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.

Let's say government can spend $100 billion today or spend the present expected value of $100 billion, stretched out over time so it is a commitment in perpetuity.  Both spending programs are financed by bonds.  So that's the same net present value of spending and the same method of finance.

The Keynesian boost to aggregate demand arises because people consider the resulting bonds to be "net wealth" even when they are not, in the sense outlined by Robert Barro (1974).  People are tricked by the government's fiscal policy, but of course the extent, timing, and nature of the trickery is hard to predict.

Is it easier to trick people "a lot all at once" or "a little bit by bit over time"?  It depends.  If you try to trick them slowly over time, temporal learning and adaptive expectations may work against the policymaker.  But if you try to trick people a lot all at once, the trick may rise over their threshold of attention, perhaps because of media coverage.  We don't know which "trick" to aggregate demand will be greater, the temporary boost to spending or the permanent boost.

One way to get a clear answer — in favor of Krugman's hypothesis that the temporary spending is more potent — is to assume that bonds as net wealth fails for a policy rule but not for a single period policy surprise (the temporary boost in spending).  In contrast, the traditional Keynesian view is to think that bonds are also net wealth in the medium run and perhaps the long run too and then we are back to not knowing whether the permanent or temporary spending boost does more for aggregate demand.  Or you might think, as I have suggested, that whether bonds are viewed as net wealth in the short run will depend on the size of the spending boost.  Many different assumptions are possible and thus many different results are possible.

Alternatively, you might compare $100 billion today (and no more) to $100 billion each year, every year.  You could call that "temporary" vs. "permanent" although I suspect the dominant effects will fall out of "small" vs. "large."

The latter, permanent boost to spending will give a bigger boost to aggregate demand overall (unless again you neuter it by applying Ricardian Equivalence to the rule but not the single period policy).  It also will lead to more crowding out.  Do note that in the early periods of this policy taxes need not rise by $100 billion for each year but rather the early installments can be paid off over time.

It is less clear whether the permanent spending boost leads to a bigger AD shift only for today.  It will if you apply the same degree of bonds as net wealth to the rule and single period policy, and if you think that the later periods of government spending will add net value, thus creating positive feedback through the long-run wealth effect.

It is also unclear if the larger, permanent spending boost creates more "stimulus per dollar" (as opposed to more stimulus in the aggregate or more stimulus for the single period).  That will depend on whether we are in the range where the stimulus has increasing returns to scale (maybe a certain critical mass is needed, as I believe Mark Thoma has suggested), constant returns to scale, or diminishing or even negative returns to scale, because of eventual crowding out. 

Overall the Keynesian effects can mean either the permanent or the temporary spending boost has a bigger effect and there are also a number of ways of defining what a "bigger effect" might mean.  This analysis has more variations than does the Poisoned Pawn Sicilian.

Perhaps Krugman is drawing from Barro's 1981 JPE paper on government purchases, which does indeed derive the stated result, but that is no longer the dominant approach. Circa 1990, Aiyagari, Christiano, and Eichenbaum note:

On pp.4-5 they explain why Barro is incomplete. 

Overall I find these debates confusing.  I wonder for instance if Krugman's blog example is actually comparing tax finance to debt finance, rather than temporary vs. permanent spending shocks.  (Note also that Krugman is making a claim about demand or effective "stimulus" rather than output and employment, although I am taking the latter as what matter.)

Those of you with lots of time on your hands can ponder whether the "permanent vs. temporary" debates compare "$100 billion this year vs. $100 billion for each year to come" and/or "$100 billion this year vs. the present value of $100 billion spread out over time, in perpetuity," and whether all cited articles and blog posts are making exactly the same comparisons.

Results in this area usually can be modified by further assumptions.  I think of this as the central paper, published in the JME 1999.  Admittedly it is for a small open economy but the key result is:

Moreover, permanent increases in government expenditures have larger
positive labor supply and output effects than temporary fiscal policies.

Again, I don't have faith in these models and I believe agnosticism is the correct stance.  The point is not about who is wrong and who is right but rather how treacherous these analytical waters can be.  Beware! 

In any case there is hardly an overwhelming brief in favor of the stimulative powers of the temporary spending increase.  The best case for the temporary boost is I think the public choice argument that it is better to get it over with more quickly, so as to limit corruption of the government.

Addendum: Megan McArdle adds comments on her contribution to the debate.

Second addendum: You'll find a response from Paul Krugman here.  I'll note it is he that introduced the framework of Milton Friedman and the permanent income hypothesis, not I.  If you look at the literature as a whole, it can go either way whether the permanent or temporary increase in government spending is more potent.  Krugman's own example doesn't demonstrate his point that the temporary increase is stronger, as it compared debt-based to tax-based finance rather than permanent vs. temporary.

Here is my column on the social changes occasioned by recessions.  Of course recessions are mostly bad and this one is no exception.  Still, one underappreciated fact is that health outcomes appear to improve in recessions, not get worse (even though health care access and coverage decline):

Sure, it's stressful to miss a paycheck, but eliminating the stresses of a job may have some beneficial effects. Perhaps more
important, people may take fewer car trips, thus lowering the risk of
accidents, and spend less on alcohol and tobacco. They also have more
time for exercise and sleep, and tend to choose home cooking over fast
food.  In a 2003 paper, “Healthy Living in Hard Times,” Christopher J. Ruhm, an economist at the University of North Carolina
at Greensboro, found that the death rate falls as unemployment rises.
In the United States, he found, a 1 percent increase in the
unemployment rate, on average, decreases the death rate by 0.5 percent.

In this recession the consumption of the wealthy is taking a bigger hit than is usually the case in a downturn:

In any recession, the poor suffer the most pain. But in cultural
influence, it may well be the rich who lose the most in the current
crisis. This downturn is bringing a larger-than-usual decline in
consumption by the wealthy.

The shift has been documented by Jonathan A. Parker and Annette Vissing-Jorgenson, finance professors at Northwestern University, in their recent paper,
“Who Bears Aggregate Fluctuations and How? Estimates and Implications
for Consumption Inequality.” Of course, people who held much wealth in
real estate or stocks
have taken heavy losses. But most important, the paper says, the labor
incomes of high earners have declined more than in past recessions, as
seen in the financial sector.

Popular culture’s catering to the
wealthy may also decline in this downturn. We can expect a shift away
from the lionizing of fancy restaurants, for example, and toward more
use of public libraries. Such changes tend to occur in downturns, but
this time they may be especially pronounced.