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.