Open economies can borrow resources from the rest of the world and lend them abroad. This way a temporary income shortfall can avoid a sharp contraction of consumption and investment. Similarly, a country with ample savings can lend and participate in productive investment project oversees. Because international borrowing and lending are possible, there is no reason for an economy’s consumption and investment to be closely tied to its current output.
The change in the net foreign assets of a country (the change in the value of its net claims on the rest of the world) is called the current account balance. The latter is said to be in surplus if the economy as a whole is lending, and in deficit if the economy is borrowing. The current account balance over period t is defined as
where is the value of the economy’s net foreign assets at the end of a period t. Equivalently:
where is the country’s national product, is the interest earned on foreign assets acquired by the economy, is the private consumption, is the government consumption and is the investment.
Note also that the national saving is defined as
Hence . The national saving in excess of domestic capital formation flows into net foreign asset accumulation. So do protective measures (such as trade tariffs) improve the current account? That depends on how those measures affect savings and investment.
Note that the current account balance is equivalently the net exports of good and services. A country with positive net exports must be acquiring foreign assets of equal value while a country with negative net exports must be borrowing an equal amount to finance its deficit.
So when does a country becomes bankrupt?
We know that (by combining the first two formulas)
Now assuming no fixed end of time for the country while imposing the no-ponzi scheme condition (i.e. – the debt should not increase faster than the interest rate i.e. this constraint prevents over-accumulation of debt) we get (by forward substitution):
where is the economy’s trade balace. The latter is the net amount of output of the economy’s transfers to foreigners each period. Hence according to the previous formula the economy’s transfers to foreigners must equal the value of their initial debt to them. This condition is satisfied, if an only if, the country pays off any initial debt through sufficiently high surpluses in its trade balance.
Assume that the output and the debt both grow at a standard rate g. Then
which leads to
Thus a growing economy can run perpetual current account deficits and still maintain a constant debt to output ratio. To do so the country need pay out only the excess of the interest rate over the growth rate. Additionally, note that the ratio measures the burden a foreign debt imposes on the economy. The higher the burden the higher the likelihood of bankruptcy.
My notes are based on the following textbook: