McCallum rule
Based on Milton Friedman's approach , Bennett McCallum developed a rule that also takes into account the development of the speed of rotation . Since the central bank only has direct control over central bank money, he only uses this money supply aggregate in his equation (central bank money supply = ZBG) McCallum bases his considerations on the quantity theory just like Friedman : (1.0) M × V = P × Y With M = money supply, V = velocity of circulation, P = price level, Y = real national product If one expresses this identity (1.0) in growth rates, and solving for ∆M, one obtains: (1.1) ∆M = π + ∆Y-∆V_M (P) becomes to (π), since the change in the price level corresponds to inflation. If you now note the correct monetary aggregate follows:
(1.2) ∆ZBG = π + ∆Y-∆V_ZBG If one expresses the money (creation) multiplier as growth rates, the result is: (1.3) ∆M = ∆m + ∆ZBG if one puts (1.1) and (1.2) in (1.3) follows: (1.4) π + ∆Y-∆V_M = ∆m + π + ∆Y-∆V_ZBG
-∆V_M=∆m-∆V_ZBG
∆V_ZBG=∆V_M+ ∆m bzw:
(1.5) π + ∆Y-∆V_M = ∆m + π + ∆Y-∆V_ZBG McCallum chooses 0% for inflation and 3% for real development (long-term average growth in the USA). The target value for the nominal GNI is then 0.74% for the quarter. The target value for the monetary base can thus be defined: Values in (1.2) ∆ZBG = 0.0074-∆V_ZBG
The average value of the last 16 quarters is used for the rate of circulation of the monetary base.
(1.6)∆ZBG= 0,0074-1/(16 ) ∑_(i=1)^16▒〖∆V_(ZBG,t-i) 〗
As a final step, the formula is supplemented with a countercyclical component. This is expressed by the difference between the actual GNI growth rate of the previous period (Y_ (t-1) ^ N) and the target value for nominal growth (Y ^ (N *)).
(1.6) ∆ZBG = 0.0074-1 / (16) ∑_ (i = 1) ^ 16▒ 〖∆V_ (ZBG, ti)〗 + λ ∙ (ln 〖Y〗 ^ (N *) - ln 〖 Y〗 _ (t-1) ^ N)
λ = speed of adjustment of monetary policy (for the USA 0.25) From this the following recommendation for action can be derived for the central bank: If the value of the nominal GNI in the previous period is below its trend value, the growth rate of the monetary base should be increased, and vice versa.