Monetary Realism

Understanding The Modern Monetary System…

Saving, Stock/Flow Consistency, and Kalecki


Here are some of the equations and interpretations that flow from the basic national income accounting identity.

C + I + G + (X – M) = C + S + T                     (1)

This is the national income accounting identity.


(S – I) = (G –T) + (X – M)                                (2)

This is one form of the corresponding 3 sector financial balance model. It says that private sector saving is the source of net finance for the government deficit and the international capital account deficit.


S = I + (S – I)                                            (3)

This says that private sector saving is the source of finance for investment and net finance for the other two sectors. The term (S – I) is the compact form of the full expression noted in (2) above. The unusual form of the equation is for purposes of highlighting the distinction between physical and financial uses of funds from saving.


I = S + (T – G) + (M – X)                               (4)

This says that investment is funded by three sources of saving – private sector saving, government saving, and foreign saving. Among other things it says that, given the presence of government and foreign sector saving contributions, the term S must cover the saving contributed by the remaining sector, which is the private sector. In particularly, S does NOT stand for household saving, a fact that will become more pertinent further below. Note that the phrase “funded by” does not refer to macroeconomic causality, which flows primarily from investment to saving (refer to the Andy Harless post referenced in the long post link just below).

These four equations are mutually compatible and derivable from each other.

Thus, S is private sector saving in a 3 sector model – the same model that gives rise to the 3 sector financial balances model prominently used by MMT, and discussed at length here:

The private sector decomposes into the household sector and the business sector.

And private sector saving decomposes into household saving and business saving.


Let S = HS + FS

HS = household saving = household income after taxes and consumption

FS = business saving = undistributed gross profit (depreciation plus retained earnings)

(See the note below regarding depreciation. All equations hold net of depreciation as well, when specifications for I and S reflects that level of netting.)

From above,

I = S + (T – G) + (M – X)                                                                           (4)

 Substitute the two components of S:

I = (HS + FS) + (T – G) + (M – X)                                                                      (5)


FS = I – (HS + (T – G) + (M – X))                                                                    (6)



Business gross profit = undistributed gross profit + distributed profit

Business gross profit = FS + DIV (dividends)

Adding DIV to both sides of (6),

Business gross profit = I – (HS + (T – G) + (M – X))        + DIV                (7)

= investment – household saving – government saving – foreign saving + dividends


This is a modern version of the Kalecki profit equation

See the following interesting posts referencing the Kalecki profit equation by Ramanan and Cullen Roche (via Pragmatic Capitalism):

The Kalecki profit equation has an interesting characteristic. Dividends are included twice in the equation – once in their explicit role and once in an embedded role as a contributor to national income. To the degree that dividends flow through to household income in particular, they are a marginal contributor to household saving, other things equal. One has to be careful of this when using the Kalecki equation as a check on either backward explanation or forward projection of corporate profits. There are many moving pieces here, and dividends are one of them, and they can move in more than one place in the equation.

Meanwhile, a third MMT leader, Professor Bill Mitchell, has weighed in (albeit indirectly) on the subject of saving in the same context that was the subject of the long post. (H tip, Ramanan)

See question 1 here:

There, he defines private sector saving as identically zero for the case of a closed, balanced budget economy.

What’s going on here? The equations noted above show consistency across parent national income accounting, the 3 sector financial balance model, and the Kalecki profit equation. There is nothing in those equations to suggest that private sector saving is identically zero in a balanced, closed economy. Under such conditions, S = I is straightforward, and nothing suggests that I is identically zero.

The professor appears to make the following adjustments:

First, he assumes (implicitly or explicitly) that all business profit is distributed to households. In connection with this, he specifies S at one point as household saving rather than private sector saving. But S is private sector saving in the parent national accounting model and therefore must be private sector saving in the 3 sector model that is derived from it.

Second, he assumes that investment constitutes dissaving. That is, investment is treated the same as consumption for purposes of determining residual saving by sector. When one combines that assumption with the preceding assumption that all business profit is distributed to households, it becomes the case that the business sector dissaves in total if gross investment exceeds depreciation.

Moreover, given budget balance and closure assumptions, the business sector dissaves in the exact same amount that the household sector saves. Therefore, from the consolidated private sector perspective, investment dissaving reverses household saving, and saving for the consolidated private sector becomes identically zero. That is the Professor’s effective position on private sector saving, I think.

And the consequence of that assumption is that the private sector must accumulate NFA in order to save, and the other two sectors (most likely the government sector) must deliver NFA to the private sector in order for it to save at all. One might interpret this as it becomes necessary for the assumed balanced, closed economy to be opened up to other sectors, in order for the private sector to save at all, according to the Professor’s characterization of saving.

So that appears to be his view on private sector saving.

However, the accumulation of household saving over time leads to a conflicting conclusion:

First, when businesses pay out all their profit as dividends to households (again, in the balanced, closed economy), they generally pay cash. That increases the book value size of household balance sheets. Assets increase by the cash dividend, and household net worth increases in book value terms. This is a transfer of book value net worth from the equity account of business to the comparable account of households. This is the balance sheet effect of a flow of income from business to households via dividends.

Households then have the option of reinvesting cash received from dividends in new financial claims issued by business – common stock, for example. But such reinvestment happens automatically in any event. Cash received from dividends in the form of bank deposits is a financial claim issued by banks, which are part of the business sector. And since we are assuming a balanced budget, closed economy, there is no avenue whereby that automatic effect can “leak” outside the private sector. Households have the option to change the counterparty for that claim within the private sector (e.g. new stock versus a bank deposit) but they have no option other than to “reinvest” their cash dividend in some private sector claim, even if that decision is only the default choice of the bank deposit that is initially associated with the dividend payment.

The result of all this is that with the assumption of 100 per cent dividend payout of business profit, the business sector issues financial claims and the household sector accumulates them. In other words, the business sector issues NFA and the household sector accumulates the same NFA. Indeed, that latter effect is the change in the household net financial asset position that results from the income that matches the original investment flow net of depreciation for the accounting period (This is due to the Harless type of causality referenced earlier).

Thus, the result is that business has issued NFA financial claims and households hold the same NFA financial claims (claims could be either debt or equity).

Let’s assume a single period model, whereby the income flows described for the period accumulate to a balance sheet position at the end of the period. Consider just the marginal effect of new investment. The result:

Business balance sheet:

Investment Asset / NFA liability


Household balance sheet:

NFA asset / Net worth


Consolidated private sector balance sheet:

Investment Asset / Net worth


That seems OK.

But there is a problem.

The problem is that private sector saving of zero for the period (according to the Professor) has somehow accumulated to a cumulative private sector savings stock equal to a non-zero outstanding investment stock. The net worth account is that accumulation of saving by definition, and it matches the accumulation of investment.

This is a contradiction of required accounting logic. It means that the accounting system as constructed is internally inconsistent. The cause of the contradiction is the assumption that investment is dissaving. This is stock/flow inconsistency. The essence of accounting for net asset value is the accumulation of net worth over time. This is contradicted by treating investment as dissaving for the current period.

Unfortunately, employing such methodology can lead to statements like:

“The sectoral balances show that if the external sector is in balance and the government is able to achieve a fiscal balance, then the private domestic sector must also be in balance. This means that the private domestic sector is spending exactly what they earn and so overall are not saving.”



MMT originally used the term “net saving” in referring to (S – I), or current period private sector saving net of investment. By contrast, in the national accounts context, net saving refers to (gross) saving net of depreciation on outstanding investment stock. But whether saving and investment are tracked at the gross or net level of national accounts, the difference between current period saving and investment is the same. If depreciation is subtracted from gross flows, it must be subtracted from both investment and saving sides to maintain accounting coherence. Accordingly, although duplication of the “net” terminology is unfortunate, it isn’t really a substantive issue in referring to the MMT originated concept and usage of “net saving” as current period saving net of investment (however unevenly that usage is now applied).

The issue discussed in this post concerns the question of the relationship of saving to investment, regardless of which level of national accounts, gross or net, is operative in the analysis of such flows. Therefore, there should not be a substantive issue in distinguishing conceptually between these two different applications of the term “net”.

Thus, the MMT context for use of “net saving” does not directly concern the use of the same term in the national accounts context. The issue for MMT is that of unusual flexibility in the way it uses the terms “saving” and “net saving” in MMT’s own chosen context.

Improvements that reduce such terminological overlap between either MMT or MMR and national accounts are desirable. But the existing intra-MMT usage issue noted here shouldn’t be confused with the separate issue of overlapping terminology between MMT and national accounts usage. I’d say the importance of the first dynamic considerably exceeds that of the second, such as occurs in the example above.

Here are two posts on the subject of related national accounts classification and terminology:



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66 Responses

  1. PFitzSimon says

    One parameter overlooked here is the private sector debt. I believe the S in the national account equation refers to whether the national aggregate debt gets increased or decreased over the one year measurement period. That is , all income not used for consumption including real investment or to pay taxes, can be viewed as paying down existing debt. If S is positive you pay down debt if S is negative you increment the aggregate private sector debt.

  2. jrbarch says

    RE Cullen Roche March 29, 2012 at 1:31 am & Michael Sankowski March 29, 2012 at 6:35 am

    Your antithesis the WSJ has 36M page views per month: Google 1B, Tumblr 15B, WikiM 7B, HuffPo 1B, NYTimes 30M, FB 1 Trillion – how has that changed anything? The internet is a veritable ocean of misinformation and out of date ‘facts’ ( probably just quoted some). Gross might have lost a battle but not the ideological war – I do appreciate the efforts made by MMT/R and others. I don’t think anybodys purpose and inner motivation should be swept aside, nor should they be denigrated simply because of differences in meaning and symbol – most people want something better for more than just themselves. All of this stuff just happens in your heads – I know it impacts on what is happening on the outside, but there is more to a human being than a little bubble of mind, ego and thoughts. When bubble rages against bubble, the casualty is always what is.

    From a simple human perspective I would nominate and prioritise:

    1) contentment
    2) being useful
    3) learning and growing

    as relevant to human existence. As to:

    1) ‘What you are looking for is already inside of you’ – that’s been the message over the millenia;
    2) Everywhere you look are opportunities;
    3) See 1 & 2.

    Granted if there is FE PS and sustainable production then that satisfies one conditional aspect of people’s physical needs – and that’s that. No more, no less. You can feed people fish, but that does not fulfill them as human beings! Neither does FE PS & production/innovation creativity/art …. they are ‘expressions’ ….

    Do you think I would be elected on those ‘political realities’? The human realities are always shoved aside – the world of thoughts mostly serve to eclipse understanding, of WHO WE ARE!! We act like we are little puppets; slaves to FE PS production ect – dependent upon TPTB. This is not true ….

    To me, its always deeper than economics or politics. We are whole beings ….

    Was wondering about that actually: politics is just one aspect of human nature – can’t quite understand why you guys would want to separate yourselves conceptually from it? As above, separations only happen in the mind …. ?? I guess I think MMT/R should be highly politicised (socialised, economised, turned into a musical – crikey, you can make a religion out of it if you like if that helps)!!!

  3. Frank in midtown says

    Technically, the “Savings” rate is the cash left over to be used by the partial reserve banking system. A substantial amount of what modern households do to create networth (SS, IRA’s, 401k’s) are newer than NIP accounting and end up as I and C even though they will be I and C again when distributed.

  4. Ramanan says


    I sorta remember you pointing out issues the first time Keen came up with this definition.

  5. JKH says

    “I guess there’s a self referencing problem with it because he defines aggregate demand in terms of incremental debt in the first place. That definition seems a bit mushy to me anyway. And there’s a further measurement problem in comparing debt increases with velocity increases. And it no doubt varies between short term and long term. So measurement overall is problematic. But it is an interesting sentence at least.”

  6. Ramanan says

    Yes understood.

    Btw, here’s quoting Marc Lavoie – he says the same thing as Krugman (I think) but in a causally correct way

    See my two comments (basically links)

  7. JKH says


    Framing it formally as “net net” would be quite complicated. Although that’s what I was getting at in my additional explanations.

  8. Ramanan says


    I guess you also said it in a comment in that long previous post in reply to Joseph on how it appears in revaluations.

    But imagine writing a post with net net saving and all that. It would have added to confusions because others would have thought you are critiquing that they don’t have depreciation.

    It’s difficult to define everything as per the full definition which Joseph correctly points. Even all of “G” is not counted in GDP etc. But that shouldn’t be an excuse for not making the distinction between saving and saving net of investment which is crucial especially given both make an appearance in the basic MMT model. So if someone wants to say something they have to use the same basic model where gross saving and saving net of depreciation collapse into one another because there is no depreciation.

    The important part is that in spite of the “angst” (in Bill’s opinion), he couldn’t come up with a proper reply and continued the same way as earlier.

  9. JKH says

    So in that sense it was an oversight of explanation and could have been improved on, so Joseph has a point (which I did acknowledge on his own site).

  10. Cullen Roche says

    I don’t see this “error” either, but I might just be a “bootlicker”. Not sure what it is about MMTers that drives their comments into the ground like this, but they could sure use a PR rep.

    Also Joseph, the whole MMR project is about being open minded and discovery. The main issue we have with MMT is that it’s rigid. There is no evolution. It is what it is. The “founders” created the bible of MMT and everyone else just has to accept the word of the lord(s).

    MMR is all about being open minded in this regard. Now, I know the accounting is not open to interpretation in the same way that other elements are, but I would assume that JKH would be open minded about any errors. I know for a fact he has been in the past so I don’t know why this time would be any different. I know from my experience that being wrong is an important part of the learning process. NO ONE HAS THE WORLD OF ECONOMICS TOTALLY FIGURED OUT. We all get things wrong on occasion. Even the very best of us. But you know what we do? We realize the mistake and work from it to form a better foundation. I write about being wrong all the time. It’s expected. But what I don’t do when I’m wrong is get all defensive, insulting and dig my heels in on a position like MMTers do (well, except in a few rare cases where I’ve been slinging MMTers mud back at them! Oops.). I mean, some MMTers have never been wrong about anything in their whole life according to them. They have the whole macro world figured out and they’ve packaged it in this one neat little box and if the world doesn’t accept the box then a storm of insults and attacks follows them….I think we should all try to be a bit more open minded and understanding here and not so quick to attack and insult….

  11. JKH says

    Another excellent post by you Ramanan:

    “This can be confusing because depreciation is a negative for net worth. The reason is that, as I have mentioned before, revaluations need to be done before end of period stocks are calculated. And it is where consumption of fixed capital will make a reappearance – subtracting from net worth due to a reduction in the value of nonfinancial assets.”

    So you could have written my 10:03.

    The fact is that I’m pretty familiar with the idea of depreciation as a source of funds and I could have made life a lot easier at this stage if I’d paid attention to that in the long post, and spent extra time on it. But I’d already cut the length by half. Also, as you say, the MMT treatment rarely mentions the depreciation factor if at all as far as I can tell, so it wasn’t front of mind in drawing out analysis, comparisons, etc.

  12. JKH says

    my 10:03?

  13. JKH says

    P.S. If I were doing an ex post indictment of myself, the best (worst?) I can attempt is that what I probably/may have done in my writing style is conflate the flow of funds properly defined to include gross saving and gross investment, before depreciation, with my own defined supplementary version that nets out depreciation. But as I’ve tried to explain, the reason for doing that is to make a short cut to the reconciliation of balance sheets, including cumulative investment, and cumulative saving or net worth – because the effect of cumulative depreciation is netted out in the stock measure of net worth or equity. Balance sheets do not reflect differential increments of value that match gross saving. So that sort of short cut is consistent with stock/flow reconciliation – whereas the Mitchell treatment of investment as dissaving isn’t.

  14. Ramanan says

    JKH March 30, 2012 at 9:30 am,

    If you don’t mind my interruption:

    I think what Joseph quoted was that he was trying to say that net saving (i.e., net of CFC) is added to net worth rather than gross saving.

    I don’t know if he realizes or not but gross saving is added in full and consumption of fixed capital is subtracted at revaluations which you probably pointed out in the earlier thread.

    Anyway apologies if some misunderstanding is created – I think he may have gotten the idea that you were using net saving from a comment of mine on his blog.

    I also wrote a post on this

  15. Ramanan says

    Joseph L,

    I thought your post and your comments were less important to the whole issue.

    If the basic model being critiqued does not talk of depreciation itself, why critique JKH’s critique which didn’t make that distinction by using either gross saving or net saving at each and every place saving appears?

    Btw, your criticism applies to MMT as well – if you haven’t realized.

    Anyway since you are done, don’t ask for you to respond.

  16. JKH says

    I’m trying to be open.

    I’ve never said I don’t make errors.

    I just don’t see what’s wrong with what you just quoted.

    It’s quite possible that my writing is condensed so that it can be misinterpreted.

    Or it may be wrong. But I don’t see it here yet, based on how I’ve explained it so far.