Do current Central Banks need to target a monetary aggregate as they set interest rates for a target inflation?
The demand for liquidity is usually defined as
$$
L(Y,i)
$$
where $Y$ is income and $i$ is the nominal interest rate. In equilibrium this equals the aggregate money supply $M$ which is function of several things, like $M_0$ the reserve rate, etc. Let us assume that everything except $i$, $M_0$ and $M = f(M_0)$ is constant. Then
$$
L(Y,i) = M = f(M_0).
$$
Demand for liquidity decreases in $i$ and $M$ increases in $M_0$. Thus for any given value of $i$ there is at most one equilibrium value of $M_0$, hence the central bank cannot simoultaneously set both $i$ and $M_0$ and always expect an equilibrium outcome. Lacking equilibrium either $i$ or $M$ will shift.