Question

Consider the accounting identity: (X – M) = (S – I) + (T – G). Define each of the individual terms in this identity. What are the implications of this identity for discussions about imbalances in global trade and capital flows?   

Answer 1

The said national income accounting identity depicts how a budget deficit can be a contributing factor to a current account deficit.

(X – M) = (S – I) + (T – G)                                                    - Given Equation

Let us consider the national accounting model of the economy:

Y = C+I +G + (X-M)                                                                                           (Equation 1)

where Y represents national income or GDP, C is consumption, I is investment, G is government spending and X–M stands for net exports. This represents GDP because all the production in an economy (the left hand side of the equation) is used as consumption (C), investment (I), government spending (G), and goods that are exported in excess of imports (NX). Another equation defining GDP using alternative terms (which in theory results in the same value is

Y= C+ S+ T                                                                          (Equation 2)

where Y is again GDP, C is consumption, S is saving, and T is taxes. This is because national income is also equal to output, and all individual income either goes to pay for consumption (C), to pay taxes (T), or is saved (S).

Now let us try to modify & simplify the equation in terms of budget deficit constraint:-

Since , Y= C+I+ G+NX      and (From Equation1)

Y -C -T = S                                    (From Equation 2)

Implies ,   S= G- T+ NX + I , which further simplifies

Taking G, T and I on the right hand side of the equation..

(S – I) + (T- G ) = NX       (   If (T-G) is negative, we have a budget deficit)

Now, assume an economy is already at potential output, that is Y is fixed. In this case, if the deficit increases, and saving remains the same, then this last equation implies that either investment (I) must fall (see crowding out effect), or net exports (NX) must fall, causing a trade deficit. Hence, a budget deficit can also lead to a trade deficit, causing a twin deficit. Though the economics behind which of the two is used to finance the government deficit can get more complicated than what is shown above, the essence of it is that if foreigners' savings pay for the budget deficit, the current account deficit grows. If the country's own citizens' savings finance the borrowing, it may cause a crowding out effect (in an economy at or near potential output, or full employment level’s ).

Another way to understand it is to consider ( X-M ) as current account deficit.

I.e. Current Account = (Private Saving – Investment) + (Taxes levied – Government Expenditure)

In the above equation, it is evident that Current account will deteriorate as government expenditure exceeds the amount of tax is collected.

Assume that there are two different markets, First consider the Foreign Exchange market. At equilibrium the quantity supplied = the quantity demanded. Thus, Imports + Capital outflow = Exports + Capital Inflow.

Rearranging this equation we find that   Imports – Exports = Capital Inflow – Capital Outflow.

Because Imports – Exports = Trade Deficit and Capital Inflow – Capital Outflow = Net Capital Inflow, we get the equation Trade Deficit = Net Capital Inflow (or Current Account deficit = Capital Account Surplus).

Now, consider market for lonable fund & investment.

Where the equilibrium is derived at.. Saving + Net Capital Inflow = Investment + Budget Deficit.

Upon Rearranging :- Budget Deficit = Saving + Trade Deficit – Investment.

Hence, in a nutshell.. if the deficit goes up then either household savings must go up, the trade deficit must go up, or private investment will decrease.