"Now this does not mean that Market Monetarists and New Keynesians suddenly agree about everything. A key difference is that for David this [fiscal policy at the ZLB] is an insurance against incompetence by the central bank, whereas Keynesians are as likely to view hitting the ZLB as unavoidable if the shock is big enough."
I want to try to clear up this last remaining difference.
At first I thought that David was right. Then I started building a little model, and convinced myself that Simon was right.
So then I changed the question, into one of more practical relevance: "How would we know in practice that the shock was big enough that Simon was right?". And I came up with Scott Sumner's answer: "If the central bank runs out of things to buy". (Maybe not Scott's actual words, but close enough.)
And then I thought to myself: "Hang on. If the central bank runs out of existing things to buy, it could always buy newly-produced things". Which is the same as Simon's answer. Because if the central bank prints money and it, or the government, uses that money to build a new bridge, that is definitely fiscal policy, as well as monetary policy.
We normally think of open market operations, where the central bank buys government bonds, as a purely monetary policy. But if a government just happened to have a very small debt/GDP ratio, the central bank would soon run out of government bonds to buy, even if the shock were very small, or even if there were no shock at all. And if the inflation target were lower, or if the NGDP level path growth target were lower, that would also mean the central bank would run out of government bonds to buy sooner. What then? Maybe the central bank should buy (an index fund of) commercial bonds as well, or/then commercial shares, or/then land, or/then existing capital goods, or/then newly-produced capital goods, like bridges.
Where exactly do you draw the line between monetary and fiscal? Does it matter?
It might matter on micro public finance/public choice grounds (is this the sort of asset we would want the government-owned central bank to own?). But if you don't want the government-owned central bank owning all that stuff, then maybe you need to increase the inflation target or NGDP level path growth target, so you get a smaller central bank. (Too dedicated a pursuit of low inflation and the optimum quantity of money leads to communism, with government ownership of everything.)
How much money should the central bank print and buy things with? As much as is necessary, to hit the NGDP target. And if it runs out of other things to buy, like government bonds, or commercial bonds, or......, then it should buy newly-produced things, if necessary. And if that means it is buying too much, and getting too big, then raise the NGDP target and the implied inflation rate and the implied tax on holding currency.
What particular things should be bought and held on the asset side of the consolidated balance sheet of the government plus central bank? That is a micro public finance question.
What particular things should be held on the unconsolidated central bank's balance sheet rather than on the government's balance sheet? That is a public choice question. If the central bank runs out of things to buy and needs to buy new bridges to hit its NGDP target, and if the government doesn't want the central bank owning bridges, the government should buy those bridges financed by issuing bonds, and let the central bank buy those bonds.
I don't think there's anything left to argue about. Except a lot of micro public finance and public choice stuff.
But I'm sure we will think of something.