Once we take account of the role of expectations, the stabilizing effects of monetary policy become even greater: If economic decision makers come to realize that the Fed is doing more to stabilize inflation, then shocks that push up inflation will lead to smaller increases in inflation expectations than in the past.
Because current inflation is affected by inflation expectations, the smaller increase in expected inflation will lead to a smaller increase in actual inflation as well. And because many shocks that may lead to inflation, such as unexpected surges in spending, also cause movements in output and employment in the same direction, the maintenance of price stability promotes the stability of the real economy.