Basic Macroeconomic Identity for an Open Economy

Let us make an in-depth study of the Basic Macroeconomic Identity for an Open Economy.

The macroeconomic identity for an open economy with government sector is Y = E = C + I + G + X-M

In an open economy with government aggregate purchase of real GDP is

Aggregate purchase – C + I + G + (X-M) … (1)

where (X – M) is the balance of trade or net export.

Aggregate production must equal aggregate purchase, which implies that

C + I + G + (X – M) = C + S + T …(2)

Since C is a component of both aggregate production and aggregate purchase, it can be subtracted from both sides of the equation to obtain the following national income accounting identity for an open economy:

I + G + (X-M) = S+ T By rearranging terms we get

(X – M) + (G -T) = S – I …(3)

Thus the sum of net export (the balance of trade) and the government budget deficit must equal the difference between desired saving and desired investment.

If there is a twin deficit — a balance of trade deficit and a budget deficit — we have the following identity:

Balance of trade deficit = S – (I + Budget deficit) … (4)

When there is a balance of trade deficit, both sides of equation (4) are negative. A balance of trade deficit implies that domestic saving falls short of the sum of desired investment and the budget deficit. The balance of trade deficit equals foreign saving that fills in the gap between domestic saving and the sum of investment and government budget deficit.

Thus equation (4) suggests that trade deficit and budget deficit are interrelated given planned investment and export demand, an increase in budget deficit (an excess of G over T) associated with each possible level of real GDP is an expansionary influence on the economy because it increases aggregate purchases (desired expenditure).

As real GDP increases, more import demand is generated in the economy. The increased import demand increases the balance of trade deficit; however the expansionary influence of the budget deficit need net increase the trade deficit — it results in a sufficient increase in private saving or a fall in planned investment.

Given planned investment to the extent that the increase in the budget deficit does not result in a substantial increase in saving, the difference must be made up by an increase in the trade deficit. In effect, this means that increases in income in the economy lead to a trade deficit because consumers chose to spend a higher percentage of their earnings on imported goods instead of saving.

If the government raise taxes to reduce budget deficit, the disposable income of the people will fall. This will reduce their spending on both domestic and imported goods. A fall in imports implies an improvement in trade balance.

An increase in taxes increases government spending. An increase in government spending due to budgetary surplus created by an increase in taxes will result in a fall in disposable income. This will lead to a fall in both consumption and saving. So the saving-investment balance will be altered.

Alternatively stated, an increase in C and S is possible if disposable income rises. This is possible if the government reduces taxes.