%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Universidade de Brasília % Tese - Modelo Geralli et all para uma Economia Aberta (Versão Rotemberg) % Orientador: Joaquim P de Andrade % Doutorando: Márcio Francisco da Silva % 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 % model blocks of eqns: 1) PATIENT HHs 2) IMPATIENT HHs 3) CAPITAL PRODUCERS 4) HOUSING PRODUCERS % 5) ENTREPRENEURS 6) BANKS 7) RETAILERS 8) LABOR MKT WITH ONE UNION FOR EACH LABOR TYPE % 9) AGGREGATION & EQUILIBRIUM 10) MONETARY POLICY %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% var lam_p % preço sombra lam_i % preço sombra lam_e % preço sombra s_ih % preço sombra s_iw % preço sombra s_e % preço sombra c_p % consumo c_i % consumo c_e % consumo h_p % imóveis h_i % imóveis h_e % imóveis h % imóveis d % depósitos b_ih % empréstimos b_iw % empréstimos b_e % empréstimos debt_ih % estoque de dívida debt_iw % estoque de dívida debt_e % estoque de dívida B % empréstimos Bstar % empréstimos Ik % investimento em capital Ih % investimento em imóveis k % capital l_p % trabalho l_i % trabalho Q % insumo importado u % taxa de utilização do capital y_e % bem intermediário y_exp % bem exportado y % bem final r_pol % taxa de juros politica monetaria r_d % taxa de juros deposito r_bih % taxa de juros empréstimo imóveis r_biw % taxa de juros empréstimo consignado r_be % taxa de juros empréstimo empresários R_b % taxa de juros empréstimo banco atacadista Rstar % taxa de juros empréstimo externo premium % premio de risco er % taxa de câmbio K_b % capital bancário pi % inflação de preços pi_star % inflação de preços externa pi_wp % inflação de salários pi_wi % inflação de salários x % preço relativo C % AGGREGATION & EQUILIBRIUM Y % AGGREGATION & EQUILIBRIUM BH w_p % salário w_i % salário q_k % preço do capital q_h % preço do imóvel J_B % lucro J_R % lucro PIW % AGGREGATION & EQUILIBRIUM ee_z % EXOGENOUS PROCESSES A_e % EXOGENOUS PROCESSES ee_j % EXOGENOUS PROCESSES %ee_prem % EXOGENOUS PROCESSES ee_qk % EXOGENOUS PROCESSES ee_qh % EXOGENOUS PROCESSES m_ih % EXOGENOUS PROCESSES (IMPATIENT LTV) m_iw % EXOGENOUS PROCESSES m_e % EXOGENOUS PROCESSES (ENTREPRENEURS LTV) eps_y % EXOGENOUS PROCESSES eps_l % EXOGENOUS PROCESSES %eps_d % EXOGENOUS PROCESSES %eps_be % EXOGENOUS PROCESSES %eps_bih % EXOGENOUS PROCESSES %eps_biw % EXOGENOUS PROCESSES eps_K_b % EXOGENOUS PROCESSES eps_premium pQ e_rpol mk_d mk_bih mk_biw mk_be ; varexo e_z e_A_e e_j e_mih e_miw e_me e_qk e_qh e_y e_erpol e_l e_eps_K_b e_eps_premium e_Rstar e_pistar e_pQ e_mk_d e_mk_be e_mk_bih e_mk_biw; % e_epsd e_epsbe e_epsbih e_epsbiw parameters a_i a_p a_e alphal alphak beta_p beta_i beta_e deltakb deltah deltak eksi_1 eksi_2 eps_lss eps_yss eps_dss eps_bihss eps_biwss eps_bess ind_w ind_p ind_d ind_be ind_bih ind_biw jh m_ihss m_iwss m_ess mk_d_ss mk_be_ss mk_bih_ss mk_biw_ss ni phi phi_pi phi_y piss piss_star phi_dih phi_diw phi_de kappa_ik kappa_ih kappa_d kappa_be kappa_bih kappa_biw kappa_kb kappa_w kappa_p rho_rpol r_bess r_bihss r_biwss r_polss Rstarss rho_ee_z rho_A_e rho_ee_j rho_mih rho_miw rho_me rho_epsy rho_e_pol rho_Rstar rho_pistar % rho_epsbiw rho_epsbe rho_epsbih rho_epsd rho_mk_d rho_mk_be rho_mk_bih rho_mk_biw rho_ee_qk rho_ee_qh rho_epsl rho_eps_K_b rho_eps_premium rho_pQ vi zeta ; % ********************* % CALIBRATED PARAMETERS % ********************* beta_p = 0.989; % beta_i = 0.96; % beta_e = beta_i; % 0.96; % 0.95; % Rstarss = 0.005; % 0.007; % piss = 1.045^0.25; % 1; % piss_star = 1.024^0.25; % 1; % 1.045^0.25; % m_ess = 0.05; % m_ihss = 0.06; % 0.07; % m_iwss = 0.1; deltak = 0.035; % 0.045; % deltah = 0.025; % 0.02; deltakb = 0.095; jh = 0.2; eps_lss = 3; phi = 1; phi_dih = 0.07; % 0.0625; phi_diw = 0.07; % 0.0625; phi_de = 0.07; % 0.0625; eps_yss = 11; ni = 0.8; alphal = 0.5; alphak = 0.3; eps_dss = - 2.62; % eps_biwss = 4.5; % 6.53; % eps_bihss = 5.36; % 6.53; % eps_bess = 2.73; % 6.53; % mk_d_ss = eps_dss/(eps_dss - 1); mk_be_ss = eps_bess/(eps_bess - 1); mk_bih_ss = eps_biwss/(eps_bihss - 1); mk_biw_ss = eps_biwss/(eps_biwss - 1); zeta = -0.1; % r_dss = (piss/beta_p - 1); r_polss = (piss/beta_p - 1) * (eps_dss - 1)/eps_dss ; % steady state gross nominal interest rate r_bess = r_polss*eps_bess/(eps_bess - 1) ; % steady state interest rate on loans to E r_bihss = r_polss*eps_bihss/(eps_bihss - 1) ; % steady state interest rate on loans to H r_biwss = r_polss*eps_biwss/(eps_biwss - 1) ; % steady state interest rate on loans to H a_i = 0.7; % 0.867003766306404 ; % coeffs(25); % a_e = a_i; % 0.0 ; % degree of habit formation: entrepreneurs a_p = a_i; % 0.0 ; % degree of habit formation: patient households kappa_p = 33.7705265016395 ; % coeffs(13); % kappa_w = kappa_p; kappa_ik = 10.0305562248008 ; % coeffs(15); % kappa_ih = 10.0305562248008 ; % coeffs(15); % kappa_d = 2.77537377104213 ; % coeffs(16); //100; % kappa_be = 7.98005959044637 ; % coeffs(17); //100; % kappa_bih = 9.04426718749482 ; % coeffs(18); //140; % kappa_biw = 9.04426718749482 ; % coeffs(18); //140; % kappa_kb = 8.91481958034669 ; % coeffs(19); % phi_pi = 2.00384780180824 ; % coeffs(20); % eksi_1 = 0.0075; % capital utilization cost parameter eksi_2 = 0.1*eksi_1; % capital utilization cost parameter vi = 0.17; //0.09; % Banking Capital ratio over Loans (Basel II) rho_ee_z = 0.5; % 0.9; % coeffs(1); % 0.385953438168178 ; rho_A_e = 0.5; % 0.9; % coeffs(2); % 0.93816527333294 ; rho_ee_j = 0.5; % 0.9; % coeffs(3); % 0.921872719102206 ; rho_me = 0.5; % 0.9; % coeffs(4); % 0.90129485520182 ; rho_mih = 0.5; % 0.9; % coeffs(5); % 0.922378382753078 ; rho_miw = 0.5; % 0.9; % coeffs(5); % 0.922378382753078 ; %rho_epsd = 0.5; % 0.9; % coeffs(6); % 0.892731352899547 ; %rho_epsbih = 0.5; % 0.9; % coeffs(7); % 0.851229673864555 ; %rho_epsbiw = 0.5; % 0.9; % coeffs(7); % 0.851229673864555 ; %rho_epsbe = 0.5; % 0.9; % coeffs(8); % 0.873901213475799 ; rho_ee_qk = 0.5; % 0.9; % coeffs(9); % 0.571692383714171 ; rho_ee_qh = 0.5; % 0.9; % coeffs(9); % 0.571692383714171 ; rho_epsy = 0.5; % 0.9; % coeffs(10); % 0.294182239567384 ; rho_epsl = 0.5; % 0.9; % coeffs(11); % 0.596186440884132 ; rho_eps_K_b = 0.5; % 0.9; % coeffs(12); % 0.813022758608552 ; rho_Rstar = 0.5; % 0.9; % coeffs(12); % 0.813022758608552 ; rho_pistar = 0.5; % 0.9; % coeffs(12); % 0.813022758608552 ; rho_pQ = 0.5; % 0.9; % coeffs(12); % 0.813022758608552 ; rho_eps_premium = 0.5; % 0.9; % coeffs(12); % 0.813022758608552 ; rho_e_pol = 0.5; % 0.9; % coeffs(12); % 0.813022758608552 ; rho_rpol = 0.5; % 0.750481873084311 ; % coeffs(21); % phi_y = 0.303247771697294 ; % coeffs(22); % rho_mk_d = 0.9; rho_mk_be = 0.9; rho_mk_bih = 0.9; rho_mk_biw = 0.9; ind_d = 0.0; % indexation deposit rates ind_be = 0.0; % indexation rates on loans to firms ind_bih = 0.0; % indexation rates on loans to households ind_biw = 0.0; % indexation rates on loans to households ind_p = 0.158112794106546 ; % coeffs(23); % ind_w = 0.300197804017489 ; % coeffs(24); % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Model equations %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% model; ////*********** 1) PATIENT HHs ********************************************************6 (1 - a_p) * exp(ee_z)*(exp(c_p) - a_p*exp(c_p(-1)))^(-1) = exp(lam_p); jh * exp(ee_j) / ( exp(lam_p) * exp(q_h) - (1 - deltah) * beta_p * exp(lam_p(+1)) * exp(q_h(+1)) ) = exp(h_p); exp(lam_p) = beta_p * exp(lam_p(+1)) * (1 + exp(r_d)) / exp(pi(+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(pi_wp) - exp(pi(-1)) ^ ind_w * piss ^ (1 - ind_w) ) * exp(pi_wp) + beta_p * exp(lam_p(+1))/exp(lam_p) * kappa_w *( exp(pi_wp(+1)) - exp(pi) ^ ind_w * piss ^ (1 - ind_w) ) * exp(pi_wp(+1))^2 / exp(pi(+1)) = 0 ; exp(pi_wp) = exp(w_p) / exp(w_p(-1)) * exp(pi); exp(c_p) + exp(q_h) * ( exp(h_p) - (1 - deltah) * exp(h_p(-1)) ) + exp(d) = exp(w_p) * exp(l_p) + (1 + exp(r_d(-1)))*exp(d(-1))/exp(pi) + exp(J_R); ////*********** 2) IMPATIENT HHs ********************************************************9 (1 - a_i)*exp(ee_z)*(exp(c_i) - a_i*exp(c_i(-1)))^(-1) = exp(lam_i); jh * (exp(ee_j)) / ( exp(lam_i) * exp(q_h) - (1 - deltah) * exp(q_h(+1)) * ( beta_i * exp(lam_i(+1)) + exp(s_ih) * exp(m_ih) * exp(pi(+1)) ) ) = exp(h_i); exp(lam_i) - beta_i * exp(lam_i(+1)) * (1 + exp(r_bih)) / exp(pi(+1)) = exp(s_ih) * (1 + exp(r_bih)); exp(lam_i) - beta_i * exp(lam_i(+1)) * (1 + exp(r_biw)) / exp(pi(+1)) = exp(s_iw) * (1 + exp(r_biw)); (1 - exp(eps_l)) * exp(l_i) + exp(l_i)^(1 + phi) / exp(w_i) * exp(eps_l) / exp(lam_i) - kappa_w *( exp(pi_wi) - exp(pi(-1)) ^ ind_w * piss ^ (1 - ind_w) ) * exp(pi_wi) + beta_i * exp(lam_i(+1))/exp(lam_i) * kappa_w *( exp(pi_wi(+1)) - exp(pi) ^ ind_w * piss ^ (1 - ind_w) ) * exp(pi_wi(+1))^2 / exp(pi(+1)) = 0 ; % exp(w_i) = (exp(l_i)^phi)/(exp(lam_i) + exp(s_iw)*exp(m_iw)); exp(pi_wi) = exp(w_i) / exp(w_i(-1)) * exp(pi); exp(c_i) + exp(q_h) * (exp(h_i) - (1 - deltah) * exp(h_i(-1))) + (1 + exp(r_bih(-1)))*exp(debt_ih(-1))/exp(pi) + (1 + exp(r_biw(-1)))*exp(debt_iw(-1))/exp(pi) = exp(w_i) * exp(l_i) + exp(debt_ih) + exp(debt_iw); (1 + exp(r_bih)) * exp(b_ih) = exp(m_ih) * exp(q_h(+1)) * (1 - deltah) * exp(h_i) * exp(pi(+1)) - exp(debt_ih); (1 + exp(r_biw)) * exp(b_iw) = exp(m_iw) * exp(w_i(+1)) * exp(l_i(+1)) * exp(pi(+1)) - exp(debt_iw); exp(debt_ih) = (1 - phi_dih)*exp(debt_ih(-1)) + exp(b_ih); exp(debt_iw) = (1 - phi_diw)*exp(debt_iw(-1)) + exp(b_iw); ////*********** 3) CAPITAL PRODUCERS *****************************************************2 exp(k) = (1 - deltak) * exp(k(-1)) + ( 1 - kappa_ik/2 * (exp(Ik)*exp(ee_qk)/exp(Ik(-1)) - 1)^2 ) * exp(Ik) ; 1 = exp(q_k) * ( 1 - kappa_ik/2 * (exp(Ik)*exp(ee_qk)/exp(Ik(-1)) - 1)^2 - kappa_ik * (exp(Ik) * exp(ee_qk)/exp(Ik(-1)) - 1) * exp(Ik) * exp(ee_qk)/exp(Ik(-1)) ) + beta_e * exp(lam_e(+1)) / exp(lam_e) * exp(q_k(+1)) * kappa_ik * (exp(Ik(+1))*exp(ee_qk(+1))/exp(Ik) - 1) * exp(ee_qk(+1)) * (exp(Ik(+1))/exp(Ik))^2 ; ////*********** 4) HOUSING PRODUCERS *****************************************************2 exp(h) = (1 - deltah) * exp(h(-1)) + ( 1 - kappa_ih/2 * (exp(Ih) * exp(ee_qh)/exp(Ih(-1)) - 1)^2 ) * exp(Ih) ; 1 = exp(q_h) * ( 1 - kappa_ih/2 * (exp(Ih)*exp(ee_qh)/exp(Ih(-1)) - 1)^2 - kappa_ih * (exp(Ih) * exp(ee_qh)/exp(Ih(-1)) - 1) * exp(Ih) * exp(ee_qh)/exp(Ih(-1)) ) + beta_e * exp(lam_e(+1)) / exp(lam_e) * exp(q_h(+1)) * kappa_ih * (exp(Ih(+1))*exp(ee_qh(+1))/exp(Ih) - 1) * exp(ee_qh(+1)) * (exp(Ih(+1))/exp(Ih))^2 ; ////************ 5) ENTREPRENEURS *********************************************************11 (1 - a_e)*(exp(c_e) - a_e*exp(c_e(-1)))^(-1) = exp(lam_e); jh * (exp(ee_j)) / ( exp(lam_e) * exp(q_h) - (1 - deltah) * exp(q_h(+1)) * ( beta_e * exp(lam_e(+1)) + exp(s_e) * exp(m_e) * exp(pi(+1)) ) ) = exp(h_e); exp(s_e) * exp(m_e) * exp(q_k(+1)) * exp(pi(+1)) * (1 - deltak) + beta_e * exp(lam_e(+1)) * ( exp(q_k(+1))*(1 - deltak) + alphak * exp(y_e(+1)) * exp(u(+1))/(exp(x(+1)) * exp(k(+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 - alphal) * exp(y_e) / ( exp(l_p) * exp(x) ); exp(w_i) = (1 - ni) * (1 - alphal) * exp(y_e) / ( exp(l_i) * exp(x) ); exp(Q) = (1 - alphal - alphak)*exp(y_e)/( exp(x)*exp(er)*exp(pQ) ); exp(lam_e) - exp(s_e) * (1 + exp(r_be)) = beta_e * exp(lam_e(+1)) * (1 + exp(r_be)) / exp(pi(+1)); alphak * exp(A_e) * exp(u)^(alphak - 1) * exp(k(-1))^(alphak) * ( exp(l_p)^ni * exp(l_i)^(1 - ni) ) ^ (1 - alphal) * (exp(Q) ^ (1 - alphal - alphak) ) /exp(x) = eksi_1 + eksi_2 * (exp(u) - 1); exp(y_e) = exp(A_e) * (exp(u)*exp(k(-1)))^(alphak) * ( exp(l_p)^ni * exp(l_i)^(1 - ni) ) ^ (1 - alphal) * (exp(Q) ^ (1 - alphal - alphak) ); (1 + exp(r_be)) * exp(b_e) = exp(m_e) * ( exp(q_k(+1)) * exp(pi(+1)) * exp(k) * (1 - deltak) + exp(q_h(+1)) * exp(pi(+1)) * exp(h_e) * (1 - deltah)) - exp(debt_e); exp(c_e) + ((1 + exp(r_be(-1))) * exp(debt_e(-1)) / exp(pi) ) + (exp(w_p)*exp(l_p) + exp(w_i)*exp(l_i)) + exp(q_k) * exp(k) + exp(q_h) * (exp(h_e) - (1 - deltah)*exp(h_e(-1))) + ( eksi_1*(exp(u) - 1) + eksi_2/2*(exp(u) - 1)^2 ) * exp(k(-1)) + exp(pQ) * exp(Q) = exp(y_e) / exp(x) + exp(debt_e) + exp(q_k) * (1 - deltak) * exp(k(-1)) ; exp(debt_e) = (1 - phi_de)*exp(debt_e(-1)) + exp(b_e); ////************* 6)BANKS **************************************************************** 10 exp(K_b) * exp(pi) = (1 - deltakb) * exp(K_b(-1))/ exp(eps_K_b) + exp(J_B(-1)) ; exp(premium) = exp(-zeta*exp(er)*exp(Bstar)/exp(K_b))*exp(eps_premium); exp(b_ih) + exp(b_iw) + exp(b_e) = exp(d) + exp(K_b) + exp(er)*exp(Bstar); exp(R_b) = - kappa_kb * ( exp(K_b) / exp(B) - vi ) * (exp(K_b)/exp(B)) ^2 + exp(r_pol) ; (1 + exp(Rstar)) * exp(premium) * (1 - zeta*exp(er)*exp(Bstar)/exp(K_b)) * (exp(er(+1))/exp(er)) * (exp(pi(+1))/exp(pi_star(+1))) = 1 + exp(r_pol); - 1 + exp(mk_d)/(exp(mk_d)-1) - exp(mk_d)/(exp(mk_d)-1) * exp(r_pol)/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(+1))/exp(d)) = 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; + 1 - exp(mk_bih)/(exp(mk_bih)-1) + exp(mk_bih)/(exp(mk_bih)-1) * exp(R_b)/exp(r_bih) - kappa_bih * (exp(r_bih)/exp(r_bih(-1)) - 1 ) * exp(r_bih)/exp(r_bih(-1)) + beta_p * ( exp(lam_p(+1))/exp(lam_p) ) * kappa_bih * ( exp(r_bih(+1))/exp(r_bih) - ( exp(r_bih)/exp(r_bih(-1)))^ind_bih ) * ( (exp(r_bih(+1))/exp(r_bih))^2 ) * (exp(b_ih(+1))/exp(b_ih)) = 0; + 1 - exp(mk_biw)/(exp(mk_biw)-1) + exp(mk_biw)/(exp(mk_biw)-1) * exp(R_b)/exp(r_biw) - kappa_biw * (exp(r_biw)/exp(r_biw(-1)) - 1 ) * exp(r_biw)/exp(r_biw(-1)) + beta_p * ( exp(lam_p(+1))/exp(lam_p) ) * kappa_biw * ( exp(r_biw(+1))/exp(r_biw) - ( exp(r_biw)/exp(r_biw(-1)))^ind_biw ) * ( (exp(r_biw(+1))/exp(r_biw))^2 ) * (exp(b_iw(+1))/exp(b_iw)) = 0; % 1 - exp(eps_bih) + exp(eps_bih)*exp(R_b)/exp(r_bih) - kappa_bih * (exp(r_bih)/exp(r_bih(-1)) - 1) * (exp(r_bih)/exp(r_bih(-1))) + beta_p * (exp(lam_p(+1))/exp(lam_p)) * kappa_bih * (exp(r_bih(+1))/exp(r_bih) - 1) * ((exp(r_bih(+1))/exp(r_bih))^2) * (exp(b_ih(+1))/exp(b_ih)) = 0; % 1 - exp(eps_biw) + exp(eps_biw)*exp(R_b)/exp(r_biw) - kappa_biw * (exp(r_biw)/exp(r_biw(-1)) - 1) * (exp(r_biw)/exp(r_biw(-1))) + beta_p * (exp(lam_p(+1))/exp(lam_p)) * kappa_biw * (exp(r_biw(+1))/exp(r_biw) - 1) * ((exp(r_biw(+1))/exp(r_biw))^2) * (exp(b_iw(+1))/exp(b_iw)) = 0; % 1 - exp(eps_be) + exp(eps_be)*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; % - 1 + exp(eps_d) - exp(eps_d)*exp(r_pol)/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(+1))/exp(d)) = 0; exp(J_B) = + exp(r_bih) * exp(b_ih) + exp(r_biw) * exp(b_iw) + exp(r_be) * exp(b_e) + exp(er)*exp(Bstar) - exp(r_d) * exp(d) - (1 + exp(Rstar(-1)))*exp(premium(-1))*exp(er)*exp(Bstar(-1))/exp(pi_star) - kappa_d/2 * ( (exp(r_d)/exp(r_d(-1))-1)^2) * exp(r_d) *exp(d) - kappa_be/2 * ( (exp(r_be)/exp(r_be(-1))-1)^2) * exp(r_be)*exp(b_e) - kappa_bih/2 * ( (exp(r_bih)/exp(r_bih(-1))-1)^2) * exp(r_bih)*exp(b_ih) - kappa_biw/2 * ( (exp(r_biw)/exp(r_biw(-1))-1)^2) * exp(r_biw)*exp(b_iw) - kappa_kb/2 * ( (exp(K_b) / exp(B) - vi ) ^2) * exp(K_b); ////*********** 7)RETAILERS ************************************************************** 2 exp(J_R) = exp(y)*(1 - (1/exp(x)) - (kappa_p/2) * (exp(pi) - ( exp(pi(-1)) ^ ind_p * piss ^ (1 - ind_p) ))^2 ) ; 1 - exp(eps_y) + exp(eps_y) / exp(x) - kappa_p * (exp(pi) - ( exp(pi(-1)) ^ ind_p * piss ^ (1 - ind_p) )) * exp(pi) + beta_p*(exp(lam_p(+1))/exp(lam_p))* kappa_p * (exp(pi(+1)) - ( exp(pi) ^ ind_p * piss ^ (1 - ind_p) )) * exp(pi(+1)) * (exp(y(+1))/exp(y)) = 0; ////************ 8) AGGREGATION & EQUILIBRIUM ************************************************ 8 exp(C) = exp(c_p) + exp(c_i) + exp(c_e); exp(BH) = exp(b_ih) + exp(b_iw); exp(B) = (exp(BH) + exp(b_e)); exp(Y) = exp(y) - exp(er)*exp(pQ)*exp(Q); exp(Y) = exp(c_p) + exp(c_i) + exp(c_e) + exp(Ik) + exp(Ih) + exp(y_exp) - exp(er)*exp(pQ)*exp(Q); exp(y) = exp(c_p) + exp(c_i) + exp(c_e) + exp(Ik) + exp(Ih) + exp(y_exp); exp(h) = exp(h_p) + exp(h_i) + exp(h_e); exp(er)*exp(Bstar) = exp(y_exp)/exp(x) - exp(er)*exp(pQ)*exp(Q) - (1 + exp(Rstar(-1)))*exp(premium(-1))*exp(er)*exp(Bstar(-1))/exp(pi_star); exp(PIW) = ( exp(w_p) + exp(w_i) ) / ( exp(w_p(-1)) + exp(w_i(-1)) ) * exp(pi); ////*********** 9) TAYLOR RULE & PROFITS CB ***************************************************** 1 (1 + exp(r_pol)) = (1 + r_polss)^(1 - rho_rpol ) * (1 + exp(r_pol(-1)))^rho_rpol * (( exp(pi) / piss ) ^phi_pi * (exp(Y)/exp(Y(-1)))^phi_y ) ^ ( 1 - rho_rpol ) * exp(e_rpol) ; ////*********** 10) EXOGENOUS PROCESSES ****************************************************12 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_ih) = (1 - rho_mih) * m_ihss + rho_mih * exp(m_ih(-1)) + e_mih; exp(m_iw) = (1 - rho_miw) * m_iwss + rho_miw * exp(m_iw(-1)) + e_miw; exp(m_e) = (1 - rho_me) * m_ess + rho_me * exp(m_e(-1)) + e_me; %exp(eps_d) = (1 - rho_epsd) * eps_dss + rho_epsd * exp(eps_d(-1)) + e_epsd; %exp(eps_be) = (1 - rho_epsbe)* eps_bess + rho_epsbe * exp(eps_be(-1)) + e_epsbe; %exp(eps_bih) = (1 - rho_epsbih)*eps_bihss + rho_epsbih * exp(eps_bih(-1)) + e_epsbih; %exp(eps_biw) = (1 - rho_epsbiw)*eps_biwss + rho_epsbiw * exp(eps_biw(-1)) + e_epsbiw; exp(ee_qk) = 1 - rho_ee_qk * 1 + rho_ee_qk * exp(ee_qk(-1)) + e_qk; exp(ee_qh) = 1 - rho_ee_qh * 1 + rho_ee_qh * exp(ee_qh(-1)) + e_qh; exp(eps_y) = (1 - rho_epsy) * eps_yss + rho_epsy * exp(eps_y(-1)) + e_y; exp(eps_l) = (1 - rho_epsl) * eps_lss + rho_epsl * 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; exp(e_rpol) = (1 - rho_e_pol) * 1 + rho_e_pol * exp(e_rpol(-1)) + e_erpol; exp(eps_premium) = (1 - rho_eps_premium)*1 + rho_eps_premium* exp(eps_premium(-1)) + e_eps_premium; exp(Rstar) = (1 - rho_Rstar)* Rstarss + rho_Rstar * exp(Rstar(-1)) + e_Rstar; exp(pi_star) = (1 - rho_pistar)* piss_star + rho_pistar * exp(pi_star(-1)) + e_pistar; exp(pQ) = (1 - rho_pQ)* 1 + rho_pQ * exp(pQ(-1)) + e_pQ; 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_bih) = (1 - rho_mk_bih)* mk_bih_ss + rho_mk_bih * exp(mk_bih(-1)) + e_mk_bih; exp(mk_biw) = (1 - rho_mk_biw)* mk_biw_ss + rho_mk_biw * exp(mk_biw(-1)) + e_mk_biw; end; //model initval; lam_p = log(2.3464); lam_i = log(11.1645); lam_e = log(6.8762); s_ih = log(0.1562); s_iw = log(0.1383); s_e = log(0.0283); c_p = log(0.4262); c_i = log(0.0896); c_e = log(0.1454); h_p = log(2.3859); h_i = log(0.2836); h_e = log(0.4559); h = log(2.3859 + 0.2836 + 0.4559); d = log(0.1386); b_ih = log(0.0151); b_iw = log(0.0088); b_e = log(0.1850); debt_ih = log(phi_dih*0.0151); debt_iw = log(phi_dih*0.0088); debt_e = log(phi_de*0.1850); Bstar = log(0.0111); k = log(3.7945); l_p = log(0.7779); l_i = log(0.8484); Q = log(0.3306); u = 0.0; % taxa de utilização do capital y_e = log(1.0638); y_exp = log(0.2); r_pol = log(r_polss); % taxa de juros politica monetaria r_d = log(r_dss); % taxa de juros deposito r_bih = log(r_bihss); % taxa de juros empréstimo imóveis r_biw = log(r_biwss); % taxa de juros empréstimo consignado r_be = log(r_bess); % taxa de juros empréstimo empresários R_b = log(r_polss); % taxa de juros empréstimo banco atacadista Rstar = log(0.005); % taxa de juros empréstimo externo premium = log(1.0102); er = log(0.5850); K_b = log(0.0638); pi = log(piss); % inflação de preços pi_star = log(piss_star); % inflação de preços externa pi_wp = pi; % log(piss); % inflação de salários pi_wi = pi; % log(piss); % inflação de salários w_p = log(0.4973); w_i = log(0.1140); q_k = 0.0; % preço do capital q_h = 0.0; % preço do imóvel pQ = 0.0; J_B = log(0.0068); J_R = log(0.0975); ee_z = 0.0; % EXOGENOUS PROCESSES A_e = 0.0; % EXOGENOUS PROCESSES ee_j = 0.0; % EXOGENOUS PROCESSES ee_qk = 0.0; % EXOGENOUS PROCESSES ee_qh = 0.0; % EXOGENOUS PROCESSES e_rpol = 0.0; % EXOGENOUS PROCESSES eps_K_b = 0.0; % EXOGENOUS PROCESSES eps_premium = 0.0; % EXOGENOUS PROCESSES m_ih = log(m_ihss); % EXOGENOUS PROCESSES (IMPATIENT LTV) m_iw = log(m_iwss); % EXOGENOUS PROCESSES m_e = log(m_ess); % EXOGENOUS PROCESSES (ENTREPRENEURS LTV) eps_y = log(eps_yss); % EXOGENOUS PROCESSES eps_l = log(eps_lss); % EXOGENOUS PROCESSES %eps_d = -0.9632; % log(eps_dss); % EXOGENOUS PROCESSES %eps_be = 1.0043; % log(eps_bess); % EXOGENOUS PROCESSES %eps_bih = 1.6790; % log(eps_bihss); % EXOGENOUS PROCESSES %eps_biw = 1.5041; % log(eps_biwss); % EXOGENOUS PROCESSES x = log(eps_yss/(eps_yss - 1)); % preço relativo C = log(0.4262 + 0.0896 + 0.1454); Y = log(0.8787); PIW = pi; % AGGREGATION & EQUILIBRIUM B = log(0.0151 + 0.0088 + 0.1850); BH = log(0.0151 + 0.0088); Ik = log(deltak*3.7945); Ih = log(deltah*(2.3859 + 0.2836 + 0.4559)); y = log(1.0721); mk_d = log(mk_d_ss); mk_be = log(mk_be_ss); mk_bih = log(mk_bih_ss); mk_biw = log(mk_biw_ss); end; steady; check; model_diagnostics; /* disp(' ');disp('%%% Display some SS results (BK model): %%%%') SSincome = exp(Y); disp(['total income in ss: ',num2str(SSincome)]); disp(['C/Y: ',num2str(exp(C)/exp(Y))]); disp(['Ik/Y: ',num2str(exp(I)/exp(Y))]); disp(['Ih/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(['bih/(bih + be + biw)(%): ',num2str(exp(b_ih)/(exp(b_ih) + exp(b_iw) + exp(b_e))*100)]); disp(['biw/(bih + be + biw)(%): ',num2str(exp(b_iw)/(exp(b_ih) + exp(b_iw) + exp(b_e))*100)]); disp(['be/(bih + be + biw)(%): ',num2str(exp(b_e)/(exp(b_ih) + exp(b_iw) + 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(['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))]); */ shocks; //estimated st.dev. var e_z = 0.01^2; % 0.0144^2; var e_A_e = 0.01^2; % 0.185807999596714^2; var e_j = 0.01^2; % 0.0658^2; var e_me = 0.01^2; %0.0034^2; var e_mih = 0.01^2; % 0.0023^2; var e_miw = 0.01^2; % 0.0023^2; %var e_epsd = 0.01^2; % 0.0488^2; %var e_epsbih = 0.01^2; % 0.0051^2; %var e_epsbiw = 0.01^2; % 0.0051^2; %var e_epsbe = 0.01^2; % 0.1454^2; var e_qk = 0.01^2; % 0.0125^2; var e_qh = 0.01^2; % 0.0125^2; var e_erpol = 0.01^2; % 0.0013^2; var e_y = 0.01^2; % 1.0099^2; var e_l = 0.01^2; % 0.3721^2; var e_eps_K_b = 0.01^2; % 0.050^2; var e_eps_premium = 0.01^2; %0.050^2; var e_Rstar = 0.01^2; % 0.050^2; var e_pistar = 0.01^2; % 0.050^2; var e_mk_d = 0.01^2; % 0.050^2; var e_mk_be = 0.01^2; %0.050^2; var e_mk_bih = 0.01^2; % 0.050^2; var e_mk_biw = 0.01^2; % 0.050^2; end; // Stochastic simulations stoch_simul(order = 1,irf = 20);