I'm not sure further progress will be made on what to me seems like
a largely semantic debate. Krugman is making perfectly sensible economic arguments but then making a
semantic leap to claim he has proven something about permanent vs.
temporary. He hasn't, as I'll consider in a moment. But don't worry, the more important substantive
issue is government spending vs. tax cuts and on that I agree with
Krugman that very often tax cuts don't get you much stimulus.
Now let's turn to the details of the exchange.
Krugman argues, correctly, that fiscal policy can create a "bonds are net wealth effect" and also a "new bridge is built effect," and his post stresses the latter. But playing up the "bridge effect" does not shift the evaluative balance between permanent vs. temporary fiscal policy, as both can be used to build useful things and indeed that is one element of the analysis which I have been explicitly holding constant across the two alternatives. (I've not been denying the potential productivity of bridges or how gdp is calculated.)
Krugman also calls forth a "size of expenditure" effect (which is not in my view a true permanent vs. temporary comparison, but still let's go ahead and say it is). He writes:
The question then is how much of that direct increase in government demand is offset by a fall in private consumption because people expect their future taxes to be higher; obviously that offset is smaller if they think the bridge is a one-time expense than if they think there will be a bridge built every year. That’s why temporary government spending has a bigger effect.
Even there I am not convinced, and that is because of the very last sentence of the paragraph. If the government builds more bridges rather than fewer bridges, yes private consumption goes down more in the former case. But if each bridge is valuable, the net stimulus (which is what matters) doesn't have to go down. In this setting, with varying expenditure across the two cases, the permanent fiscal policy easily can have both more crowding out and more net stimulus. Krugman is citing the higher crowding out but there is no demonstration (or even argument) of a smaller net stimulus from the permanent fiscal policy. It still can go either way and no, figuring out the net effect isn't simple.
Oddly, my position in this debate is that, within a Keynesian framework, "doing more over time" can in the theoretical sense work out in favor of stimulus. It is thus instructive to see MR and Krugman commentators attacking my "right wing" position or Krugman's "left wing" position; it's a sign they don't understand what is being debated. Krugman himself already mentioned that he was arguing under the rubric of Milton Friedman so I'll claim Keynes. Keynes himself was a bigger fan of permanent than temporary fiscal policy and he thought it could provide ongoing stimulus by providing ongoing value for the dollar. In this sense I am arguing for the theoretical coherence of the truly Keynesian view, even though when it comes to practice I am skeptical on public choice and Hayekian grounds.
Addendum: Here is Megan McArdle's response.