This paper uses a stochastic simulation of a DSGE model of the Czech economy to study the macroeconomic consequences of inflation target setting when interest rates are constrained by the zero lower bound. The distortions of this constraint depend non-linearly on the inflation target. For an inflation target of two percent the costs are negligible, but they increase steeply with lower target values. The largest impact is on the average values of output, consumption and investment; inflation is only slightly influenced. The volatility of all the variables considered increases significantly, but only for inflation targets that are close to zero. An inflation target of four percent does not bring additional benefits either in terms of lower volatility or in terms of higher average values.