# Explaining the net capital outflow - trade balance identity

In an open economy, the following equation always holds, it is an identity:

$S-I=NX$ where $S-I$ represents net capital outflow and $NX$ represents trade balance (net exports).

This equation tells us that there is an inextricable link between the financial markets and the markets for goods and services. But how can we explain it and why is it true, intuitively?

I believe this is the intuition:

What do people use to buy foreign goods?

Either they have to offer domestic goods or they have to offer domestic assets.


What do people use to make foreign investments?

Either they have to offer domestic goods or they have to offer domestic assets.


So if a country sells more exports than it buys imports then it must be that it is buying more foreign assets than they are selling domestic assets. Otherwise whey would be exchanging both less domestic assets and less domestic goods for both more foreign assets and more foreign assets. But since that's the entire set of things usable for trade, that's not possible.

Start with savings: S private = Y - C - T and S government = T - G. Net exports will not affect savings. So, given that Y = C + I + G + NX, total savings is S = C + I + G + NX - C - T + T - G which means S = I + NX or NX = S - I. Intuitively, exports are like capital imports (and vic versa).