Federal Reserve Chair Janet Yellen just testified to Congress for the first time, calming markets with assurances about the economy and the central bank's stimulus.

As usual, Congress showed how it doesn't understand the Fed, its role or its powers by asking questions and leveling accusations about issues the central bank has no control over, says Fortune's Christopher Matthews.

"Twice a year, the chair of the Federal Reserve submits herself to questioning from the House Financial Services Committee, and twice a year Congress embarrasses itself by misunderstanding the role and powers of the central bank," he writes.

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For instance, Rep. Randy Neugebauer, R-Texas, called the Fed a "deficit enabler" because of its bond-buying program. The program — now cut to $65 billion a month — entailed purchasing $85 billion a month of mortgage and government bonds.

However, it's Congress's job to set federal spending and the deficit, Matthews notes. The Fed's job is to set interest rates, attain low inflation and low unemployment.

Several Congressmen complained about the trend of increasing income inequality, saying the Fed's bond-purchases disproportionally helped the wealthy.

Yet the Fed lacks the power to solve the inequality issue. Even if its stimulus helps the rich more than others, "it doesn't do anything to make the poor worse off," Matthews says. "Does it make sense," he asks, "not to do it because it helps some people more than others? "

Who does have to power to decrease income inequality? Congress.

Some Congressmen complained the Fed is hurting retirees. By keeping interest rates low, they charge, the Fed is suppressing their interest earnings.

While retirees may be suffering, young workers and business owners have also been suffering in an economy with high unemployment and tight credit, Matthews states.

Congress, not the Fed, can use the tax code or Social Security to help retirees, he argues.

Yellen told the House Financial Services Committee Tuesday that income inequality is growing because more Americans lack the skills businesses demand, according to The Business Journals' Washington Bureau Chief Kent Hoover. Good-paying jobs for low-skilled workers are disappearing due to technological changes and global competition.

"That's not the Fed's role, however. The best thing the Fed can do to improve the job market is to boost economic growth," writes Hoover.

"It's up to other policymakers — Congress, the president, governors and mayors — to address the skills gap that's trapping too many Americans in low-paying jobs or no jobs at all.

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