Will Barack Obama win re-election? Well, that depends mainly on the economy.

If the economy surges, he’s likely to win. If it lurches into a recession, he will quite probably lose. And if it simply muddles along at a sluggish pace, more or less as it has been doing for months now, the election could easily be a photo finish.

Those are the latest projections of Ray C. Fair, the Yale economics professor who has been studying the economy’s effect on American elections for decades.

His current calculations, which he shared with me last week, show President Obama with 50.17 percent of the vote, giving him a margin so small that it falls within the 2.5 percent “standard error” of the equations. “That means it’s too close to call,” Professor Fair says.

He doesn’t know the identity of the Republican nominee, but no matter. It wouldn’t effect his projections anyway, nor would the issues in the coming campaign. His calculations are based almost entirely on actual economic performance.

“It’s the economy, stupid,” the old James Carville line from the 1992 presidential campaign, is the title of the first chapter of Professor Fair’s book, “Predicting Presidential Elections and Other Things,” first published in 2002. A new edition is out, and it includes his preliminary thinking about the 2012 election.

“It’s very difficult to defeat an incumbent president if the economy is reasonably strong,” he said in an interview. And regardless of the personalities of the candidates, he has found that the strength of the economy — and whether it is improving or worsening as the election approaches — comes close to explaining the results of most presidential elections.

While his projections show Mr. Obama leading by a hair, they depend on a fairly sanguine economic forecast, which Professor Fair acknowledges is far from certain. The logic of his forecast is clear, though, and it has usually proved reasonably accurate. It is based on transparent economic models that have been extensively peer-reviewed.

On his Web site, fairmodel.econ.yale.edu, he maintains models of the economy and of its effects on presidential and Congressional elections. There are even do-it-yourself modules that let you plug in your own assumptions about the economy. The site will crunch those numbers for you and issue fresh predictions about the 2012 election.

In November 2010, when I wrote about Professor Fair’s early projections for 2012, his equations showed President Obama winning by a healthy margin. That’s because, at the time, his econometric projections were even more optimistic, showing annualized growth of per capita real gross domestic product of 3.69 percent for the first three quarters of 2012.

His current projections show annualized growth in that period of 3.02 percent. And they show only one strong quarter — one with a growth rate above 3.2 percent — in the president’s first three years in office, compared with six such quarters in the earlier estimate.

That still puts President Obama ahead in November, according to the model, but with a margin of error big enough to decide a close election. That reduces the practical, if not the intellectual, usefulness of his forecasting.

One reason for this big margin of error is that the quadrennial history of American presidential elections provides too small of a sample for more precise statistical analysis. The other reason is that this type of analysis goes only so far.

“I’m not attempting to do the job of a political scientist,” Professor Fair says. “I’m just assuming that there’s a historical regularity in the effect of the economy on how people vote, and I’m trying, through the use of econometrics, to estimate what that regularity is, and to use it to make a prediction.”

The data, going back to the election of 1916 — won by Woodrow Wilson, the Democratic incumbent — shows a “fairly remarkable” correlation between the economy and electoral results, he says. A pure economic analysis “seems to explain a very great deal” about politics, Professor Fair says.

It may, in fact, explain some difficulties that Republicans in Congress now face in positioning themselves for the election. Consider the last-minute decision to extend the payroll tax cut and unemployment benefits for just the first two months of 2012.

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