highly annoying case where the "D matrix" is non-zero. About 90% of the annoyance factor of controls proofs deals with that case.

(c) Brian Romanchuk 2016


  1. These are a bit related to the paradox of profits.

    Even without investment spending, it's possible for households to save and businesses to run profits ... if we worry about "change in inventories".

    Like this and the linked post:

  2. As a non-economist who has been reading economics blogs for six or seven years, one of my main observations on economists is that they fail to agree even basic terminology and then disagree constantly on more advanced topics because they are talking about different things. Soon war breaks out. The epicentre of this confusion is the identity:

    I = S

    for a two-sector economy with businesses and households. Note that it is not the identity which is confused. It is the economists who are confused.

    I have observed four major disagreements between economists on the terms in this identity.

    1. Economists disagree about what is and what is not investment.
    2. Economists disagree about what is and what is not saving.
    3. Economists disagree about which of the two sectors is doing the saving.
    4. Economists disagree about whether the identity covers the whole economy or just the GDP part.

    Note that in your previous post on Cullen Roche’s book, you say that “he lumps private equity under "investment" and pretty well all else financial activity as "savings". In other words, he has his own idiosyncratic view of both investment and saving. Also, he sees saving as involving non-GDP activities such as buying shares on the stock market whereas Keynes original identity seems to have been about GDP only. This is typical of the economics and finance professions. No wonder that you guys get nowhere in trying to persuade the rest of the world of the benefits of Post-Keynesian economics.

    EKH makes the same two or three points over and over in the endless stream of comments he leaves across many blogs, and he makes them in a tone which is guaranteed to get him ignored. Nevertheless, one of the points he makes relates to my third point of observed disagreement.

    There are two basic interpretations of who is doing the saving.

    Interpretation 1:

    I (B) = S (H)

    This says that only businesses invest and only households save.

    Interpretation 2:

    I (B) = S (H) + S (B)


    I (B) – S (B) = S (H)


    I (B) – RP (B) = S (H)

    This interpretation says that both businesses and households save and that business saving can be renamed as retained profit (RP) as in my final version of the identity above.

    Economists never make clear which of these interpretations they are following. EKH claims that most economists follow the first interpretation but that the second interpretation is correct.

    It is a simple matter to construct a toy economy with one business and a few transactions to show that interpretation 2 is the correct interpretation. Interpretation 1 is correct only when businesses make no profit or when they distribute 100% of their profits to households in dividends.

    Where I am unclear is whether EKH’s assertion that most economists follow interpretation 1 is correct. I have a horrible feeling that it might be but, as I said previously, economists define these terms so poorly that it is difficult for a neutral observer to discern a clear definition.

    Unfortunately, this all gets lost in the bad feeling created by the tone of EKH’s posts. Nevertheless, the lack of clarity on the definitions in these identities gives an outsider the impression of an entire profession lost in a confusion of its own making.

    1. (As an aside, the above comment was originally eaten by the Blogger spam filter; I had to fish it out. The filter really seems to hate long comments.)

      I cut the discussion out, but Cullen Roche's discussion of saving and investment was an attempt to get everyday usage of "saving" and "investment" closer to the formal economics definition. (Money is another such term, as in "she has a lot of money.") For simple cases, his definition would appear to work. I did question how this relates to household finances, as the tradeoff for the activities for what he calls investing was more time-related than financial. My definitional complaint was around how he treated private equity, which was inconsistent.

      Also, I would agree that economists can be sloppy around the use of "savings" and "investment"; I try to note when I am discussing the formal economic definition, and other uses can be the informal definitions. It is very difficult to write about "investing your savings in the bond market" without using those terms (even though in most cases, the usages have nothing to do with the formal definition).

      My feeling is that many market economists also follow that pattern when writing. The clue is from context; if someone starts referring to "national savings", or is referring to accounting identities, they have switched over to the formal definition. (There are some usages of "saving" in some MMT writings which does not match the usual definition, I believe.)

      Since I spent a lot of time reading market economics, I have gotten used to picking out what I think is the intended meaning. If we are looking at the formal definition, pretty much everyone agrees on the textbook definitions, where we have to look at the investment and saving for each sector. That corresponds to your second interpretation.

      However, household saving is singled out as a particular variable of interest. I do not think it is, but this is probably related to thinking about representative households and so forth. In market research, you do see some people blurring the distinction between "household savings" and "national savings", but you would not see that from people who are closer to academic writing standards (such as central bank research). Also, people who have axes to grind like blurring the distinction. For example, people in the financial industry who want to get their hands on more of peoples' savings (oops) are quite happy to equate household saving with national saving. Politicians also like arguing that measures that favour financial asset holding households will raise national savings (and hence, real investment), since that sounds better on the campaign trail than saying "give money to rich people".

    2. Jamie

      You say: “The epicentre of this confusion is the identity: I = S”

      That is correct. The I=S mess can be traced back to Keynes and has its ultimate cause in Keynes’s scientific incompetence: “His Collected Writings show that he wrestled to solve the Profit Puzzle up till the semi-final versions of his GT but in the end he gave up and discarded the draft chapter dealing with it.” (Tómasson et al., 2010, p. 12)

      MMT shares the profit blunder with Keynes. For details of the big picture see cross-references Refutation of I=S

      Egmont Kakarot-Handtke

    3. Egmont defines income from the household's point of view as:

      Household Income = Wage Income + Distributed Firm Profits

      => Y = Yw + Yd

      Whereas income is conventionally defined from the total economy point of view as:

      Income = Wages Income + Dist Firm Profs + Retained Firm Profs

      Using Yt for total income and Qre for retained firm profits:

      => Yt = Yw + Yd + Qre

      Similarly, Egmont uses household savings not total economy savings viz.:

      Household Savings = Household Income – Consumption

      i.e. using his terms:

      => Sm = Y – C

      Again it should be total economy saving:

      Total Eco. Saving = Household Income + Retained Firm Profs – Consump.

      Using St for total savings:

      => St = Y + Qre – C


      => St = Y – C + Qre

      and given Egmont defines Sm = Y – C

      => St = Sm + Qre


      => Sm = St – Qre

      Egmont uses the equation:

      Qre = I – Sm (I Egmont defines as investment)

      and substituting into this equation for Sm as above:

      => Qre = I – (St – Qre)

      => I = St

      That is, removing the definitional impediments Egmont imposes, his equations reduce to the Keynesian relationship of equality between investment and savings.

      When he says investment is never equal to savings and hence Keynes’ relationship does not hold, he is comparing apples to oranges. His definitional schema (based on the household perspective) precludes him from comparing its results from those of the schema used by Keynes (that is, the conventional aggregate accounting one).


    4. Henry,

      Thanks for helping clear that up. You spent way more time on that than I ever would...

    5. Thanks to Henry for his comment. It was very helpful. I agree that Egmont has his own terminological definitions and that is part of the problem. However, I still have an issue regarding “the schema used by Keynes (that is, the conventional aggregate accounting one)”.

      Here is Keynes from Chapter 6 of his General Theory (entitled The Definition of Income, Saving and Investment):

      “Whilst, therefore, the amount of saving is an outcome of the collective behaviour of individual consumers and the amount of investment of the collective behaviour of individual entrepreneurs, these two amounts are necessarily equal, since each of them is equal to the excess of income over consumption”.

      Also, if you do a word search for the term “profit” in Chapter 6 you will see that Keynes uses that term several times in the sub-section on income. However, it does not appear in the sub-section on saving and investment.

      As far as I can see, everyone on this thread (including Egmont in his own strident terms) agrees that business saving should be included in the I = S identity. That is what Henry calls the conventional view. However, Keynes does not seem to agree. That means that Keynes was wrong – which is Egmont’s basic point.

      If you think that Keynes is the only economist who doesn’t understand his own theory, search for a post on Simon Wren-Lewis’s blog where he imagines a conversation between himself and a confused student on this very subject (Savings Equals Investment? – published on 14 January 2012).

      Wren-Lewis (aided by Nick Rowe in the comments section) gives no indication that he includes business saving in the identity even though the student is confused precisely because he thinks that he has been taught that business investment equals household saving.

    6. Without even looking at the text, was Keynes talking about a simplified model? Ripping pieces of text out of context, particularly the General Theory, is not a useful exercise.

      Even the strongest defenders of Keynes (as did Keynes himself, I believe) would admit that the General Theory is muddled; it was a mixture of old and new theory. Worrying about slip ups in a text published decades ago is a rather pointless excercise. There are tons of textbooks published in the following decades that cover national accounting.

    7. It most certainly is not pointless if current students are still being taught (or believing that they are being taught) that business investment equals household saving. See the Wren-Lewis post.

      It is also not pointless because casual readers of economics blogs and OpEds on this subject will pick up the wrong interpretation. Economists could solve this easily by using the form

      I (B) = S (H) + S (B)

      rather than

      I = S

      which is at best ambiguous.

      The General Theory is one of the most important texts in all of economics and the chapter I am referring to is the one where he DEFINED this very terminology. If Keynes made a slip, I would have expected that later versions of the text would include some commentary pointing out the slip. Alternately, mainstream economists would point out the slip every time they comment on what Keynes wrote. However, neither of these things occurs.

      Do you think that the deliberate use of ambiguous terminology, when that terminology causes confusion in the minds of economics students and of the general public, is a useful method of propagating economic insights?

      Why do you feel the need to write posts using mathematical models to demonstrate that retained profit has a negative effect on the economy? If the simple point I am making was widely understood, there would be no need for such posts.

    8. Keynes was involved with the war effort, and negotiating the post-war monetary system, and then died shortly thereafter. Cleaning up the text of the General Theory was not possible under those circumstances. If you want commentary, you can read a modern textbook. My recommendation is "Monetary Economics" by Godley and Lavoie.

      Sure, economists of all sorts use misleading terminology when writing op eds. My style of writing does vary; but I write my primers in such a way to explain the technical concepts. As for the misleading terminology, you need to take up your complaint with the English language, and the decision to reuse common words with multiple meanings as technical terms in economics. It is decades too late to undo that decision.

      I assume you are referring to my later post. If you read the text, you will note that I wrote that the model had problems; it was an illustration of what goes wrong when one is not careful setting up a model. I will eventually write up the more realistic case, in which we have to add new inter-sector relationships (dividends).

      In any event, you need to look at *all* sectors, even your I(B) = S(H) + S(B) is a special case. "I" is national investment, "S" is national savings, and that is what profs should be teaching their students.

    9. I am not talking about the generic use of economic terminology. I am talking about the use of terminology by mainstream academic economists when they are discussing Keynes’ identities in their lectures, blogs & OpEds. Again, see the Wren-Lewis post.

      It is not necessary for Keynes to be alive for living academic economists to either add a footnote to new editions of Keynes’ text, or for them to explain Keynes’ error in their text books and lecture courses, but neither of these things occurs. Nevertheless, academic economists often suggest that students and non-economists should read the original text.

      As it happens, I already own the Godley & Lavoie book but my understanding is not the issue. I suspect that most mainstream economists have not read that book and do not recommend it to their students, so it is irrelevant to the point I am making.

      Finally, I do understand that there are other sectors. You post says that “the external and governmental sectors are assumed out of existence”, so I am merely following your lead. However, it is the I and S terms which cause the misunderstandings in these identities, so the other sectors are less important in this respect.

      Anyway, I will sign-off now as we are unlikely to reach common ground.

    10. (1) If you think Professor Wren-Lewis made a mistake somewhere, why not post a short comment on his site? (Note that your comments have been eaten by the Blogger spam filter; I had to fish them out.) I disagree with him on various substantive issues, and so I do not see any particular need for me to defend what he wrote.

      (2) I agree that many people misunderstand the I=S identity. I also think that the identity is a complete waste of time. Since it is true by definition, it makes as much sense to worry about it as it does to go around measuring right angle triangles to see that Pythagoras' Theorem still holds.

      (3) We have just reached the 70 year mark after Keynes's death. Previously, copyright laws prevented just anyone from releasing a annotated version of the General Theory; and although it still sells a decent amount of copies, I doubt that it would have been easy to negotiate exactly who was going to edit such a volume.

    11. This link opens a 32 page slide deck by Lavoie "Minsky and Godley and financial Keynesianism":

      Page 8 shows that SAVING, INVESTMENT, and GOVT SURPLUS sum to zero in a conventional flow matrix.

      Page 10 shows a flow of profits in the business sector and household sector. I don't understand the symbols applied without a description.

      Page 12 shows a balance sheet matrix where flows accumulate over time. The accumulation of profits in these simple firms would show up as in increase in household equity claims issued by the business sector.

    12. "As far as I can see, everyone on this thread (including "Egmont in his own strident terms) agrees that business saving should be included in the I = S identity. That is what Henry calls the conventional view. However, Keynes does not seem to agree. That means that Keynes was wrong – which is Egmont’s basic point."

      I'm not so sure about this.


      saving = income - consumption


      income = wages + dist'd profits + retained profits


      saving = wages + dist'd profits + retained profits - consump.

      So business saving is included in saving.

    13. And just so it is clear:

      business saving = dist'd profits + retained profits


    14. According to Egmont's interpretation of Keynes, Keynes was wrong.

      I hate to point this out, Egmont is a crackpot, and Keynes *invented* macro as a field. My suggestion is to not look at out-of-context quotes from the General Theory, and if you are deeply concerned about national accounting identies, pick up a good textbook.

    15. "Egmont is a crackpot, and Keynes *invented* macro as a field."

      Maybe he is, maybe he isn't.

      I seem to recall he draws more from Keynes of the Treatise (happy to be corrected on that) than he does from Keynes of the GT.

      All I was trying to do was perhaps/possibly disabuse Jamie of some of his/her opinions about Keynes of the GT.

      "...pick up a good textbook."

      Always up for improving my understanding. Currently reading Mabel Timlin's "Keynesian Economics" (1942) - hardly a textbook but replete with interesting insights. As you can see, my economic re-education has not advanced much beyond 1940 (and my degree in economics is vintage early 1970s). :-)


    16. Sorry, I was in a bad mood when I wrote that -- too abrupt. What I should have written is this: worrying about what Keynes wrote in 1936(?), is not the best use of our time in 2016, when we now have a fully developed system of national accounts, and textbooks explaining how they function. Since S=I is undoubtedly true within the standard framework, why are people worrying about it?

      Keynes was still in "classical economics" mode when he wrote the Treatise; the breakthrough was in the General Theory. To a certain extent Keynes of the General Theory "disproved" the earlier Keynes himself. As for the General Theory, one explanation for the difficulties with the text was that Keynes was trying to explain his theories using classical terminology. He died too soon to clear up the problems.

      In any event, I have not seen any evidence that Keynes was actually wrong about anything in the GT. All I have seen is someone ripping a random sentence of the text, without any sense of context. You have to remember that digital computers did not exist when he wrote the book, and the ability to work with complex mathematical systems was limited. Throughout the book, he had to work with simplifying assumptions in order to get tractable relationships; I see litle reason to believe that this was not the case for the sentence in question.

    17. I think I have to disagree with a some of what you said in your last comments post.

      The GT was more than just about a way of defining macroeconomic outcomes. By the time of the GT, there was an already well developed system of national accounting.

      It could be argued that the GT's partial equilibrium framework was his strength - perhaps he was not able to break away from it being only too well indoctrinated in the system himself. I think he would deride the Walrasian general equilibrium framework which generates instantaneous, eternal equilibrium. Conversely, he was interested in how an economy moved from one equilibrium position to another.

      I personally believe there is much still to be distilled from the GT. I suspect it is still largely misunderstood, owing to the later contributions/interpretations of the likes of Hicks, Hansen and Samuelson.

      I would also argue that Keynes eschewed complex mathematical systems because he believed that a macroeconomic system with its attendant and multiple feedback loops and expectational operators was near impossible to model. He was more interested in developing a mode of thinking about economic issues that enabled solution of real world problems and not so much abstract high theory, although he was perfectly and eminently capable of managing the latter.


    18. National accounting was still its infancy at the time of the publication of the GT. In the UK, Keynes had to push for the development of a lot of statistical measures as part of the war effort.

      Yes, I think it was safe to say that he had a dim view of mathematical modelling of the economy. But working from memory, he had a section where he assumes that workers spend 100% of their income, and capitalists save all of their dividend income. He did not believe that was the case, but it gave a tractable set of accounting relationships.

  3. No fun, only ignorance
    Comment on Brian Romanchuk on ‘Fun With Accounting Identities’

    You quote my derivation of the elementary accounting equation and conclude: “The root of the problem is that he has confused cash flow for profits. In a two sector economy, if one sector has a financial surplus, the other sector has to have a corresponding deficit, since the sum of financial flows has to equal zero. ... However, a financial flow is not the same thing as profits. For an economy divided between a household sector and a business sector ... there are two main cash flows out of businesses that are not expenses, and which create a wedge between cash flow and profits. 1. Dividend payments ... 2. Capital expenditures.”

    If you had followed the references that back up my argument you would have realized:
    (i) That I do NOT confuse cash flows with profits. In fact, there are two types of profit in the axiom set, viz. monetary Qm and nonmonetary Qn (2011a).
    (ii) That dividends are in the axiom set (2014).
    (iii) That investment expenditures and depreciation have been dealt with elsewhere (2011b).

    In case you sincerely want to get out from behind the curve study the working papers on SSRN.*

    Egmont Kakarot-Handtke

    Kakarot-Handtke, E. (2011a). Primary and Secondary Markets. SSRN Working
    Paper Series, 1917012: 1–26. URL
    Kakarot-Handtke, E. (2011b). Squaring the Investment Cycle. SSRN Working Paper
    Series, 1911796: 1–25. URL
    Kakarot-Handtke, E. (2014). The Profit Theory is False Since Adam Smith. What
    About the True Distribution Theory? SSRN Working Paper Series, 2511741:
    1–23. URL

    * SSRN

    1. I'm sorry, but I doubt that I will have time to read your papers in the near term. My objective is to provide a summary of (and commentary on) existing economic theory. That theory uses standard definitions for savings, investment, and profit, and are tied together by accounting identities.

      Because economists reused common words with multiple meanings, writing gets confused. This is not mathematics, where one can make up definitions somewhat arbitrarily, and expect readers to follow those definitions. As a writer, I want to use synonyms as much as possible to add variety to my text, which means I am going to stomp all over any special technical meanings of terms.

      There are entirely legitimate complaints about national accounting. But in most cases, the desire is to get closer to the notion of profits used in accounting, since that is what private sector entities look at. And in GAAP, dividends do not subtract from profits. GAAP also defines various measures of cash flow, but one needs to know more accounting in order to interpret what is going on with them, so they are discussed less often. A perfectly healthy company can have negative cash flow for quite some time before it has to do anything about it, while companies with sustained negative profits often react violently to turn the situation around. That is, GAAP profits predict behaviour.

      Why would I (or any of my readers) be interested in your profit (or savings and investment) definitions, which appear to take us even further away from GAAP?

    2. Brian Romanchuk

      Jamie summarized her post: “Nevertheless, the lack of clarity on the definitions in these identities gives an outsider the impression of an entire profession lost in a confusion of its own making.” This is not only an impression but an incontrovertible fact (2013).

      Economists are scientifically incompetent blatherers. Their very first error is to think that they are free to define whatever pleases them. This is the Humpty Dumpty delusion.* The first thing to understand in science is that the foundational concepts have to be consistently defined.

      It is a remerkable fact that physicists have defined their foundational concepts mass, force, energy, velocity, acceleration etcetera very carefully (see Newton’s axioms) and economists can until this day not even tell the difference between the measurable variables profit and income. Does it come as a surprise that economists have not figured out how the monetary economy works and that they have not achieved anything of scientific value in the past 200 years? In methodological terms, the failure of economics is ultimately caused by the inconsistent axiomatic foundations. This applies to Walrasianism, Keynesianism, Marxianism, Austrianism and, of course, to MMT.

      The accounting equations are of overriding importance because national accounting is the central precondition for empirical testing. As a matter of principle, every model has to be first of all checked against the national accounting numbers. Therefore, it is of utmost importance that the foundational concepts are consistently defined and the SAME in accounting and in theory.

      The current state of economics is that national accounting is provable false (2012) and that economic theory is axiomatically defective and that the ‘throng of superfluous economists’ (including Brian Romanchuk) has no clue and cannot rise above brain dead blathering.

      Egmont Kakarot-Handtke

      Kakarot-Handtke, E. (2012). The Common Error of Common Sense: An Essential Rectification of the Accounting Approach. SSRN Working Paper Series, 2124415: 1–23. URL
      Kakarot-Handtke, E. (2013). Confused Confusers: How to Stop Thinking Like an Economist and Start Thinking Like a Scientist. SSRN Working Paper Series, 2207598: 1–16. URL

      * See ‘Humpty Dumpty is back again’

    3. Considering my ongoing criticisms of mainstream economics, and complete lack of training in such (I was trained as an applied mathematician), I take being included as a "superfluous economist" as a back-handed compliment.

      As for the rigorous definitions in physics that have no sloppy real world usage, I think to say that the *force* of your argument is weak, as there is a considerable *mass* of evidence pointing in the other direction. As someone with actual training in higher mathematics, I find a belief that we cannot redefine words already in common usage to have a new technical meaning *irrational*.

      Many people have varied concerns with the national accounting definitions. However, they certainly are logically consistent, and correspond to at at least some behavioural models. In the real world, what matters is the GAAP profit measure, and profits as defined by income tax laws. Those measures have a number of particularities that are hard to square with simplified economic models.

    4. I can't say I follow this or what the message or conclusion is. I can say that my understanding is that a public deficit increases private sector incomes. If this income is saved , it increases consumer savings. If this income is spent, it increases business profits. If business investment approximates depreciation, the free cash flow effect is similar to the profit effect. This I learned from MMT accounting and Kalecki. It also demonstrates that more personal saving means lower profits - supporting AXEC's point as well. That's clear to me. I'm not clear as to what the debate is about.

    5. I was having some fun with the belief that the words in physics do not have secondary meanings in English. This is exactly what is happening with "investment" and "saving".

      However, to be blunt, I do not understand what the point is either, as I do not have time to read the half-dozen articles listed.

      I would argue that the consensus position among economists is:

      (1) The formal terms for "investment" and "savings" as used in the national accounts are used in a perfectly internally consistent fashion. One could invent new accounting conventions, but then no one will know what you are talking about.

      (2) How particular transactions should be classified is an open area of debate among those people who care a lot about national accounting.

      (3) I am of the opinion that the most useful accounting identity is the Kalecki Profit Equation (or Levy); other post-Keynesians may or may not agree with that. The mainstream does not spend too much time worrying about accounting identities, other than the governmental budget constraint.

      (4) In texts written by economists and "market economists" like myself, the usages of "savings" and "investment" is all over the place. However, an experienced reader should be able to tell whether "investment" corresponds to "I" in national accounting, or the informal usage from finance.

      As a result of the confused usages of "savings" and "investment" in popular writing, the "S=I" identity is a trap. The best bet is to forget about. Since an accounting identity is true by definition, you do not have to worry about testing whether particular observed data are consistent with it.

    6. System of National Acccounts (SNA) is an effort to develop stock flow consistent accounting practices for national accounting. The link below opens a 117 page pdf with Table 1 1993 SNA Framework shown on nominal page 20 and pdf page 31:

      This is a diagram showing Saving as a flow which changes levels in a Capital account and in a Financial account. I think the word "savings" has two meanings in this context. One is the difference between consumption and investment in the GDP and the other is the accumulation of financial assets and liabilities in the financial accounts.

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