Historically, slack has accounted for only a small portion of the fluctuations in inflation. Indeed, unusual aspects of the current recovery may have shifted the lead-lag relationship between a tightening labor market and rising inflation pressures in either direction.
The standard tool of central banks is the short term interest rate which they use to influence interest rates across financial markets, and thereby steer the financial conditions in the economy. During the crisis, central banks around the world reduced policy rates ferociously, and in many advanced economies the rates are at or near zero.