I decompose deviations of the Federal funds rate from a Taylor type monetary policy rule into exogenous monetary policy shocks and a time-varying inflation target. I show that the role of exogenous shocks may be exaggerated in a fixed inflation target model, and a large fraction of business cycle fluctuations attributed to them may actually be due to changes in the inflation target. A time-varying inflation target explains approximately half of the volatility normally attributed to these deviations, and consequently more than a quarter of the fluctuations in the business cycle. This contributes approximately 39% additional inflation volatility during the Great Inflation. I show that shocks to the inflation target imply a lower sacrifice ratio compared to exogenous changes in the interest rate and therefore propose a gradual adjustment of the inflation target in order to achieve monetary policy objectives.