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The first pillar of the European Central Bank's monetary strategy consists of a reference value for the medium-term growth rate of the M3 monetary aggregate (set at 4.5%). This paper examines whether the special importance given to monetary variables in the conduct of European monetary policy is warranted. Two approaches are used. On the one hand, we ask whether a stable M3 demand function has been observed in the past. On the other, we study what information this aggregate contains for calculating short- to medium-term inflation using a P-Star model.