That's the question that readers of Fivethirtyeight Economics are asking after reading a discussion of the choices facing the Federal Reserve Board. The piece told readers that the Fed could push unemployment rate down to levels where inflation began to accelerate (overshooting):
"Overshooting is risky. The Fed would risk its credibility as an inflation-fighting central bank."
The cost of keeping the unemployment rate up is that the government (through the Fed) is denying millions of people the opportunity to get jobs. The government is also putting downward pressure on the wages of the bottom half of the workforce, since their wages are especially sensitive to the unemployment rate. And the economy is losing hundreds of billions of dollars a year in lost output, since these workers could be productively employed.
Obviously Fivethirtyeight attaches great value to the Fed's credibility as an inflation-fighting central bank since it thinks that we might think this value exceeds the costs of keeping the unemployment rate high. It would be helpful to readers if it explained how high this value is and how it came to this assessment.