Suddenly, or so it seems, the U.S. economy is looking better. Things have been looking up for a while, but at this point the signs of improvement — job gains, rapidly growing G.D.P., rising public confidence — are unmistakable.

The improving economy is surely one factor in President Obama’s rising approval rating. And there’s a palpable sense of panic among Republicans, despite their victory in the midterms. They expected to run in 2016 against a record of failure; what do they do if the economy is looking pretty good?

Well, that’s their problem. What I want to ask instead is whether any of this makes sense. How much influence does the occupant of the White House have on the economy, anyway? The standard answer among economists, at least when they aren’t being political hacks, is: not much. But is this time different?

To understand why economists usually downplay the economic role of presidents, let’s revisit a much-mythologized episode in U.S. economic history: the recession and recovery of the 1980s.

On the right, of course, the 1980s are remembered as an age of miracles wrought by the blessed Reagan, who cut taxes, conjured up the magic of the marketplace and led the nation to job gains never matched before or since. In reality, the 16 million jobs America added during the Reagan years were only slightly more than the 14 million added over the previous eight years. And a later president — Bill something-or-other — presided over the creation of 22 million jobs. But who’s counting?

In any case, however, serious analyses of the Reagan-era business cycle place very little weight on Reagan, and emphasize instead the role of the Federal Reserve, which sets monetary policy and is largely independent of the political process. At the beginning of the 1980s, the Fed, under the leadership of Paul Volcker, was determined to bring inflation down, even at a heavy price; it tightened policy, sending interest rates sky high, with mortgage rates going above 18 percent. What followed was a severe recession that drove unemployment to double digits but also broke the wage-price spiral.

Then the Fed decided that America had suffered enough. It loosened the reins, sending interest rates plummeting and housing starts soaring. And the economy bounced back. Reagan got the political credit for “morning in America,” but Mr. Volcker was actually responsible for both the slump and the boom.

The point is that normally the Fed, not the White House, rules the economy. Should we apply the same rule to the Obama years?

Not quite.

For one thing, the Fed has had a hard time gaining traction in the wake of the 2008 financial crisis, because the aftermath of a huge housing and mortgage bubble has left private spending relatively unresponsive to interest rates. This time around, monetary policy really needed help from a temporary increase in government spending, which meant that the president could have made a big difference. And he did, for a while; politically, the Obama stimulus may have been a failure, but an overwhelming majority of economists believe that it helped mitigate the slump.

Since then, however, scorched-earth Republican opposition has more than reversed that initial effort. In fact, federal spending adjusted for inflation and population growth is lower now than it was when Mr. Obama took office; at the same point in the Reagan years, it was up more than 20 percent. So much, then, for fiscal policy.

There is, however, another sense in which Mr. Obama has arguably made a big difference. The Fed has had a hard time getting traction, but it has at least made an effort to boost the economy — and it has done so despite ferocious attacks from conservatives, who have accused it again and again of “debasing the dollar” and setting the stage for runaway inflation. Without Mr. Obama to shield its independence, the Fed might well have been bullied into raising interest rates, which would have been disastrous. So the president has indirectly aided the economy by helping to fend off the hard-money mob.

Last but not least, even if you think Mr. Obama deserves little or no credit for good economic news, the fact is his opponents have spent years claiming that his bad attitude — he has been known to suggest, now and then, that some bankers have behaved badly — is somehow responsible for the economy’s weakness. Now that he’s presiding over unexpected economic strength, they can’t just turn around and assert his irrelevance.

So is the president responsible for the accelerating recovery? No. Can we nonetheless say that we’re doing better than we would be if the other party held the White House? Yes. Do those who were blaming Mr. Obama for all our economic ills now look like knaves and fools? Yes, they do. And that’s because they are.