According to Reason magazine, it's hard to tell.
In theory, fiscal stimulus juices the economy through a multiplier effect, in which one dollar of borrowed government spending produces more than a dollar of overall economic gain. With a multiplier of 1.5, a stimulus of $100 million would produce $150 million in economic activity. A multiplier of 2.0 would result in double the economic jolt of the initial cash infusion. The higher the multiplier, the bigger the boost.
The problem, as I noted in my April 2013 story on the stimulus, is that no one really knows what multiplier effect of fiscal stimulus is. Reputable economists don’t even really agree about the possible range for the multiplier. Some economists think it could be in the range of 3.0 or even higher, given the right circumstances. The Congressional Budget Office puts the estimated multiplier for government purchases at somewhere between 0.5 and 2.5. A broad survey of estimates by University of California San Diego economist Valerie Ramey found that the range was usually between 0.8 and 1.5, although the data could support anywhere from 0.5 to 2.0.
. . .
Despite the wide uncertainty surrounding these estimates, they end up playing a major role in estimates of the stimulus’ effects. That’s because when economists at the White House or the Congressional Budget Office attempted to gauge the results of the stimulus, they relied heavily on measurements of inputs rather than outputs, and then used the multipliers to work from there. In other words, they looked at the amount of money spent on stimulus and then ran that through a model that included an estimated multiplier.
If you build a model that assumes a high multiplier effect, then your results will reveal that stimulus spending has a high multiplier effect. What you won’t have done is prove that stimulus spending has a high multiplier. But that’s how the government estimates of stimulus effects on jobs and economic growth work: Rather than measure real-world results, they count the spending, assume a multiplier, and then report the output.
And what if the real-world effects were, in reality, radically different? Would that show up in the reported estimates? No. When CBO Director Douglas Elmendorf was asked, “If the stimulus bill did not do what it was originally forecast to do, then that would not have been detected by the subsequent analysis?” his response was: “That’s right. That’s right.”
What we have then are highly uncertain, hard-to-pin-down multiplier estimates being used not to measure the results of stimulus, but to estimate what the results might be if those highly uncertain estimates happen to be correct. That’s not a clear failure, but it’s hardly proof of the unambiguous success the White House and its allies have claimed.
. . .
No doubt the political back and forth over the merits of stimulus will continue, and the declarations of success and failure will end up as fodder in fights over possible future fiscal policy boosts. Not much will change. That’s too bad. Because if there’s anything we should have learned from the fight over the nation’s biggest fiscal stimulus, it’s that we’ve been asking the wrong question. It’s not whether the stimulus did or did not fail, it’s whether we can ever know one way or another—and whether it's worth spending hundreds of billions of dollars on economic interventions whose results are likely to remain uncertain.
There's more at the link.
That's one reason politicians love to spend taxpayer money on things like stimulus packages. They can predict success, then obfuscate until the cows come home to prevent an in-depth, accurate, honest analysis of whether their predictions were correct or not. They can claim credit for everything good, and deny that everything bad had anything to do with their 'stimulus'. In fact, they'll usually claim that the bad would have been worse without the stimulus - but again, that's impossible to prove one way or another.
This is one of the primary ways that politicians lie. They promise things that can't be accurately or verifiably measured. If you can't measure something, you can't determine whether it was good or bad, a success or a failure, worthwhile or a waste of taxpayer money - and you can't hold accountable those behind it. Politician heaven!