Under Paul Volcker, the Fed gradually brought inflation under control by driving the economy into a deep recession. By the mid-1990s, it seemed plausible the Fed could eliminate inflation completely. But Ms. Yellen, then a new Fed governor, was among those who argued successfully that it would be better to maintain moderate inflation.

A little inflation helps the economy rebound from recessions. It gives the Fed more room to reduce borrowing costs, and it also eases necessary economic adjustments. Employers, for example, can cut costs by holding wage increases below the inflation rate.

Inflation can also brighten the economic mood by raising wages and profits more quickly.

And a little inflation also keeps the economy at a safe distance from deflation. When prices fall, growth tends to stall as people wait for even lower prices.

The current debate, however, is mostly about inflation’s role as an economic barometer.

Fed officials began the year expressing confidence that inflation was finally rebounding as the economy continued to expand. But the Fed’s preferred measure of inflation declined in the last three monthly reports, from an annualized pace of 2.1 percent in February to 1.4 percent in May. The inflation gauge is published by the Commerce Department.

Job growth remains strong, but recent reports on cautious consumer spending and business investment suggest that overall growth remains tepid. A turn toward stronger growth again has failed to materialize. The Federal Reserve Bank of Atlanta, which predicted the economy would expand at an annualized pace of 4 percent in the second quarter, now estimates second-quarter growth was 2.5 percent.

The persistent sluggishness has convinced some Fed officials to revise their thinking.

“Low inflation has been the major surprise of the era,” James Bullard, president of the Federal Reserve Bank of St. Louis, declared last April. He said he did not support any increases in the Fed’s benchmark rate until 2018, to give inflation time to recover.