Mitt Romney’s campaign would have you believe that every job lost over the past three years is President Obama’s fault. That includes the 820,000 jobs lost in January 2009, despite the fact that Obama didn’t become president until the 20th of that month. It also includes the 726,000 jobs lost in February 2009, before any of Obama’s policies had gone into effect.

It suggests Romney holds a deeply ambitious view of a president’s power to influence the labor market — a view, as we’ll see, that’s not shared by economists who were responsible for White House economic policies in recent administrations.

But Romney’s campaign also asks us to believe that every job created in Massachusetts while he was governor was Mitt Romney’s doing. Obama might deserve the blame for the jobs lost in every state on his watch, but George W. Bush, who was president during Romney’s governorship, gets no credit for the jobs created in Massachusetts during his administration.

And Romney claims that every job created by any company that Bain Capital had a hand in should also be credited to him — even if the job was created long after Romney separated from the company. Heads, I created a job; tails, you lost one.

The Obama campaign isn’t much better. It wants credit for every job created, but not for every job lost. It also wants the ideas of Democratic economists to get credit for the jobs created under Bill Clinton’s presidency (what tech bubble?) and for the GOP’s economic philosophy to take the hit for the financial crisis that began during Bush’s administration (what Clinton-era opposition to the regulation of derivatives?).

Gov. Rick Perry’s campaign, meanwhile, assigns Obama responsibility for every job lost nationwide, but Perry gets credit for every job created in Texas. Neat trick. And he, like all Republicans, wants the jobs created under President Ronald Reagan added to conservatism’s side of the ledger.

To buy much of this requires that you hold deeply ridiculous beliefs about the American economy. You must believe that Obama bears responsibility for events that predate his presidency and deserves applause for the demand created by aging cars and worn-down machinery

You must believe that Congress, which controls fiscal policy, and the Federal Reserve, which controls monetary policy, bear little or no responsibility for the economy, but that the president is the primary driver of job creation. You must believe that governors have absolute power over state economies and that global demand is irrelevant. You also must renounce belief in Christmas — or at least its influence on the consumer-driven economy.

Virtually no one really believes these things. But partisans and the press routinely act as if they are true. They comprise a useful shorthand that is arguably good for the political system: Better for presidents to believe reelection hinges on economic performance than, say, on the quality of their attack ads.

But it would be even better if voters had a consistent benchmark for judging a president’s performance. The question — and it’s a tough one — is how to separate the very real influence the president has on the economy from the myriad other factors that weigh on whether consumers spend and businesses hire. So I put the issue to an exclusive club of economists who have an unusually fine-grained understanding of what the president can and can’t do: the former chairs of the president’s Council of Economic Advisers. And I asked each the same question: How much of national job creation during a presidency can we properly attribute to the president?

“Very little,” wrote Harvard’s Martin Feldstein in an e-mail. Feldstein led the CEA under Reagan, and he didn’t see much role for the president in normal economic times. “The key is growth of population and labor force participation. Policy — primarily monetary policy — affects cyclical conditions and therefore the unemployment rate. Fiscal policy is usually irrelevant but with interest rates at the current level there has been a role for fiscal policy.”

Laura D’Andrea Tyson, a Berkeley economist who served under President Clinton, emphasized the need to consider timing in our evaluations. “There are significant lags between the time a President proposes a policy, the time it is enacted by Congress and the time necessary for it to take effect,” she wrote to me. “These lags should be taken into account in measuring the economy’s job performance under a President. The first year probably should not count at all in terms of assessing the effects of a new Administration’s policies.”

Greg Mankiw, a Harvard economist who served as CEA chair under George W. Bush, directed me to a blog post he had written on the subject. “Randomness is a fact of economic life,” Mankiw wrote, “and it would be a mistake to judge a president by the economic outcome during his administration. It is better to look at the decisions the president made, and to acknowledge that the outcome is a function of those decisions and many other factors not under his control. As an economist, I have views about what best practices are for economic policy, and I judge presidents by how closely they adhere to those principles.”

“Unfortunately,” he concluded, “that evaluation process is not quite as simple and objective as the reader might have hoped for. But I don’t think there is a better alternative.”

Austan Goolsbee, CEA chair under Obama, tried to lay out a four-part test: “Everyone kind of knows they need to ask what conditions was the person handed, what did they do, what was happening elsewhere, and what would have happened if he wasn’t there?”

But those questions, Goolsbee admitted, are tough to answer. Whatever the answer is, however, it needs to take into account that the president’s control of the economy is at best incomplete. “Despite continued scrounging around in the basement,” Goolsbee said of his time in the White House, “I was never able to find the lever you flip that lets the economy grow and create jobs.”