Target Inflation = Autonomous Inflation
If target inflation = autonomous inflation = 0, but target output is above potential output, then the Fed will reduce the real interest rate and create more output to meet its target output. This will create inflation. This is not the end of the story. Everyone in the economy is predicting zero inflation, yet the Fed is using its monetary policy to increase output and create positive inflation. Over time, people will notice that their expectations are wrong and will start to expect positive inflation instead. This results in an increase in autonomous inflation and a shift in the relationship between inflation and output. At that point the Fed will have an incentive to create still more inflation to pursue its goal of output above potential. But additional inflation is costly to the Fed because it is now moving away from its target of zero inflation. Eventually inflation will be so high that the Fed no longer wants to create more inflation to increase output. The economy will end up with a positive inflation rate, where expectations of inflation are equal to actual inflation and no one is fooled. In the end, the Fed incurs an inflation rate above its target, yet it does not succeed in creating output above potential. The final outcome involves costly inflation, but output remains at potential. Given that it cannot actually keep output above potential, the Fed would prefer zero inflation, yet it lacks the ability to commit to a zero-inflation policy. If the inflation rate is zero, the Fed has an incentive to create positive inflation.
