Consider the following four demand functions for money:(1) InM," = a, +a,InY," +a, In R, + a, In P, + ,%3D(2) InM," = B, + BInY, + B, In R, + B, In P, + u,2(3) InM, = %, +7,InY, + 7, In R, +u,,(4) InM)=6, +6, InR, +u,.where M,", Y,", R, and P, denote, respectively, aggregate nominal money demand,M,",and/P,aggregate national income, long-term interest rate, implicit price deflator. M,Y, = /stand for aggregate real money demand and aggregate real national income.These four money demand equations are estimated for the period 1949-1965 and thefollowing estimated equations are obtained:(1) InM," = 3.999+1.710lnY," – 0.608 In R, – 0.759In P, R = 0.942, SSR = 0.080(0.469)(1.801) (0.416)(0.651)(2) InM," = 3.999+1.710lnY, –0.608In R, +0.9519 In P, R² =0.942, SSR = 0.080(1.801) (0.416) (0.469)(0.651)R = 0.902, SSR = 0.081(3) InM, = 3.760 +1.683lnY, – 0.594 In R,(0.566) (0.353) (0.443)(4) In M)=2.727+0.2201n R,R = 0.129, SSR = 0.102(0.202) (0.149) Based on the above information,(a) Explain why the only difference between (1) and (2) is the coefficient of In Pt ?(b) In Model (2) test the hypothesis that the price level has no significant effect on real moneydemand using t and F statistics.(c) Which linear restrictions must be imposed on the coefficients of Model (1) in order to obtainModel (3)? Which linear restriction must be imposed to obtain Model (4)? Test the restrictions whichyield Model (3) and Model (4).

Linear regression is a statistical method that summarizes and studies the relationships between two…

Consider the following four demand functions for money: (1) InM, =a, +a̟InY," +a¸ In R_ +a¸ In P,+u, (2) InM," = B, + BInY, + B, In R, + B, In P, + u,2 (3) InM, = 7, +7,InY, + 7, In R, +u,, %3D (4) In M)=5, +5, In R +u,. where M", Y", R and P, denote, respectively, aggregate nominal money demand, and aggregate national income, long-term interest rate, implicit price deflator. M, = M." Y, =2 ,stand for aggregate real money demand and aggregate real national income. These four money demand equations are estimated for the period 1949-1965 and the following estimated equations are obtained: (1) InM," = 3.999+1.710lnY," –0.608 In R, – 0.759In P, R = 0.942, SSR = 0.080 (0.469) (0.651) (1.801) (0.416) (2) InM," = 3.999+1.710lnY, –0.608 In R, +0.9519ln P, R = 0.942, SSR =0.080 (1.801) (0.416) (0.469) (0.651) (3) InM, = 3.760+1.683lnY, – 0.5941n R, R² =0.902, SSR = 0.081 (0.566) (0.353) (0.443) M, (4) In |=2.727+0.220ln R, R =0.129, SSR =0.102 (0.202) (0.149)