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 spending 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 often express the identity in a form that groups the terms into the three sectoral balances:

      (T – G) + (S – I) + (M – X) = 0

I will not discuss this form further in the present 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 often read the third version of the identity as suggesting that private saving S encourages private investment to the extent that budget deficits (G – T) don’t crowd it out.

There is additional room for private investment, 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 domestic economy to imports, there will be net capital inflow, which in this view enables more 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 and Keynes

Kalecki points out the identity for aggregate profit, P:

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

where Cp is capitalist expenditure and Sw is worker saving.

To interpret this identity behaviorally, Kalecki observes 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 the amount of income generated in the economy. 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 one. Autonomous private investment I will (along with government expenditure and export demand) create new income, which will at the same time create private saving, tax revenue and imports.

Keynes makes a similar argument. In accordance with the marginal propensity to consume, some of the new income created by the injections will go toward further consumption as part of a multiplier process. The sum of leakages (S + T + M) will equal the sum of injections (I + G + X) at every stage of this multiplier process. Production will keep expanding until the sum of leakages (equal to injections) reaches a proportion of income that is consistent with the propensities to tax, save and import.

The analyses of Kalecki and Keynes suggest that it does not make sense to interpret private saving or a budget surplus as encouraging private investment. Provided there is excess capacity, an increase in private investment will add to income and create an equivalent amount of leakage from the circular flow of income. Similarly, inside capacity limits, government deficits will not crowd out private investment. Rather than depleting a finite pool of saving, deficit expenditure will add to income, saving and other leakages.

Implications of Kaleckian and Keynesian Analyses

Importantly, the macroeconomic explanations of Kalecki and Keynes suggest that the reconciliation of desired leakages and injections occurs independently of wages, prices and interest rates. In a two-sector closed economy without government, this work also showed more specifically that the reconciliation of saving and investment behavior has nothing to do with interest rates (see Thinking in a Macro Way). Instead, autonomous changes in investment create equivalent changes in saving, with the subsequent multiplier effects adjusting income until this higher level of saving is made consistent with saving desires of households. A similar argument concerning injections and leakages in general applies to an open economy.

It might still be wondered whether interest rates might not play the equilibrating role traditionally supposed by neoclassicals in situations where there is a change in saving behavior (such as a change in the marginal propensity to save). Consider a spontaneous attempt by households to lift their level of saving. The insights of Kalecki and Keynes indicate that the initial impact of this will be a reduction in consumption demand. This will result in a build up of unsold inventories. Firms will tend to cut back production and employment in response. This behavioral response will result in a decline in income, largely defeating the private-sector attempt to increase private saving. In the simplest two-sector model, private saving will end up being a higher proportion of a lower income, with overall saving left unchanged. In these circumstances there will be 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 it is likely that the central bank will lower nominal interest rates and so reduce 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 reduction 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, on logical grounds, 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.

Post Keynesian and MMT Insights

More recently, Post Keynesian Economics (PKE) and Modern Monetary Theory (MMT) have 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 variable. 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 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 fiscal deficits do not in themselves cause higher interest rates, and so cannot be said financially to crowd out private investment. In fact, to the contrary, fiscal 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.


The reason for differing 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.

The Kaleckian behavioral observation that economic actors can choose what they spend but not what they receive in income (or, in the case of government, extinguish in taxes) suggests that it is autonomous expenditures (private investment, government expenditure, export demand) that determine the level of saving, tax revenue and import spending.

The work of Kalecki and Keynes suggests that household saving intentions and firms’ investment plans in the two-sector model (or desired leakages and injections in the open-economy model with government) are reconciled independently of wage, price and interest-rate adjustments. Instead, the desires of the various actors are reconciled through income adjustments driven by autonomous expenditures.

Further, a spontaneous increase in private saving will result 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 government 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. Good topic. Enjoyed the part on the Kaleckian model.

    I’ve always thought the stubborn resilience of the “national saving” concept, especially on the part of financial economists, was somehow related to the fact that the following variation of the identity is often used (the right-hand side of the identity being what is refered to as “national savings”):

    Investment = Private Saving + Government Surplus + Foreign Saving

    Notice also that this variation predisposes the reader to think positively of the government surplus.

  2. It’s always struck me as fairly obvious that this idea that ‘investment’ magically appears out of nowhere is complete nonsense. The debates today elsewhere seem to be convinced that there is a huge dam of investment waiting to happen and all they have to do is provide the right amount of money via ‘green banks’ or other such nonsense.

    As anybody who runs a business knows you simply don’t invest in anything unless you can see a fat profit at the end of it. Find a need and fill it, etc, etc. But the fat profit has to come first – that is the driver.

    I found it intensely amusing that the UK government is getting shirty about the ‘abuse’ of Feed-in-Tariffs for the production of green energy. Apparently some enterprising firms have started leasing fields to put solar panels in. Now the government department concerned is complaining about running out of money and they are thinking of changing the legislation to ban this investment.

    What hasn’t clicked with them is *why* people were investing – the big fat profit that you get from FiTs.

    Macro still has to be consistent with the micro impulses.

  3. Thanks, Peter. I will be re-reading this several times to make sure I understand it as best I can. I believe knowing where objections to our reasoning are coming from will allow us to better argue our point (and even contribute to our own better understanding.)
    One question. You say: Longer nominal rates could also be set by the central bank if it so desired and “the central bank can maintain whatever nominal interest-rate target is desired irrespective of fiscal policy and the inflationary implications of fiscal settings” I’ve seen this claim in other MMT blogs and while I understand why it is true for short term interest rates, I am not entirely sure why this would be the case for long term rates. Are we talking about adjusting supply of long term debt to hit any target rate?

  4. Peter D: Yes, your interpretation is correct regarding the yield curve. I don’t think anyone is suggesting such a policy is necessary or desirable, since from an MMT perspective the impact of interest rates on aggregate demand is uncertain and weak in any case. The main point is that interest rates are ultimately at the discretion of policymakers, and not forced on them by markets.

  5. Say the external sector is in balance, or we’re looking at a closed economy.

    Then investment = private savings + budget surplus.

    But if the nongovernment and government sector balance — one sector’s surplus is the other’s deficit. Then wouldn’t private savings + budget surplus equal zero? Wouldn’t investment always be zero?


  6. Hi, g. Welcome.

    In a closed economy, the non-government sector contains just the private sector (businesses and households). By definition, the budget deficit will equal net private saving:

    (G – T) = (S – I)

    or as you wrote it:

    I = S + (T – G)

    If the budget is balanced, then S = I, but S and I don’t need to be zero. What will be zero is the private-sector balance, (S – I).

  7. Interesting stuff, but I am still not grasping it all. I wish “I” and “S” were defined. “I” in my mind, real investment consists of the creation of fixed capital and inventory, while nominal investment is the prices we assign to these molecules and services. Is that more or less correct?

    I take it the identity explains an ex-post condition?

    The saving/excess inventory relationship is one where initially workers are paid for producing things. They can save that income in period A. In period B, unless they spend that income to purchase what they created, then the result is excess inventory?

    So S=I only in a closed economy with no gov?

    Why is there no “C” in “I + G + X = S + T + M” ?

    Lastly (related to another one of your posts), why is govt debt needed to reduce total non-govt debt? Perhaps it is more accurate to say govt debt is needed to reduce non-govt debt without non-govt defaults?


  8. Hi, Diatom. Welcome. Yes, investment refers to gross private investment demand and includes purchases of plant and machinery as well as inventories. Saving is that part of income, Y, not consumed, so S = Y – C. And, yes, the accounting identities are ex post. They do not necessarily imply equilibrium. For example, if firms sell less than they expect, there will be an unanticipated build up in inventories, which counts as part of I, even though it wasn’t part of planned investment.

    In a closed economy with no government, S = I, as you correctly write.

    In the open-economy framework with government, the injections equals leakages identity is arrived at by rearranging the following identity:

    GDP = C + I + G + X – M

    Here, GDP = Y + T, where Y is disposable (after tax) income and T is tax revenue. So we have:

    Y + T = C + I + G + X – M

    => Y – C + T + M = I + G + X

    Notice that Y – C = S, so that leaves S + T + M = I + G + X.

    Regarding your final question, if we rearrange the leakages equals injections identity, we have:

    (G – T) = (S – I) – (X – M)

    The LHS is the budget deficit. The RHS is the non-government surplus. It includes net private saving and foreign saving. Whenever there is a budget deficit, there will be a corresponding non-government surplus. Government debt is the accumulation of past budget deficits. Non-government net financial wealth (accumulated savings) is the mirror image of government debt.

    If the government runs a budget surplus, the non-government has to run down net financial wealth to the extent that tax obligations exceed income received from government spending. If the government persists with surpluses in a trade-deficit economy, it will increasingly push the private sector (households and firms) into running down past savings then going increasingly into debt.

  9. Thanks for the link to billy blog’s post on Kalecki. Also, regarding the capital controversy, did the realisation that interest rate adjustment wasn’t all that effective contribute somewhat to the rise of monetarism shortly thereafter? If not, did the end of gold convertability have anything to do with the prominence of money supply theories?

    BTW, brillant blog. Great while listening to good music and drinking a cold one.

  10. circuit: Thanks. Glad you’re enjoying the blog.

    From my understanding, the rise of monetarism had more to do with the empirical observation of a strong correlation between the broader money supply (currency plus private demand deposits) and prices, in combination with a political opening due to the stagflation of the 1970s which brought into question the neoclassical synthesis. The monetarists argued that causation runs from exogenous money to prices, and so inflation could be controlled through control of the money supply. When targeting of monetary aggregates proved difficult or impossible, there was a move to interest-rate targeting.

    I may be mistaken, but I don’t think the capital debates had much to do with the changes in perspective and policy approaches of the orthodoxy. Mainly I think the implications of the capital debates were ignored or avoided. For example, “single commodity” models don’t face the problems that arise with heterogeneous capital. Some economists chose to use these and test them empirically.

    I’m sure there are others who drop in here from time to time who know a lot more about the debates of that period.

  11. Peter, that answered all my questions but the last one well. What I was trying to get at with the last one is private debt can be run up without the government’s help (other than supplying reserves). However private sector debt can’t ever be paid down unless govt runs deficits or there are defaults. T or F?

    For example, when bank loans are repaid deposits are destroyed. This makes the remaining deposits more scarce and the likelihood of borrowers getting their hands on that money to repay debt less likely. Private debt makes the economy more fragile. The only way for the non-gov sector to deleverage (without defaulting) is for the govt to spend more than income which it is far better suited to do than the non-govt sector thanks to the central bank. Am I thinking clearly?

  12. Diatom: I hope you don’t mind if I use a simplified framework. Hopefully it will make things clearer.

    Initially, suppose there is just a two-sector closed economy with no government. S = I by definition, so there can be no net private saving. However, that is in aggregate. There could still be debt problems for individuals. It’s just that in aggregate the entire private sector (whole economy in this simple case) is neither in deficit nor surplus.

    Now, suppose there is a closed economy with government. So (G – T) = (S – I) by definition.

    If the government’s budget is balanced, net private saving will be zero. Once again, there can be some individuals in debt stress even though overall the private sector is neither in deficit nor surplus.

    If the government runs a budget surplus, the private sector will be in deficit. It is likely that more individuals will get into debt stress. The bigger the surplus, the more likely it is that some individuals will get into debt stress.

    All this is “other factors remaining equal”.

    But there are other factors as well, which may not be equal. For instance, the degree of income inequality is likely to influence the extent to which people get themselves into debt. Institutional and regulatory factors can also influence how many people get too far into debt. And so on.

    So the likelihood of debt problems rises the longer the government runs surpluses.

    In terms of paying off private debt, budget deficits will make it more likely that more people can manage their debt levels. For example, many people can pay their mortgages as long as they have a job, but if they become unemployed, they are stuck. The government can use deficit expenditure to maintain higher employment levels, and this reduces the number of people who will find themselves in this situation.

    In terms of your second paragraph, banks are not constrained in their lending by deposits or reserves. They are constrained by the demand for loans from credit-worthy borrowers and capital adequacy. Loans create deposits. Banks will lend if the borrower appears to have a good chance of paying back the loan. That will be more likely if economic activity is strong. Household members will then be less likely to lose their jobs and firms will be more likely to turn a sufficient profit on their operations. This makes them better credit risks.

    The latter part of your second paragraph makes sense. If there is a high level of debt stress in the private sector, there are only really two options: an orderly write down of debts; or budget deficits to enable net private saving and the repayment of debts.

  13. So the logic behind (S-I) to represent the private sector surplus is because in an open economy with a govt, both X and G can feed S? Then you subtract I because it represents what is owed to private savers?

    Something so simple on the surface is complex, or I am just slow, probably a both. 🙂 Thanks for your help.

  14. Thanks very much for the response and additional info. I’m always interested in learning about developments in economic thought from the 60s and 70s.

  15. Hmm no response, I wonder if I’ve gone passed my too (two?) stoopid question limit.

    I’ve been trying to understand this equation but still am confused-
    (S-I)=0. In a closed economy with no govt. So in laymens terms businesses invest $100 and this is what is saved by the private sector. Since business is down $100 and recipients of biz spending are up $100 there is no new dollar saving.

    Then substituting (Y-C) for S
    (Y-C)-I=0. So in this story businesses invest $100 then what?

    Finally why does S=I. I googled around for it and there is no satisfying answers. Whatever businesses produce is saved?

    Hope you’ll forgive my dumb questions, I’m not an economist.

  16. It just hit me,
    Businesses invest $100, consumers from income can buy up to $100. So Y can be $200. Consumption will be $100 and investment $100. So ($200-$100)-$100=0.
    Did I get it??

  17. Y is income, C is consumption, and S is savings. What is not consumed (spent) out of income is saved (left over after all spending). The answer to “why” is that this is a definition. Don’t get too carried away with the terminology. It is just used to build a simple conceptual model of what happens in an economy.

    Here is a simple way to think about this. A farmer grows corn. The harvest (income) is divided into feed corn (consumption) and seed corn (savings). The seed corn (savings) are planted (invested) next spring in a new harvest (income prime).

  18. Sorry for the delay in responding, Diatom. You seem to have figured out the answers to some of your questions. I will do a post on the basic identities at some point soon.

    Once you realize that S – I = Y – (C + I), you can see that net private saving is income minus private spending (consumption and investment) of the private sector.

    In the simple two-sector closed model with no government, actual S equals actual I by definition. The reason is that an unanticipated change in firms’ unsold stocks of inventories is counted as unplanned investment, and so is part of I.

    In theory, we can say investment I is equal to planned investment Ip plus unplanned investment Iu. If planned demand for goods and services equals planned supply of goods and services, there will be no unanticipated change in unsold inventory stocks, so Iu = 0 and I = Ip = S. But if planned demand for goods and services is less than planned supply, firms unsold inventories will build up more than expected, causing Iu > 0. In that case, Ip < I = S. That is, I = S, but it is not an equilibrium situation. Equilibrium requires Iu = 0. This probably still won't be clear. I'll devote a post to the topic in the very near future. Hopefully, along with any follow-up questions, that will clear things up.

  19. “Savings is income not spent by consuming or investing”
    Seems I still am not getting it. In our closed economy model with no govt there can be no net savings. But let’s say a business invests $100, consumers purchase $100 from that business so Y is $200, S is 100 and I is 100. S=I and S>0. So what gives?

    I thought I had it right in my previous comment, the business lost $100 during investment and gained $100 when consumption occured. Thus no change in S. Maybe what I am doing is assuming $100 exists at the start of this thought experiment, and it doesn’t change at the end.

  20. I guess my question is, is Y-C= S or Y-(C+I)=S? It can’t be both.

    Here is my simulation:
    Business invest $20. This gets paid to workers.
    Workers consume $100. This gets paid to business.
    So I=20, C=100 Y=120
    Businesses have +$80 Households have -$80 combined they have no additional dollars.
    So Y(120)-C(100)=20=S=I ? This makes sense because S=I but not equal to zero Or
    Y(120)-(C(100)+I(20))=0=S. This makes sense because S=0 but S not equal to I.

    I feel like I’m missing one or two pieces in this puzzle, but annoyingly close.

  21. Diatom: Actual saving, S, equals actual investment:

    S = I = Y – C.

    Net private saving is actual saving minus actual investment:

    S – I = Y – (C + I).

    Buying a stock is a form of saving.

  22. Wonderful, I think I see the puzzle at last. So S can be positive with no govt and no foreign sector, but net private saving can’t. Correct?

    “Saving is that part of income, Y, not consumed, so S = Y – C”

    “Net private saving is that part of income, Y, that is not spent either by consuming, C, or investing, I.”

  23. Peter, what happens to the sectoral balances identity when the government deficit is in excess of the private sectors desire to save? Does it mean that Su — unplanned savings part if S — goes up? In other words, the public holds more “money” (NFAs) than it desires – which in turn causes inflation in the next adjustment period?

  24. Peter D: The non-government will attempt to reduce its net saving; i.e. spend more and save less. If the additional expenditure cannot be absorbed at current prices, there will be inflation.

    For example, if your scenario involves full-capacity output, the non-government attempt to reduce net saving will be inflationary. The government should cut back its deficit spending.

  25. Yes, I was just wondering what happens in terms of the accounting identity G-T=S-I (ignoring ROW for simplicity), which must hold in any given period. I guess once the private sectors tries to get rid of Su (unplanned savings) and inflation goes up, then next period the automatic stabilizers such as inflation-adjusted transfer payments kick in and G grows again, feeding the vicious cycle.

  26. The identities are usually expressed in price-deflated terms. If there is inflation, net saving in price-deflated terms is less than in nominal terms (same for the budget deficit).

  27. I’m confused now. Shouldn’t the identity hold regardless whether you adjust for inflation or not? You’ll just discount both sides. My question is this: we are justifying the MMT view that govt deficits are non-govt surpluses. The identity lends basis and justification of the view that the govt needs to supply enough NFAs for private sectors desires. But one could ask: the identity holds true always, so, what does it tell us when G-T is larger than desired S-I ? My guess would be that S grows in line with G-T and this creates the disequilibrium where the private sector tries to get rid of the unplanned part of S which causes inflation in the next period.

  28. There is only equilibrium when planned net saving equals the budget deficit. Otherwise, even though the identity holds, there is impetus for behavioral change (such as you describe).

    It is similar in the two-sector closed model. S = I by definition, but equilibrium requires Sp = Ip.

    Similarly, Y = C + I by definition, but equilibrium requires Y = Cp + Ip. Planned aggregate expenditure must equal output for there to be equilibrium.

    None of this changes the point that S = I by definition. Saving, whether planned or unplanned, still represents income not spent, and it is only possible to the extent there is actual investment. Investment, whether planned or unplanned, still represents output not consumed in the current period, and whatever form it takes, will always generate an equal amount of actual saving through income adjustments.

    Similarly, G – T = S – I by definition. Net saving, whether planned or unplanned, still represents income not spent by the non-government in the current period (it equals Y – (C + I)), and is only possible to the extent that the government deficit spends.

    I’ve attempted to elaborate further in a new post.

  29. Two questions

    In a two sector closed economy where S=I, what happens when there is saving in non-productive, value storing assets such as vacant land, gold etc. Would this still be classified as I or C?

    What impact does Quantitative Easing have. In the UK for instance, £200bn of money was created to buy government debt? Because in the year it was created, the govt deficit was around £150bn. How would the equation account for this?

  30. Forget all the econ equations if we want to sell MMT to the public skip the sectorial balances stuff and go straight up binary on folks! govt asset = govt liability, issuer savings = user debt, spending vs. saving, People think binary. This MMT stuff is so basic that it’s a crime that it doesn’t have more widespread exposure. Put the dots so ridiculously close to one another that no one gets confused.


    you know what your conclusion will be? The fundamental nature of debt for an issuer is different than that of a user. One paradigm of physics does not exist in the physical world – newtonian vs quantum – just as one paradigm of debt does not exist in the monetary world. Debt for a currency user is a burden. Debt for a currency issuer is a convenience to currency users who chose to save instead of spend in the marketplace.

    hey did i just blow your mind? yo i’m just gettin started on the MMT stuff


  31. Peter,

    I have a question that I have been pondering for a while and it has to do with the creation of surplus value. I have discussed this before, in your blog, with Ramanan.

    Refer to this figure:

    Let’s suppose a simple economy with no government and no foreign sector.

    At point E1 all “productive factors” are fully employed. When all factors are employed, net output is Y1, aggregate demand is D1 and price level is P1.

    For some reason, households decide to save more. Therefore, autonomous demand falls, from the level represented by D1, to that represented by D2.

    At price level P1 and output level Y1, supply exceeds demand.

    If, on one hand, the adjustment occurred only through price falls (from P1 to P2), output level would not change (it remains at Y1). But if output does not change, then there is no reason for factors to be not fully used: there is no factor unemployment (that is, both capital and labour).

    If, at the other hand, adjustment occurred only through output adjustment (from Y1 to Y2), the price level would not change (it remains at P1). As output falls, there is factor unemployment.

    In practice, a combination of the two things happen and the equilibrium moves from E1 towards the south-west, along the red-thick continuous line. This means that both price level and net output falls, and, obviously, there is factors unemployment, too.

    As, by hypothesis, there is no government or foreign sector, there cannot be any exogenous injection.

    Further, as savings fall because income also fell, this means the economy is stuck in this new factors-unemployment equilibrium.

    If households decided to further increase their savings, expecting to invest, the process would continue and the economy would fall into a deeper recession.

    However, the gods intervene and inject enough money to the economy to restore full employment and nothing more. As there is factors unemployment, net output could increase without significant price increase: say the equilibrium could move due east, to a point between E1 and E3. Making allowance for human fallibility, let’s include the possibility that the price level returned to P1 (and equilibrium to E1).

    Notice that net output increases without inflation because there is factors unemployment, the only thing missing is money.

    However, when net output returns to Y1 there is no more factors unemployment. Any further money injection would increase demand, say to D3. At that point, there is already full factor employment and no net output increase is possible: any adjustment has to be through a price level increase (to P3). It’s like the aggregate supply curve was vertical from net output level Y1.

    Notice that, unlike the situation where the availability of unemployed factors allows for an increase in net output without or with limited price level increase, once factors are fully employed an increase of money only leads to inflation.

    I am not sure if my graphical representation would fit the MMT picture, but at least as a pure verbal exposition, it seems to me it is compatible with MMT.

    The question I’d like to ask is this: assuming the gods were willing to inject additional money (or banks existed to create credit) how can net output increase in this simple economy once we reach full factor employment? Wouldn’t this equilibrium, without any other external factor, preclude the possibility of growth?

  32. Magpie, further growth of output beyond the (current) full-employment level is made possible chiefly by technical innovation. As you know, for Marx and Keynes influenced economists, strong demand and high employment create a strong impetus toward technical innovation.

    There are other possibilities. A change in anything that is categorized as a supply-side factor can shift the supply curve. One example would be an increase in population.

    Most heterodox economists would probably object to an AS-AD type model, especially at the macro level. For instance, the aggregate-supply schedule being steeply upward sloping at less than full employment reflects a neoclassical assumption of diminishing marginal returns. The basis for a downward-sloping (rather than vertical or ill defined) aggregate-demand schedule is also weak, especially in a closed economy without government, in light of the capital debates and aggregation problems.

  33. magpie, Neil Wilson has dealt with this pretty extensively in various comments and posts. The natural tendency, so to speak, is for markets to respond to demand signals by expanding. When the limits of present resources are reached, there is a strong incentive to innovate in order to beat the next competitor to market with additional, perhaps superior supply. So innovation is not only a matter or more but also of better. That takes the game to a whole new level. Companies are continually trying to stay ahead of the game by innovating because as soon as they do, they know the game of catch up begins and some of those competitors are thinking leapfrogging. So demand is really everything in a capitalistic economy that can only sustain itself by growing through innovation and productivity increases, in that survival is based on progress. Most economists don’t seem to get this dynamic with their static models.

  34. Peter,

    “For instance, the aggregate-supply schedule being steeply upward sloping at less than full employment reflects a neoclassical assumption of diminishing marginal returns.”

    That’s precisely what I am doing. I’m trying to think like a neoclassical.

    When we are on E1 all factors are fully employed and they are rewarded in proportion to their contributions; capital, too. This is what the neoclassical theory says.

    Leaving aside technical change (which is exogenous and essentially unpredictable in neoclassical economy) or population growth (which is a long run phenomenon, as Malthus understood: even if they are sent to the mines when they are 10yo, workers still take 10 years to join the labour force) and considering that (i) capital is already rewarded in proportion to its current contribution and (ii) that additional savings could throw us back into recession, where does growth come from in the neoclassical economy?

    Forget what Marx said. Put on a neoclassical economist’s hat and try to answer without using the word “surplus value”.

    I couldn’t. But maybe it’s just me and I am unimaginative.

  35. @Tom Hickey.

    I agree with pretty much everything you said. But my agreement is a poor achievement: I already believed that on an intuitive way.

    I know neoclassical economics is full of contradictions. I live those contradictions every day. But it’s not enough that I know; I need to explain them and put my finger and say: this is crap because of this and this.

    What I am trying to do is to critique neoclassical economics. I know this will sound unbearably presumptuous of me and it probably is: but Marx did just that. That’s why the subtitle of Das Kapital was a critique of political economy.

    He studied what at his time was the state of the art in economic theory and then took great pleasure putting his fingers in the open wounds.

    Prof. Mitchell, for one, is a great help in this sense, but not even him is enough. I want more: I want to go myself and tell those people, in my own words, that they don’t fool me.

    I may be poor, I may not have a good job, I may be only a fucking wog, and I will die all but forgotten, but I am better than them because I know more than them. That’s why I took the Big Challenge.

    It is not those big people who are the Atlases carrying the weight of the world in their shoulders, it is the little, shitty, poor, ignored people.

  36. @magpie

    Marx criticized the political economy of his time, which included economic rent. In fact, economic rent was front and center. Marx amplified that understanding.

    The neoclassical model not only assumes there is no economic rent, but also it depends on there not being any economic rent. That assumption is the major reason for its inadequacy in my view, since, as Smith, Ricardo, and Marx observed, economic rent is the name of the game. As result it is just advocacy for neoliberalism, which is based on rent-seeking and rent extraction, in short parasitism.

    This is what the public needs to come to understand and appreciate the implications of. Inequality in the distribution of wealth and power is not the result of rewarding merit but rather of rent-seeking and rent extraction, in other words, socio-economic parasitism that is largely traceable to duplicity and corruption.

  37. Magpie, sorry, I didn’t connect your question with your challenge to read neoclassical stuff. Yes, as you say, in earlier neoclassical models, growth is exogenous. In the long run, a higher saving rate, reflecting exogenously given intertemporal preferences, will cause a higher rate of growth by inducing greater investment (more rapid capital accumulation and/or technical innovation) through the price mechanism, most notably the movement of the market-determined rate of interest to a new, lower natural rate.

    However, from the 1980s onwards, there have also been neoclassical endogenous growth models. These usually focus on investment in human capital or innovation, and generally assume some degree of monopoly power.

    I may as well also address how a temporary short-run situation of unemployment, caused by an increase in the rate of saving, is automatically resolved through the price mechanism in neoclassical theory. The increase in the rate of saving shifts AD down and to the left, causing it to intersect an upward-sloping short-run aggregate-supply (SRAS) schedule at a level of output below full employment.

    If money wages and prices are flexible, a spontaneous adjustment to full employment takes place through a fall in money wages, which results in a rightward/downward shift of SRAS until it intersects the new, lower AD at the full-employment level of output, designated by the vertical long-run aggregate-supply (LRAS) schedule. The price level will be lower than before convergence.

    If money wages are downwardly sticky, the situation is resolved through monetary or fiscal stimulus that shifts AD up and to the right until full employment is restored. The effect of this is to reduce the real wage, since money wages are taken as given along a particular SRAS schedule and the price level is higher once full employment is restored.

    Lastly, while on neoclassical theory, you are correct to wonder about profit. In full-employment equilibrium, where each factor is remunerated in accordance with its marginal productivity, economic profit will be zero, usually interpreted to mean that profit is equal to the rate of interest. In the short run, perfectly competitive firms can receive positive economic profit, but this is competed away once full-employment equilibrium is established.

  38. “Magpie, sorry, I didn’t connect your question with your challenge to read neoclassical stuff.”

    Never mind.

    “However, from the 1980s onwards, there have also been neoclassical endogenous growth models.”

    I’ve heard about the older models, like Harrod-Domar and Solow; not about these newer endogenous growth ones. But while I see the relation, it was not what I was trying to figure out.

    What really caught my attention is this paper by Gunnar Tomasson and Dirk Bezemer: What is the Source of Profit and Interest? A classical conundrum reconsidered

    Their general thematic, it seems to me, is somewhat similar to the Bellfiore and Passarella paper.

    The Tomasson and Bezemer paper is interesting (they propose credit as a mechanism facilitating the realization of surplus value into monetary profits), but I think they are completely mistaken in their interpretation of Say’s Law (which is another subject that has captured my attention).

    “Lastly, while on neoclassical theory, you are correct to wonder about profit. In full-employment equilibrium, where each factor is remunerated in accordance with its marginal productivity, economic profit will be zero, usually interpreted to mean that profit is equal to the rate of interest. In the short run, perfectly competitive firms can receive positive economic profit, but this is competed away once full-employment equilibrium is established.”

    In their paper Tomasson and Bezemer express as the “Profit Puzzle” what I was already wondering: how can there be positive economic profits, if capital is compensated for its contribution to net output.

    They also speak of the related problem of growth. They call it the “Expansion Enigma”: if profits tend to zero, then there should be no accumulation.

    By the way, although I find the neoclassical definition of profit absurd, my understanding of it is as accounting profits, net of opportunity costs. Say, the economic rate profit of the best investment alternative is its accounting rate of profit, less the accounting rate of profit of the second best investment alternative; and so on. The idea being that to undertake the best investment alternative, the capitalist must forsake the second best. Is this interpretation correct?

  39. By the way, although I find the neoclassical definition of profit absurd, my understanding of it is as accounting profits, net of opportunity costs. Say, the economic rate profit of the best investment alternative is its accounting rate of profit, less the accounting rate of profit of the second best investment alternative; and so on. The idea being that to undertake the best investment alternative, the capitalist must forsake the second best. Is this interpretation correct?

    Yes. Correct.

  40. 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.

  41. 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.

  42. 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]”

  43. 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.

  44. 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.

  45. 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.

  46. 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.

  47. 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.

  48. @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.

Comments are closed.