The Fed’s bond purchases have generated considerable controversy. Critics, including Mr. Taylor and Mr. Warsh, argued at the time that the Fed was trying too hard to revive growth, and that it was instead stoking the fires of inflation. Those criticisms proved to be misplaced. Others argue the purchases were simply ineffective.

Ms. Yellen said Friday, as she has previously, that the purchases helped jump-start the economy.

“The evidence strongly suggests that forward rate guidance and securities purchases — by substantially lowering borrowing costs for millions of American families and businesses and making overall financial conditions more accommodative — did help spur consumption and business spending, lower the unemployment rate, and stave off disinflationary pressures,” she said.

She added, however, that the Fed still needed to show that it could end the program.

“We have met the first challenge and have made good progress to date in meeting the second,” Ms. Yellen said.

The Fed is not selling its bond holdings. As the bonds mature, it has used the proceeds to buy new bonds. Now it is gradually reducing the reinvestment, removing the rest of the money from circulation.

Ms. Yellen also defended a law that allows the Fed to pay interest on some of the money that banks deposit at the Fed.

Congressional Republicans have criticized those payments as an unnecessary subsidy to the financial industry. But Ms. Yellen said the law enabled the Fed to manage its retreat.

As the Fed bought bonds from banks, it paid them by increasing their reserve balances. That made it impossible to raise interest rates in the traditional manner, which is based on the scarcity of those reserves.