David Leonhardt writes in the New York Times :
Just look at the outside evaluations of the stimulus. Perhaps the best-known economic research firms are IHS Global Insight, Macroeconomic Advisers and Moody’s Economy.com. They all estimate that the bill has added 1.6 million to 1.8 million jobs so far and that its ultimate impact will be roughly 2.5 million jobs. The Congressional Budget Office, an independent agency, considers these estimates to be conservative.
Sounds pretty reassuring. The three best-known economic research firms come up with similar estimates and they’re conservative according to the CBO.
I don’t think this is true. I’m not sure what Leonhardt is referring to. But in November, the CBO estimated the impact  of the stimulus as of September, 2009. They said this:
CBO has estimated the law’s impact on employment and economic output using evidence about how previous similar policies have affected the economy and various mathematical models that represent the workings of the economy. On that basis, CBO estimates that in the third quarter of calendar year 2009, an additional 600,000 to 1.6 million people were employed in the United States, and real (inflation-adjusted) gross domestic product (GDP) was 1.2 percent to 3.2 percent higher, than would have been the case in the absence of ARRA (see Table 1 ). Those ranges are intended to reflect the uncertainty of such estimates and to encompass most economists’ views on the effects of fiscal stimulus.
That estimate of job creation is embarrassingly imprecise and the 1.6 million number would not be a conservative estimate but rather the high end estimate.
I cannot find another analysis by the CBO. Perhaps they have done something else more recently. (EDIT: And the estimates above are for only the 3rd quarter of ’09. So maybe if you extended them even the lower bound might get up to 1.6 million)
But even so, the CBO estimate of the impact of the stimulus is not meaningful and neither, I would guess, are the estimates by the other research firms.
Here is what the CBO said  about their estimates:
CBO’s current estimates differ only slightly from those CBO prepared in March 2009. At that time, CBO projected that in the third quarter of 2009, U.S. employment would be higher by 600,000 to 1.5 million people with ARRA than it would be without the law, and real GDP would be 1.1 percent to 3.0 percent higher. CBO’s new estimates reflect small revisions to earlier projections of the timing and magnitude of changes to spending and revenues under ARRA.
The “estimates” differ only slightly because the estimates are just a repeat of the forecast made just after the stimulus passed:
CBO has also examined incoming data on output and employment during the period since ARRA’s enactment. However, those data are not as helpful in determining ARRA’s economic effects as might be supposed, because isolating the effects would require knowing what path the economy would have taken in the absence of the law. Because that path cannot be observed, the new data add only limited information about ARRA’s impact.
It’s awkward that the path cannot be observed. But then what is the meaning of the estimates?
And the best part:
Economic output and employment in the spring and summer of 2009 were lower than CBO had projected at the beginning of the year. But in CBO’s judgment, that outcome reflects greater-than-projected weakness in the underlying economy rather than lower-than-expected effects of ARRA.
That would be one interpretation. The other is that the model doesn’t work very well.
UPDATE: Arnold Kling makes a similar argument here  and does it very nicely.