Without knowing where the economy was headed in the absence of the stimulus, it’s impossible to judge what it contributed just from what happened afterward. That’s why empirical economists rely on other approaches.

One is to look at history. The stimulus legislation, technically known as the American Recovery and Reinvestment Act of 2009, was a mixture of tax cuts for families and businesses; increased transfer payments, like unemployment insurance; and increased direct government spending, like infrastructure investment. A growing literature examines the effects of such tax cuts and increases in government spending over history and across countries, and the overwhelming conclusion is that fiscal stimulus raises employment and output in the near term.

When the Congressional Budget Office or leading private forecasters assess what the Recovery Act contributed, they use these estimates from history. They multiply the amounts of different types of stimulus in the act by their usual historical effects. This method suggests that at its peak, the act raised employment by about 1 million to 3 1/2 million jobs, compared with what would have happened without it.

But history isn’t destiny. It’s possible that the various elements of the Recovery Act worked better or worse than similar measures in the past. That’s why a cottage industry has emerged of researchers looking explicitly at the recent experience.

The most successful of these studies focus on the variation in Recovery Act spending across states. Some of this variation resulted from differences in the recession’s severity. For example, there was much more spending on unemployment insurance in Michigan than in Wyoming, because unemployment rose much more in Michigan. We wouldn’t want to look at that variation and say Recovery Act spending caused unemployment to be higher, because causation clearly ran in the other direction.