%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Secretaria do Tesouro Nacional - STN % Modelo Novo Keynesiano inspirado em Gerali et. al. (2010) % Autor: Márcio Francisco da Silva % Agentes: 1 - Familias Pacientes, 2 - Famílias Impacientes, 3 - Empresários, % 4 - Sindicatos, 5 - Bancos, 6 - Produtores de capital, % 7 - Produtores de Imóveis, 8 - Produtores de Bens finais, 9 - Governo, 10 - Setor externo %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% var A_e % Choque tecnológico B % Empréstimo às famílias e firmas b_e % Empréstimo às firmas b_i % Empréstimo às famílias, colateral b_iw % Empréstimo às famílias, consignado Bg % Empréstimo ao governo Bstar % Empréstimo externo C % Consumo das famílias e empresários c_e % Consumo dos empresários c_i % Consumo das famílias impacientes c_p % Consumo das famílias pacientes dbgg % Divida Bruta do governo geral d_p % depósitos das famílias ee_j % Choque, preferencia por imóveis ee_qh % Choque, investimento em imóveis ee_qk % Choque, investimento em capital privado ee_z % Choque, preferencia por consumo eps_Ig % Choque, investimento em capital público eps_g % Choque, gasto público eps_K_b % Choque, investimento em capital bancário eps_l % Elasticidade de substituição entre tipos de trabalho eps_premium % Choque, premio de risco eps_y % Elasticidade de substituição entre tipos de bens er % Taxa de câmbio real G % Consumo do governo h % Estoque de imóveis, total h_e % Estoque de imóveis, empresários h_i % Estoque de imóveis, famílias impacientes h_p % Estoque de imóveis, famílias pacientes I % Investimento em capital privado Ih % Investimento em imóveis Ig % Investimento em capital público j_B % Lucro dos bancos J_R % Lucro das firmas K % Capital privado K_b % Capital bancário Kg % Capital público l_i % Mão-de-obra, impaciente l_p % Mão-de-obra, paciente lam_e % preço-sombra lam_i % preço-sombra lam_p % preço-sombra m_e % Razão loan-to-value, empresários m_i % Razão loan-to-value, famílias m_iw % Razão debt-to-income mk_be % Mark-up de taxa de juros, empréstimo para as firmas mk_bh % Mark-up de taxa de juros, empréstimo para as farmílias mk_bw % Mark-up de taxa de juros, empréstimo para as famílias mk_d % Mark-down de taxa de juros, depósitos pie % Inflação doméstica de preços pie_star % Inflação externa pie_wi % Inflação de salários, mão-de-obra da família impaciente pie_wp % Inflação de salários, mão-de-obra da família paciente PIW % Inflação de salários pQ % Preço do insumo importado premium % Prêmio de risco Q % Insumo importado q_h % Preço dos imóveis q_k % Preço do capital R_b % Taxa de juros, interbancário r_be % Taxa de juros, empréstimo às firmas r_bh % Taxa de juros, empréstimo às famílias r_bw % Taxa de juros, empréstimo às famílias r_d % Taxa de juros, depósitos r_gov r_ib % Taxa de juros, política monetaria r_k % Retorno do capital Rstar % Taxa de juros externa s_e % preço-sombra s_i % preço-sombra s_iw % preço-sombra tauy % Alíquota de imposto T % Receita de impostos u % Taxa de utilização do capital w_i % Salário, família impaciente w_p % Salário, família paciente x % Preço relativo do bem intermediário Y % PIB y % VBA y_e % Produto intermediário y_exp % Exportações ystar % Renda externa Value_p % Utilidade, família paciente Value_i % Utilidade, família impaciente Value_e % Utilidade, empresários Value_t % Utilidade, total prob fator ; 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_miw e_mk_bw e_qh e_pQ e_pie_star e_Rstar e_ystar e_eps_premium e_Ig e_tauy e_g; parameters beta_p j phi beta_i m_i_ss beta_e m_e_ss eksi_1 eksi_2 // HOUSEHOLDS & ENTREPRENEURS a_i a_p a_e ni // HOUSEHOLDS & ENTREPRENEURS eps_l_ss kappa_w // HOUSEHOLDS (labor params) eps_d eps_bh eps_be // BANKS mk_d_ss mk_bh_ss mk_be_ss r_be_ss r_bh_ss r_k_ss // BANKS (SS) 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 // SHOCKS rho_mk_d rho_mk_be rho_mk_bh rho_ee_qk rho_eps_l rho_eps_K_b // SHOCKS ind_d ind_be ind_bh // OTHERS deltah eps_bw mk_bw_ss r_bw_ss kappa_ih kappa_bw ind_bw m_iw_ss rho_miw rho_mk_bw rho_ee_qh Rstar_ss ystar_ss pie_star_ss alphak alphal chi tau zeta rho_ystar rho_pie_star rho_Rstar rho_pQ rho_eps_premium kappa_ig deltag teta_iy teta_ib teta_g etag tauy_ss growth rho_tauy rho_ig rho_g recup dbgg_sus ; % ********************* % CALIBRATED PARAMETERS % ********************* alphak = 0.4; alphal = 0.5; beta_p = 0.989; //0.9943; % discount factor patient households beta_i = 0.96; //0.975; "Iacoviello 2005" % 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 = 0.06;//0.15;//0.7 ; % loan-to-value ratio impatient households m_e_ss = 0.007;//0.085;//0.35 ; % loan-to-value ratio entrepreneurs m_iw_ss = 0.1; eps_d = -2.62;//-12.624223124295;//-1.46025; % elast. of subst. of deposits eps_bh = 5.36;//5.3561509445936;// eps_be = 2.73;//2.7328233013319;// eps_bw = 4.5; 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_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_bw_ss = eps_bw/(eps_bw - 1); eps_y_ss = 11; //6; % eps_l_ss = 3; //5; % ni = 0.8; % wage share of patient households deltak = 0.025; % 0.035; // % depreciation rate for physical capital deltah = 0.025; delta_kb = 0.095; //0.094364024331655; deltag = 0.01; % 0.015; % piss = 1;//1.045^0.25; // % steady state gross inflation rate pie_star_ss = 1; r_ib_ss = (piss/beta_p - 1) * (eps_d-1)/eps_d ; % steady state gross nominal interest rate 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_bw_ss = (eps_bw/(eps_bw - 1))*r_ib_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; % steady state rental rate of capital Rstar_ss = 0.005; eksi_1 = r_k_ss; % capital utilization cost parameter eksi_2 = 0.1*r_k_ss; % capital utilization cost parameter vi = 0.17; //0.09; % Banking Capital ratio over Loans (Basel II) 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 ind_bw = ind_bh; rho_ee_z = 0.98; rho_A_e = 0.598; rho_ee_j = 0.636; rho_me = 0.459; rho_mi = 0.556; rho_mk_d = 0.936; rho_mk_bh = 0.132; rho_mk_be = 0.564; rho_ee_qk = 0.937; rho_eps_y = 0.517; rho_eps_l = 0.547; rho_eps_K_b = 0.627; rho_miw = 0.57; rho_mk_bw = 0.129; rho_ee_qh = 0.992; rho_ystar = 0.994; rho_pie_star = 0.809; rho_Rstar = 0.261; rho_pQ = 0.955; rho_eps_premium = 0.295; rho_tauy = 0.5; rho_ig = 0.5; rho_g = 0.5; kappa_p = 84.66; % 33.7705265016395 ; kappa_w = 65.605; % 33.7705265016395 ; kappa_i = 3.217; % 10.0305562248008 ; kappa_d = 6.459; % 2.77537377104213 ; kappa_be = 0.221; % 7.98005959044637 ; kappa_bh = 7.139; % 9.04426718749482 ; kappa_kb = 0.385; % 8.91481958034669 ; kappa_ih = 4.274; % 10.0305562248008 ; kappa_bw = 13.301; % 9.04426718749482 ; kappa_ig = 10.0305562248008 ; phi_pie = 1.79; % 2.00384780180824 ; rho_ib = 0.517; % 0.750481873084311 ; phi_y = 0.173; % 0.303247771697294 ; ind_p = 0.956; % 0.158112794106546 ; ind_w = 0.808; % 0.300197804017489 ; a_i = 0.915; % 0.867003766306404 ; a_e = 0.0 ; % degree of habit formation: entrepreneurs a_p = 0.0 ; % degree of habit formation: patient households ystar_ss = 2; zeta = -0.1; chi = 0.1; tau = -1.1; etag = 0.0805; % 0.2321; % teta_iy = 0.08; % 0.07; % 0.27; % teta_ib = 0.025; % 0.01; % 0.5; % tauy_ss = 0.0355; % 0.03; % 0.025; % growth = 0.02; % 0.0273; % teta_g = 0.04; % recup = 0.9; dbgg_sus = 1.2; //%------------------------------------------------------------ //% Model equations //%------------------------------------------------------------ model; ////*********** 1) PATIENT HHs ********************************************************6 (1-a_i)*ee_z*(c_p - a_i*c_p(-1))^(-1) = lam_p; j * ee_j / h_p - lam_p * q_h + (1 - deltah) * beta_p * lam_p(+1) * q_h(+1) = 0; // lam_p = beta_p * lam_p(+1) * (1 + r_d) / pie(+1); // (1 - eps_l) * l_p + l_p ^(1+phi) / w_p * eps_l/lam_p - kappa_w *( pie_wp - pie(-1) ^ ind_w * piss ^ (1-ind_w) ) * pie_wp + beta_p * lam_p(+1)/lam_p * kappa_w *( pie_wp(+1) - pie ^ ind_w * piss ^ (1-ind_w) ) * pie_wp(+1) ^2 / pie = 0 ; pie_wp = w_p / w_p(-1) * pie; c_p + q_h * ( h_p - (1 - deltah)*h_p(-1) ) + d_p = (1 - tauy) * (w_p * l_p + J_R) + (1+r_d(-1))*d_p(-1)/pie ; ////*********** 2) IMPATIENT HHs ********************************************************7 (1-a_i)*ee_z*(c_i - a_i*c_i(-1))^(-1) = lam_i; j * ee_j / h_i - lam_i * q_h + (1 - deltah) * ( beta_i * lam_i(+1) * q_h(+1) + s_i * m_i *q_h(+1) * pie(+1) ) = 0; // lam_i - beta_i * lam_i(+1) * (1 + r_bh) / pie(+1) = s_i * (1 + r_bh); // lam_i - beta_i * lam_i(+1) * (1 + r_bw) / pie(+1) = s_iw * (1 + r_bw); // (1 - eps_l) * l_i + eps_l * l_i^(1 + phi) / (w_i * (lam_i + m_iw * s_iw)) - kappa_w *( pie_wi - pie(-1) ^ ind_w * piss ^ (1 - ind_w) ) * pie_wi + beta_i * (lam_i(+1) + s_iw(+1) + m_iw(+1))/(lam_i + s_iw + m_iw) * kappa_w *( pie_wi(+1) - pie ^ ind_w * piss ^ (1 - ind_w) ) * pie_wi(+1)^2 / pie(+1) = 0 ; pie_wi = w_i / w_i(-1) * pie; c_i + q_h * (h_i - (1 - deltah) * h_i(-1)) + (1 + r_bh(-1))*b_i(-1)/pie + (1 + r_bw(-1))*b_iw(-1)/pie = (1 - tauy) * w_i * l_i + b_i + b_iw ; (1 + r_bh) * b_i = m_i * q_h(+1) *h_i * pie(+1); // (1 + r_bw) * b_iw = m_iw * w_i(+1) * l_i(+1) * pie(+1); // ////*********** 3) CAPITAL PRODUCERS ***************************************************** (K) = (1-deltak) * (K(-1)) + ( 1 - kappa_i/2 * ( (I)* (ee_qk)/ (I(-1)) - 1)^2 ) * (I) ; 1 = (q_k) * ( 1 - kappa_i/2 * ( (I)* (ee_qk)/ (I(-1)) - 1)^2 - kappa_i * ( (I)* (ee_qk)/ (I(-1)) - 1) * (I)* (ee_qk)/ (I(-1)) ) + beta_e * (lam_e(+1)) / (lam_e) * (q_k(+1)) * kappa_i * ( (I(+1))* (ee_qk(+1))/ (I) - 1) * (ee_qk(+1)) * ( (I(+1))/ (I))^2 ; // ////*********** 3) HOUSING PRODUCERS ***************************************************** h = (1 - deltah) * h(-1) + ( 1 - kappa_ih/2 * ( Ih*ee_qh/ I(-1) - 1)^2 ) * Ih ; 1 = (q_h) * ( 1 - kappa_ih/2 * ( (Ih)* (ee_qh)/ (Ih(-1)) - 1)^2 - kappa_ih * ( (Ih)* (ee_qh)/ (Ih(-1)) - 1) * (Ih)* (ee_qh)/ (Ih(-1)) ) + beta_e * (lam_e(+1)) / (lam_e) * (q_h(+1)) * kappa_ih * ( (Ih(+1))* (ee_qh(+1))/ (Ih) - 1) * (ee_qh(+1)) * ( (Ih(+1))/ (Ih))^2 ; // ////************ 4) ENTREPRENEURS ********************************************************* (1-a_i)*ee_z*( c_e - a_i* (c_e(-1)))^(-1) = lam_e; s_e * m_e * q_k(+1) * pie(+1) * (1 - deltak) + beta_e * lam_e(+1) * ( (q_k(+1))*(1-deltak) + ((1 - tauy(+1))*r_k(+1))* (u(+1)) - ( eksi_1*( (u(+1))-1) + eksi_2/2*( ( u(+1) - 1)^2 ) ) ) = lam_e * q_k ; j * ee_j / h_e - lam_e * q_h + (1 - deltah) * ( beta_e * lam_e(+1) * q_h(+1) + s_e * m_e *q_h(+1) * pie(+1) ) = 0; w_p = (1 - tauy)*ni * alphal * y_e / ( l_p * x ); w_i = (1 - tauy)*(1 - ni) * alphal * y_e / ( l_i * x ); er*pQ = (1 - tauy)*(1 - alphak - alphal) * y_e / ( Q * x ); lam_e - s_e * (1 + r_be) = beta_e * lam_e(+1) * (1 + r_be) / pie(+1); // (1 - tauy)*r_k = eksi_1 + eksi_2 * (u - 1);// c_e + ((1 + r_be(-1)) * (b_e(-1)) / pie ) + q_h * (h_e - (1 - deltah) * h_e(-1)) + w_p * l_p + w_i * l_i + q_k * K + ( eksi_1*( u - 1 ) + eksi_2/2*( u - 1 )^2 ) * K(-1) + er*pQ*Q = (1 - tauy)*y_e / x + b_e + q_k * (1 - deltak) * K(-1) ; y_e = A_e * (Kg(-1)^etag) * (u * K(-1))^(alphak) * ( (l_p)^ni * (l_i)^(1 - ni) ) ^ (alphal) * (Q)^ (1 - alphak - alphal); (1 + r_be) * b_e = m_e * ( q_k(+1) * pie(+1) * K * (1 - deltak) + q_h(+1) * pie(+1) * h_e * (1 - deltah) ); // r_k = alphak * A_e * (Kg(-1)^etag) * (u)^(alphak - 1) * (K(-1))^(alphak - 1) * ( (l_p)^ni * (l_i)^(1 - ni) ) ^ (alphal) * (Q)^ (1 - alphak - alphal) / x; ////************* 5)BANKS **************************************************************** R_b = r_gov ; // Eq. alterada para gerar choque no Kb K_b * pie = (1 - delta_kb) * K_b(-1)/ eps_K_b + j_B(-1) ; // Eq. alterada para gerar choque no Kb b_i + b_iw + b_e + Bg = d_p + er*Bstar + K_b; // Premio de risco premium = exp(-zeta*er*Bstar/K_b)*eps_premium; // Paridade das taxas de juros (1 + Rstar) * premium * (1 - zeta*er*Bstar/K_b) * (er(+1)/er) * (pie(+1)/pie_star(+1)) = 1 + r_gov; /// PRICING in terms of MK /// - 1 + (mk_d)/( (mk_d)-1) - (mk_d)/( (mk_d)-1) * (r_ib)/ (r_d) - kappa_d * ( (r_d)/ (r_d(-1)) - 1 ) * (r_d)/ (r_d(-1)) + beta_p * ( (lam_p(+1))/ (lam_p) ) * kappa_d * ( (r_d(+1))/ (r_d) - ( (r_d)/ (r_d(-1)))^ind_d ) * ( ( (r_d(+1))/ (r_d))^2 ) * ( (d_p(+1))/ (d_p)) = 0;// + 1 - (mk_be)/( (mk_be)-1) + (mk_be)/( (mk_be)-1) * (R_b)/ (r_be) - kappa_be * ( (r_be)/ (r_be(-1)) - 1 ) * (r_be)/ (r_be(-1)) + beta_p * ( (lam_p(+1))/ (lam_p) ) * kappa_be * ( (r_be(+1))/ (r_be) - ( (r_be)/ (r_be(-1)))^ind_be ) * ( ( (r_be(+1))/ (r_be))^2 ) * ( (b_e(+1))/ (b_e)) = 0;// 30 + 1 - (mk_bh)/( (mk_bh)-1) + (mk_bh)/( (mk_bh)-1) * (R_b)/ (r_bh) - kappa_bh * ( (r_bh)/ (r_bh(-1)) - 1 ) * (r_bh)/ (r_bh(-1)) + beta_p * ( (lam_p(+1))/ (lam_p) ) * kappa_bh * ( (r_bh(+1))/ (r_bh) - ( (r_bh)/ (r_bh(-1)))^ind_bh ) * ( ( (r_bh(+1))/ (r_bh))^2 ) * ( (b_i(+1))/ (b_i)) = 0;// + 1 - (mk_bw)/( (mk_bw)-1) + (mk_bw)/( (mk_bw)-1) * (R_b)/ (r_bw) - kappa_bw * ( (r_bw)/ (r_bw(-1)) - 1 ) * (r_bw)/ (r_bw(-1)) + beta_p * ( (lam_p(+1))/ (lam_p) ) * kappa_bw * ( (r_bw(+1))/ (r_bw) - ( (r_bw)/ (r_bw(-1)))^ind_bw ) * ( ( (r_bw(+1))/ (r_bw))^2 ) * ( (b_iw(+1))/ (b_iw)) = 0;// j_B = + r_bh * b_i + r_bw * b_iw + r_be * b_e + er * Bstar - r_d * d_p - Bg + (1 + r_gov(-1)) * Bg(-1) - kappa_d/2 * ( ( r_d / r_d(-1) - 1)^2) * r_d * d_p - kappa_be/2 * ( ( r_be / r_be(-1) - 1)^2) * r_be * b_e - kappa_bh/2 * ( ( r_bh / r_bh(-1) - 1)^2) * r_bh * b_i - kappa_bw/2 * ( ( r_bw / r_bw(-1) - 1)^2) * r_bw * b_iw - kappa_kb/2 * ( ( K_b / K_b(-1) - 1 )^2) * K_b - (1 + Rstar(-1)) * premium(-1) * er * Bstar(-1); ////*********** 6)RETAILERS ************************************************************** J_R = y*(1 - (1/ x) - (kappa_p/2) * ( (pie) - ( (pie(-1)) ^ ind_p * piss ^ (1-ind_p) ))^2 ) ; 1 - (eps_y) + (eps_y) / (x) - kappa_p * ( (pie) - ( (pie(-1)) ^ ind_p * piss ^ (1-ind_p) )) * (pie) + beta_p*( (lam_p(+1))/ (lam_p))* kappa_p * ( (pie(+1)) - ( (pie) ^ ind_p * piss ^ (1-ind_p) )) * (pie(+1)) * ( (y(+1))/ (y)) = 0; // 34 ////************ 7) AGGREGATION & EQUILIBRIUM ************************************************ C = c_p + c_i + c_e; y_exp = chi*(1/er)^(-tau) * ystar; y_exp - er * pQ * Q - ((1 + Rstar(-1))/pie_star) * premium(-1) * er * Bstar(-1) = er * Bstar - er * Bstar(-1)/pie_star; h = h_p + h_i + h_e; // B = b_i + b_iw + b_e; // % y = C + ( K - (1-deltak)* K(-1)) + ( h - (1 - deltah)* h(-1)) + Kg - (1 - deltag)* Kg(-1) + G + y_exp; y = C + q_k*( K - (1-deltak)* K(-1)) + q_h*( h - (1 - deltah)* h(-1)) + Kg - (1 - deltag)* Kg(-1) + G + y_exp; Y = y - er * pQ * Q; PIW = ( w_p + w_i ) / ( w_p(-1) + w_i(-1) ) * pie; ////*********** 8) GOVERNMENT ***************************************************** (1 + r_ib) = (1 + r_ib_ss)^(1 - rho_ib ) * (1 + r_ib(-1))^rho_ib * (( pie / piss ) ^phi_pie * ( (Y)/ (Y(-1)))^phi_y ) ^ ( 1 - rho_ib ) * (1+e_r_ib) ;// 48 Ig = teta_iy*Y(-1) - teta_ib*Bg(-1) + eps_Ig; Kg = (1 - deltag) * Kg(-1) + ( 1 - kappa_ig/2 * (Ig/ Ig(-1) - 1)^2) * Ig ; G = teta_g * Y(-1) + eps_g; T = tauy*(w_p*l_p + w_i*l_i + J_R + y_e/x); prob = max(0, (dbgg(-1) - dbgg_sus)/dbgg(-1)); r_gov = (1 + r_ib)*(1 - recup*prob(+1))/(1 - prob(+1)) - 1; Bg/Y = ((1 + r_gov(-1))/((1 + growth)*pie))*Bg(-1)/Y(-1) + Ig/Y + G/Y - tauy*(w_p*l_p + w_i*l_i + J_R + y_e/x)/Y ; ////*********** 9) EXOGENOUS PROCESSES ****************************************************12 ee_z = (1 - rho_ee_z) * 1 + rho_ee_z * ee_z(-1) + e_z; A_e = (1 - rho_A_e) * 1 + rho_A_e * A_e(-1) + e_A_e; ee_j = (1 - rho_ee_j) * 1 + rho_ee_j * ee_j(-1) + e_j; m_i = (1 - rho_mi) * m_i_ss + rho_mi * m_i(-1) + e_mi; m_iw = (1 - rho_miw) * m_iw_ss + rho_miw * m_iw(-1) + e_miw; m_e = (1 - rho_me) * m_e_ss + rho_me * m_e(-1) + e_me; mk_d = (1 - rho_mk_d) * mk_d_ss + rho_mk_d * mk_d(-1) + e_mk_d; mk_be = (1 - rho_mk_be) * mk_be_ss + rho_mk_be * mk_be(-1) + e_mk_be; mk_bh = (1 - rho_mk_bh) * mk_bh_ss + rho_mk_bh * mk_bh(-1) + e_mk_bh; mk_bw = (1 - rho_mk_bw) * mk_bw_ss + rho_mk_bw * mk_bw(-1) + e_mk_bw; ee_qk = (1 - rho_ee_qk) * 1 + rho_ee_qk * ee_qk(-1) + e_qk; ee_qh = (1 - rho_ee_qh) * 1 + rho_ee_qh * ee_qh(-1) + e_qh; eps_y = (1 - rho_eps_y) * eps_y_ss + rho_eps_y * eps_y(-1) + e_y; eps_l = (1 - rho_eps_l) * eps_l_ss + rho_eps_l * eps_l(-1) + e_l; eps_K_b = (1 - rho_eps_K_b)* 1 + rho_eps_K_b* eps_K_b(-1) + e_eps_K_b; eps_premium = (1 - rho_eps_premium)* 1 + rho_eps_premium* eps_premium(-1) + e_eps_premium; pQ = (1 - rho_pQ) * 1 + rho_pQ * pQ(-1) + e_pQ; Rstar = (1 - rho_Rstar) * Rstar_ss + rho_Rstar * Rstar(-1) + e_Rstar; ystar = (1 - rho_ystar) * ystar_ss + rho_ystar * ystar(-1) + e_ystar; pie_star = (1 - rho_pie_star)* pie_star_ss + rho_pie_star* pie_star(-1) + e_pie_star; eps_Ig = (1 - rho_ig) * 0 + rho_ig * eps_Ig(-1) + e_Ig; eps_g = (1 - rho_g) * 0 + rho_g * eps_g(-1) + e_g; tauy = (1 - rho_tauy) * tauy_ss + rho_tauy * tauy(-1) + e_tauy; ////*********** 10) Funções Valor **************************************************** Value_e = (1 - a_i)*ee_z*log(c_e - a_i*c_e(-1)) + ee_j*j*log(h_e) + beta_e*Value_e(+1); Value_p = (1 - a_i)*ee_z*log(c_p - a_i*c_p(-1)) + ee_j*j*log(h_p) - ((l_p)^(1 + phi))/(1 + phi) + beta_p*Value_p(+1); Value_i = (1 - a_i)*ee_z*log(c_i - a_i*c_i(-1)) + ee_j*j*log(h_i) - ((l_i)^(1 + phi))/(1 + phi) + beta_i*Value_i(+1); %Value_t = (1/3)*Value_e + (1/3)*Value_p + (1/3)*Value_i; Value_t = (c_e/C)*Value_e + (c_p/C)*Value_p + (c_i/C)*Value_i; dbgg = Bg/(Y + Y(-1) + Y(-2) + Y(-3)); fator = ((1 + r_gov(-1))/((1 + growth)*pie)) - 1; end; initval; pie = 1; pie_wp = 1; pie_wi = 1; PIW = 1; u = 1; q_k = 1; q_h = 1; ee_z = 1; A_e = 1; ee_j = 1; ee_qk = 1; eps_K_b = 1; ee_qh = 1; eps_premium = 1; pQ = 1; pie_star = 1; Rstar = Rstar_ss; ystar = ystar_ss; r_d = piss/beta_p -1; r_bh = r_bh_ss; r_bw = r_bw_ss; r_be = r_be_ss; R_b = r_ib_ss; r_ib = r_ib_ss; r_k = r_k_ss; x = 1.1; mk_d = mk_d_ss; mk_be = mk_be_ss; mk_bh = mk_bh_ss; mk_bw = mk_bw_ss; m_i = m_i_ss; m_e = m_e_ss; m_iw = m_iw_ss; eps_y = eps_y_ss; eps_l = eps_l_ss; tauy = tauy_ss; lam_p = 1.02896476; % lam_i = 4.958757133; % lam_e = 1.858971856; % s_i = 0.10640561; % s_iw = 0.118025935; % s_e = 0.030345278; % c_p = 0.971850581; % c_i = 0.201663436; % c_e = 0.537931759; % h_p = 5.440731035; % h_i = 0.64280628; % h_e = 1.683968144; % b_i = 0.036906915; % b_iw = 0.02294929; % b_e = 0.104646626; % d_p = -0.258150451; % w_p = 1.166289209; % w_i = 0.265322368; % y_e = 2.73559381; % y = 2.761788754; % K = 14.02069948; % l_p = 0.800046997; % l_i = 0.87920045; % Q = 0.263662797; % er = 0.884734395; % Bstar = 0.023346167; % premium = 1.005151345; % K_b = 0.401998126; % y_exp = 0.254136911; % Kg = 10.02401703; % Bg = 2.076844848; % h = h_p + h_i + h_e; I = deltak*K; Ih = deltah*h; C = c_p + c_i + c_e; B = b_i + b_e + b_iw; J_R = (1 - 1/x)*Y; j_B = delta_kb*K_b; Ig = deltag*Kg; Y = y - er*Q; G = teta_g*Y; T = tauy*(w_p*l_p + w_i*l_i + J_R + y_e/x); dbgg = 0.5624; end; //// COMPUTE THE SS ///// steady(maxit = 5000, solve_algo = 1); model_diagnostics; %%%% 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): %%%%') disp(['C/Y: ',num2str( (C)/ (Y))]); disp(['Ik/Y: ',num2str( (I)/ (Y))]); disp(['Ih/Y: ',num2str( (Ih)/ (Y))]); disp(['I/Y: ',num2str( (I + Ih)/ (Y))]); disp(['Ig/Y: ',num2str( Ig / (Y))]); disp(['K/Y: ',num2str( (K)/ (Y))]); disp(['Kg/Y: ',num2str( (Kg)/ (Y))]); disp(['H/Y: ',num2str( (h)/ (Y))]); disp(['G/Y: ',num2str( G / (Y))]); disp(['Impostos/Y: ',num2str( tauy*(w_p*l_p + w_i*l_i + J_R + y_e/x) / (Y))]); disp(['erBstar/Y: ',num2str( er*Bstar/ (Y))]); disp(['Exp/Y: ',num2str( y_exp/ (Y))]); disp(['Imp/Y: ',num2str( er*pQ*Q/ (Y))]); disp(['r_d (%annual): ',num2str( (r_d)*400)]); disp(['r_ib (%annual): ',num2str( (r_ib)*400)]); disp(['r_gov (%annual): ',num2str( (r_gov)*400)]); disp(['r_bh (%annual): ',num2str( (r_bh)*400)]); disp(['r_bw (%annual): ',num2str( (r_bw)*400)]); disp(['r_be (%annual): ',num2str( (r_be)*400)]); disp(['bi/(bi+biw+be)(%): ',num2str( b_i /( b_i + b_iw + b_e)*100)]); disp(['biw/(bi+biw+be)(%): ',num2str( b_iw /( b_i + b_iw + b_e)*100)]); disp(['be/(bi+biw+be)(%): ',num2str( b_e /( b_i + b_iw + b_e)*100)]); disp(['D/Y: ',num2str( (d_p)/ (Y))]); disp(['K_b/B: ',num2str( (K_b)/ (B))]); disp(['K_b/Y: ',num2str( (K_b)/ (Y))]); disp(['B/Y: ',num2str( (B)/ (Y))]); disp(['DBGG: ',num2str( dbgg )]); disp(['Utilidade: ',num2str( Value_t)]); shocks; //estimated st.dev. var e_z = 0.385^2; % 0.0144^2; var e_A_e = 0.1759^2; % 0.185807999596714^2; var e_j = 3.6008^2; % 0.0658^2; var e_me = 0.2801^2; % 0.0034^2; var e_mi = 0.8502^2; % 0.0023^2; var e_miw = 0.8415^2; % 0.0023^2; var e_mk_d = 1.7323^2; % 0.0488^2; var e_mk_bh = 0.9062^2; % 0.0051^2; var e_mk_bw = 0.050^2; % 0.0051^2; var e_mk_be = 4.4625^2; % 0.1454^2; var e_qk = 0.7344^2; % 0.0125^2; var e_qh = 0.4777^2; % 0.0125^2; var e_r_ib = 0.13^2; % 0.0013^2; var e_y = 1.0754^2; % 1.0099^2; var e_l = 1.0198^2; % 0.3721^2; var e_eps_K_b = 0.6341^2; var e_pQ = 0.3063^2; var e_eps_premium = 0.3209^2; var e_Rstar = 0.3248^2; var e_ystar = 0.4146^2; var e_pie_star = 0.2902^2; var e_Ig = 0.3232^2; var e_tauy = 0.1528^2; var e_g = 0.2023^2; end; /* stoch_simul(order=1,irf=20) A_e B b_e b_i b_iw Bg Bstar C c_e c_i c_p d_p dbgg ee_j ee_qh ee_qk ee_z eps_Ig eps_K_b eps_l eps_premium eps_y er G h h_e h_i h_p I Ih Ig j_B J_R K K_b Kg l_i l_p m_e m_i m_iw mk_be mk_bh mk_bw mk_d pie pie_star pie_wi pie_wp PIW pQ premium Q q_h q_k R_b r_be r_bh r_bw r_d r_ib r_gov r_k Rstar tauy T u w_i w_p x Y y y_e y_exp ystar; */ //%------------------------------------------------------------ //% BAYESIAN ESTIMATION //%------------------------------------------------------------ //% defining which dataseries are used in estimation varobs C I Y Q y_exp pie G r_ib dbgg; % estimated_params ; //% Initial conditions PRIOR shape MEAN STD rho_tauy , , beta_pdf, 0.50, 0.25 ; //0.80, 0.10 ; rho_ig , , beta_pdf, 0.50, 0.25 ; //0.80, 0.10 ; rho_g , , beta_pdf, 0.50, 0.25 ; //0.80, 0.10 ; dbgg_sus , , normal_pdf, 1.20, 1.0 ; end; estimation(datafile = dados_stn3 ,mode_compute = 6 ,mh_jscale = 0.30 ,presample = 1 ,prefilter = 0 ,prior_trunc = 1e-14 ,mh_replic = 600000 ,mh_nblocks = 2 ,filtered_vars ,lik_init = 1 ,order = 1 ,mode_check ,irf = 20 ,bayesian_irf ,forecast = 40 ,tex ); shock_decomposition(parameter_set = posterior_mode) Y I Ig C pie r_ib G dbgg;