I think that the extremely thoughtful David Glasner may have gotten one wrong.
David Glasner wrote:
I Figured Out What Scott Sumner Is Talking About « Uneasy Money: Paul Krugman and Simon Wren-Lewis pounced on this assertion, arguing that Ricardian equivalence actually reinforces the stimulative effect of government spending financed by taxes, because consumption smoothing implies that a temporary increase in taxation would cause current consumption to fall by less than would a permanent increase in taxation…. Now this response by Krugman and Wren-Lewis was just a bit opportunistic and disingenuous, the standard explanation for a balanced-budget multiplier equal to one having nothing to do with the deferred effect of temporary taxation. Rather, it seems to me that Krugman and Wren-Lewis were trying to show that they could turn Ricardian equivalence to their own advantage…
This was not what I understood Krugman and Wren-Lewis to be doing.
What I thought that they were doing was this: suppose that there is no consumption smoothing and no balanced-budget multiplier: that households have a target level of savings independent of their income and wealth, so that raising their taxes by $1 leads them to cut back the present value of consumption spending not by $(1-s) but by the full $1.
Now add consumption smoothing. This period's government purchases go up by $1. This period's private consumption spending goes down by $r. There is a short-term stimulative effect of fiscal policy, even without a balanced-budget multiplier.
The thing from Robert Lucas that made them howl--that made me howl back in April 2009--was Robert Lucas's invocation of a permanent-income consumption-smoothing argument to claim that $1 of government purchases now would be offset by $1 of reduced private consumption spending now, something that is not true in any model I know of with consumption smoothing.