// 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 // 9 blocks: 1) PATIENTs 2) IMPATIENTs 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 // THIS VERSION: April 20th, 2009 // 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) - All equations in exp form // This is the full version (monop. competitive banking sector & BANK capital à la Gerali with sticky rates) ////////////////////////////KILLING THE LABOUR MARKET RIGIDITIES////////////////////////////// /////////////SS calculated from the Gerali model %grid_vi = [ 0.09*1.02 : 0.01 : 0.10 ] ; %[n4, n_grid_vi ] = size(grid_vi) ; counter = 0; %for i4 = 1:n_grid_vi; %load steady_state_Y1_baseline.txt; var c_p // 1 h_p // 2 d_p // 3 l_p // 4 lam_p // 5 J_R // 6 j_B // 7 c_i // 9 h_i // 10 b_i // 11 l_i // 12 lam_i // 13 s_i // 14 I // 16 q_k // 17 c_e // 18 k_e // 19 l_pd // 20 l_id // 21 b_ee // 22 y_e // 23 lam_e // 24 s_e // 25 d_b // 26 b_h // 27 b_e // 28 r_d // 29 r_bh // 30 r_be // 31 R_b // 32 K_b // 33 pie // 34 x // 35 C // 36 Y // 37 D // 38 BE // 39 BH // 40 B // 41 w_p // 42 w_i // 43 J_B // 44 q_h // 45 K // 46 r_ib // 48 r_k // 49 ee_z // 50 A_e // 51 ee_j // 52 mk_d // 53 mk_be // 54 mk_bh // 55 ee_qk // 56 m_i // 57 m_e // 58 eps_y // 59 Y1 // 61 spr_b // 62 rr_e // 63 aux1 // 64 vi // 65 L // 66 weight_BH // 67 weight_BE // 68 k_ratio ; // 69 varexo e_A_e e_j e_l e_me e_mi e_mk_be e_mk_bh e_mk_d e_r_ib e_qk e_y e_z; //13 varexo parameters beta_p j phi beta_i m_i_ss beta_e m_e_ss alpha // HOUSEHOLDS & ENTREPRENEURS h a_i a_p a_e gamma_p gamma_i gamma_e ni pi_share // HOUSEHOLDS & ENTREPRENEURS eps_d eps_bh eps_be // BANKS mk_d_ss mk_bh_ss mk_be_ss r_be_ss r_bh_ss r_d_ss r_k_ss // BANKS (SS) gamma_b beta_b delta_kb 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 vi_ss x_ss R_b_ss // STEADY STATE rho_ee_z rho_A_e rho_ee_j rho_mi rho_me rho_eps_y // SHOCKS rho_mk_d rho_mk_be rho_mk_bh rho_ee_qk rho_eps_l // SHOCKS mu_qp mu_dp mu_cp mu_qi mu_ci mu_bi mu_ke mu_be mu_ce mu_jb ; // Steady state households & entrepreneurs % ********************************************************************************** % estimated parameters are set at the median of the posterior marginal distributions % ********************************************************************************** beta_p = 0.994550000000000 ; % calibrated ok beta_i = 0.975000000000000 ; % calibrated ok beta_b = 0.940050000000000 ; % calibrated <-- beta_e = 0.975000000000000 ; % calibrated ok j = 0.203000000000000 ; % calibrated ok phi = 1.500000000000000 ; % calibrated ok m_i_ss = 0.750000000000000 ; % calibrated ok m_e_ss = 0.400000000000000 ; % calibrated ok alpha = 0.340000000000000 ; % calibrated ok (=1-0.66) h = 1.000000000000000 ; % calibrated ok a_i = 0.8 ; % estimated a_p = 0.000000000000000 ; % calibrated a_e = 0.000000000000000 ; % calibrated gamma_p = 1.000000000000000 ; % calibrated gamma_i = 1.000000000000000 ; % calibrated gamma_e = 1.000000000000000 ; % calibrated ni = 0.800000000000000 ; % calibrated eps_l_ss = 5.000000000000000 ; % calibrated ok kappa_w = 99.8983 ; % estimated eps_d = -1.1 ; % calibrated ok eps_bh = 5.85 ; % calibrated ok-default: 5.85 for 25% liquidity proxy (14bp):4.935/for 50%: 5.29 eps_be = 4.85 ; % calibrated ok-default: 4.85 for 25% liquidity proxy (14bp):3.935/for 50%: 4.29 mk_d_ss = eps_d / (eps_d - 1); % 0.571697789960578 ; % calibrated mk_bh_ss = eps_bh / (eps_bh - 1); % 1.401533321911910 ; % calibrated mk_be_ss = eps_be / (eps_be - 1); % 1.401533321911910 ; % calibrated gamma_b = 1.000000000000000 ; % calibrated deltak = 0.040000000000000 ; % calibrated ok piss = 1.000000000000000 ; % calibrated vi_ss = 0.1 ; % calibrated eps_y_ss = 8.90000000000000 ; % calibrated ok h = 1 ; % calibrated kappa_kb = 11.0683 ; % estimated kappa_p = 28.6502 ; % estimated ind_p = 0.1605 ; % estimated ind_w = 0.2757 ; % estimated kappa_i = 10.1822 ; % estimated kappa_d = 3.5030 ; % estimated kappa_be = 9.3638 ; % estimated kappa_bh = 10.0867 ; % estimated rho_ib = 0.7686 ; % estimated phi_pie = 1.9816 ; % estimated phi_y = 0.3459 ; % estimated rho_ee_z = 0.9390 ; % estimated rho_A_e = 0.9390 ; % estimated rho_ee_j = 0.909222967643905 ; % estimated rho_mi = 0.938578931344182 ; % estimated rho_me = 0.910171380445550 ; % estimated rho_eps_y = 0.256295678347778 ; % estimated rho_mk_d = 0.859494657527038 ; % estimated rho_mk_be = 0.810106816126432 ; % estimated rho_mk_bh = 0.777287054862844 ; % estimated rho_ee_qk = 0.440993407158326 ; % estimated rho_eps_l = 0.677034135657493 ; % estimated r_ib_ss = (piss/beta_p - 1) * (eps_d-1)/eps_d ; R_b_ss = r_ib_ss ; r_be_ss = R_b_ss * mk_be_ss ; r_bh_ss = R_b_ss * mk_bh_ss ; r_d_ss = r_ib_ss * mk_d_ss ; r_k_ss = -(1-deltak)-m_e_ss*(1-deltak)*piss/beta_e*(1/(1+r_be_ss)-beta_e/piss)+1/beta_e; eksi_1 = r_k_ss; eksi_2 = 0.1*r_k_ss; eps_b = mean([eps_bh,eps_be]); pi_share = 0.35; % share of bank profits payed out to patient households delta_kb = r_ib_ss/vi_ss * (1-pi_share)*(eps_d - eps_b + vi_ss * eps_d*(eps_b-1))/((eps_b-1)*(eps_d-1)); x_ss = (eps_y_ss / (eps_y_ss - 1)) ; mu_qi = (j / (1 - beta_i * (1-m_i_ss) - ((m_i_ss * piss)/(1+r_bh_ss)))) ; mu_ci = (gamma_e * (1-alpha) * (1-ni)) / (gamma_i * x_ss * (1 - (m_i_ss * mu_qi * piss / (1+r_bh_ss)) + m_i_ss * mu_qi)) ; mu_bi = (m_i_ss * mu_qi * mu_ci * piss) / (1 + r_bh_ss) ; mu_ke = alpha / r_k_ss ; mu_be = m_e_ss * piss * (1-deltak) * mu_ke / (1 + r_be_ss) ; mu_ce = (alpha - mu_ke * (deltak + m_e_ss * (1-deltak) * (1 - (piss/(1+r_be_ss))))) ; mu_qp = j / (1 - beta_p) ; mu_dp = (gamma_b/gamma_p * ((gamma_e/gamma_b)*(delta_kb - r_ib_ss * mk_be_ss)/(delta_kb - r_ib_ss * mk_d_ss) * mu_be + (gamma_i / gamma_b) * (delta_kb - r_ib_ss * mk_be_ss)/(delta_kb - r_ib_ss * mk_d_ss) * mu_bi)) ; mu_cp = (((gamma_e/gamma_p)*(1-alpha)*(1-ni) + mu_dp * ((1-beta_p)/beta_p) + (x_ss - 1) + pi_share * (r_ib_ss * (mk_bh_ss * (gamma_i/gamma_b) * mu_bi + mk_be_ss * (gamma_e/gamma_b) * mu_be - mk_d_ss * (gamma_p/gamma_b) * mu_dp))) / x_ss) ; mu_jb = (r_ib_ss * (mk_bh_ss * (gamma_i/gamma_b) * mu_bi + mk_be_ss * (gamma_e/gamma_b) * mu_be - mk_d_ss * (gamma_p/gamma_b) * mu_dp)) ; model; ////*********** 1) PATIENT HHs ******************************************************** (1-a_i)*exp(ee_z)*(exp(c_p) - a_i*exp(c_p(-1)))^(-1) = exp(lam_p);//x j * (exp(ee_j)) / exp(h_p) - exp(lam_p) * exp(q_h) + beta_p * exp(lam_p(+1)) * exp(q_h(+1)) = 0; //x exp(lam_p) = beta_p * exp(lam_p(+1)) * (1+exp(r_d)) / exp(pie(+1)); //x exp(w_p) * exp(lam_p) = (exp(l_p) ^ (phi)) ; 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 + pi_share*exp(j_B(-1))/(gamma_p*exp(pie));//x // ////*********** 2) IMPATIENT HHs ********************************************************5 (1-a_i)*exp(ee_z)*(exp(c_i) - a_i*exp(c_i(-1)))^(-1) = exp(lam_i);//x 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;//x // exp(lam_i) - beta_i * exp(lam_i(+1)) * (1+exp(r_bh)) / exp(pie(+1)) = exp(s_i) * (1+exp(r_bh)); //x exp(w_i) * exp(lam_i) = (exp(l_i) ^ (phi)); 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) ;//x // (1+exp(r_bh)) * exp(b_i) = exp(m_i) * exp(q_h(+1)) * exp(h_i) * exp(pie(+1)); //x // ////*********** 3) CAPITAL PRODUCERS *****************************************************11 exp(K) = (1-deltak) * exp(K(-1)) + ( 1 - kappa_i/2 * (exp(I)*exp(ee_qk)/exp(I(-1)) - 1)^2 ) * exp(I) ;//x 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 ; //x // 15 ////************ 4) ENTREPRENEURS *********************************************************13 (1-a_i)*(exp(c_e) - a_i*exp(c_e(-1)))^(-1) = exp(lam_e);//x 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(lam_e) * exp(q_k) ;//x // exp(w_p) = ni * (1-alpha) * exp(y_e) / ( exp(l_pd) * exp(x) );//x exp(w_i) = (1-ni) * (1-alpha) * exp(y_e) / ( exp(l_id) * exp(x) );//x exp(lam_e) - exp(s_e) * (1+exp(r_be)) = beta_e * exp(lam_e(+1)) * (1+exp(r_be)) / exp(pie(+1));//x // 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) = exp(y_e) / exp(x) + exp(b_ee) + exp(q_k) * (1-deltak) * exp(k_e(-1)) ;//x // 20 exp(y_e) = exp(A_e) * (exp(k_e(-1)))^(alpha) * ( exp(l_pd)^ni * exp(l_id)^(1-ni) ) ^ (1-alpha);//x (1+exp(r_be)) * exp(b_ee) = exp(m_e) * exp(q_k(+1)) *exp(pie(+1)) * exp(k_e) * (1-deltak); //x// exp(r_k) = alpha * exp(A_e) * exp(k_e(-1))^(alpha-1) * ( exp(l_pd)^ni * exp(l_id)^(1-ni) ) ^ (1-alpha) /exp(x);//x // ////************* 5)BANKS ****************************************************************22 exp(R_b) = - kappa_kb * ( exp(K_b) / exp(B) - exp(vi) ) * (exp(K_b)/exp(B)) ^2 + exp(r_ib) ;//x exp(K_b) * exp(pie) = (1-delta_kb) * exp(K_b(-1)) + (1-pi_share)*exp(j_B(-1)) ;//x gamma_b * exp(d_b) = gamma_p * exp(d_p) ;//x gamma_b * exp(b_h) = gamma_i * exp(b_i) ;//x gamma_b * exp(b_e) = gamma_e * exp(b_ee);//x (exp(b_h) + exp(b_e)) = ( exp(d_b) + exp(K_b) ) ; %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(Y1)/exp(Y1(-4)) )^( ( 1 - 0.92 ) )* exp( vi(-1) )^0.92;//x exp(weight_BH) = ( 1 ^( 1-0.94 ) ) * ( exp(Y1) / exp(Y1(-4)) )^( ( 1 - 0.94 ) * ( - 10 * 1 ) ) * exp( weight_BH(-1) )^0.94;//x exp(weight_BE) = ( 1 ^( 1-0.92 ) ) * ( exp(Y1)/exp(Y1(-4)) )^(( 1 - 0.92 ) * ( - 15 * 1 ))* exp( weight_BE(-1) )^0.92;// 31 /// 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) - 1 ) * ( (exp(r_d(+1))/exp(r_d))^2 ) * (exp(d_b(+1))/exp(d_b)) = 0;//x + 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) - 1 ) * ( (exp(r_be(+1))/exp(r_be))^2 ) * (exp(b_e(+1))/exp(b_e)) = 0;//x + 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) - 1 ) * ( (exp(r_bh(+1))/exp(r_bh))^2 ) * (exp(b_h(+1))/exp(b_h)) = 0;//x 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) - exp(vi) ) ^2) * exp(K_b);//x // 35 ////*********** 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 ) ;//x 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;//x // 37 ////************ 7) AGGREGATION & EQUILIBRIUM ************************************************ exp(C) = gamma_p * exp(c_p) + gamma_i * exp(c_i) + gamma_e * exp(c_e);//x exp(BH) = gamma_b * exp(b_h);//x exp(BE) = gamma_b * exp(b_e);//x exp(B) = ( exp(weight_BH) * exp(BH) + exp(weight_BE) * exp(BE) );//x // exp(D) = gamma_p * exp(d_p) ;//x // oppure: (gamma_b * exp(d_b)) exp(Y) = gamma_e * exp(y_e);//x // exp(J_B) = gamma_b * exp(j_B);//x // gamma_e * exp(l_pd) = gamma_p * exp(l_p);//x gamma_e * exp(l_id) = gamma_i * exp(l_i);//x h = gamma_p * exp(h_p) + gamma_i * exp(h_i);//x // exp(K) = gamma_e * exp(k_e);//x // exp(Y1) = exp(C) + 1 * (exp(K)-(1-deltak)*exp(K(-1))) ;//x // //exp(Y) = exp(C) + exp(q_k) * (exp(K)-(1-deltak)*exp(K(-1))) + delta_kb * exp(K_b(-1)) // + (eksi_1*(exp(u)-1) + eksi_2/2*((exp(u)-1)^2)) // + 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)) // ; //x //50 ////*********** 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) ;//x ////*********** 9) EXOGENOUS PROCESSES **************************************************** exp(ee_z) = 1 - rho_ee_z * 1 + rho_ee_z * exp(ee_z(-1)) + e_z;//x exp(A_e) = 1 - rho_A_e * 1 + rho_A_e * exp(A_e(-1)) + e_A_e;//x exp(ee_j) = 1 - rho_ee_j * 1 + rho_ee_j * exp(ee_j(-1)) + e_j;//x exp(m_i) = (1-rho_mi) * m_i_ss + rho_mi * exp(m_i(-1)) + e_mi;//x exp(m_e) = (1-rho_me) * m_e_ss + rho_me * exp(m_e(-1)) + e_me;//x exp(mk_d) = (1-rho_mk_d) * mk_d_ss + rho_mk_d * exp(mk_d(-1)) + e_mk_d;//x exp(mk_be) = (1-rho_mk_be) * mk_be_ss + rho_mk_be * exp(mk_be(-1)) + e_mk_be;//x exp(mk_bh) = (1-rho_mk_bh) * mk_bh_ss + rho_mk_bh * exp(mk_bh(-1)) + e_mk_bh;//x exp(ee_qk) = 1-rho_ee_qk * 1 + rho_ee_qk * exp(ee_qk(-1)) + e_qk;//x exp(eps_y) = (1-rho_eps_y) * eps_y_ss + rho_eps_y * exp(eps_y(-1)) + e_y;//x 61 ////*********** 10) AUXILIARY VARIABLES ***************************************************** exp(rr_e) = exp(l_pd)^ni * exp(l_id)^(1-ni);//x exp(aux1) = exp(j_B) ;//x exp(k_ratio) = exp(K_b) / ( exp(BH) + exp(BE) );//x exp(L) = exp(BH) + exp(BE) ;//x exp(spr_b) = 0.5*exp(r_bh) + 0.5*exp(r_be) - exp(r_d);//x // 66 end; //model initval; x = x_ss ; q_k = 1 ; A_e = 1 ; %y_e = A_e * k_e^alpha * (l_pd^ni * l_id ^(1-ni))^(1-alpha) ; y_e = 1 ; q_h = mu_qp * (c_p / h_p) ; r_d = (piss/beta_p -1) ; d_p = mu_dp * (y_e / x) ; c_p = mu_cp * y_e ; q_h = mu_qi * (c_i / h_i) ; c_i = mu_ci * y_e ; b_i = mu_bi * (y_e / x) ; r_bh = r_bh_ss ; k_e = mu_ke * (y_e / (q_k * x)) ; b_ee = mu_be * (y_e / x) ; c_e = mu_ce * (y_e / x) ; r_be = r_be_ss ; J_R = (x - 1) * (y_e / x) ; I = deltak * K ; J_B = (delta_kb / (1-pi_share)) * K_b ; J_B = mu_jb ; Y = C + q_k * deltak * K + delta_kb * K_b ; h_p = (mu_qp * mu_cp)/(mu_qp * mu_cp + mu_qi * mu_ci) ; h_i = (mu_qi * mu_ci)/(mu_qp * mu_cp + mu_qi * mu_ci) ; end; shocks; //estimated st.dev. var e_z = 0.0152683462770726^2; var e_A_e = 0.00512426105215156^2; var e_j = 0.0666521707690898^2; var e_me = 0.00325455234425937^2; var e_mi = 0.00243843645883989^2; var e_mk_d = 0.0302568470883558^2; var e_mk_bh = 0.123519101019487^2; var e_mk_be = 0.00723910778720155^2; var e_qk = 0.0131631984802325^2; var e_r_ib = 0.00157434820106446^2; var e_y = 0.620300719165277^2; var e_l = 0.434843841701844^2; end; options_.nograph = 1; options_.nomoments = 0; options_.noprint = 1; %stoch_simul(order=1,irf=40) Y1 Y C I B q_h q_k J_B BE BH K_b k_ratio L pie spr_b r_bh r_be r_d r_ib D h_i h_p vi; 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)); 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)); % 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 % varexo e_A_e e_eps_K_b e_j e_l e_me e_mi e_mk_be e_mk_bh e_mk_d e_r_ib e_qk e_y e_z; % 1 2 3 4 5 6 7 8 9 10 11 12 13 %end;