Dynare 2013 10 6 Ver. 2.07 1 2 1.1 Dynare Dynare............... 2 1.2 Octave............................... 2 1.3..................... 4 2 4 3 Dynare 5 3.1 RBC.mod.............. 5 3.2 tmodel2.mod......... 16 3.3 NK Linear.mod, NK Linear stoch.mod. 19 3.4 Dynare..................... 22 4 Dynare NK Linear EST2.mod 23 4.1............................ 23 4.2............................... 25 4.3 mod................... 26 4.4............................ 29 http://www.rhasumi.net/wiki/ 1
1 2 Octave/MATLAB Dynare Dynare Octave/MATLAB 1.1 Dynare Dynare Dynare DSGE 3 4 Dynare Octave MAT- LAB Dynare stable release http://www.dynare.org/download 1.2 Octave Octave GNU Dynare Octave MATLAB *1 Octave Windows *2 MinGW Microsoft Visual Studio 2 MinGW Octave Octave Dynare *1 MATLAB MathWorks *2 MATLAB 2
1 Octave Octave-3.6.2.exe - http://octave.sourceforge.net/ Windows Octave Windows Octave exit 3
1.3 Dynare Octave/MATLAB.txt Dynare.mod Octave/MATLAB.m *3 DSGE Dynare mod mod Dynare Octave/MATLAB Dynare Octave/MATLAB *4 2 Octave Dynare mod 3.1.2 RBC mod Dynare 4.3.1 RBC mod RBC.mod C:\work\dsge *5 main.m addpath C:\dynare\4.3.1\matlab cd C:\work\dsge dynare RBC m main.m RBC.mod Octave 3 Octave Octave/Dynare RBC.mod *3 Windows 7 *4 Octave/MATLAB *5 \ Yen Y= 4
2 Octave main dynare RBC 3 Dynare 3.1 RBC.mod 3.1.1 DSGE 1. 2. a 3. 4. 5. a Dynare 4 3 RBC w t = (γ + 1) µl γ t C t (1) C t+1 = β (r t+1 δ + 1) C t (2) Y t = A t Kt α L 1 α t (3) w t = (1 α) A t Kt α L α t (4) r t = αa t Kt α 1 L 1 α t (5) K t+1 = Y t + (1 δ) K t C t (6) ln (A t+1 ) = ρ ln (A t ) + e t+1 (7) *6 *6 4 5
1. 1 2 C t C L t L K t K Y t Y w t w r t r A t A e t e 2 RBC 1 RBC 2. 3 α alpha 0.3 β beta 0.99 δ delta 0.025 µ mu 1.0 γ gamma 1.0 ρ AR(1) rho 0.9 3 RBC 3. (1) (7) 7 6
4. *7 A = 1 (8) r = β 1 + δ 1 (9) K ( ) 1 r L = α 1 A (10) α Y ( ) K α L = A L (11) C L = Y L δ K L (12) ( ) K w = (1 α)a α (13) { w L = (γ + 1)µ L } 1 γ+1 ( C L ) 1 γ+1 Dynare *8 (14) 5. t = 0 t = 1 e 1 = 0.05 5% *9 3.1.2 1 5 mod RBC.mod 1. var varexo 2. parameters 3. model *7 4 *8 Octave fsolve *9 4.8771% 7
4. initval steady check 5. simul m % mod // * 10 1. var varexo // 1. var C L K Y w r A; varexo e; 2. 2 parameters // 2. parameters alpha beta delta mu gamma rho; // alpha = 0.3; beta = 0.99; delta = 0.025; mu = 1.0; gamma = 1.0; rho = 0.9; *10 mod Octave/MATLAB mod % 8
3. model model model; end; t + 1 C(+1) t 1 A( 1) t + 1 K t A t 2 (6) (7) K t = Y t 1 + (1 δ) K t 1 C t 1 (15) ln (A t ) = ρ ln (A t 1 ) + e t (16) K t+1 A t+1 model * 11 // 3. model; w/c = (gamma+1)*mu*l^gamma; C(+1)/C = beta*(r(+1)-delta+1); Y = A*K^alpha*L^(1-alpha); w = (1-alpha)*A*K^alpha*L^(-alpha); r = alpha*a*k^(alpha-1)*l^(1-alpha); K = Y(-1)+(1-delta)*K(-1)-C(-1); log(a) = rho*log(a(-1)) + e; end; 4. initval Dynare star *11 log exp 9
// 4. Astar = 1; rstar = 1/beta + delta - 1; K_L = (rstar/alpha/astar)^(1/(alpha-1)); Y_L = Astar*K_L^alpha; C_L = Y_L-delta*K_L; wstar = (1-alpha)*Astar*K_L^alpha; Lstar = (wstar/(gamma+1)/mu)^(1/(gamma+1))*c_l^(-1/(gamma+1)); Kstar = K_L*Lstar; Ystar = Y_L*Lstar; Cstar = C_L*Lstar; // Dynare initval; C = Cstar; L = Lstar; K = Kstar; Y = Ystar; w = wstar; r = rstar; A = Astar; end; steady Dynare * 12 Dynare *12 initval steady Dynare steady histval 10
// Dynare steady; // [Cstar; Lstar; Kstar; Ystar; wstar; rstar; Astar] ans = Dynare ans = STEADY-STATE RESULTS: C 1.31577 L 0.667162 K 14.3013 Y 1.6733 w 1.75566 r 0.035101 A 1 ans = 1.315771 0.667162 14.301334 1.673304 1.755665 0.035101 1.000000 check // check; EIGENVALUES: check 1 11
C(+1) r(+1) 2 rank * 13 The rank condition is verified. EIGENVALUES: Modulus Real Imaginary 3.204e-020 3.204e-020 0 5.318e-018-5.318e-018 0 0.9 0.9 0 0.9482 0.9482 0 1.065 1.065 0 Inf Inf 0 There are 2 eigenvalue(s) larger than 1 in modulus for 2 forward-looking variable(s) The rank condition is verified. 5. t = 0 t = 1 e 1 = 0.05 5% simul perfect foresight solution periods=150 t = 151 periods var C t C t = 0 151 152 *13 Blanchard and Kahn [1980] 12
// 5. // shocks; var e; periods 1; values -0.05; end; // simul(periods=150); Dynare Octave/MATLAB simul 13
// C1 = (C./Cstar-1)*100; L1 = (L./Lstar-1)*100; K1 = (K./Kstar-1)*100; Y1 = (Y./Ystar-1)*100; w1 = (w./wstar-1)*100; r1 = (r-rstar)*100; A1 = (A./Astar-1)*100; I1 = ((Y-C)./(Ystar-Cstar)-1)*100; // figure(1) subplot(2,2,1) plot(0:50, A1(1:51)); title( A ) subplot(2,2,2) plot(0:50, Y1(1:51)); title( Y ) subplot(2,2,3) plot(0:50, C1(1:51)); title( C ) subplot(2,2,4) plot(0:50, K1(1:51)); title( K ) figure(2) subplot(2,2,1) plot(0:50, L1(1:51)); title( L ) subplot(2,2,2) plot(0:50, I1(1:51)); title( I ) subplot(2,2,3) plot(0:50, w1(1:51)); title( w ) subplot(2,2,4) plot(0:50, r1(1:51)); title( r ) 14
2 e 1 = 0.05 2 RBC.mod 2 * 14 csv *14 print( filename.eps, -depsc2 ) 15
csvwrite( rbc_rslt.csv,[c, L, K, Y, w, r, A]); RBC.mod rbc rslt.csv csv csv EXCEL 3.2 tmodel2.mod 3 mod 3.2.1 3.1.1 1. 4 5 C t C K t K τ c,t tauc 0 0 τ k,t tauk 0 0.1 g t g 0.1 0.1 4 5 2. 6 α alpha 0.3 β beta 0.99 δ delta 0.25 A t At 1.0 6 16
3. (1 + τ c,t+1 )C t+1 = β [ (1 τ k,t+1 )αa t+1 Kt+1 α 1 (1 + τ c,t )C t (17) K t+1 = A t Kt α + (1 δ)k t C t g t (18) 4. Dynare 5. t = 0 t = 10 τ k,t 0.1 t = 1 τ c,t 3.2.2 1 5 mod tmodel2.mod 1. var varexo 2. parameters 3. model 4. initval 5. endval steady 6. check 7. simul 3. 3.1 RBC initval t = 0 initval steady Dynare initval Dynare * 15 Dynare *15 3.1 t = 0 *12 17
// 4. initval; C = 1; K = 1; tauc = 0; tauk = 0; g = 0.1; end; steady; endval Dynare steady Dynare // 5. endval; C = 1; K = 1; tauc = 0; tauk = 0.1; g = 0.1; end; steady; check 3.1 18
t = 0 t = 10 τ k,t 0.1 t = 1 // 7. shocks; var tauk; periods 1:9; values 0; end; simul(periods=31); 3.3 NK Linear.mod, NK Linear stoch.mod 5 Dynare 3.3.1 3.1.1 4. 1. 7 8 ˆx t GDP x π t ppi â t a î t ii v t vv ν t â t+1 â t nu 7 e t e ε t eps 8 19
2. 9 β beta 0.99 γ gamma 1 ϱ varrho 0.8 κ κ = (1 ϱ)(1 ϱβ)(γ+1) ϱ kappa ϕ π phi pi 1.5 ϕ y GDP phi y 0.5 ρ A AR(1) rho A 0.9 ρ v AR(1) rho v 0.9 9 3. π t = βπ t+1 + κˆx t (19) ˆx t = ˆx t+1 (î t π t+1 ) + ν t (20) î t = ϕ π π t + ϕ y ˆx t + v t (21) v t+1 = ρ v v t + ε t+1 (22) â t+1 = ρ A â t + e t+1 (23) ν t = â t+1 â t (24) 4. * 16 5. t = 0 t = 1 +5% *16 20
3.3.2 3.1.2 initval steady simul stoch simul simul shocks; var e; periods 1; values 0.05; end; simul(periods=150); stoch simul shocks; var e = 5^2; end; stoch_simul(order=1, irf = 100) x ii ppi a v; 6 * 17 stoch simul RBC stoch.mod * 18 *17 1 mod simul NK Linear.mod stoch simul NK Linear stoch.mod stoch simul 1 *18 Dynare 21
3.4 Dynare simul stoch simu 2 Deterministic Simulation Stochastic Simulation 22
4 Dynare NK Linear EST2.mod DSGE Dynare * 19 Dynare MCMC M-H 4.1 DSGE 1. 2. 3. 4. 5. 6. 1. π t = βπ t+1 + κˆx t (25) ˆx t = ˆx t+1 (î t π t+1 ) + (ρ A 1)â t (26) î t = (1 + ϕ π )π t + ϕ y ˆx t + v t (27) v t+1 = ρ v v t + u t+1 (28) â t+1 = ρ A â t + ε t+1 (29) x obs t x obs = ˆx t (30) π obs t π obs = π t + ϵ π,t (31) (i obs t ī obs )/4 = î t (32) *19 Dynare 23
* 20 2. ˆx t GDP x π t ppi â t a î t ii v t v 10 e t e u t u ϵ π,t errppi 11 3. β beta 0.99 4. γ 1.0 0.5 ϱ 0.8 0.1 ϕ π 0.5 0.25 ϕ y 0.5 0.25 GDP ρ A 0.8 0.05 AR(1) ρ v 0.8 0.1 AR(1) σ ε 0.5 0.5 ε t σ u 0.5 0.5 u t σ ϵπ 0.5 0.5 ϵ π,t 12 *20 7 24
5. GDP x obs t i obs t 3 GDP ; πt obs 6. MCMC 20,000 2 0.25 * 21 4.2 x act t π act t i act t = x obs t x obs (33) = π obs t π obs (34) = (i obs t ī obs )/4 (35) x act t, πt act, i act t mod script dataset.m *21 DSGE 25
script dataset.m EO90 = csvread( EO90.csv, 1, 1); GAP0 = EO90(:,1); PGDP0 = EO90(:,2); IRS0 = EO90(:,3); PC_PGDP0 = [NaN; (PGDP0(2:end)./PGDP0(1:end-1)-1)*100]; tt = 2:77; MGAP = mean(gap0(tt)); MPC_PGDP = mean(pc_pgdp0(tt)); MIRS = mean(irs0(tt)); GAP = GAP0(tt)-MGAP; PC_PGDP = PC_PGDP0(tt)-MPC_PGDP; IRS4 = (IRS0(tt)-MIRS)*0.25; x = GAP; ppiact = PC_PGDP; ii = IRS4; save dset.mat x ppiact ii; csv EO90.csv GDP (33) (35) x act t, πt act, i act t x, ppiact, ii dset.mat mat MATLAB mod 4.3 mod mod NK Linear EST2.mod 1. var varexo 2. parameters 26
3. model 4. estimated params 5. varobs 6. estimation 1. 3 var x ppi a ii v ppiact; varexo e u errppi; ppiact 3. 2. 3 // 2. parameters beta gamma varrho phi_pi phi_y rho_a rho_v; // beta = 0.99; 3. (31) π act t = π t + ϵ π,t (36) π act t ppiact κ kappa # model 27
model(linear); # kappa = (1-varrho)*(1-varrho*beta)*(gamma+1)/varrho; ppi = beta*ppi(+1)+kappa*x; x = x(+1)-(ii-ppi(+1))+(rho_a-1)*a; ii = (phi_pi+1)*ppi + phi_y*x + v; a = rho_a*a(-1) + e; v = rho_v*v(-1) + u; ppiact = ppi + errppi; end; ˆx t, πt act, î t mod x, ppiact, ii dset.mat 4. 12 // 4. estimated_params; gamma, gamma_pdf, 1, 0.5; varrho, beta_pdf, 0.8, 0.1; phi_pi, gamma_pdf, 0.5, 0.25; phi_y, gamma_pdf, 0.5, 0.25; rho_a, beta_pdf, 0.8, 0.05; rho_v, beta_pdf, 0.8, 0.1; stderr e, inv_gamma_pdf, 0.5, 0.5; stderr u, inv_gamma_pdf, 0.5, 0.5; stderr errppi, inv_gamma_pdf, 0.5, 0.5; end; 5. 3. ˆx t, πt act, î t 28
// 5. varobs x ppiact ii; 6. estimation datafile dset mh replic MCMC 20,000 mh nblocks 2 mh drop 0.25 mh jscale M-H acceptation rate 0.2 0.5 0.7 0.3 // 6. estimation(datafile=dset, mh_replic=20000, mh_nblocks=2, mh_drop = 0.25, mh_jscale=0.7); 4.4 mat mod 2 29
ESTIMATION RESULTS Log data density is -130.702306. parameters prior mean post. mean conf. interval prior pstdev gamma 1.000 0.8754 0.2309 1.5030 gamma 0.5000 varrho 0.800 0.9262 0.9040 0.9468 beta 0.1000 phi_pi 0.500 0.4078 0.1039 0.7118 gamma 0.2500 phi_y 0.500 0.2417 0.0771 0.3963 gamma 0.2500 rho_a 0.800 0.9582 0.9408 0.9751 beta 0.0500 rho_v 0.800 0.8789 0.8531 0.9042 beta 0.1000 standard deviation of shocks prior mean post. mean conf. interval prior pstdev e 0.500 2.3409 1.4877 3.1567 invg 0.5000 u 0.500 0.3609 0.2081 0.5040 invg 0.5000 errppi 0.500 0.4302 0.3709 0.4911 invg 0.5000 Total computing time : 0h02m00s 30