It’s being called the “battle of the beards” — Paul Krugman vs. Ben Bernanke. Both are eminent (and bearded) economists: Bernanke, chairman of the Federal Reserve Board; Krugman, a Nobel Prize winner and a prominent New York Times columnist. Krugman accuses Bernanke of being too timid in fighting high unemployment and slow economic growth. Bernanke calls Krugman’s policy proposals “reckless.” What’s going on?

Beyond the rhetoric, there’s a serious debate about the Federal Reserve. A decade ago, the Fed was widely seen as all-knowing and powerful. It could cushion business cycles, defuse financial crises and ensure prosperity. No more. Almost everyone thinks unemployment (8.1 percent in April) is declining too slowly. By year-end 2013, it will still be somewhere between 7 and 8.1 percent, according to top Fed officials’ latest estimates.

The Fed hasn’t been passive. Since late 2008, it has kept overnight interest rates just above zero. During the 2008-09 financial crisis, its emergency loans to banks and money market funds averted a broader collapse. The Fed also bought more than $2.5 trillion of Treasury bonds and mortgage-related securities in an effort to lower long-term interest rates (studies suggest a decline of 0.7 percentage points or more) and boost stock prices, as investors seek higher returns.

But these heroic exertions haven’t yet ignited a robust recovery.

What we need now — and what the Fed could supply, says Krugman — is a bit more inflation. This would spur growth and job creation, he argues. The Fed now strives to keep inflation around 2 percent annually, a low level that it views as reassuring the public. Krugman wants the Fed to raise its target range to 3 to 4 percent for five years.

“You’d make borrowing more attractive. Sitting on cash would be less attractive,” he says. The logic is straightforward. If prices rise 4 percent instead of 2, consumers and businesses have an incentive to buy now and avoid higher prices later. If interest rates don’t increase (or increase less than inflation), then “real” rates — adjusted for inflation — fall; again, that makes borrowing more appealing.

Higher inflation would also erode the “real” value of debt. With a lighter debt burden, households and businesses would feel freer to spend. Another channel would be a cheaper dollar on foreign exchange markets, making U.S. exports less expensive and imports more expensive. (Krugman minimizes this channel, because he thinks Europe and Japan should also pursue higher inflation.)

Besides Krugman, some other economists advocate higher inflation. But not Bernanke.

Without naming Krugman, he responded at an April 25 news conference: “Does it make sense to actively seek a higher inflation rate in order to achieve . . . a slightly increased pace of reduction in the unemployment rate? The view [of top Fed policymakers] is that that would be very reckless.”

Bernanke argued that the belief that the Fed keeps inflation down (what economists call the “anchoring” of inflationary expectations) tends to be self-fulfilling. If companies think inflation will stay low, they refrain from large price increases that might weaken their competitiveness. This then allows the Fed to be more aggressive in cutting interest rates to fight unemployment. If inflationary expectations shifted, as they might under Krugman’s proposal, the flexibility could be lost.

Although Bernanke didn’t say so, there are other reasons Krugman’s policy could backfire. Consider:

●Prices might increase faster than wages, reducing workers’ purchasing power and (probably) dampening spending.

●Experiencing higher inflation, consumers might become more fearful of the future and, to protect against the unknown, might increase saving and reduce spending — the opposite of what Krugman intends. This happened in the 1970s, although at higher inflation rates than Krugman proposes.

●Something similar could happen in financial markets. Investors — not knowing whether inflation would return to 2 percent and fearing it might go higher than 4 percent — might demand much higher interest rates to prevent erosion of their money. This, too, would undermine Krugman’s strategy.

None of this is preordained. Krugman’s theory could be right. It responds to an understandable urge to do something about the feeble recovery and the millions left without work and hope. But in this debate, I side with Bernanke. Flirting with more inflation is treacherous. If inflation expectations change, the consequences are hard to predict. The double-digit inflation in the late 1970s (peak: 13 percent) resulted from well-intended mistakes and unleashed many damaging side effects.

What we should have learned since 2008 is that the Federal Reserve can’t do everything and overambitious goals guarantee disappointment. The larger lesson is that economists have exaggerated their understanding and control of the economy. People often don’t act according to academic theories. There isn’t a proper policy response for every need. This captures our frustration.