%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Choques petroleros y política monetaria %%% %%% Análisis de un modelo DSGE para la economía colombiana %%% %%% Gonzalo Jiménez Murcia %%% %%% Universidad de los Andes %%% %%% Enero de 2017 %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Primera parte - preámbulo (variables endógenas, variables exógenas y parámetros) var p_OIL, y_OIL, R_ast, R_f, b_ast, lambda_1, c, h, w, R, q, c_T, p_T, c_NT, p_NT, y_T, z_T, h_T, z_NT, fi_NT, h_NT, y_NT, OIL_IN, PSI, PI_NT, ZETA, p_NT_hat, I, PI, z_I, y, p_T_ast, PI_T, OIL_OUT, Dev_nom, PI_ast, p_OIL_OBS, y_OBS, PI_OBS, I_OBS, Dev_nom_OBS; varexo e_p_OIL, e_y_OIL, e_R_f, e_z_T, e_z_NT, e_z_I, e_p_T_ast, e_PI_ast; parameters beta, ro_p_OIL, p_OIL_bar, ro_y_OIL, y_OIL_bar, omega, b_ast_par, ro_R_f, R_f_bar, chi, sigma, gama, varteta, ro_z_T, z_T_bar, ro_z_NT, z_NT_bar, alfa, fi, teta, PI_bar, eta_PI, eta_y, ro_z_I, z_I_bar, ro_p_T_ast, p_T_ast_bar, ro_PI_ast, PI_ast_bar, delta, p_OIL_ee, y_OIL_ee, R_ast_ee, R_f_ee, b_ast_ee, lambda_1_ee, c_ee, h_ee, w_ee, R_ee, q_ee, c_T_ee, p_T_ee, c_NT_ee, p_NT_ee, y_T_ee, z_T_ee, h_T_ee, z_NT_ee, fi_NT_ee, h_NT_ee, y_NT_ee, OIL_IN_ee, PSI_ee, PI_NT_ee, ZETA_ee, p_NT_hat_ee, I_ee, PI_ee, z_I_ee, y_ee, p_T_ast_ee, PI_T_ee, OIL_OUT_ee, Dev_nom_ee, PI_ast_ee; beta = 1 / ((1+0.025)^(1/4)); % Implica una tasa de interés real de 2,5% anual ro_p_OIL = 0.9829; p_OIL_bar = 0.17; %%% ro_y_OIL = 0.4996; y_OIL_bar = 0.17; %%% omega = 0.0544; b_ast_par = 0.6; ro_R_f = 0.8432; R_f_bar = 1 / beta; %chi; sigma = 0.6085; gama = 0.3; varteta = 0.78; ro_z_T = 0.8324; z_T_bar = 1; ro_z_NT = 0.8910; %z_NT_bar; alfa = 0.98; fi = 0.5762; teta = 6; PI_bar = 1.03^(1/4); eta_PI = 1.3859; eta_y = 0; ro_z_I = 0.4977; z_I_bar = 1; ro_p_T_ast = 0.8555; p_T_ast_bar = 1; ro_PI_ast = 0.33; PI_ast_bar = PI_bar; delta = 1.5; % Definición del estado estacionario del modelo h_ee = log(0.3); p_T_ee = log(1); p_OIL_ee = log(p_OIL_bar); %(1) y_OIL_ee = log(y_OIL_bar); %(2) R_f_ee = log(R_f_bar); %(4) R_ast_ee = log(exp(R_f_ee)); %(3) b_ast_ee = log(b_ast_par); %(3) R_ee = log(1 / beta); %(7) p_NT_ee = log(1); %(12) z_T_ee = log(z_T_bar); %(14) p_NT_hat_ee = log(1); %(23) z_I_ee = log(z_I_bar); %(25) I_ee = log(((1 / beta) * PI_bar) * (exp(z_I_ee)^(1 / (1 - ro_z_I)))); %(24) p_T_ast_ee = log(p_T_ast_bar); %(28) PI_ast_ee = log(PI_ast_bar); %(35) w_ee = log(exp(z_T_ee) * exp(p_T_ee)); %(15) q_ee = log(exp(p_T_ee) / exp(p_T_ast_ee)); %(27) PI_ee = log(exp(I_ee) / exp(R_ee)); %(31) PI_NT_ee = log(exp(PI_ee)); %(32) PI_T_ee = log(exp(PI_ee)); %(33) c_ee = log((exp(w_ee) * exp(h_ee)) + (exp(q_ee) * exp(b_ast_ee)) + (exp(q_ee) * exp(p_OIL_ee) * exp(y_OIL_ee)) - (exp(R_ast_ee) * exp(q_ee) * exp(b_ast_ee))); %(9) %chi = exp(w_ee) / (exp(h_ee)^sigma); %(6) % GHH. chi = exp(w_ee) / (exp(h_ee)^sigma); %(6) lambda_1_ee = log(1 / exp(c_ee)); %(5) % KPR. lambda_1_ee = log(1 / exp(c_ee)); %(5) % GHH. lambda_1_ee = log((exp(c_ee) - (chi * ((exp(h_ee)^(1 + sigma)) / (1 + sigma))))^(-delta)); %(5) c_T_ee = log(gama * exp(c_ee) * (exp(p_T_ee)^(-varteta))); %(10) c_NT_ee = log((1 - gama) * exp(c_ee) * (exp(p_NT_ee)^(-varteta))); %(11) y_NT_ee = log(exp(c_NT_ee)); %(30) ZETA_ee = log(exp(y_NT_ee) / (1 - (fi * beta))); %(21) PSI_ee = log(((teta - 1) / teta) * (exp(ZETA_ee) * exp(p_NT_hat_ee))); %(22) fi_NT_ee = log((1 - (fi * beta)) * (exp(PSI_ee) / exp(y_NT_ee))); %(20) h_NT_ee = log((alfa * exp(p_NT_ee) * exp(fi_NT_ee) * exp(y_NT_ee)) / exp(w_ee)); %(17) OIL_IN_ee = log(((1 - alfa) * exp(p_NT_ee) * exp(fi_NT_ee) * exp(y_NT_ee)) / (exp(q_ee) * exp(p_OIL_ee))); %(18) z_NT_ee = log(exp(y_NT_ee) / ((exp(h_NT_ee)^alfa) * (exp(OIL_IN_ee)^(1 - alfa)))); %(19) h_T_ee = log(exp(h_ee) - exp(h_NT_ee)); %(29) y_T_ee = log(exp(z_T_ee) * exp(h_T_ee)); %(13) y_ee = log((exp(p_T_ee) * exp(y_T_ee)) + (exp(p_NT_ee) * exp(y_NT_ee)) + (exp(p_OIL_ee) * exp(y_OIL_ee))); %(26) OIL_OUT_ee = log(exp(y_OIL_ee) - exp(OIL_IN_ee)); %(34) Dev_nom_ee = log(exp(PI_ee) / exp(PI_ast_ee)); %(36) chi = (exp(lambda_1_ee) * exp(w_ee)) / (exp(h_ee)^sigma); %(6) % KPR. chi = (exp(lambda_1_ee) * exp(w_ee)) / (exp(h_ee)^sigma); %(6) z_NT_bar = exp(z_NT_ee); %(16) %%% Segunda parte - Descripción del modelo model; p_OIL = (ro_p_OIL * p_OIL(-1)) + ((1 - ro_p_OIL) * log(p_OIL_bar)) + e_p_OIL; %(1) y_OIL = (ro_y_OIL * y_OIL(-1)) + ((1 - ro_y_OIL) * log(y_OIL_bar)) + e_y_OIL; %(2) exp(R_ast) = exp(R_f) + (omega * (exp(exp(b_ast) - b_ast_par) - 1)); %(3) R_f = (ro_R_f * R_f(-1)) + ((1 - ro_R_f) * log(R_f_bar)) + e_R_f; %(4) exp(lambda_1) = 1 / exp(c); %(5) % KPR. exp(lambda_1) = 1 / exp(c); %(5) % GHH. exp(lambda_1) = (exp(c) - (chi * ((exp(h)^(1 + sigma)) / (1 + sigma))))^(-delta); %(5) exp(lambda_1) = (chi * (exp(h)^sigma)) / exp(w); %(6) % KPR. exp(lambda_1) = (chi * (exp(h)^sigma)) / exp(w); %(6) % GHH. exp(w) = chi * (exp(h)^sigma); %(6) exp(lambda_1) = beta * exp(lambda_1(+1)) * exp(R); %(7) exp(lambda_1) = beta * exp(lambda_1(+1)) * exp(R_ast) * (exp(q(+1)) / exp(q)); %(8) exp(c) = (exp(w) * exp(h)) + (exp(q) * exp(b_ast)) + (exp(q) * exp(p_OIL) * exp(y_OIL)) - (exp(R_ast(-1)) * exp(q) * exp(b_ast(-1))); %(9) exp(c_T) = gama * exp(c) * (exp(p_T)^(-varteta)); %(10) exp(c_NT) = (1 - gama) * exp(c) * (exp(p_NT)^(-varteta)); %(11) 1 = (gama * (exp(p_T)^(1 - varteta))) + ((1 - gama) * (exp(p_NT)^(1 - varteta))); %(12) exp(y_T) = exp(z_T) * exp(h_T); %(13) z_T = (ro_z_T * z_T(-1)) + ((1 - ro_z_T) * log(z_T_bar)) + e_z_T; %(14) exp(w) = exp(z_T) * exp(p_T); %(15) z_NT = (ro_z_NT * z_NT(-1)) + ((1 - ro_z_NT) * log(z_NT_bar)) + e_z_NT; %(16) exp(h_NT) = (alfa * exp(p_NT) * exp(fi_NT) * exp(y_NT)) / exp(w); %(17) exp(OIL_IN) = ((1 - alfa) * exp(p_NT) * exp(fi_NT) * exp(y_NT)) / (exp(q) * exp(p_OIL)); %(18) exp(y_NT) = exp(z_NT) * (exp(h_NT)^alfa) * (exp(OIL_IN)^(1 - alfa)); %(19) exp(PSI) = (exp(fi_NT) * exp(y_NT)) + (fi * beta * (exp(lambda_1(+1)) / exp(lambda_1)) * ((exp(PI_NT(+1)) / exp(PI_NT))^teta) * exp(PSI(+1))); %(20) exp(ZETA) = exp(y_NT) + (fi * beta * (exp(lambda_1(+1)) / exp(lambda_1)) * ((exp(PI_NT(+1)) / exp(PI_NT))^(teta - 1)) * exp(ZETA(+1))); %(21) exp(p_NT_hat) = (teta / (teta - 1)) * (exp(PSI) / exp(ZETA)); %(22) exp(PI_NT) = ((fi * (exp(PI_NT(-1))^(1 - teta))) + ((1 - fi) * ((exp(p_NT_hat) * exp(PI_NT))^(1 - teta))))^(1 / (1 - teta)); %(23) exp(I) = (exp(I(-1))^ro_z_I) * ((((1 / beta) * PI_bar) * ((exp(PI) / PI_bar)^eta_PI) * ((exp(y) / steady_state(exp(y)))^eta_y))^(1 - ro_z_I)) * exp(z_I); %(24) z_I = (ro_z_I * z_I(-1)) + ((1 - ro_z_I) * log(z_I_bar)) + e_z_I; %(25) exp(y) = (exp(p_T) * exp(y_T)) + (exp(p_NT) * exp(y_NT)) + (exp(p_OIL) * exp(y_OIL)); %(26) exp(p_T) = exp(q) * exp(p_T_ast); %(27) p_T_ast = (ro_p_T_ast * p_T_ast(-1)) + ((1 - ro_p_T_ast) * log(p_T_ast_bar)) + e_p_T_ast; %(28) exp(h) = exp(h_T) + exp(h_NT); %(29) exp(y_NT) = exp(c_NT); %(30) exp(R) = exp(I) / exp(PI(+1)); %(31) exp(p_NT) = exp(p_NT(-1)) * (exp(PI_NT) / exp(PI)); %(32) exp(p_T) = exp(p_T(-1)) * (exp(PI_T) / exp(PI)); %(33) exp(y_OIL) = exp(OIL_IN) + exp(OIL_OUT); %(34) PI_ast = (ro_PI_ast * PI_ast(-1)) + ((1 - ro_PI_ast) * log(PI_ast_bar)) + e_PI_ast; %(35) exp(Dev_nom) = (exp(q) / exp(q(-1))) * (exp(PI) / exp(PI_ast)); %(36) p_OIL_OBS = p_OIL - p_OIL(-1); %(37) y_OBS = y - y(-1); %(38) PI_OBS = PI - steady_state(PI); %(39) I_OBS = I - steady_state(I); %(40) Dev_nom_OBS = Dev_nom - steady_state(Dev_nom); %(41) end; %%% Tercera parte - Declaración de variables observables varobs p_OIL_OBS, y_OBS, PI_OBS, I_OBS, Dev_nom_OBS; %%% Cuarta parte - Valores iniciales (estado estacionario) initval; %steady_state_model; h = h_ee; p_T = p_T_ee; p_OIL = p_OIL_ee; y_OIL = y_OIL_ee; R_f = R_f_ee; R_ast = R_ast_ee; b_ast = b_ast_ee; R = R_ee; p_NT = p_NT_ee; z_T = z_T_ee; p_NT_hat = p_NT_hat_ee; z_I = z_I_ee; I = I_ee; p_T_ast = p_T_ast_ee; PI_ast = PI_ast_ee; w = w_ee; q = q_ee; PI = PI_ee; PI_NT = PI_NT_ee; PI_T = PI_T_ee; c = c_ee; lambda_1 = lambda_1_ee; c_T = c_T_ee; c_NT = c_NT_ee; y_NT = y_NT_ee; ZETA = ZETA_ee; PSI = PSI_ee; fi_NT = fi_NT_ee; h_NT = h_NT_ee; OIL_IN = OIL_IN_ee; z_NT = z_NT_ee; h_T = h_T_ee; y_T = y_T_ee; y = y_ee; OIL_OUT = OIL_OUT_ee; Dev_nom = Dev_nom_ee; p_OIL_OBS = 0; y_OBS = 0; PI_OBS = 0; I_OBS = 0; Dev_nom_OBS = 0; end; resid; steady; check; %return; %%% Quinta parte - Choques shocks; var e_p_OIL; stderr 0.1591; var e_y_OIL; stderr 0.0041; var e_R_f; stderr 0.0017; var e_z_T; stderr 0.007; var e_z_NT; stderr 0.0078; var e_z_I; stderr 0.0038; var e_p_T_ast; stderr 0.0035; var e_PI_ast; stderr 0.0535; end; %%% Sexta parte - Computación del modelo stoch_simul(irf=40,order=1);