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 Comments on "Saving, Stock/Flow Consistency, and Kalecki"

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Btw JKH,

This post discusses Kalecki:

and says:

“which says in English, that gross profits after tax (Pn) equals gross investment (I), plus the budget deficit (G – T), plus the export surplus (NX), plus capitalists’ consumption (Cp) minus workers’ saving (Sw).”

which is a strange way of putting it. Can you check?

I am sure of your equation (7) and my equation on FU, not the above.

For, instead of using household plus firms, it uses workers plus capitalists which for a first step is fine but later? (i.e., if capitalists keep guzzling like there is no tomorrow, do they keep making more profits???)


Yes, I believe that’s the/an original version. It’s why I put “modern” in front of the equation in the post here. I really only wanted to touch on Kalecki, to emphasize the robust connection between investment and saving from multiple sources (almost like an anti-sector financial balances approach). But I think the difference between the original and the modern must be a very interesting story in itself. Workers today are vested as quasi capitalists, via their own saving process.


Yes I understand the reason you put it as modern.

Nontheless, I have a feeling the old/non-modern equation is incorrect.



Looks nice.

Btw, I myself had pointed out the net terminology before the last two links in your post popped up – directly highlighting data from FoF but not making an issue out of it!:

Yes, the importance of the first dynamic considerably exceeds the other as per your post.


How about solving for Household saving (adding in wages as a factor) to give some insight if the government spending has found its way largely into wages/household or predominately into corporate profits.

Cullen Roche

This is another tremendous piece of work JKH. Thanks.