Misinterpreting the Sectoral Balances

The government deficit equals the non-government surplus, by definition. Although the relationship is straightforward, it often meets with resistance. It might be worth reflecting on the orthodox interpretation of the identity and the problems with it.

This post is prompted by a comment by Peter D:

This point – that the govt. deficit = non-govt. surplus – seems so self-evident once you think about it that it keeps amazing me how on earth anybody could dispute it. Can you identify what exactly prevents people from appreciating this point? And it is not only laymen. I am not an economist, but the sectoral balances identity G-T=S-I+M-X is supposedly taught in any introductory macroeconomics course, is it not? If so, how could economists fail to understand this? Is there something we are missing?

Others may have different explanations for the resistance to this interpretation of the identity. If so, I’d be interested in reading them. For me, two points spring to mind. One is the way the identities are usually presented in introductory textbooks and presumably lectures. The other is the different causation usually attributed to the variables in the identity by neoclassical economists. As with any identity, the sectoral balances equation shows a relationship that must hold by definition, but says nothing in itself about causation.

Textbook Presentation

In introductory textbooks, the student is typically presented with the identity in one or more of the following alternative forms at different points in the presentation:

          GDP = C + I + G + (X – M)

    I + G + X = S + T + M

            I = S – (G – T) – (X – M)

The first version of the identity stresses the components of demand that contribute to GDP. The second version highlights the equality of actual injections and actual leakages. The third version breaks up the private-sector balance in a way that hints at a neoclassical understanding of causation that should not have survived the contributions of Kalecki and Keynes, nor the Cambridge Capital Controversy.

Economists using the sectoral-balances framework, including MMT proponents, instead express the identity in a more enlightening form that groups the terms into the three sectoral balances:

      (G – T) = (S – I) – (X – M)

I will not be discussing this interpretation further in this post, since it is the usual one dealt with here and at other MMT blogs. For a discussion of the sectoral-balances approach, see this post by Scott Fullwiler and the links provided in it.


Neoclassicals read the third version of the identity as suggesting that private saving S leaves room for private investment to the extent that budget deficits (G – T) don’t crowd it out.

There is additional room, in this view, to the extent the country runs a capital account surplus (which will occur if there is a current account deficit, M > X). Strictly speaking, the current account deficit, CAD, is equal to imports minus exports plus net income payments. I’ll just assume, for simplicity, that CAD = M – X. By identity, the CAD equals the capital account surplus, KAS. This is because, if there is a net leakage out of the economy, there will be net capital inflow, which in this view provides additional room for private investment.

The neoclassical perspective becomes easier to follow if we write the third version of the identity as:

            I = S – BD + KAS

where BD is the budget deficit.


            I = S + BS + KAS

where BS is the budget surplus. This is read by neoclassicals as suggesting that private saving, S, and public “saving”, BS – or “national saving”, S + BS – leave room for private investment.

In the long run, it is then supposed that private investment will adjust to the level of “national saving” through real interest-rate adjustments.

This view of causation has been discredited by the work of Kalecki and Keynes, and also by the capital debates.


Kalecki points out the identity for aggregate profit, P:

            P = Cp + I + (G – T) – Sw + (X – M)

where Cp is capitalist expenditure out of profit and Sw is worker saving out of wages.

To interpret this identity behaviorally, Kalecki points out that capitalists can choose what they spend but not what they earn. The same logic applies to other economic agents. Workers cannot control what they ultimately save, since their saving will depend on income. The government can choose what it spends but not ultimately the tax revenue it receives, since tax revenue depends on income. Lastly, the foreign sector does choose its expenditure (export demand) but not import spending, which depends on domestic income.

The variables in the profit identity that are completely subject to choice within the domestic economy are therefore I and G. The capitalists’ choice of I and the government’s choice of G will together help to determine the level of income, which in turn will determine the endogenous variables, including P.

The profit identity is simply a different version of the same accounting identity discussed previously. To see this, we can rearrange to get:

  P – Cp + Sw = I + (G – T) + (X – M)

Note that (P – Cp) is that part of profit not consumed, i.e. capitalist saving out of profit. So the left-hand side of the identity is capitalist saving out of profit plus worker saving out of wages. In other words, private saving, S. So we have:

            S = I + (G – T) + (X – M)

         => I = S + BS + KAS

However, from Kalecki’s analysis, the appropriate interpretation of causation differs from the neoclassical reasoning. Autonomous private investment I will (along with government expenditure and export demand) determine income, which in turn will determine private saving, tax revenue and imports. Through a multiplier process, the sum of leakages (S + T + M) will adjust to the sum of injections (I + G + X) via income adjustments.

Kalecki’s analysis shows that it does not make sense to interpret private saving or a budget surplus as leaving room for private investment. Provided there is excess capacity, an increase in private investment will generate the necessary leakages. At the same time, budget deficits will not crowd out private investment. Rather than depleting a finite pool of saving, deficit expenditure adds to income, saving and other leakages.

Implications of Kalecki’s Analysis

Importantly, Kalecki’s aggregate analysis revealed that the equality between leakages and injections occurs independently of wages, prices and interest rates. In a two-sector closed economy without government, his work also showed more specifically that the equality of saving and investment has nothing to do with interest rates (see Thinking in a Macro Way). Instead, autonomous changes in investment bring about a multiplied change in income that adjusts saving to investment (in the two-sector model) or leakages to injections (in the open-economy model with government included).

This then raises questions about why interest rates might not play the equilibrating role traditionally supposed by neoclassicals. The insights of Kalecki and Keynes indicate that the initial impact of an increase in private saving is a reduction in consumption demand. This results in a build up of unsold inventories. Firms will tend to cut back production and employment in response. This behavioral response results in a decline in income, defeating the private-sector attempt to increase private saving. At the same time, there is little impetus for firms to increase investment when unsold inventories are building up as a result of weak demand. There is already excess capacity without firms adding even more through additional investment. The much likelier outcome is simply that the attempt to increase private saving will be thwarted by negative income adjustments.

Even though nominal interest rates may fall, reducing the nominal cost of borrowing, expected revenues are also likely to fall due to the weak demand. On top of that, deflationary pressures and expectations of deflation may prevent the nominal interest-rate reduction from translating into lower real interest rates. So there is no guarantee that real interest rates will fall, even if such a real reduction in rates could be relied upon to induce an increase in private investment to match the higher intended private saving. In neoclassical terms, there could be real interest-rate “stickiness”.

Cambridge Capital Controversy

But the problem with neoclassical causation goes deeper than this. Neoclassicals traditionally argued that provided real interest rates did adjust, this would ensure private investment moved to the level sufficient to absorb full-employment saving. Once full employment was established, it would then be impossible for investment to be increased without a corresponding decrease in consumption to allow for extra saving to make room for the investment. In the long run, it was claimed, the real rate of interest would at last come to the fore to equilibrate investment and saving, even though it was conceded that income adjustments played the role identified by Kalecki and Keynes in the short run. Although the initial impact of increased private saving might be a reduction in output and income, the neoclassicals argued that eventually real interest rates would restore full employment at a higher level of saving and investment.

The capital debates demonstrated that this is not the case. There is no monotonic inverse relation between the real rate of interest and private investment. For instance, Paul Samuelson, the leading neoclassical participant in the debate, conceded the following:

The phenomenon of switching back at a very low interest rate to a set of techniques that had seemed viable only at a very high interest rate involves more than esoteric difficulties. It shows that the simple tale told by Jevons, Böhm-Bawerk, Wicksell and other neoclassical writers — alleging that, as the interest rate falls in consequence of abstention from present consumption in favour of future, technology must become in some sense more ’roundabout,’ more ‘mechanized’ and ‘more productive’ — cannot be universally valid. (“A Summing Up”, Quarterly Journal of Economics vol. 80, 1966, p. 568. This quote is reproduced from the link provided above.)

The capital debates made clear that there is no basis for supposing real interest-rate adjustments can be relied upon to adjust investment to a higher level of saving, including in the long run.

MMT Insights

More recently, MMT has demonstrated that in a modern monetary system interest rates are not determined in the way neoclassicals have traditionally supposed. Operationally, the short-term nominal interest rate is an exogenous policy choice. Longer nominal rates could also be set by the central bank if it so desired, but otherwise tend to move in line with shorter rates on the basis of inflationary expectations and arbitrage.

Prices and inflation are also susceptible to strong policy influence through fiscal policy. As the monopoly issuer of its own fiat currency, the government’s spending choices and level of net spending ultimately determine the price level. Exogenous changes in fiscal policy can be made if the price level is rising faster than preferred.

The interest-rate target of the central bank (nominal rate) is therefore a policy variable. The inflation rate is also largely policy determined. Moreover, the central bank can maintain whatever nominal interest-rate target is desired irrespective of fiscal policy and the inflationary implications of fiscal settings. This means that the real rate of interest is also ultimately a policy variable.

One important implication is that budget deficits do not cause higher interest rates, and so cannot be said to crowd out private investment. In fact, to the contrary, budget deficits in isolation would drive the short-term interest rate to zero due to an influx of reserves. If the central bank is intent on targeting a positive nominal rate, it needs to step in to maintain its target.


One reason for different interpretations of the sectoral balances identity is ongoing disagreement over causation. However, the neoclassical view of causation has been discredited by Kalecki, Keynes and the capital debates, and also relies on arguments that do not apply to a modern monetary system.

Kalecki’s behavioral observation that capitalists and governments can choose what they spend but not what they earn or receive in tax revenue makes clear that it is autonomous expenditures (private investment, government expenditure, export demand) that determine the level of saving, tax revenue and import spending.

Kalecki’s work also makes clear that saving and investment in the two-sector model (or leakages and injections in the open-economy model with government) come into equality independently of wage, price and interest-rate adjustments. The connection, rather, is through income changes that adjust leakages to injections.

The insights of Kalecki and Keynes indicate that a spontaneous increase in private saving results in a build up of unsold inventories and cutbacks in production and income that are likely to thwart the additional intended private saving. Falling demand and income are not conducive to a strengthening in private investment. In this context, falling nominal interest rates may not be sufficient to induce increased expenditure. If prices are also falling, it is not even clear that the real rate of interest will fall.

However, even if the real rate of interest did fall, the capital debates have made clear that there is no valid basis for supposing that this will induce an increase in investment sufficient to absorb the higher intended saving.

Finally, MMT shows that it would be operationally impossible for budget deficits to cause financial crowding out of private investment. When there is deficit expenditure, the central bank has to step in to prevent the short-term rate falling to zero whenever its interest-rate target is positive.

61 thoughts on “Misinterpreting the Sectoral Balances

  1. Another of Hudson’s points: As the rate of profit falls, there is a shift from productive investment to rent-seeking, which has been going on in the US for some time, as shown by the expansion of the financial sector’s contribution to GDP and the decline of the productive sector.

  2. Interesting. The Marxist economist Andrew Kliman makes a similar argument on the basis of Marx’s ‘law of the tendential fall in the rate of profit’ (LTFRP). I discussed this in relation to the lead up to the crisis in an early post, and related it to the MMT position focused on effective demand and informed by the sectoral balances approach :

    Marx’s theory, and Kliman’s study, suggest that the increasing tendency toward speculative rather than productive investment is due to the drying up of profitable productive investments. The result has been relatively weak growth in GDP (compared with the immediate post-war period), and a consequent recourse to more and more speculation as financial capital seeks higher returns, creating a level of private debt that is unsustainable in relation to real-value creation (or GDP growth).

    A related post further touches on interconnections between profitability and effective demand.

  3. This is a reason that Michael Hudson successfully called the approaching crisis.

    From Wikipedia_Michael Hudson

    “Hudson’s April 2006 Harper’s cover story, “The $4.7 Trillion Pyramid: Why Social Security Won’t Be Enough to Save Wall Street,” helped defeat the Bush administration’s attempt to privatize Social Security by showing its aim of steering wage withholding into the stock market to reflate stock market prices for the benefit of insiders and speculators – and to sell to the pension funds. His May 2006Harper’s cover story, “The New Road to Serfdom: An illustrated guide to the coming real estate collapse,” was the first major national article forecasting – in precise chart form – the bursting of the real estate bubble and its consequences for homeowners and state and local government solvency.[4]”

  4. Ok, sir. Please explain it to me as if you were explaining things to retarded folk.
    All transactions within the private sector net to 0? Correct? If so, do all transactions within the private sector and foreign sector combined net to 0?
    If this expression holds true (S-I)+(G-T)+(X-M)=0, then it would have to, right?
    Bear in mind, I suck at math.
    Since the government deficit equals the net surplus of the nongovernment sector in a given fiscal year, then vice-versa must also be true. The government surplus equaling the net deficit of the nongovernment sector. Correct?
    If for instance, I have a budget surplus of 100 dollars, a foreign surplus of 120 dollars and I don’t know the private sector balance (X). Then, -100=X-(120), X=100-120, then, X=(-20). The private sector is shouldering the deficit. Correct?
    Then why is Randall Wray NOT identifying this problem in his brief analysis of Argentina’s situation. Here’s the article: http://www.economonitor.com/lrwray/2012/10/09/mmt-argentina-and-views-on-inflation/
    Why isn’t he recognizing the Argentinian’s government surplus as the problem to employment? Unemployment is, after all, a macroeconomic and monetary phenomenon – because taxation creates unemployment of money paying jobs. And public spending employs the unemployed originally created by taxation. Furthermore, why is Randy ignoring in the article, the scarcity of pesos in the economy. Fin fine fine fine fine, with foreign currency obtained from a positive trade balance one can slash off private or public debt owed in foreign currency. But the fact remains, that the government surplus equals the net deficit of the nongovernment sector. Argentinian households can’t net save in pesos, if the government is running the wrong vertical transactions over time (namely, running surpluses instead of deficits).
    Please, sir. Don’t ignore my comment. Thank you.

  5. Hi Serban. The position of any individual sector will be offset by the combined positions of all other sectors. So, for example, the surplus of the domestic private sector will be offset by the combined position of the government and external sectors. The same is true of any smaller sub-sector. That is, its position will be offset by the combined positions of all other sub-sectors in the economy.

    In the case of Argentina, Randall Wray mentions in the linked post that for much of the period since going off the currency board, the country was running a current account surplus. This made it possible for the domestic private sector to be in surplus even though the government was running budget surpluses. This, in fact, occurred because the current account surplus was larger than the government surpluses.

    Rearranging the identity:

    (S – I) = (G – T) + (X – M)

    Or in words:

    Domestic Private Sector Surplus = Government Deficit + Net Exports

    So, there are two sources for a domestic private sector surplus: government deficits or net exports (roughly equal to current account surpluses). Note the following passage in Wray’s post:

    What about deficits and debts? The current account was consistently in deficit under the Neoliberals—running around $10 billion annually. After the crisis it was in surplus, reaching as high as $10 billion before the Global meltdown; by 2011 it had fallen to zero. The current account surpluses allowed the country to accumulate significant international reserves—reaching over $50 billion by 2010 (falling thereafter—a point to be briefly discussed later). Government has been running large primary fiscal surpluses—on the order of 3% of GDP. … Household indebtedness is an extremely low 8.4% of GDP (versus 39% in Chile and 87% in the US). That is not too surprising: with a current account surplus larger than the budget surplus the private sector has been running a surplus that allowed it to pay off debt and accumulate savings

    If you haven’t read it already, a more introductory post on the sectoral balances is Budget Deficits and Net Private Saving.

  6. Thank you for the speedy reply, sir. However, I am still confused. A net exporter of goods means net savings in foreign currency, correct? So, if (S-I)=(G-T)+(X-M), then using the figures in my previous example: (S-I)= (-100) + 120. (S-I)=20. Knowing each balance of the 3 sectors, all 3 of them must balance out to 0, according to this equation (S-I)+(G-T)+(X-M)=0
    But it doesn’t, does it? A -100 (budget surplus) plus 20 (private sector surplus) plus 120 (foreign surplus) does not net to 0. The only way it can respect the sectoral balance equation, is if the government surplus equals the net deficit of the nongovernment sector. Meaning, that with a government surplus (-100) and a foreign surplus of (120), the private sector has to be in deficit (-20). -120 + 120 nets to 0.
    Again, if the trade balance surplus is larger than the budget surplus, how on earth can the private sector be in surplus? If this is the case, then the 3 sectors combined do not net to 0.

  7. Follow up. A friend of mine resolved my confusion on Wray’s statement. I didn’t know that positive net exports meant a deficit for the foreign sector. Damn math and conflicting semantics. Thank you for your time, sir.

  8. First, who cares about Net Financial Assets? Why would people want more Treasury securities when that money could be put to work elsewhere? If business has no use for these savings, then economically speaking, they shouldn’t exist, or at least shouldn’t earn a return.

    Second, this analysis neglects to consider that its definition of a budget deficit/surplus differs considerably from the government’s definition. Surplus revenue isn’t destroyed by the government; rather, it is returned to the economy in the form of debt repayment.

  9. @myth buster
    Irrespective of government rhetoric, surplus revenue is indeed destroyed, and not “returned to the economy”, (whatever that might mean). While the US treasury sells $1 of US debt (i.e. US treasury bills) for every $1 in federal budget deficits, no such reverse operation occurs for budget surpluses.

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