An estimated monetary policy VAR with 1993:IV-2008:III Euro data returns an insignificant response of inflation and a borderline significant reaction of the output gap to monetary policy shocks identified with the widely employed Cholesky restrictions. We replicate this evidence with a Monte Carlo exercise, in which the true responses of inflation and the output gap, according to an estimated DSGE model which we use as data-generating process, are negative. Consequently, insignificant macroeconomic reactions to policy shocks as documented by a smallscale Cholesky-VAR for the Euro area do not necessarily point to monetary policy neutrality. Differently, the Cholesky-VAR evidence may very well be due to false short-run zero-restrictions. A data-driven discussion on this reading of the drivers of our Cholesky-VAR impulse responses versus alternative interpretations such as omitted factors and structural breaks is proposed.We thank Robert M. Kunst (Coordinating Editor) and two anonymous referees for their useful comments and suggestions. We also thank