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In a Wall Street Journal article earlier this week, Jon Hilsenrath quoted the Stanford economist Robert Hall as claiming that there hasn't been much stimulus spending because of state and local government fiscal contraction: 

Robert Hall, a Stanford University professor, says there hasn't actually been that much extra government spending overall, because the increased federal spending has been largely offset by a large contraction in state and local government outlays. By the third quarter of 2009, he notes, federal government spending added $66 billion to economic output, less than 0.5% of total output, offset by a $43.1 billion contraction in state and local government spending, he says. 

This passage gives a misleading impression of the size of the government's response to the crisis, because it omits much of Hall's analysis of the stimulus. In order to assess the impact of fiscal policy, Hall broke up all the government spending in response to the recession into the two parts that would have varying spending multipliers: direct purchases of goods and services (which in Hall's model have a higher multiplier), and increased benefits and tax cuts and rebates (which have a significantly lower multiplier).

Hilsenrath's description only accounts for spending on purchases. He leaves out the stimulus funds that flowed to benefits or tax rebates, which funds accounted for over half of the spending in the third quarter of 2009 (depending on how you count "spending." Tax rebates, for instance, would show up as lost revenue instead of increased expenditure). In his assessment, Hall includes all above-trend government spending, or fiscal expansion, as stimulus, and not just spending included in the 2009 stimulus bill. Hall's measurement of spending, which includes automatic stabilizers, is intended to give a better picture of overall fiscal stimulus.

Here, from a paper Hall sent to me, is a graph showing the the extra government purchases of goods and services, the portion of the stimulus spending that Hilsenrath refers to:

Clearly federal spending on purchases was elevated through the first quarter of 2010, while state and local spending on purchases steadily decreased. 

And here is the rest of the stimulus spending, composed of tax rebates and benefits. Note the larger scale on the left axis:

Eyeballing this second graph, it looks like the government spent about an annualized extra $200 billion on benefits in the third quarter of 2009, far more than the annualized $66 billion portion Hilsenrath mentioned in the WSJ article. 

Given that Hilsenrath has omitted a majority of the stimulus from his discussion of Hall's work, it's unclear why someone would take this passage at face value as an argument that the stimulus "worked," as David Leonhardt of the New York Times did. It's reminiscent of the liberal blogger Ezra Klein arguing that there has been no net stimulus: if you can't tell whether fiscal policy has been expansionary or not, shouldn't that introduce some doubt about whether it was effective?