%% Draft7d DSGE Model %% Declaring Endogenous Variables var % Patient households uc_p % marginal ut. consumption c_p % consumption h_p % housing d_p % deposits eh % housing demand preferences (exogenous) % DC - impatient households uc_idc % marginal ut. consumpti on c_idc % consumption h_idc % housing b_idc % idc hh mortgage debt m_idc % idc ltv (exogenous) n_idc % idc labor supply % FC - impatient households uc_ifc % marginal ut. consumption c_ifc % consumption h_ifc % housing % b_ifc % ifc hh mortgage debt l_ifc % ifc hh mortgage debt - expressed in domestic currency m_ifc % ifc ltv (exogenous) n_ifc % ifc labor supply % Entrepreneurs uc_e % marginal ut. consumption c_e % consumption k % capital b_e % entrepreneurs debt m_e % e ltv (exogenous) yw % intermediate production pw % intermediate goods price a % tfp (exogenous) u % capital utiliyation n % employment % Labor supply w % wages uc % average marginal utility % Capital producing sector q_k % real capital price i_k % capital investment % Housing producing sector q_h % real housing price i_h % housing investment h % aggregate stock of capital pi_hh % housing inflation % Final good producers y % final good production pi % inflation rate % Domestic retailers y_h % domestic production p_h % domestic production price pi_h % domestic production inflation % Importing retailers y_f % imported production p_f % imported production price pi_f % imported production inflation % Exporting retailers y_h_star % exported production p_h_star % exported production prices pi_h_star % exported production inflation % Banking sector l_star % real external funding k_b % bank capital j_b % bank profits R_bidc % idc mortgage interest rate R_bifc % ifc mortgage interest rate R_be % entrepeneurs credit interest rate R_d % deposit interest rate R_bstar % international funding interest rate v_idc % capital-to-idc assets ratio (exogenous) v_ifc % capital-to-ifc assets ratio (exogenous) v_e % capital-to-e assets ratio (exogenous) % Foreign sector y_star % external production (exogenous) pi_star % external inflation (exogenous) Rf_star % international risk free interest rate (exogenous) varrho % risk premium additional term (exogenous) %Government g % government expenditures (exogenous) T % government transfers %Central bank R % monetary policy rate %Aggregate variables q % real exchange rate y_tilde % gdp c; % aggregate consumption % 68 endogenous variables %% Exogenous Variables (shocks) varexo e_h % housing demand shock e_midc % idc ltv shock e_mifc % ifc ltv shock e_me % e ltv shock e_a % tfp shock e_vidc % capital-to-idc assets shock e_vifc % capital-to-ifc assets shock e_ve % capital-to-e assets shock e_varrho % additional rate premium term shock % Pure shocks (they do not have persistence) e_y_star % shock to foreign IS curve e_pi_star % shock to foreign Phillips curve e_rf_star % shock to foreign Taylor rule e_g % fiscal shock e_r; % monetary policy shock % 14 shocks (which allows to include 14 observed variables for estimation) %% Setting parameters parameters % Strictly calibrated parameters % Population sizes gamma_p % size of patient households gamma_idc % size of idc households gamma_ifc % size of ifc households gamma_e % size of entrepreneurs % Preferences parameters beta_p % discount factor of patient households beta_idc % discount factor of idc households beta_ifc % discount factor of ifc households beta_e % discount factor of entrepreneurs sigma_c % marginal utility of consumption parameter sigma_h % marginal utility of housing parameter sigma_n % Inverse of Frish Elasticity zeta_c % internal habit formaton parameter % Labour sector theta_w % Calvo probability zeta_w % wage indexation parameter mu_w % wage elasticity parameter % LTV ratios m_idc_ss % SS LTV of idc loans m_ifc_ss % SS LTV of ifc loans m_e_ss % SS LTV of e loans % Intermediate production sector alpha % capital share in intermediate production function Psi % standardised utilization adjustmen cost parameter Psi_1 % utilization adjustmen cost parameter of SS % Capital goods production sector delta_k % depreciation rate of capital kappa_k % capital adjustment cost parameter % Housing production sector delta_h % depreciation rate of housing kappa_h % depreciation rate of housing % Final good production sector eta % home bias parameter mu % substitutability parameter % Retailers p_h_ss % domestic retailer ss price index theta_h % domestic retailer Calvo parameter zeta_h % domestic retailer price indexation parameter p_f_ss % importing retailer ss price index theta_f % importing retailer Calvo parameter zeta_f % importing retailer price indexation parameter theta_h_star % exporting retailer Calvo parameter zeta_h_star % exporting retailer price indexation parameter mu_h_star % exporting retailer goods substitutability parameter % Interest rates R_bidc_ss % ss of idc credit rate R_bifc_ss % ss of ifc credit rate R_be_ss % ss of e credit rate R_bstar_ss % ss of external funding rate R_d_ss % ss of deposit rate R_ss % ss of monetary policy rate Rf_star_ss % ss of international risk free rate % Rest of banking sector kappa_idc % adjutment cost parameter of capital-to-idc assets ratio kappa_ifc % adjutment cost parameter of capital-to-ifc assets ratio kappa_e % adjutment cost parameter of capital-to-e assets ratio v_idc_ss % ss of capital-to-idc assets ratio v_ifc_ss % ss of capital-to-ifc assets ratio v_e_ss % ss of capital-to-e assets ratio delta_b % managing bank capital cost parameter omega_b % bank dividend policy % Aggregate variables pi_ss % ss of inflation %Foreign sector std_y_star % size of shock to foreign IS curve std_pi_star % size of shock to foreign Phillips curve std_rf_star % size of shock to foreign Taylor rule rho_y_star % autoregressive term for foreign output rho_pi_star % autoregressive term for foreign inflation rho_rf_star % autoregressive term for foreign interest rate Psi_b % interest rate premium varrho_ss % interest rate premium additional term pi_star_ss % ss foreign inflation % Central Bank phi_r % persistance parameter phi_pi % inflation stabilization parameter phi_y % output stabilization parameter % Compound parameters beta_hat % average beta gamma_hat % aggregate size of households % Ratios ----- c_ytilde % aggregate consumption / gdp cp_ytilde % patient household consumption / gdp cidc_ytilde % idc household consumption / gdp cifc_ytilde % ifc household consumption / gdp ce_ytilde % entrepreneur consumption / gdp cp_c % patient household consumption / aggregate consumption cidc_c % idc household consumption / aggregate consumption cifc_c % ifc household consumption / aggregate consumption ce_c % entrepreneur consumption / aggregate consumption hp_h % patient household housing / aggregate housing hidc_h % idc household housing / aggregate housing hifc_h % ifc household housing / aggregate housing h_ytilde % aggregate housing / gdp ih_ytilde % housing investment / gdp hidc_ytilde % idc housing / gdp hifc_ytilde % ifc housing / gdp b_kb % total credit / bank capital ytilde_kb % gdp / bank capital b_ytilde % total credit /gdp D_ytilde % deposits / gdp bidc_b % idc credit / gdp sbifc_b % ifc credit /gdp be_b % e credit /gdp bidc_ytilde % idc mortgage credits / gdp sbifc_ytilde % ifc mortgage credits / gdp be_ytilde % e credits / gdp D_kb % deposits / bank capital lstar_kb % foreing bank debt / bank capital yh_share % yh / (yh + yhstar) yhstar_share % yhstar / (yh + yhstar) t_ytilde % transfer / gdp pyw_ytilde % intermediate production / gdp yh_ytilde % domestic production / gdp yf_ytilde % imports / gdp qyhstar_ytilde % exportes / gdp ik_ytilde % investment / gdp wage_ytilde % labour income / gdp g_ytilde % government expenditures / gdp lstar_ytilde % foreign debt / gdp y_ytilde % absortion / gdp % Estimated parameters for exogenous process rho_h % autochorrelation of preferences shock std_h % size of shock to housing preferences rho_midc % autochorrelation of idc ltv std_midc % size of shock to idc ltv rho_mifc % autochorrelation of ifc ltv std_mifc % size of shock to ifc ltv rho_me % autochorrelation of e ltv std_me % size of shock to e ltv rho_a % autochorrelation of tfp std_a % size of shock to tfp rho_vidc % autochorrelation of capital-to-idc assests ratio std_vidc % size of shock to capital-to-idc assests ratio rho_vifc % autochorrelation of capital-to-ifc assests ratio std_vifc % size of shock to capital-to-idc assests ratio rho_ve % autochorrelation of capital-to-e assests ratio std_ve % size of shock to capital-to-e assests ratio rho_varrho % autochorrelation of rate premium parameter std_varrho % size of shock to rate premium parameter rho_g % autochorrelation of government expenditures std_g % size of shock to government expenditures std_r; % size of monetary policy shock %% Calibration %------------------------------- %Calibrated parameter %------------------------------- % Preferences parameters gamma_p=0.45; gamma_idc=0.20; gamma_ifc=0.15; gamma_e=0.20; % Preferences parameters beta_idc=0.975; beta_ifc=0.975; beta_e=0.98; sigma_c=2; sigma_h=3.5; sigma_n=3.5; zeta_c=0.75; % Labour sector theta_w=0.75; zeta_w=0.40; mu_w=0.1; % LTV ratios m_idc_ss=0.7; m_ifc_ss=0.7; m_e_ss=0.6; % Intermediate production alpha=0.3; Psi=0.2; %Brzoza % Capital goods delta_k=0.025; kappa_k=0.2; % Housing production delta_h=0.0125; kappa_h=0.02; % Final good production eta=0.77; mu=1; % Retailers p_h_ss=1; %Brzoza theta_h=0.75; zeta_h=0.85; p_f_ss=1; %Brzoza theta_f=0.95; zeta_f=0.75; theta_h_star=0.10; zeta_h_star=0.50; mu_h_star=1; %Foreign sector std_y_star=0.01; std_pi_star=0.01; std_rf_star=0.01; rho_y_star=0.8; rho_pi_star=0.8; rho_rf_star=0.8; Psi_b=0.001; % Central Bank phi_r=0.70; phi_pi=1.50; phi_y=0.50; % Aggregate variables pi_ss=1.0275^(1/4); % Rest of banking kappa_idc=1.0; %To be estimated? kappa_ifc=1.0; %To be estimated? kappa_e=1.0; %To be estimated? v_idc_ss=1.61; v_ifc_ss=1.49; v_e_ss=0.16; delta_b=0.025; omega_b=1; %To be estimated? %Interest Rates R_ss=1.0376^(1/4); Rf_star_ss=1.0144^(1/4); varrho_ss=0; pi_star_ss=Rf_star_ss * pi_ss / R_ss; % National Accounting Ratios y_ytilde=0.98; c_ytilde=0.64; g_ytilde=0.11; ik_ytilde=0.22; qyhstar_ytilde=0.25; yf_ytilde=0.23; lstar_ytilde=0.35; % Banking system ratios b_kb=1/0.134; b_ytilde=0.25; bidc_b=0.08; sbifc_b=0.09; be_b=0.83; D_ytilde=0.04; %------------------------------- % Compound parameters %------------------------------- % Interest rates R_bidc_ss=R_ss; R_bifc_ss=R_ss; R_be_ss=R_ss; R_d_ss=R_ss; R_bstar_ss=Rf_star_ss + varrho_ss; % Aggregate variables beta_p=pi_ss/R_ss; gamma_hat=gamma_p+gamma_idc+gamma_ifc; beta_hat=(gamma_p/gamma_hat)*beta_p + (gamma_idc/gamma_hat)*beta_idc + (gamma_ifc/gamma_hat)*beta_ifc; Psi_1=beta_e^(-1)-(1-delta_k)-((beta_e*R_be_ss)^(-1)-pi_ss^(-1))*m_e_ss*(1-delta_k)*pi_ss; %Brzoza % Banking system ratios ytilde_kb=(1/b_ytilde)*b_kb; bidc_ytilde=b_ytilde*bidc_b; sbifc_ytilde=b_ytilde*sbifc_b; be_ytilde=b_ytilde*be_b; D_kb=D_ytilde*ytilde_kb; lstar_kb=b_kb - D_kb - 1; % Housing ratios ih_ytilde=y_ytilde-c_ytilde-ik_ytilde-g_ytilde; h_ytilde=(1/delta_h)*ih_ytilde; hidc_ytilde=(1/gamma_idc)*((m_idc_ss*(1-delta_h)*pi_ss)^(-1))*R_bidc_ss*bidc_ytilde; hifc_ytilde=(1/gamma_ifc)*((m_ifc_ss*(1-delta_h)*pi_ss)^(-1))*R_bifc_ss*sbifc_ytilde; hidc_h=hidc_ytilde/h_ytilde; hifc_h=hifc_ytilde/h_ytilde; hp_h=(1/gamma_p)*(1-gamma_idc*hidc_h-gamma_ifc*hifc_h); % National Accounting ratios yh_ytilde=((y_ytilde^(1/(1+mu)) - ((1-eta)^(mu/1+mu))*((yf_ytilde)^(1/(1+mu))))*(1/eta)^(mu/(1+mu)))^(1+mu); yh_share=yh_ytilde/(yh_ytilde+qyhstar_ytilde); yhstar_share=qyhstar_ytilde/(yh_ytilde+qyhstar_ytilde); t_ytilde=g_ytilde/gamma_hat; pyw_ytilde=(alpha*delta_k)^(-1)*Psi_1*ik_ytilde; wage_ytilde=1-alpha; % Consumption ratios cidc_c=(gamma_idc*c_ytilde)^(-1)*(gamma_idc*wage_ytilde-gamma_idc*hidc_h*ih_ytilde-(R_bidc_ss/pi_ss - 1)*bidc_ytilde - gamma_idc*t_ytilde); cifc_c=(gamma_ifc*c_ytilde)^(-1)*(gamma_ifc*wage_ytilde-gamma_ifc*hifc_h*ih_ytilde-(R_bifc_ss/pi_ss - 1)*sbifc_ytilde - gamma_ifc*t_ytilde); ce_c=(gamma_e*c_ytilde)^(-1)*(pyw_ytilde-ik_ytilde-wage_ytilde+(1 - R_be_ss/pi_ss)*be_ytilde); cp_c=(1-gamma_idc*cidc_c-gamma_ifc*cifc_c-gamma_e*ce_c)/gamma_p; cp_ytilde=cp_c*c_ytilde; cidc_ytilde=cidc_c*c_ytilde; cifc_ytilde=cifc_c*c_ytilde; ce_ytilde=ce_c*c_ytilde; % Estimated parameters rho_h=0.6; std_h=0.01; rho_midc=0.6; std_midc=0.01; rho_mifc=0.6; std_mifc=0.01; rho_me=0.6; std_me=0.01; rho_a=0.6; std_a=0.01; rho_vidc=0.6; std_vidc=0.01; rho_vifc=0.6; std_vifc=0.01; rho_ve=0.6; std_ve=0.01; rho_varrho=0.6; std_varrho=0.01; rho_g=0.6; std_g=0.01; std_r=0.01; %% The DSGE Model (linear version) model(linear); % =========== Patient households =========== % 1 Marginal utility uc_p= -(sigma_c/(1-zeta_c))*(c_p - zeta_c*c_p(-1)); % 2 Euler equation uc_p= uc_p(+1) + R_d - pi(+1); % 3 Housing demand sigma_h*h_p = -uc_p - q_h + ((beta_p*(1-delta_h))/(1-beta_p*(1-delta_h)))*(pi_hh(+1)-R_d)+ eh; % 4 Housing price inflation pi_hh = q_h- q_h(-1) + pi; % =========== IDC households =========== % 5 Marginal utility uc_idc= -(sigma_c/(1-zeta_c))*(c_idc - zeta_c*c_idc(-1)); % 6 Housing demand (1-beta_idc*(1-delta_h)+(1-delta_h)*(beta_idc-pi_ss/R_bidc_ss)*m_idc_ss)*(eh - sigma_h*h_idc) = uc_idc + q_h + (1-delta_h)*m_idc_ss*beta_idc*uc_idc(+1) +(1-delta_h)*((beta_idc-(pi_ss/R_bidc_ss))*m_idc_ss)*(q_h(+1) + m_idc) - (1-delta_h)*m_idc_ss*(pi_ss/R_bidc_ss)*(pi(+1) + uc_idc - R_bidc)-(1-delta_h)*beta_idc*(uc_idc(+1)+q_h(+1)); % 7 Labour supply w = uc_idc - sigma_n*n_idc; % 8 IDC borrowing constraint R_bidc + b_idc = m_idc + q_h(+1) + pi(+1) + h_idc; % 9 IDC budget constraint gamma_idc*(cidc_ytilde)*c_idc + gamma_idc*(hidc_h)*(ih_ytilde)*(q_h + (1/delta_h)*h_idc - ((1-delta_h)/delta_h)*h_idc(-1))+(R_bidc_ss/pi_ss)*(bidc_ytilde)*(R_bidc(-1)+b_idc(-1)-pi)=gamma_idc*wage_ytilde*(w+n_idc)+(bidc_ytilde)*b_idc-gamma_idc*(t_ytilde)*T; % =========== IFC households =========== % 10 Marginal utility uc_ifc= -(sigma_c/(1-zeta_c))*(c_ifc - zeta_c*c_ifc(-1)); % 11 Housing demand (1-beta_ifc*(1-delta_h)+(1-delta_h)*m_ifc_ss*pi_ss*((beta_ifc/pi_star_ss)-(1/R_bifc_ss)))*(eh - sigma_h*h_ifc) = uc_ifc + q_h + (1-delta_h)*m_ifc_ss*beta_ifc*(pi_ss/pi_star_ss)*(uc_ifc(+1)+q(+1)-q-pi_star(+1)+pi(+1)) +(1-delta_h)*m_ifc_ss*pi_ss*((beta_ifc/pi_star_ss)-(1/R_bifc_ss))*(q_h(+1)+m_ifc)-(1-delta_h)*m_ifc_ss*(pi_ss/R_bifc_ss)*(pi(+1) + uc_ifc - R_bifc)-(1-delta_h)*beta_ifc*(uc_ifc(+1)+q_h(+1)); % 12 Labour supply w = uc_ifc - sigma_n*n_ifc; % 13 IFC borrowing constraint R_bifc + l_ifc = m_ifc + q_h(+1) + pi(+1) + h_ifc; % 14 IFC budget constraint gamma_ifc*(cifc_ytilde)*c_ifc + gamma_ifc*(hifc_h)*(ih_ytilde)*(q_h + (1/delta_h)*h_ifc - ((1-delta_h)/delta_h)*h_ifc(-1))+(R_bifc_ss/pi_star_ss)*(sbifc_ytilde)*(R_bifc(-1)+l_ifc(-1)+q-q(-1)-pi_star)=gamma_ifc*wage_ytilde*(w+n_ifc)+(sbifc_ytilde)*l_ifc-gamma_ifc*(t_ytilde)*T; % =========== Entrepreneurs =========== % 15 Marginal utility uc_e = -(sigma_c/(1-zeta_c))*(c_e - zeta_c*c_e(-1)); % 16 Labour demand w = pw + a + alpha*u + alpha*(k(-1)-n); % 17 Capital utilization u = Psi*(pw + a + (1-alpha)*(n-u-k(-1))); % 18 Euler equation q_k = (1-delta_k)*beta_e*(q_k(+1) + (uc_e(+1) - uc_e)) + beta_e*Psi_1*(uc_e(+1) - uc_e + (1/Psi)*u(+1)) + m_e_ss*(1-delta_k)*pi_ss*(((1/R_be_ss)-(beta_e/pi_ss))*(m_e + q_k(+1)) -(1/R_be_ss)*(R_be - pi(+1)) -(beta_e/pi_ss)*(uc_e(+1) - uc_e)); % 19 Borrowing constraint R_be + b_e = m_e + q_k(+1) + pi(+1) + k; % 20 Production function yw = a + alpha*(u + k(-1))+(1-alpha)*n; % 21 Budget constraint gamma_e*(ce_ytilde)*c_e = pyw_ytilde*(pw + yw) + ((1-delta_k)/delta_k)*(ik_ytilde)*(q_k + k(-1)) + (be_ytilde)*b_e - (wage_ytilde)*(w + n)- (1/delta_k)*(ik_ytilde)*(q_k + k)-(Psi_1/delta_k)*(ik_ytilde)*u - (R_be_ss/pi_ss)*(be_ytilde)*(R_be(-1)+b_e(-1)-pi); % =========== Labor packer =========== % 22 Average marginal utility uc = ((gamma_idc*((cidc_c)^(-sigma_c)))/((gamma_idc*(cidc_c)^(-sigma_c))+(gamma_ifc*(cifc_c)^(-sigma_c))+ (gamma_p*(cp_c)^(-sigma_c))))*uc_idc + ((gamma_ifc*((cifc_c)^(-sigma_c)))/((gamma_idc*(cidc_c)^(-sigma_c))+(gamma_ifc*(cifc_c)^(-sigma_c))+ (gamma_p*(cp_c)^(-sigma_c))))*uc_ifc + ((gamma_p*((cp_c)^(-sigma_c)))/((gamma_idc*(cidc_c)^(-sigma_c))+(gamma_ifc*(cifc_c)^(-sigma_c))+ (gamma_p*(cp_c)^(-sigma_c))))*uc_p; % 23 Wages (theta_w/(1-theta_w))*(w-w(-1)+pi-zeta_w*pi(-1)) = ((1-beta_hat*theta_w)/(1+sigma_n*((1+mu_w)/mu_w)))*(sigma_n*n - uc - w) + ((beta_hat*theta_w)/(1-theta_w))*(w(+1)-w+pi(+1)-zeta_w*pi); % =========== Capital goods producers =========== % 24 Capital price i_k = (kappa_k/(1+beta_p))*q_k + (beta_p/(1+beta_p))*i_k(+1) + (1/(1+beta_p))*(i_k(-1)); % 25 Capital accumulation k = (1-delta_k)*k(-1) + delta_k*i_k; % =========== Housing producers =========== % 26 Housing price i_h = (kappa_h/(1+beta_p))*q_h + (beta_p/(1+beta_p))*i_h(+1) + (1/(1+beta_p))*(i_h(-1)); % 27 Housing accumulation h = (1-delta_h)*h(-1) + delta_h*i_h; % =========== Final goods producers =========== % 28 Homogenous final good (this equation is not considered by Brzoza) % y = (eta^(mu/(mu+1)))*((yh_y)^(1/(mu+1)))*y_h + ((1-eta)^(mu/(mu+1)))*((yf_y)^(1/(mu+1)))*y_f; % 29 Demand for domestic intermediate goods y_h = -((1+mu)/mu)*p_h + y; % 30 Demand for imported intermediate goods y_f = -((1+mu)/mu)*p_f + y; % 31 Inflation pi = (1-eta)*((p_f_ss)^(-1/mu))*(pi_f+p_f(-1)) + (eta)*((p_h_ss)^(-1/mu))*(pi_h+p_h(-1)); % =========== Domestic retailers =========== % 32 Domestic goods inflation pi_h = pi + p_h - p_h(-1); % 33 Domestic goods prices (theta_h/(1+theta_h))*(p_h + pi - p_h(-1) - zeta_h*pi(-1))=(1-beta_p*theta_h)*(pw-p_h) + (beta_p*theta_h/(1-theta_h))*(p_h(+1) - p_h + pi(+1) - zeta_h*pi); % =========== Importing retailers =========== % 34 Imported goods inflation pi_f = pi + p_f - p_f(-1); % 35 Imported goods prices (theta_f/(1+theta_f))*(p_f + pi - p_f(-1) - zeta_f*pi(-1))=(1-beta_p*theta_f)*(q-p_f) + (beta_p*theta_f/(1-theta_f))*(p_f(+1) - p_f + pi(+1) - zeta_f*pi); % =========== Exporting retailers =========== % 36 Demand for exported intermediate goods y_h_star = - ((1+mu_h_star)/mu_h_star)*p_h_star + y_star; % 37 Exported goods inflation pi_h_star = pi_star + p_h_star - p_h_star(-1); % 38 Exported goods prices (theta_h_star/(1+theta_h_star))*(p_h_star + pi_star - p_h_star(-1) - zeta_h_star*pi_star(-1))=(1-beta_p*theta_h_star)*(pw-q-p_h_star)+(beta_p*theta_h_star/(1-theta_h_star))*(p_h_star(+1)-p_h_star+pi_star(+1)- zeta_h_star*pi_star); % =========== Banking sector =========== % 39 First order conditions R_bidc = R - (kappa_idc / R_ss) * ((v_idc_ss)^3)* (k_b - b_idc) + (kappa_idc / R_ss) * ((v_idc_ss)^3)* v_idc; // 40 R_bifc = R - (kappa_ifc / R_ss) * ((v_ifc_ss)^3)* (k_b - l_ifc) + (kappa_ifc / R_ss) * ((v_ifc_ss)^3)* v_ifc; // 41 R_be = R - (kappa_e / R_ss) * ((v_e_ss)^3)* (k_b - b_e) + (kappa_e / R_ss) * ((v_e_ss)^3)* v_idc; // 42 R_d = R; % 43 Bank balance sheet condition k_b = (1/v_idc_ss)*b_idc + (1/v_ifc_ss)*l_ifc + (1/v_e_ss)*b_e - D_kb*d_p - lstar_kb*l_star; % 44 Bank capital accumulation pi_ss*(k_b + pi) = (1 - delta_b)*k_b(-1) + (pi_ss - (1-delta_b))*j_b(-1); % 45 Bank profits ((pi_ss-(1-delta_b))/omega_b) * j_b = R_ss*((1/v_idc_ss)*R_bidc + (1/v_ifc_ss)*R_bifc + (1/v_e_ss)*R_be - D_kb*R - (lstar_kb*(pi_star_ss/pi_ss))*R_bstar) + (R_ss-1)*((1/v_idc_ss)*b_idc + (1/v_ifc_ss)*(l_ifc) + (1/v_e_ss)*b_e - D_kb*d_p) - ((R_ss*pi_star_ss/pi_ss)-1)*lstar_kb*l_star; % 46 UIP condition R - R_bstar = q(+1) - q + pi(+1) - pi_star(+1); % =========== Foreign sector =========== % 47 y_star = rho_y_star * y_star(-1) + e_y_star; % 48 pi_star = rho_pi_star * pi_star(-1) + e_pi_star; % 49 Rf_star = rho_rf_star * Rf_star(-1) + e_rf_star; % 50 Interest rate premium R_bstar = (Rf_star_ss / R_bstar_ss) * Rf_star + (Psi_b/R_bstar_ss)*(l_star - y_tilde) + (1 - (Rf_star_ss / R_bstar_ss))*varrho; % =========== Government =========== % 51 Government expenditures g = rho_g*g(-1) + e_g; % 52 Government budget constraint g=T; % =========== Central bank =========== // 53 R = phi_r*R(-1) + (1-phi_r)*(phi_pi*pi + phi_y*y_tilde) + e_r; % =========== Market clearing =========== % 54 Final goods market clearing condition (y_ytilde)*y = (c_ytilde)*c + (ik_ytilde)*i_k + (ih_ytilde)*i_h + (g_ytilde)*g + (Psi_1/delta_k)*(ik_ytilde)*u; % 55 Consumption aggregation c = gamma_p*(cp_c)*c_p + gamma_idc*(cidc_c)*c_idc + gamma_ifc*(cifc_c)*c_ifc + gamma_e*(ce_c)*c_e; % 56 Intermediate homegenous goods market clearing yw = (yh_share)*y_h + (yhstar_share)*y_h_star; % 57 Housing market clearing h(-1) = gamma_p*(hp_h)*h_p + gamma_idc*(hidc_h)*h_idc + gamma_ifc*(hifc_h)*h_ifc; % 58 Balance of payments (p_f_ss*yf_ytilde)*(p_f + y_f) + (lstar_ytilde)*(R_ss/pi_ss)*(q - q(-1) - pi_star + l_star(-1) + R_bstar(-1)) = (qyhstar_ytilde)*(q+ p_h_star + y_h_star) + (lstar_ytilde)*l_star; % 59 GDP definition y_tilde = (y_ytilde)*y + (qyhstar_ytilde)*(p_h_star + y_h_star + q) - (p_f_ss*yf_ytilde)*(p_f + y_f); % =========== Exogenous processes =========== // 60 eh = rho_h*eh(-1) + eh; // 61 m_idc = rho_midc*m_idc(-1) + e_midc; // 62 m_ifc = rho_mifc*m_ifc(-1) + e_mifc; // 63 m_e = rho_me*m_e(-1) + e_me; // 64 a = rho_a*a(-1) + e_a; // 65 v_idc = rho_vidc*v_idc(-1) + e_vidc; // 66 v_ifc = rho_vifc*v_ifc(-1) + e_vifc; // 67 v_e = rho_ve*v_e(-1) + e_ve; // 68 varrho = rho_varrho*varrho(-1) + e_varrho; end; %% Initial Values (check ss values of somes variables) initval; uc_p=0; c_p=0; h_p=0; d_p=0; eh=0; uc_idc=0; c_idc=0; h_idc=0; b_idc=0; m_idc=0; n_idc=0; uc_ifc=0; c_ifc=0; h_ifc=0; l_ifc=0; m_ifc=0; n_ifc=0; uc_e=0; c_e=0; k=0; b_e=0; m_e=0; yw=0; pw=0; a=0; u=0; n=0; w=0; uc=0; q_k=0; i_k=0; q_h=0; i_h=0; h=0; pi_hh=0; y=0; pi=0; y_h=0; p_h=0; pi_h=0; y_f=0; p_f=0; pi_f=0; y_h_star=0; p_h_star=0; pi_h_star=0; l_star=0; k_b=0; j_b=0; R_bidc=0; R_bifc=0; R_be=0; R_d=0; R_bstar=0; v_idc=0; v_ifc=0; v_e=0; y_star=0; pi_star=0; Rf_star=0; varrho=0; g=0; T=0; R=0; q=0; y_tilde=0; c=0; end; %% Declaring shocks parametrisation shocks; var e_h; stderr std_h; var e_midc; stderr std_midc; var e_mifc; stderr std_mifc; var e_me; stderr std_me; var e_a; stderr std_a; var e_vidc; stderr std_vidc; var e_vifc; stderr std_vifc; var e_ve; stderr std_ve; var e_varrho; stderr std_varrho; var e_y_star; stderr std_y_star; var e_pi_star; stderr std_pi_star; var e_rf_star; stderr std_rf_star; var e_g; stderr std_g; var e_r; stderr std_r; end; %% Final Commands resid(1); steady; check; model_diagnostics; stoch_simul(irf=10);