Short & Simple 15 – The Sectoral Balances Identity

We saw, in part 14, that government spending increases the net financial assets of non-government, whereas taxes do the reverse. The level of net financial assets at a point in time is a stock. The change in net financial assets over the period is the result of flows.

In the case of a government deficit, in which government spends more into the economy over the period than it taxes out, non-government will spend less than its income, with the flow of saving adding to its stock of net financial wealth. Net financial assets will increase.

When, instead, government runs a surplus, taxing more out of the economy than it spends into it, non-government will spend more than its income, by either running down past savings or borrowing. The flow of dissaving (i.e. negative saving) will subtract from the non-government’s stock of net financial wealth. Net financial assets will decrease.

An easy way to think of this is that government spending involves crediting bank accounts whereas taxes involve debiting bank accounts. So when the government spends more than it taxes (running a deficit), non-government bank accounts are credited more than they are debited, and non-government savings increase. The reverse occurs when government runs a surplus.

In general, the government’s financial balance is matched dollar for dollar by the non-government’s financial balance, but with the signs reversed. The sector that spends less than its income is said to have maintained a financial surplus over the period. The sector that spends more than its income has run a financial deficit.

The result that the government’s deficit is the non-government’s surplus follows as a matter of accounting. It is true by definition. In itself, it says nothing about causation.

Macroeconomists formulate theories by combining accounting identities with particular behavioral assumptions. The accounting identities are indisputable (provided we accept the principles of accounting). But behavioral assumptions are contestable.

In earlier parts of the series, it has been argued that spending creates income. Even so, it could be that non-government spending behavior drives the government’s fiscal balance, or instead that the government’s fiscal decisions drive the non-government’s financial outcome. It will be supposed in this series that once government has set its fiscal policy (including tax rates and spending measures), it is the spending decisions of non-government that determine which sector runs a deficit, and which sector runs a surplus. The idea here is that non-government spending decisions, by affecting income, affect the amount of tax payments. This is because, for given tax rates, the amount taxed out of the economy rises and falls automatically with income.

We will return to questions of causation in the next installment of the series. In the remainder of this one, the basis for the accounting identity is explained.

Recall that Gross Domestic Product (GDP) can be expressed as the sum of various categories of expenditure:

GDP = Private Consumption + Private Investment + Government Spending + Exports – Imports

Or in symbols:

GDP = C + I + G + X – M

We can think of the expenditures as coming from three sectors: government, which spends G; the domestic private sector, which spends C and I; and non-residents who spend X on domestic production and generate M by selling foreign output to residents. The latter two sectors are what we often group together as non-government.

Now, GDP includes income that will go to taxes. Since tax payments affect the financial positions of the three sectors, we need to take this into account.

Also, because GDP includes only income generated by domestic production, it excludes income received by residents on the basis of foreign production while including income received by foreigners on the basis of domestic production. Some residents do work overseas and receive employee compensation, and some receive dividend payments on shares in foreign companies or interest on treasuries issued by foreign governments. These are all examples of primary income flows. There can also be current transfers, with nothing of economic value provided in exchange, such as a pension paid to a domestic resident by a foreign government. These are referred to as secondary income flows. Conversely, there are foreigners who receive primary and secondary income flows from the domestic economy. Since these income flows affect the financial positions of the various sectors, we need to include them as well. This can be done by including a term for net primary and secondary income flows. This term represents the sum of the balances on the primary and secondary income accounts. The primary income balance reflects net primary income flows (i.e. primary income derived by residents from foreign production minus primary income derived by foreigners from domestic production). The secondary income balance reflects net secondary income flows.

Adding the primary income balance to GDP gives a measure called Gross National Income, denoted GNI. Adding the secondary income balance to GNI gives a measure called Gross National Disposable Income, denoted GNDI. It is a measure of the total income received by residents. If we denote the sum of net primary and secondary income flows F, we have:

GNDI = GDP + F = C + I + G + X – M + F

Subtracting taxes (T) from the left and right-hand sides of this expression (which preserves the equality) gives:

GNDI – T = C + I + G – T + X – M + F

This expression can be rearranged as follows:

(GNDI – T – C – I) + (T – G) + (M – X – F) = 0

In the first bracketed part of the expression, GNDI – T is disposable income, and C and I are the expenditures of the domestic-private sector. So this part of the expression represents the domestic-private sector’s disposable income minus its expenditure. In other words, it is the domestic-private financial balance.

The terms inside the second set of brackets represent the government’s financial balance. These terms represent the difference between taxes and government spending, known as the fiscal balance.

The terms inside the third set of brackets represent the foreign sector’s financial balance. These terms represent the income that foreigners receive from selling output to the domestic economy (M), minus the amount they spend on domestic output (X), minus the net primary and secondary income flows (F) going in the form of wages, interest, dividends and current transfers to residents of the domestic economy.

Subtracting C from disposable income (GNDI – T) leaves that part of disposable income that is not consumed. This is private saving (S = GNDI – T – C). So the first bracketed part of the expression can be rewritten S – I. This enables us to write:

(S – I) + (T – G) + (M – X – F) = 0

This is the sectoral balances identity. In words:

Domestic Private Balance + Government Balance + Foreign Balance = 0

The balances of the three sectors cancel each other out. If one sector spends less than its income, maintaining a positive balance (a surplus), at least one of the other sectors must run a negative balance (a deficit).

The result can be aggregated a bit more by combining the domestic-private and foreign sectors into the Non-Government Sector. The identity then becomes:

Non-Government Balance + Government Balance = 0

This result is consistent with what was stated earlier. Specifically, whatever the non-government balance happens to be, the government’s balance must be its mirror image.

If the non-government manages to maintain a financial surplus, then by definition the government will be running a deficit. In doing so, non-government will accumulate net financial assets over the period and increase its stock of net financial wealth.

 
Further Reading

More in-depth treatments of the sectoral balances identity, as well as some background material on causation, are provided in:

Bill Mitchell – Flow-of-Funds and Sectoral Balances

L. Randall Wray – MMP Blog 2: The Basics of Macro Accounting

L. Randall Wray – MMT, Sectoral Balances and Behavior

Share

14 thoughts on “Short & Simple 15 – The Sectoral Balances Identity

  1. Hi Peter,

    Minor point.

    I think the system of national accounts (ie the 2008 SNA) no longer uses GNP. Income, such as interest income from assets held abroad is hardly production. So the phrase GNI is used.

  2. Hi,

    From an international perspective, I think it would be even better to follow the latest IMF nomenclature, linking the National Income and Product Accounts to the balance of payments accounts:

    GDP + Primary Income Balance (Factor payments from nonresidents minus Factor payments to nonresidents) = GNI (Gross National Income)

    GNI + Secondary Income Balance (current transfers from nonresidents minus current transfers to nonresidents) = GNDI (Gross National Disposable Income).

    That’s the nomenclature that the IMF staff is now teaching to Finance Ministry and Central Bank officials all over the world (https://www.imf.org/external/np/ins/english/learning.htm )

    Best regards,

    José

  3. This is an excellent post. Can you identify the appropriate BEA data to graph the results? I usually go to Gov net borrowing + Private net borrowing + Net exports. That gives a nice symmetric graph, but Net exports is not really the same as Current account, so the exercise is a bit off.

  4. Daniel M. Have a look at https://theminskys.org/usa-2017-q1-sectoral-balances-update/ for the USA case, which is a bit confusing for a lay audience.

    In the UK the best example is Neil Wilson’s chart at http://www.3spoken.co.uk/2016/04/uk-sectoral-balances-q4-2015.html It shows the basic five sectors more clearly. The reference to “foreign balance” in sector accounts is normally titled by your BEA and the UK ONS as the “rest of world”. Neil splits non-financial corporations from financial corporations, which together with the household sector, is the aggregate private balance.

    There are for me, two interesting points on Neil’s chart. The year 2001; the financial sector is loaning out money (running a deficit) such that it is funding the government’s budget surplus, and paying for the imports (foreigners amassing a surplus of Pounds Sterling) and the savings accounts of the households.

    In 2010, the UK government budget deficit of near 11% of GDP (as a result of the crash), is funding everybody else and his dog!!!

    PS. Your BEA has a good explainer at https://www.bea.gov/national/pdf/nipa_primer.pdf

  5. @Egmont

    Was reading some of your material. Seems your formulas are proving what I have discovered – its not mathematically possible for every entity (which is capable of becoming bankrupt) to be solvent all at the same time.

    We sometimes play monopoly at home where we get one player (the custodian) who controls one of the properties but does not own it. Because they control that property they also prevent a monopoly.of that group. This player never gets any money nor pays any out, they just roll the dice and move around for the fun of it. At the end of the game there is still always one winner. But then we ask, well who came second and its always the custodian because they still have a place to live.

  6. Dean

    Peter Copper asserts: “The accounting identities are indisputable (provided we accept the principles of accounting).”

    Fact is
    ― accounting is elementary mathematics,
    ― MMTers do not understand the underlying math of accounting,#1
    ― the accounting equations of MMT are provably false,#2
    ― these are the correct accounting identities:

    Qm≡C+G-Yw profit Qm, business sector
    Sm≡Yw-T-C saving Sm, household sector
    Bm≡T-G budget surplus Bm, government sector
    ::::::::::::::::::::::
    Qm+Sm+Bm=0,

    ― for THREE sectors, proper accounting yields THREE sectoral balances which add up to zero,
    ― it is either mathematical incompetence or fraud that profit does not appear in the MMT accounting identities,
    ― Peter Cooper violates the principles of accounting.

    Take away: As far as Peter Copper only parrots Bill Mitchell and Randall Wray the charge of scientific incompetence applies to these spokespersons of MMT.#3

    Egmont Kakarot-Handtke

    #1 A tale of three accountants
    https://axecorg.blogspot.de/2017/07/a-tale-of-three-accountants.html

    #2 The Common Error of Common Sense: An Essential Rectification of the Accounting Approach
    https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2124415

    #3 For the full-spectrum debunking of MMT see cross-references
    http://axecorg.blogspot.de/2017/07/mmt-cross-references.html

  7. Yeah, Im not arguing with anyone on the underlying math of accounting…all I really care about is proving to those that matter that its not mathematically possible for everyone to be solvent and you have demonstrated this along with a few others (proudhon and collingwood to name a couple).

  8. Dean

    You say: “Yeah, I’m not arguing with anyone on the underlying math of accounting…all I really care about is proving to those that matter that its not mathematically possible for everyone to be solvent …”

    There are opinion and brain-dead blather. This is called politics. There are knowledge and proof. This is called science.

    MMT belongs to the first category. Peter Cooper’s discussion about the sectoral balance identity demonstrates beyond any doubt that MMT is economics from suckers for suckers.

    Note that you contradict yourself in one sentence. You care about proof but not about the underlying mathematics of accounting. What does your proof, then, consist in?

    Egmont Kakarot-Handtke

  9. “What does your proof, then, consist in?”

    Your formula…business sector profit = household dissaving…you proved it for me.

    Cheers

  10. “Most people say that it is the intellect which makes a great scientist. They are wrong: it is character.” [Albert Einstein]

    Take a look at Alby’s character: – Albert Einstein Quotes

  11. Hi all

    Earlier I commented on some material Egmont had linked to. It motivated me to write a piece on 100% solvency and if it was possible. Even though Egmont’s formula ‘business profits = household dissaving’ would be proof of this fact, it is obvious to me formulas are not enough. Strangely enough a friend of mine (who is following a similar cause to me) came round for a visit and when I brought up this subject he himself had to admit that he never ever considered the question and as such was unable to reconcile in his mind why 100% solvency was not possible. To add to this, when I suggested that ‘exchange’ itself is over-croweded, i.e. there is an inherent cost in exchange which exchange itself cannot meet, he also found he could not reconcile it. I tried to explain to him that the two are linked. Because exchange itself is based on competition, then its not possible for everyone to be winning (winning means being solvent – losing means being insolvent) all at the same time, therefore 100% solvency is not possible.

    I wrote this piece in an attempt to explain why 100% solvency is not possible if we ‘all’ continue to treat human needs as commodities.

    https://livewithoutmoneylawfully.wordpress.com/is-100-solvency-possible/

    I purposely ask for any demonstration as to why I am wrong. Can anyone show that 100% solvency is possible whilst we ‘all’ continue to treat human needs as commodities?

    Cheers

Leave a Reply

Your email address will not be published. Required fields are marked *