In the fourth quarter of 2012, the CBO estimates, stimulus effects caused between 100,000 and 800,000 people to be employed over what would have happened absent the stimulus. By the end of 2013, the CBO's low-end estimate shows that the stimulus' effect on economic activity will be gone.
Last year, the CBO revised its economic modeling to account for the possibility that the stimulus was far less effective than they had previously estimated. In doing so, they cut their low-end estimate for the stimulus' effectiveness in half. This report has left the CBO's stimulus multiplier estimates effectively unchaged.
As the stimulus' effectiveness dies down, attention turns to the estimates of long-run effects of the legislation. And this is where the CBO's warnings take a dark turn. CBO's estimates are that ARRA will depress economic activity in the long run, by between zero and 0.2% of GDP. "ARRA's long-run impact on the economy will stem primarily from the resulting increase in government debt," the report warns. "In the long run, each dollar of additional debt crowds out about a third of a dollar's worth of private domestic capital." Still, the CBO is optimistic about some of the stimulus' effects, hoping that road and infrastructure investments will pay off.The CBO takes an explicitly Keynesian framework to its stimulus analysis - that government spending has more economic effect in a recession and recovery than it does during an economic boom. For a good framework to think about this, Matt Mitchell at the Mercatus Center pulled a very good summation of recent research on if government spending helps or crowds out private economic activity:
Mitchell's analysis also includes some caveats, like that multipliers tend to be smaller as a potential stimulus gets larger and that "multipliers are smaller in economies that are burdened by high levels of government debt."
The CBO's median multiplier estimates are generally around 1.5, but due to uncertainty they provide a very, very wide range. Some of the most influential economists in the world believe the multiplier is nonexistant, while members of President Obama's economic team believe there's an incredibly high multiplier specifically for tax cuts. The final word on President Obama's stimulus is still to be written, but the CBO's analysis is one of many valuable points of reference.