As the U.S. economy increasingly sends mixed signals about the strength of its recovery, the significant  sparring  over the efficacy of the stimulus has regained an urgent relevance (papers, in PDF, available respectively here  and here ; the FT summarizes a wide range of opinions here ). The latest salvo in the stimulus wars has been the battle between the so-called strucs versus cycs , with the former claiming that worker mismatches are the central problem in the current anemic labor market, while the latter dispute that cyclical factors are more to blame.[*] Of course, such theoretical stances are not only academic, since they inform and implicitly shape one's preferred policy response.
Rather than wade into the morass of the U.S. case, it is perhaps helpful to consider the bigger global context. After all, the financial crisis and subsequent slowdown instigated many governments around to the world to implement fiscal stimuli, of which America's and China's were merely the most prominent. It is perhaps useful to examine the association between the size of the stimuli---as measured by the size of the stimulus packages that governments implemented---and subsequent growth, to tease out whether there are any systematic patterns in the relationship.
At first glance, the relationship appears to be positive (see figure, top): this seems to vindicate the pro-stimulus camp, at least at the international level. This first impression, however, is deceiving. The positive slope is almost entirely due to the presence one outlier: and you guessed it---China. The size of China's stimulus, of course, has been the subject of much debate, with many observers claiming that the large stimulus had mainly been a reclassification of planned expenditures as stimulus. Repeating the exercise without the two big outliers, China and Saudi Arabia (which had pitifully little growth-bang for the buck in their $400 billion stimulus), and the positive relationship basically disappears (see figure, bottom). The bottom line is not so much that a large fiscal stimulus has either a positive or a negative effect on subsequent growth, but rather that---at the crude cross-country level---it is difficult to tease out any significant effect altogether.[†]
Source: Grail Research (stimulus data) and IMF IFS  (growth data).
Notes: Stimulus data are for late 2008 to early 2009, while growth data are for 2009 (with the exception of Kenya, Kuwait, Mongolia, Nigeria, Serbia, where data are only available for 2008). Excluded outliers are China and Saudi Arabia, but the bottom figure is essentially the same by excluding only China.
Of course, this picture is somewhat incomplete. After all, much consternation has been made about the tradeoff between debt and deficits vis-a-vis the efficacy of a stimulus; in particular, Carmen Reinhart , among others, has repeatedly  warned  of the complicating effects posed by high debt burdens on stimulus and growth. The IMF has also recently noted  the more general point that the post-crisis response to countercyclical macroeconomic policies are conditioned by pre-crisis vulnerabilities.[‡]
So let's try to provide a slightly more nuanced picture of the impact of fiscal stimulus, based on countries' external debt/GDP exposure. Slicing the data into countries with little external debt (< 10% GDP), moderate external debt (10-30% GDP), and high external debt (>30% GDP), we see that the growth impact of a stimulus is either negligible or slightly positive when countries have lower debt levels, but this turns negative when debt levels exceed a certain threshold (see figures). Similar pictures accrue when we use domestic debt (from BIS SecStats ) instead of external debt, and when we combine the two measures into total public debt; with the difference being in the specific thresholds where the impact seems to shift from positive to negative. Interestingly, for total public debt, the contingent effect of a stimulus seems to comport with Reinhart and Rogoff's debt thresholds: there is a positive effect of a stimulus in countries with debt/GDP ratios of below 60%, little effect for countries up to 90%, and a negative effect in countries above 90%.[§]
Stimulus data are for late 2008 to early 2009, while growth data are for 2009 (with the exception of Kenya, Kuwait, Mongolia, Nigeria, Serbia, where data are only available for 2008). Debt data are gross external general government debt, for the 2008H1.
Now, it is important to be modest about how much we can draw from the above analysis. After all, the crude methodology above does not account for endogeneity and simultaneity concerns, the causal mechanisms have not been laid out, and the data do not account for the phasing in of stimulus packages. Moreover, we lack a counterfactual of how events would have played out in each country, had the stimulus package been absent, along with whether monetary policies may have played a complementary role. That said, it is useful to draw some tentative conclusions from the exercise.
Perhaps the best way to interpret the findings is that the size of fiscal stimulus, by our chosen measure, has a fairly limited impact on contemporaneous output growth. Moreover, to the extent that the fiscal package is actually accompanied by a nontrivial share of actual spending, the early effects of the stimulus have a fairly minimal impact on growth. This second conclusion should be qualified: since the early stages of a stimulus phase-in typically occurs in the deepest depths of a recession, it could well be that growth simply would have been worse. Finally, debt thresholds seem to matter for evaluating whether a stimulus is likely to have a growth impact or not. Generally speaking, when the debt burden gets too large, any positive growth effect of a stimulus appears to be washed away by the concerns that the country really shouldn't be taking on more debt.
In sum, fiscal stimulus does not appear to be the silver bullet that many of its most vociferous proponents would hope for it to be. That said, it would be both premature and irresponsible to declare that fiscal stimuli around the world are misguided. Rather, the wisdom of pursuing a stimulus is dependent on a whole range of factors, not least the extent to which a country already has fiscal space to enact such stimuli.
Postscript: Elsewhere at the Bank, Raj Nallari has also pointed out  how the international jobs picture has not responded to fiscal stimuli as much as desired. Fritzi Koehler-Geib and her coauthors also make the point that there are tipping points  after which debt can affect growth.
*. Amidst the sturm und drang, what Krugman  and DeLong  both miss, in my view, is the that mismatches in just two segments of the labor market can in fact induce broader unemployment, when general equilibrium effects are taken into account. Thus, when the mass of unemployed workers in the construction sector find it difficult to be reabsorbed into, say, the booming healthcare sector, overall aggregate demand may nonetheless be depressed if spending increases in the booming sector is not matched by the decline in the contracting sector. This could happen if there are sticky wages or habit persistence, or even the simple fact that workers in the booming sector do not have the time to increase their spending (remember, they are expanding their working hours as a consequence of the unexpected boom in their sector). With the shrinkage in aggregate spending, there is an accompanying contraction in employment in other labor market sectors unrelated to the two sectors where misallocation occurred. While this does not  necessarily rehabilitate Austrian business cycle theory  in full, it does nonetheless allow for the mismatch element that the two professors are so quick to denigrate.
†. This point can be made very slightly more formally. While the bivariate regression on the full sample has a statistically significant (at the 5 percent level) coefficient on the stimulus variable, the coefficients on the restricted sample (excluding outliers) is insignificant. The coefficient (standard error) in the full sample is 0.062 (0.03), for N = 66. The coefficients (standard errors) in the restricted sample without China only and without both China and Saudi Arabia are 0.028 (0.03) and 0.043 (0.05), N = 65 and N = 64, respectively.
‡. The IMF paper, however, concentrates on the size of reserve holdings as their central measure of vulnerability. Since reserve size has not featured in much of the contemporary debate on fiscal policy, we defer to their findings in that regard, and concentrate instead on the impact of debt instead.
§. The formal results in this case are somewhat more disappointing, however, with small sample sizes typically rendering the coefficients insignificant in most specifications. However, the signs of the coefficients are stable: the coefficients on the stimulus variable is positive, while that on debt is negative. When interacted, the coefficient on debt usually turns small and positive, but is dominated by the coefficient on the interaction term.