The system of basic indicators of the national product makes it possible to derive a number of macroeconomic identities. The basic macroeconomic identity (income identity) reflects the equality of income and expenditure:
Y=C+I+G+Xn,
where Y is income, which is equal to GNP.
Other important identities are used in macroeconomic analysis.
The identity of savings and investments can be deduced as follows. For simplicity, consider first a closed economy in which there is no public sector, and, consequently, taxes. Then:
Spending on GNP = Consumption + Investment
By definition of savings, we can write:
Income, or GNP, measured by income = Savings + Consumption
Since the expenditure on GNP and the income derived from the production of GNP are equal, then, equating the right parts of the equations, we have:
C+I=S+C, or I=S
This simple identity becomes more complicated with the introduction to the analysis of the state and the outside world.
Aggregate savings are divided into private (Sp), public (Sg) and rest of the world savings (Sr):
S = Sp + Sg + Sr
Private savings are equal to the sum of income (Y), transfers (TR), interest on public debt (N) less taxes (T) and consumption (C):
Sp = (Y + TR + N – T) – C
Government savings are defined as:
Sg = (T – TR – N) – G
The state’s savings, if they are a positive value, constitute a budget surplus. If they are negative, this indicates the presence of a budget deficit (BD).
BD =– Sg
The savings of the outside world (the rest of the world) in the simplest definition are equal to the income that the outside world receives from our imports (M), minus the costs of our exports (X):
Sr = M – X, or Sr = – Xn
The savings of the outside world can be used to buy financial assets in our country, to reduce foreign debt, and then we have an inflow of capital into the country.
Equality of savings and investment is true for the economy as a whole, but not necessarily for each of the sectors (private, public, external world). For example, investment can also grow with a reduction in private and public savings due to an increase in capital inflows from abroad:
Sp +Sg +Sr = (Y + TR + N – T) – C + (T – TR – N) – G + (–Xn),
Sp + Sg + Sr = Y – C – G – Xn;
S = I.
Savings can be used both to invest in real assets and to increase financial assets. Suppose, for simplicity, that there are two types of financial assets: government bonds and cash. Bonds and cash are liabilities (liabilities) of the state and assets of the private sector. Government savings can then be used either to cover public debt or to reduce the money supply.
Sg = –(ΔM)
Sg = –(ΔM + ΔB)
where ΔM is the change in the money supply,
ΔB is the change in the amount of government bonds issued.
This expression is called the identity of the state budget. If there is a budget deficit, it can be financed by the issue of money or bonds:
BD = –Sg, or BD = ΔM + ΔB.
Private savings can also be used both to increase real assets and remain in the form of government bonds or cash.
Sp = I + ΔM + ΔBp
The savings of the rest of the world, similarly, can be used to buy our country’s government bonds, and then we have:
Sr = ΔBr
The sum of the three types of savings in terms of their use will again give us a certain identity:
S = I.
It is assumed that all bonds issued by the state (ΔB) are bought either by the private sector (ΔBp) or by foreigners (ΔBr), i.e. ΔB = ΔBp + ΔBr.