// miu_4e.dyn // Dynare program for MIU model of Chapter 2 // Monetary Theory and Policy, 4th ed., by Carl E. Walsh // The MIT Press. 2015 var Z U Y C K INV N R M I MUC PI; varexo EPZ EPU; parameters A B ALPHA BETA ETA DELTA GAMMA OMEGA1 OMEGA2 SIGMA_Z SIGMA_M SIGMA_V; parameters RHOZ RHOU THETA PHI UPSILON phi NSS YK CK NKSS KSS CSS RSS ISS MSS XSS; ALPHA = 0.36; DELTA = 0.019; BETA = 0.989; ETA = 1; THETA = 1.0138; % THETA implies quarterly growth rate of money equal to 1.38%. % money_demand_percapita.rpf % GRLFM1 is growth rate (at quarterly rate) of M1. %Statistics on Series GRLFM1 %Quarterly Data From 1985:01 To 2014:04 %Observations 120 %Sample Mean 1.384221 Variance 2.590167 %Standard Error 1.609400 SE of Sample Mean 0.146917 PHI = 2; B = 9; % B = 9 is implied by Ireland (2009) and (M1/P)/C = 0.7811. NSS = 1/3; // Implied parameters YK = (1/ALPHA)*((1/BETA) - 1 + DELTA); CK = YK - DELTA; NKSS = (YK)^(1/(1-ALPHA)); KSS = NSS/NKSS; CSS = CK*KSS; RSS = 1/BETA; ISS = (RSS*THETA - 1); UPSILON = ISS/(1+ISS); // A chosen to target M1/C = 0.7811 for quarterly rates // See MTP_Ch2_4e.m // M1 divided by C at quarter rates: mean 1985:1-2014:1 equals 0.7811 A = 1/(1 + UPSILON*(0.7811^B)); MSS = CSS*((A*UPSILON)/(1-A))^(-1/B); XSS = A*(CSS^(1-B)) + (1-A)*(MSS^(1-B)); GAMMA = A*(CSS^(1-B))/XSS; OMEGA1 = (B - PHI)*GAMMA - B; OMEGA2 = (B - PHI)*(1-GAMMA); // Parameters for exogenous processes SIGMA_Z = 0.34; RHOZ = 0.95; RHOU = 0.69; phi = 0; SIGMA_M = 1.17; % standard deviation of money growth rate. Units: Percent %Linear Regression - Estimation by Least Squares %Dependent Variable GRLFM1 %Quarterly Data From 1985:01 To 2014:04 %Usable Observations 120 %Degrees of Freedom 118 %Centered R^2 0.4752601 %R-Bar^2 0.4708132 %Uncentered R^2 0.6994553 %Mean of Dependent Variable 1.3842206067 %Std Error of Dependent Variable 1.6093997316 %Standard Error of Estimate 1.1707614837 %Sum of Squared Residuals 161.74052929 %Regression F(1,118) 106.8733 %Significance Level of F 0.0000000 %Log Likelihood -188.1827 %Durbin-Watson Statistic 2.1460 % % Variable Coeff Std Error T-Stat Signif %************************************************************************************ %1. Constant 0.4329143027 0.1410325118 3.06961 0.00266006 %2. GRLFM1{1} 0.6893456888 0.0666810433 10.33796 0.00000000 % Innovation variance of money growth shock set so that s.d. of money % growth matches SIGMA_M. SIGMA_V = ((1-RHOU^2)*(SIGMA_M)^2 - ((phi^2)/(1-RHOZ^2))*(SIGMA_Z^2))^.5; model(linear); Z = RHOZ*Z(-1) + EPZ; U = RHOU*U(-1)+ phi*Z(-1) + EPU; Y = ALPHA*K(-1) + (1-ALPHA)*N + Z; YK*Y = CK*C + DELTA*INV; K = (1 - DELTA)*K(-1) + DELTA*INV; (1 + (ETA*NSS/(1-NSS)))*N = Y + MUC; R = ALPHA*YK*(Y(+1) - K); MUC = OMEGA1*C + OMEGA2*M; MUC = R + MUC(+1); M = C - (1/B)*((1-ISS)/ISS)*I; M = M(-1) + U - PI; I = R + PI(+1); end; steady; check; shocks; var EPZ; stderr SIGMA_Z; var EPU; stderr SIGMA_V; end; ///////////////////////////////////////// // Computing Theoretical Moments and IRF's //////////////////////////////////////// // Baseline parameters stoch_simul(order=1,ar=1,irf=60,graph,print); OOPT.MODELS.MIU_1 = oo_; save OOPT_MIU_1;