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One popular idea in "Keynesian economics" is that the government should balance its budget over the course of the business cycle, running deficits for stimulus during recessions, then surpluses in booms to bring down the debt.

This is a bad strategy, because it neglects /1
the interconnectedness of financial positions in the economy.

One entity's spending is another's income; so for somebody to run a surplus, somebody else has to run a deficit. So if we say "gov should run a surplus," what does that imply about private financial positions? /2
In the US, because of structural factors that aren't going away anytime soon, we nearly always run deficits against the rest of the world (the trade/current account deficit), meaning that we send income overseas that doesn't come back as spending. /3
That means that for the US private sector balance to be positive (a surplus), the gov sector balance has to be negative (a deficit) and it has to be at least as large as the losses to the foreign sector (the gov deficit ≥ the current account deficit). /4
The private sector doesn't need to be in surplus at all times. But we also wouldn't expect it to be continually in deficit - that would imply, on net, ever-worsening financial positions in the private sector, running down saved assets and/or issuing new IOUs. /5
So what happens to the private sector if the gov "balances its budget over the cycle"? In recessions, depending on the size of the gov deficit, the private sector will be balanced or running small surpluses (because the foreign deficit cancels out some/all of the gov deficit). /6
But in booms, the private sector would be deeply in the red (deficit), because the gov surpluses would be subtracting income out of the private sector, while the foreign sector is doing it too. /7
So if the gov spends half its time in deficit and half in surplus, that implies that the private sector is spending nearly all of its time in deficit! That's not sustainable.

No doubt, people advocating this policy haven't thought it through. If you ask them, /8
"1. should the gov balance its budget over the cycle?" and "2. should we have a policy of keeping the private sector in deficit most of the time?" they will probably answer yes to 1, no to 2, without realizing that in the US 1 implies 2! /9
The alternative policy that solves this is based on "Functional Finance": the gov should run whatever budget position is needed to keep the economy at full employment while keeping prices stable, at all times. That will be deficits sometimes, and surpluses other times /10
The point is that the budget should *always* be tailored to the needs of the economy - and not some arbitrary financial worry like "the debt is too big." If the budget is tuned to the economy, then the debt can't get "too big." /Fine
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