In any case, the Fed has succeeded in driving down unemployment, which is perhaps the strongest defense against the reverse Robin Hood argument, since the single most powerful means of reducing income inequality is to reduce the number of people who have no income.

Josh Bivens, director of research and policy at the left-leaning Economic Policy Institute, delivered that defense at Brookings. Mr. Bivens has sounded the alarms about inequality in recent years, but he said the Fed’s stimulus campaign was not to blame. Compared with an alternate reality in which the Fed would have done nothing, he said it was clear that the stimulus campaign reduced inequality by increasing employment.

“Successful macroeconomic stabilization is strongly progressive,” Mr. Bivens said.

Even the Fed’s impact on asset prices was arguably progressive, he said. While the Fed drove up stock prices, most of which are owned by the wealthy, it also increased the value of housing, which is mostly owned by the middle class.

Indeed, Mr. Bivens said he had compared the impact of the Fed’s campaign with the Obama administration’s 2010 fiscal stimulus and found no evidence of a larger impact on inequality. The means were different, but the impact was more or less the same.

A second paper presented at Brookings reached a similar conclusion: “Contrary to much of the recent rhetoric, looser monetary policy helps the middle class and middle-aged at the expense of the wealthy aged,” wrote the economists Matthias Doepke and Veronika Selezneva of Northwestern University and Martin Schneider of Stanford.

This, however, is a stronger case than Mr. Bernanke himself was willing to make.

Mr. Bernanke argued instead that the impact on inequality was beside the point. The Fed acted to improve the nation’s prosperity. The impact on inequality was “complex and uncertain,” but whether positive or negative, it was most likely small. And if there is a negative impact, he suggested it should be offset by fiscal policy.