// My adjusted model based on Gerali et al. (2010) // 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 // 8 blocks: 1) PATIENTs 2) IMPATIENTs 3) CAPITAL PRODUCERS 4) ENTREPRENEURS 5) BANKS 6) RETAILERS // 7) AGGREGATION & EQUILIBRIUM 8) EXOGENOUS PROCESSES grid_vi = ( 0.09*1.02 : 0.01 : 0.10 ) ; [n4, n_grid_vi ] = size(grid_vi) ; counter = 0; //------------------------------------------------------------------------- // 1. Declaration of endogenous and exogenous variables //------------------------------------------------------------------------- var c_p h_p d_p l_p J_R c_i h_i b_i l_i I q_k c_e k_e l_pd l_id b_ee y_e d_b b_h b_e r_d r_bh r_be K_b pie x C Y D BE BH B w_p w_i J_B j_B q_h K A_e ee_j m_i m_e eps_y Y1 vi weight_BH weight_BE u; // 48 variables varexo e_A_e e_j e_me e_mi e_y e_r_ib; // 5 varexo //------------------------------------------------------------------------- // 2. Declaration of parameters //------------------------------------------------------------------------- parameters beta_p j phi beta_i m_i_ss beta_e m_e_ss alpha h gamma_p gamma_i gamma_e gamma r_k_ss psi_b delta_kb kappa_kb eps_y_ss kappa_p zeta kappa_i deltak piss vi_ss rho_A_e rho_ee_j rho_mi rho_me rho_eps_y xi_1 xi_2 x_ss mu_qp mu_k mu_qi mu_ci mu_dp mu_cp mu_ce y_e_ss rho_ib phi_pie phi_y r_ib_ss eps_d r_ss; //------------------------------------------------------------------------- // 3. Parameter calibration //------------------------------------------------------------------------- beta_p = 0.994550000000000 ; beta_i = 0.975000000000000 ; beta_e = 0.975000000000000 ; j = 0.203000000000000 ; phi = 1.500000000000000 ; rho_mi = 0.938578931344182 ; rho_me = 0.910171380445550 ; m_i_ss = 1/(1-rho_mi) ;%?? m_e_ss = 1/(1-rho_me) ;%?? %m_i_ss = 0.750000000000000 ; %m_e_ss = 0.400000000000000 ; alpha = 0.340000000000000 ; h = 1.000000000000000 ; gamma_p = 0.4000000000000000 ; gamma_i = 0.4000000000000000 ; gamma_e = 0.200000000000000 ; gamma = 0.800000000000000 ; psi_b = 1.000000000000000 ; delta_kb = 0.049000000000000 ; deltak = 0.040000000000000 ; piss = 1.000000000000000 ; q_k_ss = 1.000000000000000 ; vi_ss = 0.090000000000000 ; eps_y_ss = 8.90000000000000 ; kappa_kb = 11.0683 ; kappa_p = 28.6502 ; zeta = 0.1605 ; kappa_i = 10.1822 ; rho_A_e = 0.9390 ; rho_ee_j = 0.909222967643905 ; rho_mi = 0.938578931344182 ; rho_me = 0.910171380445550 ; rho_eps_y = 0.256295678347778 ; y_e_ss = 1 ; rho_ib = 0.7686 ; phi_pie = 1.9816 ; phi_y = 0.3459 ; eps_d = -1.1 ; r_ss = 1/beta_p -1; r_ib_ss = (piss/beta_p - 1) * (eps_d-1)/eps_d ; r_k_ss = -(1-deltak)-m_e_ss*(1-deltak)*piss/beta_e*(1/(piss/beta_p)-beta_e/piss)+1/beta_e; xi_1 = r_k_ss ; xi_2 = 0.1 * r_k_ss ; x_ss = eps_y_ss / (eps_y_ss - 1) ; mu_qp = j / (1-beta_p); mu_k = (alpha*beta_e) / (1 - beta_e*(1-deltak) - (m_e_ss * (1-deltak) * (beta_p - beta_e))); mu_qi = j / (1-(beta_i * (1-m_i_ss)) - (m_i_ss * beta_p)); mu_ci = (gamma_e*(1-alpha)*(1-gamma)) / (gamma_i*(1-mu_qi*m_i_ss*(beta_p-1))); mu_dp = ((gamma_p/gamma_e) * (mu_k*m_e_ss*beta_p*(1-deltak)) + ((gamma_p/gamma_i) * (mu_qi*m_i_ss*beta_p*mu_ci))); mu_cp = ((1-alpha) * gamma * gamma_e / gamma_p) + (gamma_e*(x_ss-1)) + (mu_dp * (beta_p-1) / beta_p); mu_ce = alpha + mu_k * ((m_e_ss*(beta_p-1)*(1-deltak))-deltak); //------------------------------------------------------------------------- // 4. The MODEL //------------------------------------------------------------------------- model; ////*********** 1) PATIENT HHs ******************************************************** (exp(q_h) / exp(c_p)) = ((j * (exp(ee_j))) / exp(h_p)) + ((beta_p * exp(q_h(+1))) / exp(c_p(+1))); 1 / exp(c_p) = beta_p * ((1+exp(r_d)) / (exp(pie(+1)) * exp(c_p(+1)))); exp(w_p) = (exp(l_p) ^ (phi)) * exp(c_p); 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) ; //4 ////*********** 2) IMPATIENT HHs ******************************************************** (exp(q_h) / exp(c_i)) = ((j * (exp(ee_j))) / exp(h_i)) + ((exp(m_i) * exp (q_h(+1)) * exp(pie(+1))) / ((1+exp(r_bh)) * (exp(c_i)))) + ((beta_i * (exp (q_h(+1)) * (1-exp(m_i)))) / (exp(c_i(+1)))); exp(w_i) = (exp(l_i) ^ (phi)) * exp(c_i); ((1+exp(r_bh)) * exp(b_i)) = (exp(m_i) * exp(q_h(+1)) * exp(h_i) * exp(pie(+1))); 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) ; //8 ////*********** 3) CAPITAL PRODUCERS ***************************************************** exp(K) = ((1-deltak) * exp(K(-1))) + ( 1 - kappa_i/2 * (exp(I)/exp(I(-1)) - 1)^2 ) * exp(I) ; 1 / exp(q_k) = ( 1 - kappa_i/2 * (exp(I)/exp(I(-1)) - 1)^2 - kappa_i * (exp(I)/exp(I(-1)) - 1) * (exp(I)/exp(I(-1))) ) + (beta_e * (exp(c_e) / exp(c_e(+1))) * (exp(q_k(+1)) / exp(q_k)) * kappa_i * (exp(I(+1))/exp(I) - 1) * (exp(I(+1))/exp(I))^2) ; // 10 ////************ 4) ENTREPRENEURS ********************************************************* exp(w_p) = ((1-alpha) * gamma * exp (y_e)) / ( exp(l_pd) * exp(x) ); exp(w_i) = ((1-alpha) * (1-gamma) * exp(y_e)) / ( exp(l_id) * exp(x) ); (xi_1 + xi_2 * exp(u-1)) = (alpha * exp(A_e) * (exp(k_e(-1)) * exp(u))^(alpha-1) * ( exp(l_pd)^(gamma) * exp(l_id)^(1-gamma) ) ^ (1-alpha)) / exp(x); (exp(q_k) / exp(c_e))-(((exp(m_e) * exp(q_k(+1)) * exp(pie(+1)) * (1-deltak)) / ((1+exp(r_be)) * exp(c_e)))) = beta_e * (1 / exp(c_e(+1))) * (((alpha * exp(A_e(+1)) * exp(k_e)^(alpha-1) * exp(u(+1))^(alpha) * ( exp(l_pd)^(gamma) * exp(l_id)^(1-gamma) ) ^ (1-alpha)) / exp(x(+1))) + exp(q_k(+1)) * (1-deltak)-(xi_1*(exp(u(+1))-1)+(xi_2/2)*(exp(u(+1))-1)^2) - (exp(m_e) * exp(q_k(+1)) *(1-deltak))); exp(y_e) = exp(A_e) * (exp(k_e(-1)) * exp(u))^(alpha) * ( exp(l_pd)^gamma * exp(l_id)^(1-gamma) ) ^ (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(c_e) + ((1+exp(r_be(-1))) * exp(b_ee(-1)) / exp(pie) ) + (exp(w_p)*exp(l_p) + exp(w_i)*exp(l_i)) + exp(q_k) * exp(k_e) + (xi_1*(exp(u)-1)+(xi_2/2)*(exp(u)-1)^2) = (exp(y_e) / exp(x)) + exp(b_ee) + exp(q_k) * (1-deltak) * exp(k_e(-1)) ; //17 ////************* 5)BANKS **************************************************************** exp(r_be) = - kappa_kb * ( exp(K_b) / exp(B) - exp(vi) ) * (exp(K_b)/exp(B)) ^2 + exp(r_d) ; exp(r_bh) = - kappa_kb * ( exp(K_b) / exp(B) - exp(vi) ) * (exp(K_b)/exp(B)) ^2 + exp(r_d) ; exp(K_b) * exp(pie) = (1-delta_kb) * exp(K_b(-1)) + exp(j_B(-1)) ; psi_b * exp(d_b) = gamma_p * exp(d_p); psi_b * exp(b_h) = gamma_i * exp(b_i); psi_b * exp(b_e) = gamma_e * exp(b_ee); %(exp(b_h) + exp(b_e)) = ( exp(d_b) + exp(K_b) ) ; //24 %exp(vi) = ((vi_ss)^( 1-0.92 ) ) * ( (exp(b_h)+ exp(b_e))/exp((Y1(-4))) )^( (1-0.92)*0.1 )* exp( vi(-1) )^0.92 ;% Countercyclical Capital Buffer Equation exp(vi) = ( vi_ss ^( 1-0.92 ) ) * ( exp(Y)/exp(Y(-4)) )^( ( 1 - 0.92 ) )* exp( vi(-1) )^0.92; exp(weight_BH) = ( 1 ^( 1-0.94 ) ) * ( exp(Y1) / exp(Y1(-4)) )^( ( 1 - 0.94 ) * ( - 10 * 1 ) ) * exp( weight_BH(-1) )^0.94; exp(weight_BE) = ( 1 ^( 1-0.92 ) ) * ( exp(Y1)/exp(Y1(-4)) )^(( 1 - 0.92 ) * ( - 15 * 1 ))* exp( weight_BE(-1) )^0.92; exp(j_B) = exp(r_bh) * exp(b_h) + exp(r_be) * exp(b_e) - exp(r_d) * exp(d_b) - kappa_kb/2 * ( ( exp(K_b) / exp(B) - exp(vi) ) ^2) * exp(K_b); //28 not including % countercyclical cbe ////*********** 6)RETAILERS ************************************************************** exp(J_R) = exp(Y) * (1 - (1/exp(x)) - (kappa_p/2) * (exp(pie) - ( (exp(pie(-1)) ^ zeta) * (piss ^ (1-zeta)) ))^2 ) ; 1 - exp(eps_y) + exp(eps_y) / exp(x) - kappa_p * (exp(pie) - ( exp(pie(-1)) ^ zeta * piss ^ (1-zeta))) * exp(pie) + beta_p * (exp(c_p) / exp(c_p(+1)))* kappa_p * (exp(pie(+1)) - ( exp(pie) ^ zeta * piss ^ (1-zeta))) * exp(pie(+1)) * (exp(Y(+1))/exp(Y)) = 0; //%30 ////************ 7) AGGREGATION & EQUILIBRIUM ************************************************ exp(C) = gamma_p * exp(c_p) + gamma_i * exp(c_i) + gamma_e * exp(c_e); exp(BH) = psi_b * exp(b_h); exp(BE) = psi_b * exp(b_e); exp(B) = ( exp(weight_BH) * exp(BH) + exp(weight_BE) * exp(BE) ); exp(D) = gamma_p * exp(d_p); exp(Y) = gamma_e * exp(y_e); exp(J_B) = psi_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))) ; exp(Y) = exp(C) + exp(q_k) * (exp(K)-(1-deltak)*exp(K(-1))) + (delta_kb + kappa_kb/2* ( exp(K_b) / exp(B) - exp(vi) ) ^2)* exp(K_b(-1)) + (xi_1*(exp(u)-1) + xi_2/2*((exp(u)-1)^2))* exp(k_e(-1))+ kappa_p/2 * ( exp(pie) - ( exp(pie(-1)) ^ (zeta) * piss ^ (1-zeta) ))^2 * exp(Y); //43 ////*********** 8) TAYLOR RULE & PROFITS CB ***************************************************** (1+exp(r_d)) = (1+r_ss)^(1-0) * (1+exp(r_d(-1)))^rho_ib * (( exp(pie) / piss) ^phi_pie * (exp(Y)/exp(Y(-1)))^phi_y ) ^ (1-rho_ib) * exp(e_r_ib) ;// 43 ////*********** 9) EXOGENOUS PROCESSES ********************************************************** 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(eps_y) = (1-rho_eps_y) * eps_y_ss + rho_eps_y * exp(eps_y(-1)) + e_y; //48 end; //------------------------------------------------------------------------- // 5. Initial guesses for steady state computation //------------------------------------------------------------------------- %initval; %c_p = mu_cp * (y_e_ss / x_ss) ; %h_p = (gamma * mu_qp * mu_cp) / ((gamma * mu_qp * mu_cp) + ((1-gamma) * mu_qi * mu_ci)) ; %q_h = mu_qp * (c_p / h_p) ; %d_p = mu_dp * (y_e_ss / x_ss) ; %c_i = mu_ci * (y_e_ss / x_ss) ; %h_i = ((1-gamma) * mu_qi * mu_ci) / ((gamma * mu_qp * mu_cp) + ((1-gamma) * mu_qi * mu_ci)) ; %q_h = mu_qi * (c_i / h_i) ; %b_i = mu_qi * m_i_ss * beta_p * c_i ; %k_e = mu_k * (y_e_ss / (x_ss * q_k_ss)) ; %b_ee = mu_k * m_e_ss * beta_p * (1-deltak) * (y_e_ss / x_ss) ; %c_e = mu_ce * (y_e_ss / x_ss) ; %I = deltak * k_e ; %j_B = 0 ; %y_e_ss = 1; %end; resid (1); steady ; check; //------------------------------------------------------------------------- // 6. Specification of shocks //------------------------------------------------------------------------- shocks; var e_A_e = 0.00512426105215156^2; var e_j = 0.0666521707690898^2; var e_mi = 0.00243843645883989^2; var e_me = 0.00325455234425937^2; var e_y = 0.620300719165277^2; var e_r_ib = 0.00157434820106446^2; end; %ramsey_policy (periods=100,order=1,planner_discount=((beta_p^gamma_p) * (beta_i^gamma_i) * (beta_e^gamma_e))) ; %planner_objective gamma_p * (log (c_p) + j * log (h_p) - ((l_p^(1+phi))/(1+phi))) + gamma_i * (log (c_i) + j * log (h_i) - ((l_i^(1+phi))/(1+phi))) + gamma_e * (log (c_e)); stoch_simul(periods=10000, irf=100);