% This .mod file solves in Dynare the model from my paper ''Welfare gains from unvonventional monetary policy at the zero lower bound'' % Linear Quadratic Approach % (c) Nikolas Kontogiannis, Department of Economics, University of Leicester %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Necessary Notation: % For any generic variable X_t: % X_t denotes the level of variable X at time t. % X_flext denotes the level of variable X at time t, when prices are % flexible and output is at its natural level. % X_ss denotes the steady state. % X_hat = logX_t - logX_ss, % X_flex = logX_flext - logX_ss, % X_tilde = X_hat - X_flex, is the log-deviation from the flexible price % equilibrium %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%% Declaration of Variables %%%%%%%%%%%%%%%%%%%%%%%%% var %%%%%%%%%%%%%% HATS (log-deviations from the steady-state) %%%%%%%%%%%%%%%% R_hat % real interest rate QNOM_hat % nominal interest rate Pi % inflation, given in absolute deviaton from its steady-state (See Walsh chapter 2) Phi_hat % real marginal cost A_hat % productivity Psi_hat % quality of capital Spread_hat % the spread or the difference between the real interest of lending and borrowing (natural or Wicksellian rates) %%%%%%%%% TILDES (log-deviations from flexible price equilibrium) %%%%%%%%% Y_tilde % output I_tilde % investment (new capital) K_tilde % capital stock R_tilde % real interest rate log-deviation from the Wicksellian interest Z_tilde % gross profit per unit of capital use Q_tilde % capital (asset) price D_tilde % households' deposits S_tilde % total securities issued NW_tilde % banks' net worth (capital) RK_tilde % real interest of banks' lending Theta_tilde % leverage ratio, private intermediation VD_tilde % banks' marginal value from lending Mu_tilde % banks' excess value of lending (marginal benefit from lending - marginal cost from borrowing) Omega_tilde % stochastic marginal value of net worth SP_tilde % securities issued privately SG_tilde % securities issued by government Varrho_tilde % unconventional policy instrument ThetaC_tilde % leverage ratio from total intermediation (private and governmental) Spread_tilde % the spread or the difference between the real interest of lending and borrowing KAUXLAG_tilde % auxiliary variable for capital to substitute K (-1) in the welfare criterion % FLEXIS (flexible price equilibrium log-deviation from the steady-state)%% Y_flex % flexible price equilibrium level of output. This is the natural level of output since the steady-state is efficient I_flex % natural level of investment K_flex % natural level of capital R_flex % Wicksellian real interest rate (See Walsh chapter 8) Z_flex % gross profits per unit of capital use Q_flex % capital (asset) price associated with investment' natural level D_flex % households' deposits S_flex % total securities issued NW_flex % banks' net worth (capital) RK_flex % real interest of banks' lending Theta_flex % leverage ratio, private intermediation VD_flex % banks' marginal value from lending Mu_flex % banks' excess value of lending (marginal benefit from lending - marginal cost from borrowing) Omega_flex % stochastic marginal value of net worth SP_flex % securities issued privately SG_flex % securities issued by government Varrho_flex % unconventional policy instrument ThetaC_flex % leverage ratio from total intermediation (private and governmental) Spread_flex % the spread or the difference between the real interest of lending and borrowing (natural or Wicksellian rates) YAUXLEAD_flex IAUXLEAD_flex; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%% Declaration of the Shocks %%%%%%%%%%%%%%%%%%%%%%%% varexo E_A % productivity shock E_Psi; % capital quality shock %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%% Declaration of the Parameters %%%%%%%%%%%%%%%%%%%% parameters %%%% Because the model is linearised by hand, the steady-state of %%%% the level of variables is declared as parameter. %%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%% Steady-State of levels, expressed as parameters %%%%%%%%%%%% C_ss % consumption R_ss % real interest rate N_ss % labour or measure of participation to work QNOM_ss % nominal interest rate Phi_ss % real marginal cost Y_ss % output of final goods A_ss % productivity K_ss % capital stock I_ss % investment (new capital) Psi_ss % quality of capital Z_ss % gross profits per unit of capital use Q_ss % capital (asset) price D_ss % households' deposits S_ss % total securities issued NW_ss % banks' net worth (capital) RK_ss % real interest of banks' lending Theta_ss % leverage ratio, private intermediation VD_ss % banks' marginal value from lending Mu_ss % banks' excess value of lending (marginal benefit from lending - marginal cost from borrowing) Omega_ss % stochastic marginal value of net worth SP_ss % securities issued privately SG_ss % securities issued by government Varrho_ss % unconventional policy instrument Spread_ss % the spread or the difference between the real interest of lending and borrowing NWK_ss % the steady state of the ratio NW/K (useful to find the steady-state) DK_ss % the steady state of the ratio D/K (useful to find the steady-state) YK_ss % the steady state of the ratio Y/K (useful to find the steady-state) CK_ss % the steady state of the ratio C/K (useful to find the steady-state) %%%%%%%%%%%%%%%%%%%%%%%%% Structural Parameters %%%%%%%%%%%%%%%%%%%%%%%%%%% beta % static discount factor alpha % capital share varphi % Frisch inverse elasticity of labour delta % depreciation of capital gamma % elasticity of substitution among the differentiated goods delta_p % elasticity of inflation wrt the real marginal cost M % markup chi % parameter in convex adjustment cost function omega % degree of nominal price rigidity, to match quarterly data rho_a % degree of autocorrelation, productivity shock rho_psi %d egree of autocorrelation, capital quality shock sigma %survival rate of bankers xi % transfer to entering bankers, perfect interbank lambda % fraction of divertable assets %%%%%%%%%%%%%%%%%%%%%%%%%%% Monetary Policy Parameters %%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%% Conventional Monetary Policy %%%%%%%%%%%%%%%%%%%%%%% kappa_y % elasticity of nominal interest rate w.r.t. output kappa_pi % elasticity of nominal interest rate w.r.t. inflation rho_q %%%%%%%%%%%%%%%%%%%% Unconventional Monetary Policy %%%%%%%%%%%%%%%%%%%%%%% %kappa_varrhoH % strength of unconventional monetary policy, the goal is the spread_hat kappa_varrhoF % strength of unconventional monetary policy, the goal is the spread_flex kappa_varrhoT % strength of unconventional monetary policy, the goal is the spread_tilde %%%%%%%%%%%%%%%%%%%% Weights of the central bank's welfare criterion %%%%%%%%%%%%%%%%%%%% (objective function) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% delta_1 delta_2 delta_3 delta_4 delta_5 delta_6 delta_7 delta_8; %%% Declaration of the parameter and the steady-state (levels) values %%%%% %%% Notice that the steady-state has been solved with the use of Fsolve %%% (matlab) for another model. Since I have not changed the value of %%% lambda, here I copy these values. IF someone wants to change lambda %%% manually, then the Fsolve must be used to calculate the new %%% steady-state, since the value of mu will change. Here, I choose lambda %%% to hit a steady state of spread equal to 0.0025 (quarterly) %%%%%%%%%%% %%%%%%%%%%%%%%%%%%% Standard NK model parameters calibration %%%%%%%%%%%%%% beta=0.99; % static discount factor alpha=0.33; %capital share varphi=0; %Frisch inverse elasticity of labour delta=0.025; %depreciation of capital gamma=6; %elasticity of substitution among the differentiated goods (to match the markup) M=gamma/(gamma-1); %markup omega=0.75; %degree of nominal price rigidity, to match quarterly data delta_p=((1-omega*beta)*(1-omega)/(omega)); %elasticity of inflation wrt the real marginal cost chi=1; % parameter in convex adjustment cost function %%%%%%%%%%%% Financial intermediation model parameters calibration %%%%%%%% sigma=0.97; %survival rate of bankers xi=0.003; %transfer to entering bankers, perfect interbank lending lambda=0.383; %fraction of divertable assets (to hit the spread of 100 basis points) %%%%%%%%%%% Steady-state (levels) calibration. Given as parameters as the model is log-linearised by hand %%%%%%% R_ss=1/beta; % the SS from euler equation. Useful to find the R_ss NWK_ss=0.2683; % from Fsovle. See above Omega_ss=1.4146; % from Fsolve. See above. RK_ss=1.0126; % from Fsolve. lambda was chosen to hit the spread_ss =0.0025 quarterly Theta_ss=3.7269; % from Fsolve; Mu_ss= 0.0034; % from Fsolve. Notice that the expression for mu_ss is quadratic. But mu=max[>0, 0] so chose the positive value DK_ss=1-NWK_ss; % from the ss equations of the financial intermediation Spread_ss=RK_ss-R_ss; % chosen to hit a target of 0.0025 QNOM_ss=R_ss-1; % Fisher equation Psi_ss=1; % steady-state of quality of capital shock A_ss=1; % steady-state of productivity shock Q_ss=1; % price of new-capital good (tobin's q) steady-state, calculated from capital good producers optimal decision Phi_ss=1/M; % price flexibility value of real marginal cost (inverse of mark-up) VD_ss=Omega_ss; % at the steady state VD = Omega Z_ss=(RK_ss - (1-delta))*Q_ss; YK_ss=(1/(alpha*Phi_ss))*Z_ss; CK_ss=YK_ss - delta; N_ss=(Phi_ss*(1-alpha)*YK_ss*(CK_ss)^(-1))^(1/(1+varphi)); K_ss=(N_ss)*(YK_ss)^((-1/(1-alpha))); I_ss=delta*K_ss; C_ss=CK_ss*K_ss; Y_ss=YK_ss*K_ss; S_ss=K_ss; NW_ss=NWK_ss*K_ss; D_ss=DK_ss*K_ss; Varrho_ss=0.1; SP_ss=(1-Varrho_ss)*S_ss; SG_ss=S_ss-SP_ss; %%%%%%%%%%%%%%%%%%%% Policy parameters calibration %%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%% Conventional policy calibration %%%%%%%%%%%%%%%%%%%% kappa_pi=1.5; kappa_y=0.5/4; rho_q=0.2; %%%%%%%%%%%%%%%%%%%% Unconventional policy calibration %%%%%%%%%%%%%%%%%%%% kappa_varrhoT=100; %kappa_varrhoH=0; kappa_varrhoF=100; %%%%%%%%%%%%%%%%%%%%% autocorrelation of the shocks %%%%%%%%%%%%%%%%%%%%%% rho_a=0.95; rho_psi=0.66; %%%%%%%%%%%%%%%%%%%% Calculation of the weights of the central bank's welfare criterion %%%%%%%%%%%%%%%%%%%%(objective function). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% delta_1 = (gamma/2)*((delta_p)/(1-delta_p)); delta_2 = (1/2)*(Y_ss/C_ss)*(((alpha+varphi)/(1-alpha))); delta_3 = (1/2)*(I_ss*Y_ss)/(C_ss^2); delta_4 = ((alpha^2)*(1+varphi)*Y_ss)/(2*(1-alpha)*C_ss); delta_5 = (alpha*Y_ss/C_ss)*((1+varphi)/(1-alpha)); delta_6 = 2*delta_3; delta_7 = (K_ss*Y_ss)/(C_ss^2); delta_8 = (alpha*Y_ss)/C_ss; model (linear); %%%%%%%%%%%%%%%% Standard New Keynesian model with capital %%%%%%%%%%%%%%%% Y_tilde = Y_tilde(+1) - (I_ss/Y_ss)*(I_tilde(+1) - I_tilde) - R_tilde; % Dynamic IS expressed in tilde R_tilde = R_hat - R_flex; R_flex = Y_flex(+1) - Y_flex - (I_ss/Y_ss)*(I_flex(+1) - I_flex); % Expression for Wicksellian interest rate R_hat = QNOM_hat - Pi(+1); % Fisher equation (((alpha+varphi)/(1-alpha)) + (Y_ss/C_ss))*Y_flex = (I_ss/C_ss)*I_flex + ((alpha*(1+varphi))/(1-alpha))*K_flex(-1) + ((1+varphi)/(1-alpha))*A_hat; % Flexible price equilibrium Pi = beta*Pi(+1) + delta_p*Phi_hat; % New Keynesian Phillips Curve Phi_hat = (((alpha+varphi)/(1-alpha)) + (Y_ss/C_ss))*Y_tilde - (I_ss/C_ss)*I_tilde - ((alpha*(1+varphi))/(1-alpha))*K_tilde(-1); % Link of real marginal cost with flexi price equil K_tilde = delta*I_tilde + (1 - delta)*K_tilde(-1); % Law of motion of capital tilde K_flex = Psi_hat(+1) + delta*I_flex + (1 - delta)*K_flex(-1); % Law of motion of capital flexi Z_tilde = Phi_hat + Y_tilde - K_tilde(-1); Z_flex = Y_flex - K_flex(-1); Q_tilde = chi*(I_tilde - I_tilde(-1)) - chi*beta*(I_tilde(+1) - I_tilde) - Q_flex + chi*(I_flex - I_flex(-1)) - chi*beta*(I_flex(+1) - I_flex) ; % Profit maximising for capital producers price Q_flex = chi*(I_flex - I_flex(-1)) - chi*beta*(I_flex(+1) - I_flex); % Profit maximising for capital producers price KAUXLAG_tilde = K_tilde(-1); YAUXLEAD_flex = Y_flex(+1); IAUXLEAD_flex = I_flex(+1); A_hat = rho_a*A_hat(-1) - E_A; % AR(1) productivity. Notice the declaration of a negative shock Psi_hat = rho_psi*Psi_hat(-1) - E_Psi; % AR(1) capital quality. Notice the declaration of a negative shock %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Monetary Policy %%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Conventional %%%%%%%%%%%%%%%%%%%%%%%%%%%% %Taylor rule should be removed when calculate ramsey/discretion policy% %QNOM_hat = rho_q*QNOM_hat(-1) + (1-rho_q)*(kappa_pi*Pi + kappa_y*Y_tilde); % Taylor rule %%%%%%%%%%%%%%%%%%%%%%%%%%% FLEX Financial Intermediation %%%%%%%%%%%%%%%%% D_flex = (Q_ss*SP_ss/D_ss)*Q_flex + (Q_ss*SP_ss/D_ss)*SP_flex - (NW_ss/D_ss)*NW_flex; % Deposits NW_flex = ((sigma+xi)*(RK_ss*Q_ss*SP_ss)/NW_ss)*(RK_flex + Q_flex(-1) + SP_flex(-1)) - (R_ss*D_ss/NW_ss)*(R_flex + D_flex(-1)); % Balance sheet Theta_flex = VD_flex + (Mu_ss/(lambda - Mu_ss))*Mu_flex; % Leverage ratio (private) VD_flex = Omega_flex (+1); Mu_flex = ((beta*Omega_ss*RK_ss)/Mu_ss)*(RK_flex(+1) - R_flex(+1)) + Omega_flex(+1); Omega_flex = ((sigma*VD_ss)/Omega_ss)*VD_flex + ((sigma*Theta_ss*Mu_ss)/Omega_ss)*(Theta_flex + Mu_flex); S_flex = K_flex; % Equilibrium in security market S_flex = ThetaC_flex + NW_flex - Q_flex; RK_flex = Psi_hat - Q_flex(-1) + (Psi_ss*Z_ss/RK_ss*Q_ss)*Z_flex + ((1-delta)*Psi_ss/RK_ss)*Q_flex; S_flex = (SP_ss/S_ss)*SP_flex + (SG_ss/S_ss)*SG_flex; SG_flex = Varrho_flex + S_flex; Spread_flex = RK_flex(+1) - R_flex(+1); ThetaC_flex = Theta_flex + (Varrho_ss/(1-Varrho_ss))*Varrho_flex; % Leverage (Total intermediation) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Monetary Policy %%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Unconventional %%%%%%%%%%%%%%%%%%%%%%%%%% Varrho_flex = kappa_varrhoF*(RK_flex(+1) - R_flex(+1)); %%%%%%%%%%%%%%%%%%%%%%%%%%% TILDE Financial Intermediation %%%%%%%%%%%%%%%%% D_tilde = (Q_ss*SP_ss/D_ss)*Q_tilde + (Q_ss*SP_ss/D_ss)*SP_tilde - (NW_ss/D_ss)*NW_tilde; % Deposits NW_tilde = ((sigma+xi)*(RK_ss*Q_ss*SP_ss)/NW_ss)*(RK_tilde + Q_tilde(-1) + SP_tilde(-1)) - (R_ss*D_ss/NW_ss)*(R_tilde + D_tilde(-1)); % Balance sheet Theta_tilde = VD_tilde + (Mu_ss/(lambda - Mu_ss))*Mu_tilde; % Leverage ratio (private) VD_tilde = Omega_tilde (+1); Mu_tilde = ((beta*Omega_ss*RK_ss)/Mu_ss)*(RK_tilde(+1) - R_tilde(+1)) + Omega_tilde(+1); Omega_tilde = ((sigma*VD_ss)/Omega_ss)*VD_tilde + ((sigma*Theta_ss*Mu_ss)/Omega_ss)*(Theta_tilde + Mu_tilde); S_tilde = K_tilde; % Equilibrium in security market S_tilde = ThetaC_tilde + NW_tilde - Q_tilde; RK_tilde = - Q_tilde(-1) + (Psi_ss*Z_ss/RK_ss*Q_ss)*Z_tilde + ((1-delta)*Psi_ss/RK_ss)*Q_tilde; S_tilde = (SP_ss/S_ss)*SP_tilde + (SG_ss/S_ss)*SG_tilde; SG_tilde = Varrho_tilde + S_tilde; Spread_tilde = RK_tilde(+1) - R_tilde(+1); Spread_hat = Spread_tilde + Spread_flex; ThetaC_tilde = Theta_tilde + (Varrho_ss/(1-Varrho_ss))*Varrho_tilde; % Leverage (Total intermediation) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Monetary Policy %%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Unconventional %%%%%%%%%%%%%%%%%%%%%%%%%% Varrho_tilde = kappa_varrhoT*(RK_tilde(+1) - R_tilde(+1)); end; /* %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% STEADY STATE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% initval; R_hat=0; % real interest rate QNOM_hat=0; % nominal interest rate Pi=0; % inflation, given in absolute deviaton from its steady-state (See Walsh chapter 2) Phi_hat=0; % real marginal cost A_hat=0; % productivity Psi_hat=0; % quality of capital Spread_hat=0; % the spread or the difference between the real interest of lending and borrowing %%%%%%%%% TILDES (log-deviations from flexible price equilibrium) %%%%%%%%% Y_tilde=0; % output I_tilde=0; % investment (new capital) K_tilde=0; % capital stock R_tilde=0; % real interest rate log-deviation from the Wicksellian interest Z_tilde=0; % gross profit per unit of capital use Q_tilde=0; % capital (asset) price D_tilde=0; % households' deposits S_tilde=0; % total securities issued NW_tilde=0; % banks' net worth (capital) RK_tilde=0; % real interest of banks' lending Theta_tilde=0; % leverage ratio, private intermediation VD_tilde=0; % banks' marginal value from lending Mu_tilde=0; % banks' excess value of lending (marginal benefit from lending - marginal cost from borrowing) Omega_tilde=0; % stochastic marginal value of net worth SP_tilde=0; % securities issued privately SG_tilde=0; % securities issued by government Varrho_tilde=0; % unconventional policy instrument ThetaC_tilde=0; % leverage ratio from total intermediation (private and governmental) Spread_tilde=0; % the spread or the difference between the real interest of lending and borrowing KAUXLAG_tilde=0; % auxiliary variable for capital to substitute K (-1) in the welfare criterion % FLEXIS (flexible price equilibrium log-deviation from the steady-state)%% Y_flex=0; % flexible price equilibrium level of output. This is the natural level of output since the steady-state is efficient I_flex=0; % natural level of investment K_flex=0; % natural level of capital R_flex=0; % Wicksellian real interest rate (See Walsh chapter 8) Z_flex=0; % gross profits per unit of capital use Q_flex=0; % capital (asset) price associated with investment' natural level D_flex=0; % households' deposits S_flex=0; % total securities issued NW_flex=0; % banks' net worth (capital) RK_flex=0; % real interest of banks' lending Theta_flex=0; % leverage ratio, private intermediation VD_flex=0; % banks' marginal value from lending Mu_flex=0; % banks' excess value of lending (marginal benefit from lending - marginal cost from borrowing) Omega_flex=0; % stochastic marginal value of net worth SP_flex=0; % securities issued privately SG_flex=0; % securities issued by government Varrho_flex=0; % unconventional policy instrument ThetaC_flex=0; % leverage ratio from total intermediation (private and governmental) Spread_flex=0; % the spread or the difference between the real interest of lending and borrowing (natural or Wicksellian rates) YAUXLEAD_flex=0; IAUXLEAD_flex=0; end; */ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% SHOCKS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% shocks; var E_Psi; stderr 0.05; /* var E_A; stderr 0.00624; var E_Psi, E_A = 1*0.05*0.00624; */ end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% SOLUTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%% OPTIMAL MONETARY POLICY %%%%%%%%%%%%%%%%%%%%% planner_objective (delta_1*(Pi^2) + delta_2*(Y_tilde^2) + delta_3*(I_tilde^2) + delta_4*(KAUXLAG_tilde^2) - delta_5*Y_tilde*KAUXLAG_tilde - delta_6*Y_tilde*I_tilde - delta_7*K_tilde*Y_flex + delta_7*K_tilde*I_flex + delta_7*K_tilde*YAUXLEAD_flex - delta_7*K_tilde*IAUXLEAD_flex - delta_8*KAUXLAG_tilde*Y_flex + delta_8*KAUXLAG_tilde*I_flex); /* %%%%%%%%%%%%%%%%%%%%%%%%%%%% Optimal Commitment %%%%%%%%%%%%%%%%%%%%%%%%%%% ramsey_policy(planner_discount=0.99)Y_tilde Pi I_tilde K_tilde; oo_.planner_objective_value */ %%%%%%%%%%%%%%%%%%%%%%%%%%%% Optimal Discretion %%%%%%%%%%%%%%%%%%%%%%%%%%% discretionary_policy(planner_discount=0.99, instruments=(QNOM_hat)); oo_.planner_objective_value /* %%%%%%%%%%%%%%%%%%%%%%%%%% Optimal simple rule %%%%%%%%%%%%%%%%%%%%%%%%%%%% check; optim_weights; Pi delta_1; Y_tilde delta_2; I_tilde delta_3; KAUXLAG_tilde delta_4; Y_tilde, KAUXLAG_tilde -delta_5; Y_tilde, I_tilde -delta_6; K_tilde, Y_flex -delta_7; K_tilde ,I_flex delta_7; K_tilde, YAUXLEAD_flex delta_7; K_tilde, IAUXLEAD_flex -delta_7; KAUXLAG_tilde, Y_flex -delta_8; KAUXLAG_tilde, I_flex delta_8; end; osr_params kappa_pi kappa_y; check; osr Pi; oo_.osr.objective_function %oo_.var */ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% IMPULSE RESPONSES %%%%%%%%%%%%%%%%%%%%%%%% /* check; stoch_simul(order=1,nomoments,periods=3000,irf=40)Spread_hat Spread_tilde Spread_flex Y_tilde Pi K_tilde I_tilde SG_tilde SP_tilde S_tilde NW_tilde NW_flex D_tilde D_flex QNOM_hat Varrho_tilde Varrho_flex; */