Economists trying to figure out how stimulative the stimulus package that Congress approved in early 2009 was have got bogged down in the sort of problem economists are always getting bogged down in: There’s no way to know what the world would have looked like sans stimulus.

“Without a counterfactual, the best we can do is fall back on our models,” write Dartmouth College economists James Feyrer and Bruce Sacerdote in a paper published by the National Bureau of Economic Research. “Unsurprisingly, the models tell the same story today that they did when arguments for and against the stimulus were being made.”

The two use what they think is the better approach of comparing states and counties that got a heavy dose of stimulus spending with those that didn’t. The difficulty with this is that one would naturally expect the places that got hardest hit by the recession to get the most money. Their solution: Historically, states with higher seniority in Congress tend to receive the most money per capita. That allowed the economists to employ a statistical technique to try and tease out the effect of spending. (Caveat: The method they used can be problematic. See here.)

What they find is that the stimulus package did boost the economy — though not by as much as the administration assumed it would when it put the plan in place. One reason why, they find, is that money spent to support education and law enforcement did little to improve employment. But programs to support low-income households were highly stimulative, as was spending on infrastructure projects.

“This all suggests that a stimulus package that did not include state level grants for local services would have been more effective per dollar than the actual stimulus package,” they write.