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Notes -
These NIPA I & S terms are probably some of the more pointlessly confusing things in macro econ. The whole thing is an identity because it starts with the basic concept: someone's spending ≡ someone's income, and then slices & dices that in various ways. The 'S' is not any colloquial version of savings, like your money in a bank account. It's "gross saving", which is a really bizarre terminology for income. Meanwhile in the usual national accounts equation, they cancel out the consumption spending & consumption income parts. So it ends up as I being non-consumption spending, and S being non-consumption income. (So even if you know this is 'spending' and 'income', the letters are literally flipped...very helpful).
In financial terms, (S-I) is the domestic private sector financial surplus. Green on this sectoral balances chart. (G-T) in red, the government deficit, is pretty clearly the 'source' of both the private sector surplus and the foreign sector financial surplus (M-X) (blue). So arranged more usefully, (G-T) ≡ (S-I) + (M-X). The foreign sector and the domestic private sector both want to earn more dollars than they spend, so the government ends up spending more dollars than they earn (aka net issuing new IOUs in the form of USD reserves/bonds/bills/notes/coins/whatever, which our households/businesses and the chinese both want to get our hands on).
I couldn't say what level of confusion Cochrane was on there, when he insinuated that the source of the government's deficit is partially the foreign sector's surplus. So in that chart, we're suggesting that if the blue goes to zero, our government won't be able to be in such a deficit? That's certainly a take. It just won't need or be forced to run such a deficit, and/or our green part of that chart will gobble up the extra dollars.
Just more confusion from Cochrane coming from the NIPA "saving" term. It would sound pretty stupid if he got this right, and properly wrote "without foreigners having large net incomes, we'll have to finance the government deficit by our domestic private sector accepting larger net incomes". Homer Simpson indeed there.
edit a few hours later: I guess I was typical-minding and literally forgot that some people might be using a 'loanable funds' framework of how money and credit could be imagined to work (as if they're finite goods), such that deficit spending requires being 'financed' by borrowing someone else's pre-existing 'savings' that they're willing to lend. The chain of logic where current accounts deficits disappearing leads to problems is still confused in multiple ways, but I guess it wasn't necessarily a confusion just from the national accounts 'S' term.
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