636 lines
16 KiB
Modula-2
636 lines
16 KiB
Modula-2
//This mod-file tests the value of the objective function in the presence of non-stationary variables
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Var
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p_U_Hat
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pi_U_Hat
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r_Hat
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r_Gap
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r_Eff
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realrate_U_Hat
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realrate_U_Eff
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realrate_U_Gap
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c_U_Gap
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c_U_Eff
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c_U_Hat
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g_U_Gap
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g_U_Eff
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g_U_Hat
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y_U_Gap
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y_U_Eff
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y_U_Hat
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l_U_Gap
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l_U_Eff
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l_U_Hat
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a_U_Hat
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p_A_Hat
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pc_A_Hat
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tt_A_Hat
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tt_A_Gap
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tt_A_Eff
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pi_A_Hat
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pic_A_Hat
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c_A_Gap
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c_A_Eff
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c_A_Hat
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g_A_Gap
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g_A_Eff
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g_A_Hat
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realrate_A_Hat
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l_A_Gap
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l_A_Eff
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l_A_Hat
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muW_A_Hat
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y_A_Gap
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y_A_Eff
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y_A_Hat
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a_A_Hat
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mc_A_Hat
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tau_A_Hat
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tau_A_Gap
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tau_A_Eff
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Kdebt_A
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p_B_Hat
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pc_B_Hat
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tt_B_Hat
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tt_B_Gap
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tt_B_Eff
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pi_B_Hat
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pic_B_Hat
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c_B_Gap
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c_B_Eff
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c_B_Hat
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g_B_Gap
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g_B_Eff
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g_B_Hat
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realrate_B_Hat
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l_B_Gap
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l_B_Eff
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l_B_Hat
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muW_B_Hat
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y_B_Gap
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y_B_Eff
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y_B_Hat
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a_B_Hat
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mc_B_Hat
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tau_B_Hat
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tau_B_Gap
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tau_B_Eff
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Kdebt_B
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;
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%DECLARATION OF EXOGENOUS VARIABLES%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Varexo
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eps_muW_A
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eps_a_A
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eps_muW_B
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eps_a_B
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;
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%DECLARATION OF PARAMETERS%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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parameters
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n
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alpha
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beta
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rho
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lambdaA
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lambdaB
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sigma
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chi
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psi
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epsilon
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muP
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gamma
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ell
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phi_GY
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phi_caps
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theta_A
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theta_B
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phi_A
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phi_B
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%%%%%%
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//Rule Parameters
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ruleR_U_y
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ruleR_U_pi
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ruleR_U_debt
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ruleG_A_y
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ruleG_A_tt
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ruleG_A_debt
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ruleG_B_y
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ruleG_B_tt
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ruleG_B_debt
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ruleT_A_y
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ruleT_A_tt
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ruleT_A_debt
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ruleT_B_y
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ruleT_B_tt
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ruleT_B_debt
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%%%%%%
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rho_a_A
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rho_a_B
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rho_muW_A
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rho_muW_B
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rho_mp
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r_SS
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muW_SS
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tau_A_SS
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DebtOutput_A_SS
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tau_B_SS
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DebtOutput_B_SS
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;
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%%%%%%%%%%%%%%%%%%%%%%%%
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%%SET PARAMETER VALUES%%
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%%%%%%CALIBRATION%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%
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n = 0.5;
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alpha = 0.4;
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beta = 0.99 ;
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rho = -log(beta);
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lambdaA = 1-(1-n)*alpha;
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lambdaB = 1-n*alpha;
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sigma = 0.4;
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chi = 3;
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psi = 0.4;
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epsilon = 11;
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muP = 1/(epsilon - 1);
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gamma = 4.5;
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ell = 11;
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phi_GY = 0.25;
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phi_caps = alpha*(gamma-(1-alpha)*(-gamma+sigma));
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theta_A = 0.75;
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theta_B = 0.75;
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phi_A = (1 - theta_A*beta)*(1 - theta_A)/(theta_A*(1 + epsilon*chi));
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phi_B = (1 - theta_B*beta)*(1 - theta_B)/(theta_B*(1 + epsilon*chi));
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//Rule Parameters
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ruleR_U_y = 0.5;
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ruleR_U_pi = 1.5;
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ruleR_U_debt = 0;
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ruleG_A_y = 0;
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ruleG_A_tt = 0;
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ruleG_A_debt = -0.05;
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ruleG_B_y = ruleG_A_y;
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ruleG_B_tt = 0;
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ruleG_B_debt = ruleG_A_debt;
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ruleT_A_y = 0;
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ruleT_A_tt = 0;
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ruleT_A_debt = 0.05;
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ruleT_B_y = ruleT_A_y;
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ruleT_B_tt = 0;
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ruleT_B_debt = ruleT_A_debt;
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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rho_a_A = 0.85;
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rho_a_B = 0.85;
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rho_muW_A = 0;
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rho_muW_B = 0;
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rho_mp = 0;
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%% STEADY STATE VALUES %%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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muW_SS = 1/(ell - 1);
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r_SS = log(1/beta);
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DebtOutput_A_SS = 4*0.6;
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DebtOutput_B_SS = 4*0.6;
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tau_A_SS = phi_GY + r_SS*DebtOutput_A_SS;
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tau_B_SS = phi_GY + r_SS*DebtOutput_B_SS;
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model(linear);
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p_U_Hat = n*p_A_Hat + (1-n)*p_B_Hat;
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pi_U_Hat = n*pi_A_Hat + (1-n)*pi_B_Hat;
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c_U_Gap = c_U_Gap(+1)- sigma*(r_Gap - pi_U_Hat(+1));
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realrate_U_Gap = realrate_U_Hat - realrate_U_Eff;
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realrate_U_Eff = ((1 + chi)/(1 + chi*(phi_GY*psi + (1 - phi_GY)*sigma)))*(a_U_Hat(+1) - a_U_Hat);
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realrate_U_Hat = r_Hat - pi_U_Hat(+1);
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r_Eff = ((1 + chi)/(1 + chi*(phi_GY*psi + (1 - phi_GY)*sigma)))*(a_U_Hat(+1) - a_U_Hat);
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r_Hat = r_Gap + r_Eff;
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// Interest rate rule
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r_Gap = ruleR_U_y*y_U_Gap(-1) + ruleR_U_pi*pi_U_Hat(-1) + ruleR_U_debt*(n*Kdebt_A(-1) + (1-n)*Kdebt_B(-1));
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c_U_Gap = n*c_A_Gap + (1-n)*c_B_Gap;
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c_U_Eff = n*c_A_Eff + (1-n)*c_B_Eff;
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c_U_Hat = n*c_A_Hat + (1-n)*c_B_Hat;
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g_U_Gap = n*g_A_Gap + (1-n)*g_B_Gap;
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g_U_Eff = n*g_A_Eff + (1-n)*g_B_Eff;
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g_U_Hat = n*g_A_Hat + (1-n)*g_B_Hat;
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y_U_Gap = n*y_A_Gap + (1-n)*y_B_Gap;
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y_U_Eff = n*y_A_Eff + (1-n)*y_B_Eff;
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y_U_Hat = n*y_A_Hat + (1-n)*y_B_Hat;
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l_U_Gap = n*l_A_Gap + (1-n)*l_B_Gap;
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l_U_Eff = n*l_A_Eff + (1-n)*l_B_Eff;
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l_U_Hat = n*l_A_Hat + (1-n)*l_B_Hat;
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a_U_Hat = n*a_A_Hat + (1-n)*a_B_Hat;
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tt_A_Hat = (p_U_Hat - p_A_Hat)/(1-n);
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pi_A_Hat = p_A_Hat - p_A_Hat(-1);
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pic_A_Hat = pc_A_Hat - pc_A_Hat(-1);
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pic_A_Hat = pi_A_Hat + (1-lambdaA)*(tt_A_Hat - tt_A_Hat(-1));
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c_A_Eff = (((1 + chi)*sigma)/(1 + chi*(phi_GY*psi + (1 - phi_GY)*sigma)))*a_U_Hat + (((1 - alpha)*(1 + chi)*sigma)/(1 + chi*(phi_GY*psi + (1 - phi_GY)*(gamma + (sigma - gamma)*(1 - 2*alpha + alpha*alpha)))))*(a_A_Hat - a_U_Hat);
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g_A_Eff = (((1 + chi)*psi)/(1 + chi*(phi_GY*psi + (1 - phi_GY)*sigma)))*a_U_Hat + (((1 + chi)*psi)/(1 + chi*(phi_GY*psi + (1 - phi_GY)*(gamma + (sigma - gamma)*(1 - 2*alpha + alpha*alpha)))))*(a_A_Hat - a_U_Hat);
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y_A_Eff = (((1 + chi)*(phi_GY*psi + (1 - phi_GY)*sigma))/(1 + chi*(phi_GY*psi + (1 - phi_GY)*sigma)))*a_U_Hat + (((1 + chi)*(phi_GY*psi + (1 - phi_GY)*(gamma + (sigma - gamma)*(1 - 2*alpha + alpha*alpha))))/(1 + chi*(phi_GY*psi + (1 - phi_GY)*(gamma + (sigma - gamma)*(1 - 2*alpha + alpha*alpha)))))*(a_A_Hat - a_U_Hat);
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l_A_Eff = y_A_Eff - a_A_Hat;
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realrate_A_Hat = r_Hat - pic_A_Hat(+1);
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tt_A_Gap = tt_A_Hat - tt_A_Eff;
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tt_A_Eff = ((1 + chi)/(1 + chi*(phi_GY*psi + (1 - phi_GY)*(gamma + (sigma - gamma)*(1 - 2*alpha + alpha*alpha)))))*((a_A_Hat - a_U_Hat)/(1-n));
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y_A_Gap = l_A_Gap;
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pi_A_Hat = beta*pi_A_Hat(+1)+ phi_A*mc_A_Hat;
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mc_A_Hat = tau_A_Gap/(1 - tau_A_SS) +(chi + 1/((1- phi_GY)*(phi_caps+sigma*(1-alpha))))* y_A_Gap - (phi_GY /((1- phi_GY)*(phi_caps+sigma*(1-alpha))))*g_A_Gap + (1/(sigma*(1- phi_GY))- 1/((1- phi_GY)*(phi_caps+sigma*(1-alpha))))* y_U_Gap - phi_GY *(1/(sigma*(1 - phi_GY)) - 1/((1- phi_GY)*(phi_caps+sigma*(1-alpha))))*g_U_Gap;
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tau_A_Hat = tau_A_Gap + tau_A_Eff;
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tau_A_Eff = - (1 - tau_A_SS)*muW_A_Hat;
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y_A_Gap = (1- phi_GY)*c_U_Gap + (1 - phi_GY)*(sigma*(1 - alpha) + phi_caps)*(1-n)*tt_A_Gap + phi_GY*g_A_Gap;
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Kdebt_A - ((1 + r_SS)/r_SS)*(tau_A_SS - phi_GY)*r_Hat= (1/beta)*(Kdebt_A(-1) - ((1 + r_SS)/r_SS)*(tau_A_SS - phi_GY)*pi_A_Hat + (phi_GY*g_A_Gap - tau_A_SS*y_A_Gap - tau_A_Gap)) + (1/beta)*(phi_GY*g_A_Eff - tau_A_SS*y_A_Eff + (1 - tau_A_SS)*muW_A_Hat) + (1/beta)*((1 + r_SS)/r_SS)*(tau_A_SS - phi_GY)*alpha*(1-n)*(tt_A_Gap(-1) -(1/(1 + r_SS))*tt_A_Gap) + (1/beta)*((1 + r_SS)/r_SS)*(tau_A_SS - phi_GY)*alpha*(1-n)*(tt_A_Eff(-1) -(1/(1 + r_SS))*tt_A_Eff);
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//FISCAL RULES
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g_A_Gap = ruleG_A_y*(y_A_Gap(-1) - y_U_Gap(-1)) + ruleG_A_tt*tt_A_Gap(-1) + ruleG_A_debt*Kdebt_A(-1);
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tau_A_Gap = ruleT_A_y*(y_A_Gap(-1) - y_U_Gap(-1)) + ruleT_A_tt*tt_A_Gap(-1)+ ruleT_A_debt*Kdebt_A(-1);
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c_A_Hat = c_A_Gap + c_A_Eff;
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g_A_Hat = g_A_Gap + g_A_Eff;
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y_A_Hat = y_A_Gap + y_A_Eff;
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l_A_Hat = l_A_Gap + l_A_Eff;
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tt_B_Hat = (p_U_Hat - p_B_Hat)/n;
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pi_B_Hat = p_B_Hat - p_B_Hat(-1);
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pic_B_Hat = pc_B_Hat - pc_B_Hat(-1);
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pic_B_Hat = pi_B_Hat + (1-lambdaB)*(tt_B_Hat - tt_B_Hat(-1));
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c_B_Eff = (((1 + chi)*sigma)/(1 + chi*(phi_GY*psi + (1 - phi_GY)*sigma)))*a_U_Hat + (((1 - alpha)*(1 + chi)*sigma)/(1 + chi*(phi_GY*psi + (1 - phi_GY)*(gamma + (sigma - gamma)*(1 - 2*alpha + alpha*alpha)))))*(a_B_Hat - a_U_Hat);
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g_B_Eff = (((1 + chi)*psi)/(1 + chi*(phi_GY*psi + (1 - phi_GY)*sigma)))*a_U_Hat + (((1 + chi)*psi)/(1 + chi*(phi_GY*psi + (1 - phi_GY)*(gamma + (sigma - gamma)*(1 - 2*alpha + alpha*alpha)))))*(a_B_Hat - a_U_Hat);
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y_B_Eff = (((1 + chi)*(phi_GY*psi + (1 - phi_GY)*sigma))/(1 + chi*(phi_GY*psi + (1 - phi_GY)*sigma)))*a_U_Hat + (((1 + chi)*(phi_GY*psi + (1 - phi_GY)*(gamma + (sigma - gamma)*(1 - 2*alpha + alpha*alpha))))/(1 + chi*(phi_GY*psi + (1 - phi_GY)*(gamma + (sigma - gamma)*(1 - 2*alpha + alpha*alpha)))))*(a_B_Hat - a_U_Hat);
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l_B_Eff = y_B_Eff - a_B_Hat;
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realrate_B_Hat = r_Hat - pic_B_Hat(+1);
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c_A_Gap = c_B_Gap + sigma*(1 - alpha)*((1-n)*tt_A_Gap-n*(tt_B_Gap));
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tt_B_Gap = tt_B_Hat - tt_B_Eff;
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tt_B_Eff = ((1 + chi)/(1 + chi*(phi_GY*psi + (1 - phi_GY)*(gamma + (sigma - gamma)*(1 - 2*alpha + alpha*alpha)))))*((a_B_Hat - a_U_Hat)/n);
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y_B_Gap = l_B_Gap; //l_B_Gap = y_B_Gap + z_B , up to a first order approximation z_B=0
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pi_B_Hat = beta*pi_B_Hat(+1)+ phi_B*mc_B_Hat;
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mc_B_Hat = tau_B_Gap/(1 - tau_B_SS) +(chi + 1/((1- phi_GY)*(phi_caps+sigma*(1-alpha))))* y_B_Gap - (phi_GY /((1- phi_GY)*(phi_caps+sigma*(1-alpha))))*g_B_Gap + (1/(sigma*(1- phi_GY))- 1/((1- phi_GY)*(phi_caps+sigma*(1-alpha))))* y_U_Gap - phi_GY *(1/(sigma*(1 - phi_GY)) - 1/((1- phi_GY)*(phi_caps+sigma*(1-alpha))))*g_U_Gap;
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tau_B_Hat = tau_B_Gap + tau_B_Eff;
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tau_B_Eff = - (1 - tau_B_SS)*muW_B_Hat;
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y_B_Gap = (1- phi_GY)*c_U_Gap + (1 - phi_GY)*(sigma*(1 - alpha) + phi_caps)*n*tt_B_Gap + phi_GY*g_B_Gap;
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Kdebt_B - ((1 + r_SS)/r_SS)*(tau_B_SS - phi_GY)*r_Hat= (1/beta)*(Kdebt_B(-1) - ((1 + r_SS)/r_SS)*(tau_B_SS - phi_GY)*pi_B_Hat + (phi_GY*g_B_Gap - tau_B_SS*y_B_Gap - tau_B_Gap)) + (1/beta)*(phi_GY*g_B_Eff - tau_B_SS*y_B_Eff + (1 - tau_B_SS)*muW_B_Hat) + (1/beta)*((1 + r_SS)/r_SS)*(tau_B_SS - phi_GY)*alpha*n*(tt_B_Gap(-1) -(1/(1 + r_SS))*tt_B_Gap) + (1/beta)*((1 + r_SS)/r_SS)*(tau_B_SS - phi_GY)*alpha*n*(tt_B_Eff(-1) -(1/(1 + r_SS))*tt_B_Eff);
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//FISCAL RULES
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g_B_Gap = ruleG_B_y*(y_B_Gap(-1) - y_U_Gap(-1)) + ruleG_B_tt*tt_B_Gap(-1) + ruleG_B_debt*Kdebt_B(-1); // function of domestic inflation since government spending is oriented only to domestic production
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tau_B_Gap = ruleT_B_y*(y_B_Gap(-1) - y_U_Gap(-1)) + ruleT_B_tt*tt_B_Gap(-1) + ruleT_B_debt*Kdebt_B(-1); // function of domenstic inflation(!?)
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c_B_Hat = c_B_Gap + c_B_Eff;
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g_B_Hat = g_B_Gap + g_B_Eff;
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y_B_Hat = y_B_Gap + y_B_Eff;
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l_B_Hat = l_B_Gap + l_B_Eff;
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%% Exogenous processes %%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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a_A_Hat = rho_a_A* a_A_Hat(-1) + eps_a_A;
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a_B_Hat = rho_a_B* a_B_Hat(-1) + eps_a_B;
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muW_A_Hat = rho_muW_A*muW_A_Hat(-1) + eps_muW_A;
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muW_B_Hat = rho_muW_B*muW_B_Hat(-1) + eps_muW_B;
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end;
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shocks;
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var eps_a_B; stderr 1;
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var eps_a_A; stderr 1;
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var eps_muW_B; stderr 1;
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var eps_muW_A; stderr 1;
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end;
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steady;
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//check; //do not use this command under optimal policy!!!
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//stoch_simul(order=1, irf=100);
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%Optimized Simple Rule (osr)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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optim_weights;
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//for country A
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pi_A_Hat (1/2)*n*(epsilon/phi_A);
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c_A_Gap (1/2)*n*(1 - phi_GY)*(1/sigma + (1 - phi_GY)*chi);
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g_A_Gap (1/2)*n*phi_GY*(1/psi + phi_GY*chi);
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tt_A_Gap (1/2)*n*(1 - phi_GY)*(gamma*alpha*(alpha - 2) + 2*phi_caps + (1 - phi_GY)*(phi_caps^2)*chi)*((1-n)^2);
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c_A_Gap, g_A_Gap (1/2)*(1/2)*n*2*phi_GY*(1 - phi_GY)*chi;
|
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c_A_Gap, tt_A_Gap (1/2)*(1/2)*n*(1 - phi_GY)*(2*alpha + 2*(1 - phi_GY)*phi_caps*chi)*(1-n);
|
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g_A_Gap, tt_A_Gap (1/2)*(1/2)*n*2*phi_GY*(1 - phi_GY)*phi_caps*chi*(1-n);
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|
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g_A_Gap, c_A_Gap (1/2)*(1/2)*n*2*phi_GY*(1 - phi_GY)*chi;
|
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tt_A_Gap, c_A_Gap (1/2)*(1/2)*n*(1 - phi_GY)*(2*alpha + 2*(1 - phi_GY)*phi_caps*chi)*(1-n);
|
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tt_A_Gap, g_A_Gap (1/2)*(1/2)*n*2*phi_GY*(1 - phi_GY)*phi_caps*chi*(1-n);
|
|
|
|
|
|
|
|
//now, the same for country B
|
|
pi_B_Hat (1/2)*(1-n)*(epsilon/phi_B);
|
|
c_B_Gap (1/2)*(1-n)*(1 - phi_GY)*(1/sigma + (1 - phi_GY)*chi);
|
|
g_B_Gap (1/2)*(1-n)*phi_GY*(1/psi + phi_GY*chi);
|
|
tt_B_Gap (1/2)*(1-n)*(1 - phi_GY)*(gamma*alpha*(alpha - 2) + 2*phi_caps + (1 - phi_GY)*(phi_caps^2)*chi)*(n^2);
|
|
|
|
c_B_Gap, g_B_Gap (1/2)*(1/2)*(1-n)*2*phi_GY*(1 - phi_GY)*chi;
|
|
c_B_Gap, tt_B_Gap (1/2)*(1/2)*(1-n)*(1 - phi_GY)*(2*alpha + 2*(1 - phi_GY)*phi_caps*chi)*n;
|
|
g_B_Gap, tt_B_Gap (1/2)*(1/2)*(1-n)*2*phi_GY*(1 - phi_GY)*phi_caps*chi*n;
|
|
|
|
g_B_Gap, c_B_Gap (1/2)*(1/2)*(1-n)*2*phi_GY*(1 - phi_GY)*chi;
|
|
tt_B_Gap, c_B_Gap (1/2)*(1/2)*(1-n)*(1 - phi_GY)*(2*alpha + 2*(1 - phi_GY)*phi_caps*chi)*n;
|
|
tt_B_Gap, g_B_Gap (1/2)*(1/2)*(1-n)*2*phi_GY*(1 - phi_GY)*phi_caps*chi*n;
|
|
|
|
end;
|
|
|
|
|
|
|
|
osr_params
|
|
|
|
|
|
ruleR_U_y
|
|
ruleR_U_pi
|
|
ruleR_U_debt
|
|
|
|
|
|
|
|
|
|
ruleG_A_y
|
|
ruleG_A_tt
|
|
ruleG_A_debt
|
|
|
|
|
|
|
|
ruleG_B_y
|
|
ruleG_B_tt
|
|
ruleG_B_debt
|
|
|
|
|
|
|
|
ruleT_A_y
|
|
ruleT_A_tt
|
|
ruleT_A_debt
|
|
|
|
|
|
|
|
ruleT_B_y
|
|
ruleT_B_tt
|
|
ruleT_B_debt
|
|
|
|
;
|
|
|
|
osr(irf=5,maxit=10000, nograph, silent_optimizer,nofunctions);
|
|
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
|
asymptotic_loss=((1/2)*n*(epsilon/phi_A))...
|
|
*oo_.var(strmatch('pi_A_Hat',M_.endo_names,'exact'),strmatch('pi_A_Hat',M_.endo_names,'exact'))+...
|
|
((1/2)*n*(1 - phi_GY)*(1/sigma + (1 - phi_GY)*chi))...
|
|
*oo_.var(strmatch('c_A_Gap',M_.endo_names,'exact'),strmatch('c_A_Gap',M_.endo_names,'exact'))+...
|
|
((1/2)*n*phi_GY*(1/psi + phi_GY*chi))...
|
|
*oo_.var(strmatch('g_A_Gap',M_.endo_names,'exact'),strmatch('g_A_Gap',M_.endo_names,'exact'))+...
|
|
((1/2)*n*(1 - phi_GY)*(gamma*alpha*(alpha - 2) + 2*phi_caps + (1 - phi_GY)*(phi_caps^2)*chi)*((1-n)^2))...
|
|
*oo_.var(strmatch('tt_A_Gap',M_.endo_names,'exact'),strmatch('tt_A_Gap',M_.endo_names,'exact'))+...
|
|
((1/2)*(1/2)*n*2*phi_GY*(1 - phi_GY)*chi)...
|
|
*oo_.var(strmatch('c_A_Gap',M_.endo_names,'exact'),strmatch('g_A_Gap',M_.endo_names,'exact'))+...
|
|
((1/2)*(1/2)*n*(1 - phi_GY)*(2*alpha + 2*(1 - phi_GY)*phi_caps*chi)*(1-n))...
|
|
*oo_.var(strmatch('c_A_Gap',M_.endo_names,'exact'),strmatch('tt_A_Gap',M_.endo_names,'exact'))+...
|
|
((1/2)*(1/2)*n*2*phi_GY*(1 - phi_GY)*phi_caps*chi*(1-n))...
|
|
*oo_.var(strmatch('g_A_Gap',M_.endo_names,'exact'),strmatch('tt_A_Gap',M_.endo_names,'exact'))+...
|
|
((1/2)*(1/2)*n*2*phi_GY*(1 - phi_GY)*chi)...
|
|
*oo_.var(strmatch('g_A_Gap',M_.endo_names,'exact'),strmatch('c_A_Gap',M_.endo_names,'exact'))+...
|
|
((1/2)*(1/2)*n*(1 - phi_GY)*(2*alpha + 2*(1 - phi_GY)*phi_caps*chi)*(1-n))...
|
|
*oo_.var(strmatch('tt_A_Gap',M_.endo_names,'exact'),strmatch('c_A_Gap',M_.endo_names,'exact'))+...
|
|
((1/2)*(1/2)*n*2*phi_GY*(1 - phi_GY)*phi_caps*chi*(1-n))...
|
|
*oo_.var(strmatch('tt_A_Gap',M_.endo_names,'exact'),strmatch('g_A_Gap',M_.endo_names,'exact'))+...
|
|
((1/2)*(1-n)*(epsilon/phi_B))...
|
|
*oo_.var(strmatch('pi_B_Hat',M_.endo_names,'exact'),strmatch('pi_B_Hat',M_.endo_names,'exact'))+...
|
|
((1/2)*(1-n)*(1 - phi_GY)*(1/sigma + (1 - phi_GY)*chi))...
|
|
*oo_.var(strmatch('c_B_Gap',M_.endo_names,'exact'),strmatch('c_B_Gap',M_.endo_names,'exact'))+...
|
|
((1/2)*(1-n)*phi_GY*(1/psi + phi_GY*chi))...
|
|
*oo_.var(strmatch('g_B_Gap',M_.endo_names,'exact'),strmatch('g_B_Gap',M_.endo_names,'exact'))+...
|
|
((1/2)*(1-n)*(1 - phi_GY)*(gamma*alpha*(alpha - 2) + 2*phi_caps + (1 - phi_GY)*(phi_caps^2)*chi)*(n^2))...
|
|
*oo_.var(strmatch('tt_B_Gap',M_.endo_names,'exact'),strmatch('tt_B_Gap',M_.endo_names,'exact'))+...
|
|
((1/2)*(1/2)*(1-n)*2*phi_GY*(1 - phi_GY)*chi)...
|
|
*oo_.var(strmatch('c_B_Gap',M_.endo_names,'exact'),strmatch('g_B_Gap',M_.endo_names,'exact'))+...
|
|
((1/2)*(1/2)*(1-n)*(1 - phi_GY)*(2*alpha + 2*(1 - phi_GY)*phi_caps*chi)*n)...
|
|
*oo_.var(strmatch('c_B_Gap',M_.endo_names,'exact'),strmatch('tt_B_Gap',M_.endo_names,'exact'))+...
|
|
((1/2)*(1/2)*(1-n)*2*phi_GY*(1 - phi_GY)*phi_caps*chi*n)...
|
|
*oo_.var(strmatch('g_B_Gap',M_.endo_names,'exact'),strmatch('tt_B_Gap',M_.endo_names,'exact'))+...
|
|
((1/2)*(1/2)*(1-n)*2*phi_GY*(1 - phi_GY)*chi)...
|
|
*oo_.var(strmatch('g_B_Gap',M_.endo_names,'exact'),strmatch('c_B_Gap',M_.endo_names,'exact'))+...
|
|
((1/2)*(1/2)*(1-n)*(1 - phi_GY)*(2*alpha + 2*(1 - phi_GY)*phi_caps*chi)*n)...
|
|
*oo_.var(strmatch('tt_B_Gap',M_.endo_names,'exact'),strmatch('c_B_Gap',M_.endo_names,'exact'))+...
|
|
((1/2)*(1/2)*(1-n)*2*phi_GY*(1 - phi_GY)*phi_caps*chi*n)...
|
|
*oo_.var(strmatch('tt_B_Gap',M_.endo_names,'exact'),strmatch('g_B_Gap',M_.endo_names,'exact'));
|
|
|
|
if abs(asymptotic_loss-oo_.osr.objective_function)>1e-10
|
|
error('Objective Function with Non-stationary Variables is wrong')
|
|
end
|
|
|
|
|