If the output gap is a good representative measure of the cyclical unemployment rate, then we are fully covered – the monetary policy equation we use to get to the interest rate includes, as best we can, the relationship between those rates and employment. If we look at how the Fed operates, we can take further comfort in our own framework.
The Fed has an inflation target of 2%, averaged over time. This averaging introduces some flexibility to not respond to inflation shocks that are temporary, just as in our flexible inflation-targeting framework. But the Fed framework does not say that when unemployment rises it will aim for a higher inflation rate.