Last week, Christina Romer, chairwoman of the White House Counsel of Economic Advisers, suggested that we think of the $787 billion American Recovery and Reinvestment Act as an extremely expensive course of antibiotics. “Suppose you go to your doctor for a strep throat,” Romer said in a speech to the Economic Club of Washington, “and he or she prescribes an antibiotic.”

If your fever goes up after you take the first pill, just as unemployment rose after the stimulus bill was enacted, that doesn’t mean “the medicine is useless,” Romer noted. It could simply be that “the illness was more serious than you and the doctor thought.”

But it’s also possible that your sore throat and fever are caused by a virus, not a bacterium, in which case the antibiotic will not help. Eventually, though, you will recover on your own, and you may mistakenly conclude that your doctor’s prescription did the trick.

Such erroneous causal inferences are always a hazard when it comes to government spending aimed at alleviating a recession. Even if most or all of the money is disbursed after the recession has ended (which is typically the case), stimulus advocates can say the recovery would have been weaker without the spending. Since there’s no readily available parallel universe in which to test that counterfactual hypothesis, they can never be conclusively refuted.

Still, Romer seems unreasonably sure that Dr. Obama’s medicine is already kicking in. Although she concedes that “the evidence from the path of the economy over time can’t settle the issue of what the effects of the Recovery Act have been,” her answer to the question posed in the title of her speech – “Is It Working?” – is “absolutely.”

I guess that depends on how you define “working.” No doubt spending billions of dollars in borrowed money has some impact on the economy. But the idea that the stimulus package played a major role in what looks like an incipient recovery that may have begun in June is belied by a couple of inconvenient facts.

First, since World War II, the length of recessions has ranged from six to 16 months, with an average of 10. The current recession officially began in December 2007, so a recovery by the second half of 2009 was always widely expected.

Second, according to ProPublica, only $73 billion of the $580 billion in stimulus spending has been disbursed so far. Another $30 billion or so has gone out in the form of tax cuts.

Romer concedes the latter portion of the stimulus does not seem to be very stimulating. She says “consumption fell slightly in the second quarter after rising slightly in the first quarter,” which “could be a sign that households are initially using the tax cut mainly to increase their saving and pay off debt.”

Is it plausible to suggest that $73 billion in stimulus spending over five months had a decisive impact on a $14 trillion economy? I say “decisive” because President Obama, back in February, presented the stimulus package as the only alternative to a never-ending recession, and last week he claimed, “We’ve rescued our economy from catastrophe.”

Even if we accept the Obama administration’s numbers, taxpayers do not seem to be getting much employment bang for their buck. Romer estimates that “employment is now about 485,000 jobs above what it otherwise would have been.” That comes out to more than $200,000 per job, which seems pretty pricey, especially since many of these jobs are temporary.

Here is where the “reinvestment” part comes into play. Administration officials say the stimulus package is all about putting Americans back to work. When asked whether this is an efficient way to do that, they claim all the work needs to be done anyway. Conversely, when asked whether all the projects are really worth the money spent on them, they cite jobs “created or saved” as a backup justification. Stimulus means never having to admit you’re wasting money.

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