The The Balance of Payments and the The Loanable Funds Market market are two views of one fact: a country's saving must pay for its investment, at home or abroad.
Key idea
$$S_{private} + (T - G) = I + NX$$ Private saving plus the government's budget balance (national saving) equals domestic investment plus net exports. When national saving falls short of investment, net exports are negative: the country borrows the difference from abroad and runs a trade deficit.
Why it works
Start from $Y = C + I + G + NX$. Households' income is spent, taxed or saved: $Y = C + S_{private} + T$ (with $T$ as taxes net of transfers). Set the two equal and cancel $C$: $S_{private} + T = I + G + NX$, so $S_{private} + (T - G) = I + NX$. It is an accounting identity: true every year in every country. It says the trade balance cannot change unless saving, investment or the government's budget balance changes too. Economists broadly agree on the identity; how saving and investment respond to policy is where they differ.
Worked examples
Worked example: Finding net exports
In billions: private saving 2,000; government budget balance −400; investment 1,900. Find NX.
- $$NX = S_{private} + (T - G) - I = 2{,}000 - 400 - 1{,}900 = -300$$
- National saving (1,600) is less than investment (1,900), so the country borrows 300 from abroad: a trade deficit of \$300 billion.
Answer: −\$300 billion
Worked example: A bigger deficit
The government's deficit grows by \$200 billion, and private saving and investment stay the same. What happens to NX?
- $(T - G)$ falls by 200, so $NX$ must fall by 200.
- In practice saving and investment also respond, so the trade balance need not move one-for-one; but something in the identity must give.
Answer: NX falls by \$200 billion
Common mistake
Treating the trade balance as separate from saving and investment. By the identity, the trade balance changes only if saving, investment or the government's budget balance changes too. Check: before predicting that a policy will change the trade balance, ask what it does to saving and investment.