Stephen M. Miller Equation(7)does not separate the effect of the excess supply f money into movements in real income and the price level. Al lowing for these differential effects, Equation(5)becomes Dlny=φ2(1-81nM-hnM) D In P 22(1-8)n MS-In Mp) whereΦ2=Φa1+Φ2,Now, dividing Equations(4,(5a),and⑤5b) byΦ1,Φal,andΦ2;, respectively, and then subtracting twice Equa- tion (4)from the sum of Equations (5a)and (5b) gives In M-In Mt=-(1/1D In T,+(1/2p2 D In y, +(1/2p22)D In P, And finally, substituting from Equation(1)results in In M=ao+aInr,+aIn y, +aaIn P, -(1/p,)D In re +(1/22)Dhy+(1/2a)DhP+∈ Now, first-differencing Equation (1)yields In M,-In Mi-1=a, D In rt-1+ a2D In y,-1 3D In Pt-1+ Et where Equation (3b)defines the adjustments in the interest rate real income, and the price level. Substituting into Equation( 8)from quations(4),(5a), and(5b)generates InMp-In Mp-1=Q(n M,-1-In Mp-1)+eE-1,(9) where =-∝1中181+(221+a32)(1-81) (10) Equation(9)represents, not surprisingly, a demand-adjusting forStephen M. Miller Equation (7) does not separate the effect of the excess supply of money into movements in real income and the price level. Al￾lowing for these differential effects, Equation (5) becomes D In qt = cP,,(l - &)(ln Mf - ln Mf) , (54 and D In P, = cP,,(l - S,)(ln Mf - In Mf) , W where apz = a21 + az2. Now, dividing Equations (4), (5a), and (5b) by aI, QS1, and $a, respectively, and then subtracting twice Equa￾tion (4) from the sum of Equations (5a) and (5b) gives In Mf - In MF = -(l/al)0 In r, + (l/2@& In yi + (l/2@.& In P, . And finally, substituting from Equation (1) results in In Mf = a0 + a,ln r, + olJn qt + ol,ln P, - (l/@&I In r, + (1/2@&I In qt + (1/2@.&0 In P, + l , . Now, first-differencing Equation (1) yields lnM:- In ME, = alD In t-,-r + ozD In gt-l + c@ In P,-I + E, - l tel , (64 (74 (8) where Equation (3b) defines the adjustments in the interest rate, real income, and the price level. Substituting into Equation (8) horn Equations (4), (Sa), and (5b) generates In Mf' - ln ME, = LR(ln Mf-, - ln ML,) + E, - Q-~, (9) where n = -a,@16, + (a&!1 + c&&)(1 - 6,) . (10) Equation (9) represents, not surprisingly, a demand-adjusting for- 568