Those of us who say that the stimulus was too small are often accused of after-the-fact rationalization: you said this would work, but now that it hasn’t, you’re just saying it wasn’t big enough. The quick answer to that accusation is that people like me said that the stimulus was too small in advance. But the longer answer is that it’s all in the math: Keynesian analysis provides numbers as well as qualitative predictions, and given reasonable projections of the economy’s path in January 2009, the proposed stimulus just wasn’t big enough. Let’s go back to the tape, January 9, 2009:

Even the C.B.O. says, however, that “economic output over the next two years will average 6.8 percent below its potential.” This translates into $2.1 trillion of lost production. “Our economy could fall $1 trillion short of its full capacity,” declared Mr. Obama on Thursday. Well, he was actually understating things. To close a gap of more than $2 trillion — possibly a lot more, if the budget office projections turn out to be too optimistic — Mr. Obama offers a $775 billion plan. And that’s not enough. Now, fiscal stimulus can sometimes have a “multiplier” effect: In addition to the direct effects of, say, investment in infrastructure on demand, there can be a further indirect effect as higher incomes lead to higher consumer spending. Standard estimates suggest that a dollar of public spending raises G.D.P. by around $1.50. But only about 60 percent of the Obama plan consists of public spending. The rest consists of tax cuts — and many economists are skeptical about how much these tax cuts, especially the tax breaks for business, will actually do to boost spending. (A number of Senate Democrats apparently share these doubts.) Howard Gleckman of the nonpartisan Tax Policy Center summed it up in the title of a recent blog posting: “lots of buck, not much bang.” The bottom line is that the Obama plan is unlikely to close more than half of the looming output gap, and could easily end up doing less than a third of the job.

In practice, it was even worse, because one of the key elements of the plan — aid to state and local governments — was cut back sharply in the Senate. We ended up with only about $600 billion of real stimulus over that two-year period.

So this wasn’t a test of fiscal stimulus, even though it has played out that way in the political arena: the whole thing was obviously underpowered from the start.