// model with: TWO WAGES; INVESTMENT ADJ. COSTS; VARIABLE CAPITAL UTILIZATION; CONSUMPTION HABITS // STICKY BANK RATES, PRICES & WAGES à la Rotemberg with indexation to both past and st.st. inflation // Banking dynamics // 9 blocks of eqns: 1) PATIENT HHs 2) IMPATIENT HHs 3) CAPITAL PRODUCERS // 4) ENTREPRENEURS 5) BANKS 6) RETAILERS 7) LABOR MKT WITH ONE UNION FOR EACH LABOR TYPE // 8) AGGREGATION & EQUILIBRIUM 9) MONETARY POLICY // BBS has all items dated (t) // Banking capital in real terms is defined as: K_B(t)/p(t) // Banking profits are defined in the model code at time (t) var c_p // 1 PATIENT HHs h_p // 2 PATIENT HHs d_p // 3 PATIENT HHs l_p // 4 PATIENT HHs lam_p // 5 PATIENT HHs J_R // 6 PATIENT HHs j_B // 7 PATIENT HHs pie_wp // 8 PATIENT HHs c_i // 9 IMPATIENT HHs h_i // 10 IMPATIENT HHs b_i // 11 IMPATIENT HHs l_i // 12 IMPATIENT HHs lam_i // 13 IMPATIENT HHs s_i // 14 IMPATIENT HHs pie_wi // 15 IMPATIENT HHs I // 16 CAPITAL PRODUCERS q_k // 17 CAPITAL PRODUCERS c_e // 18 ENTREPRENEURS k_e // 19 ENTREPRENEURS l_pd // 20 ENTREPRENEURS l_id // 21 ENTREPRENEURS b_ee // 22 ENTREPRENEURS y_e // 23 ENTREPRENEURS lam_e // 24 ENTREPRENEURS s_e // 25 ENTREPRENEURS u // 26 ENTREPRENEURS Capital utilization rate d_b // 27 BANKS b_h // 28 BANKS b_e // 29 BANKS r_d // 30 BANKS r_bh // 31 BANKS r_be // 32 BANKS R_b // 33 BANKS K_b // 34 BANKS N // 34 BANKS pie // 35 RETAILERS x // 36 RETAILERS C // 37 AGGREGATION & EQUILIBRIUM Y // 38 AGGREGATION & EQUILIBRIUM D // 39 AGGREGATION & EQUILIBRIUM BE // 40 AGGREGATION & EQUILIBRIUM BH // 41 AGGREGATION & EQUILIBRIUM B // 42 AGGREGATION & EQUILIBRIUM w_p // 43 AGGREGATION & EQUILIBRIUM w_i // 44 AGGREGATION & EQUILIBRIUM J_B // 45 AGGREGATION & EQUILIBRIUM q_h // 46 AGGREGATION & EQUILIBRIUM K // 47 AGGREGATION & EQUILIBRIUM PIW // 48 AGGREGATION & EQUILIBRIUM r_ib // 49 MONETARY POLICY r_k // 50 CAPITAL RENTAL RATE ee_z // 51 EXOGENOUS PROCESSES A_e // 52 EXOGENOUS PROCESSES ee_j // 53 EXOGENOUS PROCESSES mk_d // 54 EXOGENOUS PROCESSES mk_be // 55 EXOGENOUS PROCESSES mk_bh // 56 EXOGENOUS PROCESSES ee_qk // 57 EXOGENOUS PROCESSES m_i // 58 EXOGENOUS PROCESSES (IMPATIENT LTV) m_e // 59 EXOGENOUS PROCESSES (ENTREPRENEURS LTV) eps_y // 60 EXOGENOUS PROCESSES eps_l // 61 EXOGENOUS PROCESSES eps_K_b // 62 EXOGENOUS PROCESSES // e_N // 62 EXOGENOUS PROCESSES Y1 // 63 output a prezzi di ss rr_e // 64 Entrep. Real Rate aux1 // 65 auxiliary variable bm // 66 banks intermediation margins spr_b // 67 average bank spread (active-passive) data_C // 68 dataseries data_I // 69 dataseries data_rBH // 70 dataseries data_rBE // 71 dataseries data_rD // 72 dataseries data_rIB // 73 dataseries data_D // 74 dataseries data_BH // 75 dataseries data_BE // 76 dataseries data_PIW // 77 dataseries data_PIE // 78 dataseries data_HP // 79 dataseries data_N // 80 dataseries ; varexo e_z e_A_e e_j e_mi e_me e_mk_d e_mk_be e_mk_bh e_qk e_y e_r_ib e_l e_eps_K_b e_N; parameters beta_p j phi beta_i m_i_ss beta_e m_e_ss alpha eksi_1 eksi_2 // HOUSEHOLDS & ENTREPRENEURS h a_i a_p a_e gamma_p gamma_i gamma_e ni // HOUSEHOLDS & ENTREPRENEURS eps_l_ss kappa_w // HOUSEHOLDS (labor params) eps_d eps_bh eps_be // BANKS ind_d ind_bh ind_be // BANKS mk_d_ss mk_bh_ss mk_be_ss r_be_ss r_bh_ss r_k_ss N_ss // BANKS (SS) gamma_b beta_b delta_kb vi kappa_kb // BANKS eps_y_ss kappa_p ind_p ind_w // RETAILERS kappa_i kappa_d kappa_be kappa_bh deltak // OTHERS rho_ib phi_pie phi_y // POLICY piss r_ib_ss // STEADY STATE rho_ee_z rho_A_e rho_ee_j rho_mi rho_me rho_eps_y rho_N // SHOCKS rho_mk_d rho_mk_be rho_mk_bh rho_ee_qk rho_eps_l rho_eps_K_b // SHOCKS ; % ********************* % CALIBRATED PARAMETERS % ********************* beta_p = 0.9960; % discount factor patient households beta_i = 0.975; % discount factor impatient households beta_b = beta_p; % discount factor bankers (not used in this version of the model) beta_e = beta_i; % discount factor entrepreneurs j = 0.2; % weight of housing in utility function phi = 1.0; % inverse Frisch elasticity of labor supply m_i_ss = 0.8 ; % loan-to-value ratio impatient households m_e_ss = 0.35 ; % loan-to-value ratio entrepreneurs alpha = 0.250; % capital share in the production function eps_d = 0.02441042; % elast. of subst. of deposits eps_bh = -0.004718071; % elast. of subst. of loans to I eps_be = -0.004339128; % elast. of subst. of loans to E // eps_d = - 0.02441042; % elast. of subst. of deposits // eps_bh = 0.004718071; % elast. of subst. of loans to I // eps_be = 0.004339128; % elast. of subst. of loans to E N_ss = 0.002440489; % Average log deviation of number of banks //********* mk_d_ss = eps_d / (eps_d + 1) ; % steady state markdown on D (ok if eps_d<0; if eps_d>0 it should be eps_d/(eps_d+1) ) // mk_d_ss = eps_d / (eps_d - 1) ; // mk_bh_ss = eps_bh / (eps_bh - 1) ; % steady state markup on loans to I // mk_be_ss = eps_be / (eps_be - 1) ; % steady state markup on loans to E mk_d_ss = (- eps_d *N + eps_d) / (- eps_d *N + eps_d + N) ; % EXTENSION: steady state markdown on D mk_bh_ss = (- eps_bh *N + eps_bh) / (- eps_bh *N + eps_bh + N) ; % EXTENSION: steady state markup on loans to I mk_be_ss = (- eps_be *N + eps_be) / (- eps_be *N + eps_be + N) ; % EXTENSION: steady state markup on loans to E book_ss = 0; %-35 % steady state value of (B-M)/D in the bank balance shhet eps_y_ss = 6; % eps_l_ss = 5; % gamma_p = 1; % shares of patient households gamma_i = 1; //1/3; % shares of impatient households ni = 0.8; % wage share of patient households gamma_b = 1; //0.10; % shares of bankers gamma_e = 1; //1 - gamma_p - gamma_i; % shares of entrepreneurs deltak = 0.025; % depreciation rate for physical capital piss = 1; % steady state gross inflation rate //********* r_ib_ss = (piss/beta_p - 1) * (eps_d+1)/eps_d ; % steady state gross nominal interest rate // r_ib_ss = (piss/beta_p - 1) * (eps_d-1)/eps_d ; // r_be_ss = r_ib_ss*eps_be/(eps_be-1) ; % steady state interest rate on loans to E // r_bh_ss = r_ib_ss*eps_bh/(eps_bh-1) ; % steady state interest rate on loans to H r_ib_ss = (piss/beta_p - 1) * (- eps_d *N + eps_d + N)/(- eps_d *N + eps_d) ; r_be_ss = r_ib_ss* (- eps_be *N + eps_be) / (- eps_be *N + eps_be + N); % EXTENSION: steady state interest rate on loans to E r_bh_ss = r_ib_ss* (- eps_bh *N + eps_bh) / (- eps_bh *N + eps_bh + N) ; % EXTENSION: steady state interest rate on loans to H r_k_ss = -(1-deltak)-m_e_ss*(1-deltak)*piss/beta_e* (1/(1+r_be_ss)-beta_e/piss)+1/beta_e; % steady state rental rate of capital h = 1; % fixed supply housing eksi_1 = r_k_ss; % capital utilization cost parameter eksi_2 = 0.1*r_k_ss; % capital utilization cost parameter vi = 0.09; % Banking Capital ratio over Loans (Basel II) eps_b = mean([eps_bh,eps_be]); % delta_kb = r_ib_ss/vi * (eps_d - eps_b + vi*(eps_b-1))/((eps_b-1)*(eps_d-1)); % j_B with terms in r_ib // delta_kb = r_ib_ss/vi * (eps_d - eps_b + vi*eps_d*(eps_b-1))/((eps_b-1)*(eps_d-1)); delta_kb = r_ib_ss/vi * ((- eps_d *N + eps_d) - (- eps_b *N + eps_b) + vi*(- eps_d *N + eps_d)*(- eps_b *N + eps_b + N))/((- eps_d *N + eps_d + N)*(- eps_b *N + eps_b + N)); // EXTENSION: Changed due to new markups % ******************** % ESTIMATED PARAMETERS % ******************** kappa_p = 100; % adjustment cost parameter for prices kappa_w = 50; % adjustment cost parameter for nominal wages kappa_i = 10; % adjustment cost parameter for investment kappa_d = 110; % adjustment cost parameter for deposit rates kappa_be = 50; % adjustment cost parameter for rates on loans to firms kappa_bh = 60; % adjustment cost parameter for rates on loans to households ind_d = 0.0; % indexation deposit rates ind_be = 0.0; % indexation rates on loans to firms ind_bh = 0.0; % indexation rates on loans to households kappa_kb = 10; % adjustment cost parameter for Banking Capital (Basel II) rho_ib = 0.75; % monetary policy response to lagged interest rate phi_pie = 1.8; % monetary policy response to inflation phi_y = 0.2; % monetary policy response to output ind_p = 0.0; % degree of indexation of prices ind_w = 0.5; % degree of indexation of nominal wages to inflation a_i = 0.0; % degree of habit formation: impatient households a_e = 0.0; % degree of habit formation: entrepreneurs a_p = 0.0; % degree of habit formation: patient households rho_ee_z = 0.95; % AR(1) coefficient intertemporal preference shock rho_A_e = 0.95; % AR(1) coefficient neutral technology shock rho_ee_j = 0.95; % AR(1) coefficient housing demand shock rho_me = 0.95; % AR(1) coefficient LTV (entrepreneurs) shock rho_mi = 0.95; % AR(1) coefficient LTV (households) shock rho_mk_d = 0.0; % AR(1) coefficient banking markup (deposits) shock rho_mk_bh = 0.0; % AR(1) coefficient banking markup (loans HH) shock rho_mk_be = 0.0; % AR(1) coefficient banking markup (loans E) shock rho_ee_qk = 0.95; % AR(1) coefficient investment specific technology shock rho_eps_y = 0.0; % AR(1) coefficient cost push shock rho_eps_l = 0.0; % AR(1) coefficient labor supply shock rho_eps_K_b = 0.90; % AR(1) coefficient Bank Balance Sheet shock rho_N = 0.95; % AR(1) coefficient bank number shock //%------------------------------------------------------------ //% Model equations //%------------------------------------------------------------ // EXTENSION: // model(block, bytecode); model; ////1*********** 1) PATIENT HHs ********************************************************6 (1-a_i)*exp(ee_z)*(exp(c_p) - a_i*exp(c_p(-1)))^(-1) = exp(lam_p); // WITH rescaling. a_i used. j * (exp(ee_j)) / exp(h_p) - exp(lam_p) * exp(q_h) + beta_p * exp(lam_p(+1)) * exp(q_h(+1)) = 0; // Housing decision with rescaling parameter j exp(lam_p) = beta_p * exp(lam_p(+1)) * (1+exp(r_d)) / exp(pie(+1)); // (1 - exp(eps_l)) * exp(l_p) + exp(l_p) ^(1+phi) / exp(w_p) * exp(eps_l)/exp(lam_p) - kappa_w *( exp(pie_wp) - exp(pie(-1)) ^ ind_w * piss ^ (1-ind_w) ) * exp(pie_wp) + beta_p * exp(lam_p(+1))/exp(lam_p) * kappa_w *( exp(pie_wp(+1)) - exp(pie) ^ ind_w * piss ^ (1-ind_w) ) * exp(pie_wp(+1)) ^2 / exp(pie) = 0 ; exp(pie_wp) = exp(w_p) / exp(w_p(-1)) * exp(pie); exp(c_p) + exp(q_h) * ( exp(h_p) - exp(h_p(-1)) ) + exp(d_p) = exp(w_p) * exp(l_p) + (1+exp(r_d(-1)))*exp(d_p(-1))/exp(pie) + exp(J_R)/gamma_p ; // ////7*********** 2) IMPATIENT HHs ********************************************************7 (1-a_i)*exp(ee_z)*(exp(c_i) - a_i*exp(c_i(-1)))^(-1) = exp(lam_i); // CON rescaling j * (exp(ee_j)) / exp(h_i) - exp(lam_i) * exp(q_h) + beta_i * exp(lam_i(+1)) * exp(q_h(+1)) + exp(s_i) * exp(m_i) *exp(q_h(+1)) * exp(pie(+1)) = 0; // exp(lam_i) - beta_i * exp(lam_i(+1)) * (1+exp(r_bh)) / exp(pie(+1)) = exp(s_i) * (1+exp(r_bh)); // (1 - exp(eps_l)) * exp(l_i) + exp(l_i) ^(1+phi) / exp(w_i) * exp(eps_l)/exp(lam_i) - kappa_w *( exp(pie_wi) - exp(pie(-1))^ind_w * piss ^ (1-ind_w) ) * exp(pie_wi) + beta_i * exp(lam_i(+1))/exp(lam_i) * kappa_w *( exp(pie_wi(+1)) - exp(pie) ^ind_w * piss ^ (1-ind_w) ) * exp(pie_wi(+1)) ^2 / exp(pie) = 0; exp(pie_wi) = exp(w_i) / exp(w_i(-1)) * exp(pie); exp(c_i) + exp(q_h) * (exp(h_i) - exp(h_i(-1))) + (1+exp(r_bh(-1)))*exp(b_i(-1))/exp(pie) = exp(w_i) * exp(l_i) + exp(b_i) ; // (1+exp(r_bh)) * exp(b_i) = exp(m_i) * exp(q_h(+1)) *exp(h_i) * exp(pie(+1)); // ////14*********** 3) CAPITAL PRODUCERS ***************************************************** exp(K) = (1-deltak) * exp(K(-1)) + ( 1 - kappa_i/2 * (exp(I)*exp(ee_qk)/exp(I(-1)) - 1)^2 ) * exp(I) ; 1 = exp(q_k) * ( 1 - kappa_i/2 * (exp(I)*exp(ee_qk)/exp(I(-1)) - 1)^2 - kappa_i * (exp(I)*exp(ee_qk)/exp(I(-1)) - 1) * exp(I)*exp(ee_qk)/exp(I(-1)) ) + beta_e * exp(lam_e(+1)) / exp(lam_e) * exp(q_k(+1)) * kappa_i * (exp(I(+1))*exp(ee_qk(+1))/exp(I) - 1) * exp(ee_qk(+1)) * (exp(I(+1))/exp(I))^2 ; // 13 // 15 ////16************ 4) ENTREPRENEURS ********************************************************* (1-a_i)*(exp(c_e) - a_i*exp(c_e(-1)))^(-1) = exp(lam_e); // CON rescaling exp(s_e) * exp(m_e) * exp(q_k(+1)) * exp(pie(+1)) * (1-deltak) + beta_e * exp(lam_e(+1)) * ( exp(q_k(+1))*(1-deltak) + exp(r_k(+1))*exp(u(+1)) - ( eksi_1*(exp(u(+1))-1)+eksi_2/2*( (exp(u(+1))-1)^2 ) ) ) = exp(lam_e) * exp(q_k) ; // exp(w_p) = ni * (1-alpha) * exp(y_e) / ( exp(l_pd) * exp(x) ); exp(w_i) = (1-ni) * (1-alpha) * exp(y_e) / ( exp(l_id) * exp(x) ); exp(lam_e) - exp(s_e) * (1+exp(r_be)) = beta_e * exp(lam_e(+1)) * (1+exp(r_be)) / exp(pie(+1)); // exp(r_k) = eksi_1 + eksi_2 * (exp(u)-1);// exp(c_e) + ((1+exp(r_be(-1))) * exp(b_ee(-1)) / exp(pie) ) + (exp(w_p)*exp(l_pd) + exp(w_i)*exp(l_id)) + exp(q_k) * exp(k_e) + ( eksi_1*(exp(u)-1)+eksi_2/2*(exp(u)-1)^2 ) * exp(k_e(-1)) = exp(y_e) / exp(x) + exp(b_ee) + exp(q_k) * (1-deltak) * exp(k_e(-1)) ; // 20 exp(y_e) = exp(A_e) * (exp(u)*exp(k_e(-1)))^(alpha) * ( exp(l_pd)^ni * exp(l_id)^(1-ni) ) ^ (1-alpha); (1+exp(r_be)) * exp(b_ee) = exp(m_e) * exp(q_k(+1)) *exp(pie(+1)) * exp(k_e) * (1-deltak); // exp(r_k) = alpha * exp(A_e) * exp(u)^(alpha-1) * exp(k_e(-1))^(alpha-1) * ( exp(l_pd)^ni * exp(l_id)^(1-ni) ) ^ (1-alpha) /exp(x); // 23 ////26************* 5)BANKS **************************************************************** exp(R_b) = - kappa_kb * ( exp(K_b) / exp(B) - vi ) * (exp(K_b)/exp(B)) ^2 + exp(r_ib) ; // eq 27 exp(K_b) * exp(pie) = (1-delta_kb) * exp(K_b(-1)) + exp(j_B(-1)) ; gamma_b * exp(d_b) = gamma_p * exp(d_p) ; gamma_b * exp(b_h) = gamma_i * exp(b_i) ; gamma_b * exp(b_e) = gamma_e * exp(b_ee); exp(b_h) + exp(b_e) = exp(d_b) + exp(K_b) + eps_K_b; /// PRICING in terms of MK /// // - 1 + exp(mk_d)/(exp(mk_d)-1) - exp(mk_d)/(exp(mk_d)-1) * exp(r_ib)/exp(r_d) - kappa_d * ( exp(r_d)/exp(r_d(-1)) - 1 ) * exp(r_d)/exp(r_d(-1)) // + beta_p * ( exp(lam_p(+1))/exp(lam_p) ) * kappa_d * ( exp(r_d(+1))/exp(r_d) - ( exp(r_d)/exp(r_d(-1)))^ind_d ) * ( (exp(r_d(+1))/exp(r_d))^2 ) * (exp(d_b(+1))/exp(d_b)) = 0;// // + 1 - exp(mk_be)/(exp(mk_be)-1) + exp(mk_be)/(exp(mk_be)-1) * exp(R_b)/exp(r_be) - kappa_be * (exp(r_be)/exp(r_be(-1)) - 1 ) * exp(r_be)/exp(r_be(-1)) // + beta_p * ( exp(lam_p(+1))/exp(lam_p) ) * kappa_be * ( exp(r_be(+1))/exp(r_be) - ( exp(r_be)/exp(r_be(-1)))^ind_be ) * ( (exp(r_be(+1))/exp(r_be))^2 ) * (exp(b_e(+1))/exp(b_e)) = 0;// 30 // + 1 - exp(mk_bh)/(exp(mk_bh)-1) + exp(mk_bh)/(exp(mk_bh)-1) * exp(R_b)/exp(r_bh) - kappa_bh * (exp(r_bh)/exp(r_bh(-1)) - 1 ) * exp(r_bh)/exp(r_bh(-1)) // + beta_p * ( exp(lam_p(+1))/exp(lam_p) ) * kappa_bh * ( exp(r_bh(+1))/exp(r_bh) - ( exp(r_bh)/exp(r_bh(-1)))^ind_bh ) * ( (exp(r_bh(+1))/exp(r_bh))^2 ) * (exp(b_h(+1))/exp(b_h)) = 0;// /// CHANGES BECAUSE OF EXTENSION /// % Without taking into account that the bank influences the market rate r_d // - 1/exp(N) + 1/exp(N) * exp(mk_d)* exp(N) /(1- exp(N) - exp(mk_d) + exp(mk_d)*exp(N)) - 1/exp(N) * exp(mk_d)* exp(N) /(1- exp(N) - exp(mk_d) + exp(mk_d)*exp(N)) * exp(r_ib)/exp(r_d) // - kappa_d * ( exp(r_d)/exp(r_d(-1)) - 1 ) * exp(r_d)/exp(r_d(-1)) // + beta_p * ( exp(lam_p(+1))/exp(lam_p) ) * kappa_d * ( exp(r_d(+1))/exp(r_d) - ( exp(r_d)/exp(r_d(-1)))^ind_d ) * ( (exp(r_d(+1))/exp(r_d))^2 ) * (exp(d_b(+1))/exp(d_b)) = 0;// // + 1/exp(N) - 1/exp(N) * exp(mk_be)* exp(N) /(1- exp(N) - exp(mk_be) + exp(mk_be)*exp(N)) + 1/exp(N) * exp(mk_be)* exp(N) /(1- exp(N) - exp(mk_be) + exp(mk_be)*exp(N)) * exp(R_b)/exp(r_be) // - kappa_be * (exp(r_be)/exp(r_be(-1)) - 1 ) * exp(r_be)/exp(r_be(-1)) // + beta_p * ( exp(lam_p(+1))/exp(lam_p) ) * kappa_be * ( exp(r_be(+1))/exp(r_be) - ( exp(r_be)/exp(r_be(-1)))^ind_be ) * ( (exp(r_be(+1))/exp(r_be))^2 ) * (exp(b_e(+1))/exp(b_e)) = 0;// 30 // + 1/exp(N) - 1/exp(N) * exp(mk_bh)* exp(N) /(1- exp(N) - exp(mk_bh) + exp(mk_bh)*exp(N)) + 1/exp(N) * exp(mk_bh)* exp(N) /(1- exp(N) - exp(mk_bh) + exp(mk_bh)*exp(N)) * exp(R_b)/exp(r_bh) // - kappa_bh * (exp(r_bh)/exp(r_bh(-1)) - 1 ) * exp(r_bh)/exp(r_bh(-1)) // + beta_p * ( exp(lam_p(+1))/exp(lam_p) ) * kappa_bh * ( exp(r_bh(+1))/exp(r_bh) - ( exp(r_bh)/exp(r_bh(-1)))^ind_bh ) * ( (exp(r_bh(+1))/exp(r_bh))^2 ) * (exp(b_h(+1))/exp(b_h)) = 0;// // eq 32 - 1/exp(N) - kappa_d * ( exp(r_d)/exp(r_d(-1)) - 1 ) * exp(r_d)/exp(r_d(-1)) - kappa_d/2 * ( exp(r_d)/exp(r_d(-1)) - 1 )^2 + beta_p * ( exp(lam_p(+1))/exp(lam_p) ) * kappa_d * ( exp(r_d(+1))/exp(r_d) - ( exp(r_d)/exp(r_d(-1)))^ind_d ) * ( (exp(r_d(+1))/exp(r_d))^2 ) * (exp(d_b(+1))/exp(d_b)) = 0;// // eq 33 1/exp(N) - kappa_bh * ( exp(r_bh)/exp(r_bh(-1)) - 1 ) * exp(r_bh)/exp(r_bh(-1)) - kappa_bh/2 * ( exp(r_bh)/exp(r_bh(-1)) - 1 )^2 + beta_p * ( exp(lam_p(+1))/exp(lam_p) ) * kappa_bh * ( exp(r_bh(+1))/exp(r_bh) - ( exp(r_bh)/exp(r_bh(-1)))^ind_bh ) * ( (exp(r_bh(+1))/exp(r_bh))^2 ) * (exp(b_h(+1))/exp(b_h)) = 0;// // eq 34 1/exp(N) - kappa_be * ( exp(r_be)/exp(r_be(-1)) - 1 ) * exp(r_be)/exp(r_be(-1)) - kappa_be/2 * ( exp(r_be)/exp(r_be(-1)) - 1 )^2 + beta_p * ( exp(lam_p(+1))/exp(lam_p) ) * kappa_be * ( exp(r_be(+1))/exp(r_be) - ( exp(r_be)/exp(r_be(-1)))^ind_be ) * ( (exp(r_be(+1))/exp(r_be))^2 ) * (exp(b_e(+1))/exp(b_e)) = 0;// exp(j_B) = + exp(r_bh) * exp(b_h) + exp(r_be) * exp(b_e) - exp(r_d) * exp(d_b) - kappa_d/2 * ( (exp(r_d)/exp(r_d(-1))-1)^2) * exp(r_d) *exp(d_b) - kappa_be/2 * ( (exp(r_be)/exp(r_be(-1))-1)^2) * exp(r_be)*exp(b_e) - kappa_bh/2 * ( (exp(r_bh)/exp(r_bh(-1))-1)^2) * exp(r_bh)*exp(b_h) - kappa_kb/2 * ( (exp(K_b) / exp(B) - vi ) ^2) * exp(K_b); // ////36*********** 6)RETAILERS ************************************************************** exp(J_R) = exp(Y)*(1 - (1/exp(x)) - (kappa_p/2) * (exp(pie) - ( exp(pie(-1)) ^ ind_p * piss ^ (1-ind_p) ))^2 ) ; 1 - exp(eps_y) + exp(eps_y) / exp(x) - kappa_p * (exp(pie) - ( exp(pie(-1)) ^ ind_p * piss ^ (1-ind_p) )) * exp(pie) + beta_p*(exp(lam_p(+1))/exp(lam_p))* kappa_p * (exp(pie(+1)) - ( exp(pie) ^ ind_p * piss ^ (1-ind_p) )) * exp(pie(+1)) * (exp(Y(+1))/exp(Y)) = 0; // 34 ////38************ 7) AGGREGATION & EQUILIBRIUM ************************************************ exp(C) = gamma_p * exp(c_p) + gamma_i * exp(c_i) + gamma_e * exp(c_e); exp(BH) = gamma_b * exp(b_h); exp(BE) = gamma_b * exp(b_e); exp(B) = (exp(BH) + exp(BE)); // eq 42 exp(D) = gamma_p * exp(d_p) ; // oppure: (gamma_b * exp(d_b)) exp(Y) = gamma_e * exp(y_e); // exp(J_B) = gamma_b * exp(j_B); // gamma_e * exp(l_pd) = gamma_p * exp(l_p); gamma_e * exp(l_id) = gamma_i * exp(l_i); h = gamma_p * exp(h_p) + gamma_i * exp(h_i); // exp(K) = gamma_e * exp(k_e); // % exp(Y1) = exp(C) + 1 * (exp(K)-(1-deltak)*exp(K(-1))) + delta_kb * exp(K_b(-1)); // exp(Y1) = exp(C) + 1 * (exp(K)-(1-deltak)*exp(K(-1))) ; // //exp(Y) = exp(C) + exp(q_k) * (exp(K) - (1-deltak) * exp(K(-1))) // + delta_kb * exp(K_b(-1)) / exp(pie) // + (eksi_1*(exp(u)-1) + eksi_2/2*((exp(u)-1)^2)) * exp(k_e(-1)) // + kappa_p/2 * ( exp(pie) - ( exp(pie(-1)) ^ ind_p * piss ^ (1-ind_p) ))^2 * exp(Y) // + kappa_d/2 * ( (exp(r_d(-1))/exp(r_d(-2))-1)^2) * exp(r_d(-1)) *exp(d_b(-1)) // + kappa_be/2 * ( (exp(r_be(-1))/exp(r_be(-2))-1)^2) * exp(r_be(-1))*exp(b_e(-1)) // + kappa_bh/2 * ( (exp(r_bh(-1))/exp(r_bh(-2))-1)^2) * exp(r_bh(-1))*exp(b_h(-1)) // + kappa_kb/2 * ( (exp(K_b(-1)) / exp(B(-1)) - vi ) ^2) * exp(K_b(-1)) // + errorflag ; // exp(PIW) = ( exp(w_p) + exp(w_i) ) / ( exp(w_p(-1)) + exp(w_i(-1)) ) * exp(pie); ////51*********** 8) TAYLOR RULE & PROFITS CB ***************************************************** (1+exp(r_ib)) = (1+r_ib_ss)^(1 - rho_ib ) * (1+exp(r_ib(-1)))^rho_ib * (( exp(pie) / piss ) ^phi_pie * (exp(Y1)/exp(Y1(-1)))^phi_y ) ^ ( 1 - rho_ib ) * (1+e_r_ib) ;// ////52*********** 9) EXOGENOUS PROCESSES ****************************************************13 exp(ee_z) = 1 - rho_ee_z * 1 + rho_ee_z * exp(ee_z(-1)) + e_z; exp(A_e) = 1 - rho_A_e * 1 + rho_A_e * exp(A_e(-1)) + e_A_e; exp(ee_j) = 1 - rho_ee_j * 1 + rho_ee_j * exp(ee_j(-1)) + e_j; exp(m_i) = (1-rho_mi) * m_i_ss + rho_mi * exp(m_i(-1)) + e_mi; exp(m_e) = (1-rho_me) * m_e_ss + rho_me * exp(m_e(-1)) + e_me; // exp(mk_d) = (1-rho_mk_d) * mk_d_ss + rho_mk_d * exp(mk_d(-1)) + e_mk_d; // exp(mk_be) = (1-rho_mk_be) * mk_be_ss + rho_mk_be * exp(mk_be(-1)) + e_mk_be; // exp(mk_bh) = (1-rho_mk_bh) * mk_bh_ss + rho_mk_bh * exp(mk_bh(-1)) + e_mk_bh; // EXTENSION: Exogenous process of the markup. NEED TO CHANGE?? exp(mk_d) = (1-rho_mk_d) * mk_d_ss + rho_mk_d * exp(mk_d(-1)) + e_mk_d; // eq 58 exp(mk_be) = (1-rho_mk_be) * mk_be_ss + rho_mk_be * exp(mk_be(-1)) + e_mk_be; exp(mk_bh) = (1-rho_mk_bh) * mk_bh_ss + rho_mk_bh * exp(mk_bh(-1)) + e_mk_bh; exp(ee_qk) = 1-rho_ee_qk * 1 + rho_ee_qk * exp(ee_qk(-1)) + e_qk; exp(eps_y) = (1-rho_eps_y) * eps_y_ss + rho_eps_y * exp(eps_y(-1)) + e_y; exp(eps_l) = (1-rho_eps_l) * eps_l_ss + rho_eps_l * exp(eps_l(-1)) + e_l; exp(eps_K_b) = (1-rho_eps_K_b)* 1 + rho_eps_K_b* exp(eps_K_b(-1)) + e_eps_K_b; // EXTENSION: New process of number of banks introduced exp(N) = (1-rho_N) * N_ss + rho_N * exp(N(-1)) + e_N; // eq 64 ////65*********** 10) AUXILIARY VARIABLES *****************************************************4 exp(rr_e) = (1+exp(r_be))/exp(pie(+1)) - 1; exp(aux1) = exp(C) + 1 * (exp(K)-(1-deltak)*exp(K(-1))); exp(bm) = (exp(b_h(-1))/(exp(b_h(-1))+exp(b_e(-1))) * exp(r_bh(-1)) + exp(b_e(-1))/(exp(b_h(-1))+exp(b_e(-1))) * exp(r_be(-1))) - exp(r_d(-1)); exp(spr_b) = 0.5*exp(r_bh) + 0.5*exp(r_be) - exp(r_d); //64 ////69*********** 11) MEASUREMENT EQUATIONS (VARIABLES TAKEN TO THE DATA) ******************************13 data_C = C - steady_state(C); data_I = I - steady_state(I); data_rBH = exp(r_bh) - r_bh_ss; data_rBE = exp(r_be) - r_be_ss; data_rD = exp(r_d) - (piss/beta_p - 1); data_rIB = exp(r_ib) - r_ib_ss; data_D = D - steady_state(D); data_BH = BH - steady_state(BH); data_BE = BE - steady_state(BE); data_PIW = exp(PIW) - piss; data_PIE = exp(pie) - piss; //data_PIE = exp(pie) * exp(pie(-1)) * exp(pie(-2)) * exp(pie(-3)) - piss; data_HP = q_h - steady_state(q_h); // EXTENSION: Number of banks, new observable data_N = N - steady_state(N); end; //model initval; /////////// Initial values. Spain Extension /////////////////// c_p = -0.10314 ; h_p = -0.0524999 ; d_p = 1.29143 ; l_p = -0.263578 ; lam_p = 0.10314 ; J_R = -1.50576 ; j_B = -3.73481 ; c_i = -1.90526 ; h_i = -2.97308 ; b_i = 0.656068 ; l_i = -0.055665 ; lam_i = 1.90526 ; s_i = -2.23308 ; I = -1.87535 ; c_e = -2.26228 ; k_e = 1.81353 ; l_pd = -0.263578 ; l_id = -0.055665 ; b_ee = 0.72836 ; y_e = 0.285995 ; lam_e = 2.26228 ; s_e = -1.93617 ; d_b = 1.29143 ; b_h = 0.656068 ; b_e = 0.72836 ; r_d = -5.51745 ; r_bh = -4.69582 ; r_be = -4.59701 ; R_b = -5.42671 ; // r_d = 1.1 ; // r_bh = 1.3 ; // r_be = 1.3 ; // R_b = 1.2 ; K_b = -1.01914 ; pie = -3.44179E-16 ; x = 0.182322 ; C = 0.144011 ; Y = 0.285995 ; D = 1.29143 ; BE = 0.72836 ; BH = 0.656068 ; B = 1.38601 ; w_p = -0.143575 ; w_i = -1.73778 ; J_B = -3.73481 ; q_h = 3.86138 ; K = 1.81353 ; r_ib = -5.42205 ; // r_ib = 1.05 ; r_k = -3.09259 ; mk_d = log(mk_d_ss) ; mk_be = log(mk_be_ss) ; mk_bh = log(mk_bh_ss) ; m_i = log(m_i_ss) ; m_e = log(m_e_ss) ; Y1 = 0.268651 ; rr_e = -4.59701 ; aux1 = 0.268651 ; bm = -5.18344 ; spr_b = -5.1865 ; eps_y = 1.79176 ; eps_l = log(eps_l_ss) ; data_C = 0 ; data_I = 0 ; data_rBH = 0 ; data_rBE = 0 ; data_rD = 0 ; data_rIB = 0 ; data_D = 0 ; data_BH = 0 ; data_BE = 0 ; data_PIW = 0 ; data_PIE = 0 ; data_HP = 0 ; // EXTENSION: // mk_d = 0.908907246 ; // mk_be = 2.292598027 ; // mk_bh = 2.076970128 ; N = 0.002440489; data_N = 0 ; ///////////////////////////////////////// end; fprintf('\n...solve for the SS...\n') % steady(solve_algo=0); steady(solve_algo=4,maxit=100000); resid(1); %%%% get the SS values %%%% ss_vector = oo_.steady_state; n_vars = length(ss_vector); ss_cell = mat2cell(ss_vector,ones(1,n_vars)); tmp = [M_.endo_names,ones(n_vars,1)*44]'; varnames = ['[',tmp(:)',']']; eval([varnames,' = deal(ss_cell{:});']) disp(' ');disp('%%% Display some SS results (BK model): %%%%') SSexpenditures = exp(C) + exp(q_k) * (exp(K)-(1-deltak)*exp(K)) + ... + delta_kb * exp(K_b) / exp(pie) + ... + (eksi_1*(exp(u)-1) + eksi_2/2*((exp(u)-1)^2))*exp(k_e) + ... + kappa_kb/2 * ( (exp(K_b) / exp(B) - vi ) ^2) * exp(K_b); SSincome = exp(Y); disp(['expenditures in ss: ',num2str(SSexpenditures)]); disp(['total income in ss: ',num2str(SSincome)]); disp(['C/Y: ',num2str(exp(C)/exp(Y))]); disp(['I/Y: ',num2str(exp(I)/exp(Y))]); disp(['K/Y: ',num2str(exp(K)/exp(Y))]); disp(['r_d (%annual): ',num2str(exp(r_d)*400)]); disp(['r_ib (%annual): ',num2str(exp(r_ib)*400)]); disp(['r_bh (%annual): ',num2str(exp(r_bh)*400)]); disp(['r_be (%annual): ',num2str(exp(r_be)*400)]); disp(['spread(%annual): ',num2str(exp(spr_b)*400)]); disp(['bh/(bh+be)(%): ',num2str(exp(b_h)/(exp(b_h)+exp(b_e))*100)]); disp(['be/(bh+be)(%): ',num2str(exp(b_e)/(exp(b_h)+exp(b_e))*100)]); disp(['B/Y: ',num2str(exp(B)/exp(Y))]); disp(['D/Y: ',num2str(exp(D)/exp(Y))]); disp(['K_b/B: ',num2str(exp(K_b)/exp(B))]); disp(['K_b/Y: ',num2str(exp(K_b)/exp(Y))]); disp(['delta_kb: ',num2str(delta_kb)]); disp(['check_i: ',num2str(beta_i*(1+exp(r_bh))/piss)]); disp(['check_e: ',num2str(beta_e*(1+exp(r_be))/piss)]); disp(['w_i*l_i: ',num2str(exp(w_i)*exp(l_i))]); disp(['w_p*l_p: ',num2str(exp(w_p)*exp(l_p))]); disp(['w_i: ',num2str(exp(w_i))]); disp(['w_p: ',num2str(exp(w_p))]); %------------------------------------------------------------ % Check indeterminacy with STOCH_SIMUL %------------------------------------------------------------ check; % return; Std_e = [0.0025 0 0 0 0 0 0 0 0 % r_ib 0 0.20 0 0 0 0 0 0 0 % A_e 0 0 0.537 .90 .90 .90 .90 0 0 % e_mk_be 0 0 .90 0.01 .90 .90 .90 0 0 % m_e 0 0 .90 .90 0.44 .90 .90 0 0 % e_mk_b 0 0 .90 .90 .90 0.01 .90 0 0 % m_i 0 0 .90 .90 .90 .90 0.6422 0 0 % e_mk_d 0 0 0 0 0 0 0 0.10 0 % e_j 0 0 0 0 0 0 0 0 0.000756]; % BB shocks; var e_r_ib = Std_e(1,1)^2; var e_A_e = Std_e(2,2)^2; % var e_mk_be = Std_e(3,3)^2; % var e_me = Std_e(4,4)^2; var e_mk_bh = Std_e(5,5)^2; var e_mi = Std_e(6,6)^2; var e_mk_d = Std_e(7,7)^2; var e_j = Std_e(8,8)^2; % var e_j = 0.001^2; end; // Stochastic simulations % options_.nograph = 1; % options_.nomoments = 1; % options_.noprint = 1; stoch_simul(order=1,irf=20) C I Y r_ib r_be r_d pie B D K r_k PIW q_h J_B K_b; % return //%------------------------------------------------------------ //% BAYESIAN ESTIMATION //%------------------------------------------------------------ //% defining which dataseries are used in estimation varobs data_C data_I data_rBH data_rBE data_rD data_rIB data_D data_BH data_BE data_PIW data_PIE data_HP data_N; load(['data',filesep,'Data_spain.mat']); % load dataseries from file % load(['data',filesep,'end_period_MRO.txt']); % load dataseries from file % mro = (1+end_period_MRO./100).^0.25 - mean( (1+end_period_MRO./100).^0.25 ); % delete initial/final dates if there are NaN in the data used ... BEG_OBS = 2; % 2003:Q1 END_OBS = length(DATES); % 2013:Q4 DATES = DATES(BEG_OBS:END_OBS,:); datadescr.DATES = DATES; datadescr.MODEL = M_.fname; % give the dataseries the names listed in the 'varobs' command ... dataseries.data_C = C_HP (BEG_OBS:END_OBS); datadescr.data_C = 'Real Consumption'; dataseries.data_I = I_HP (BEG_OBS:END_OBS); datadescr.data_I = 'Real Investment'; dataseries.data_rBH = RBH (BEG_OBS:END_OBS) - mean(RBH (BEG_OBS:END_OBS)); datadescr.data_rBH = 'Interest rate on loans to households'; dataseries.data_rBE = RBE (BEG_OBS:END_OBS) - mean(RBE (BEG_OBS:END_OBS)); datadescr.data_rBE = 'Interest rate on loans to firms'; dataseries.data_rD = RD (BEG_OBS:END_OBS) - mean(RD (BEG_OBS:END_OBS)); datadescr.data_rD = 'Interest rate on deposits'; dataseries.data_rIB = EONIA (BEG_OBS:END_OBS) - mean(EONIA (BEG_OBS:END_OBS)); datadescr.data_rIB = 'Short-term interest rate'; dataseries.data_D = DR_HP (BEG_OBS:END_OBS); datadescr.data_D = 'Real deposits'; dataseries.data_BH = BHR_HP (BEG_OBS:END_OBS); datadescr.data_BH = 'Real loans to households'; dataseries.data_BE = BER_HP (BEG_OBS:END_OBS); datadescr.data_BE = 'Real loans to firms'; dataseries.data_PIW = PIW (BEG_OBS:END_OBS) - mean(PIW (BEG_OBS:END_OBS)); datadescr.data_PIW = 'Wage inflation'; dataseries.data_PIE = PIE (BEG_OBS:END_OBS) - mean(PIE (BEG_OBS:END_OBS)); datadescr.data_PIE = 'Inflation (q/q)'; dataseries.data_HP = HP_HP (BEG_OBS:END_OBS); datadescr.data_HP = 'Real house prices'; dataseries.data_N = N_HP (BEG_OBS:END_OBS); datadescr.data_N = 'Banking competition'; //% saving the renamed series for Dynare save ('data/DYNARE_estimdata','-STRUCT','dataseries') estimated_params ; //% Initial conditions PRIOR shape MEAN STD stderr e_z , 0.010, inv_gamma_pdf, 0.0100, 0.05 ; stderr e_A_e , 0.007, inv_gamma_pdf, 0.0100, 0.05 ; stderr e_j , 0.020, inv_gamma_pdf, 0.0100, 0.05 ; stderr e_me , 0.0030, inv_gamma_pdf, 0.0100, 0.05 ; stderr e_mi , 0.0041, inv_gamma_pdf, 0.0100, 0.05 ; stderr e_mk_d , 0.09, inv_gamma_pdf, 0.0100, 0.05 ; stderr e_mk_bh , 0.0049, inv_gamma_pdf, 0.0100, 0.05 ; stderr e_mk_be , 0.0835, inv_gamma_pdf, 0.0100, 0.05 ; //10 stderr e_qk , 0.0136, inv_gamma_pdf, 0.0100, 0.05 ; stderr e_r_ib , 0.0020, inv_gamma_pdf, 0.0100, 0.05 ; stderr e_y , 0.90, inv_gamma_pdf, 0.0100, 0.05 ; stderr e_l , 0.348, inv_gamma_pdf, 0.0100, 0.05 ; stderr e_eps_K_b , 0.008, inv_gamma_pdf, 0.0100, 0.05 ; // EXTENSION: Estimate the std of the innovation of new process stderr e_N , 0.008, inv_gamma_pdf, 0.0100, 0.05 ; rho_ee_z , 0.55, beta_pdf, 0.80, 0.10 ; rho_A_e , 0.95, beta_pdf, 0.80, 0.10 ; rho_ee_j , 0.98, beta_pdf, 0.80, 0.10 ; rho_me , 0.95, beta_pdf, 0.80, 0.10 ; rho_mi , 0.95, beta_pdf, 0.80, 0.10 ; rho_mk_d , 0.95, beta_pdf, 0.80, 0.10 ; rho_mk_bh , 0.85, beta_pdf, 0.80, 0.10 ; rho_mk_be , 0.85, beta_pdf, 0.80, 0.10 ; rho_ee_qk , 0.55, beta_pdf, 0.80, 0.10 ; rho_eps_y , 0.80, beta_pdf, 0.80, 0.10 ; rho_eps_l , 0.60, beta_pdf, 0.80, 0.10 ; rho_eps_K_b , 0.80, beta_pdf, 0.80, 0.10 ; kappa_p , 50, gamma_pdf, 50, 20 ; kappa_w , 50, gamma_pdf, 50, 20 ; kappa_i , 4.5, gamma_pdf, 2.5, 1.0 ; kappa_d , 10, gamma_pdf, 10, 2.5 ; kappa_be , 3, gamma_pdf, 3, 2.5 ; kappa_bh , 6, gamma_pdf, 6, 2.5 ; kappa_kb , 5, gamma_pdf, 10.0, 5.0 ; phi_pie , 2.0, gamma_pdf, 2.0, 0.5 ; rho_ib , 0.75, beta_pdf, 0.75, 0.10 ; phi_y , 0.2, normal_pdf, 0.10, 0.15 ; ind_p , 0.20, beta_pdf, 0.50, 0.15 ; ind_w , 0.25, beta_pdf, 0.50, 0.15 ; a_i , 0.6, beta_pdf, 0.50, 0.10 ; end; estimation(datafile='data/DYNARE_estimdata' ,mode_compute = 9 %9 // ,mode_file = '' ,mh_jscale = 0.2 ,presample = 1 ,prefilter = 0 ,prior_trunc = 1e-14 ,mh_replic = 200 %put 500 for test and a big number (like 100000) when serious ,mh_nblocks = 1 %put 1 for test and 5 or 10 when serious ,filtered_vars ,lik_init = 2 % 1 ,order = 1 ,mode_check ) C I Y1 r_ib r_be r_bh r_d pie B D J_B K_b; save([M_.fname '_results.mat'],'oo_','M_','estim_params_','options_','dataseries','datadescr');