A rising government deficit will always allow the private domestic sector to increase its overall saving in nominal terms.
Answer: False
The answer is False.
If the external balance is zero (that is, net exports equal zero) then there is a one-to-one correspondence between the government balance and the private domestic sector balance such that, for example, a 2 per cent fiscal deficit must be associated with a 2 per cent private domestic sector balance surplus.
So in this circumstance the answer would be true.
But things get complicated when we introduce positive or negative external balances. Then a 2 per cent fiscal deficit might be associated with a 3 per cent external deficit and so the private domestic sector balance will be in deficit overall (spending greater than income).
Saving might still be positive but overwhelmed by spending which means that overall the sector is in deficit.
So the answer is only true if the fiscal deficit is larger (as a percent of GDP) than the external balance and growing faster.