// Basic New Keynesian Model under optimal discretion policy

 
var
x,   //  1.Output Gap
pi,  //  2.Inflation
i,   //  3.Nominal interest rate 
r,   //  4.Real interest rate
rn,  //  5.Natural interest rate
z,   //  6.Technology shock
u;   //  7.Cost Push Shock


varexo e_z e_u;

parameters
beta,    // Subjective discount factor
eta,     // Labor supply coef. in utility function
sigma,   // Consumption index coef. in utility function
omega,   // Calvo parameter (Fraction of firms not adjusting prices)
kappa,   // Inflation elasticity w.r.t output gap
rho_z,   // Tech. Shock persistance
sde_z,   // Standard deviation for tech. shock
rho_u,   // Cost push shock persistance
sde_u,   // Stadard deviation for cost push shock
lambda,   // Weight on output gap in the policy objective
epsilon; // Elasticity of substitution between consumption goods

// Deep Parameters Calibration
beta    = 0.99;
eta     = 1.0; 
sigma   = 1.0;
omega   = 0.8;
rho_z   = 0.9;
sde_z   = 1.0;
rho_u   = 0.001;
sde_u   = 1.0;
epsilon = 6;

// Implied Parameters
kappa = (sigma + eta)*(1-omega)*(1-omega*beta)/omega;
//lambda = (kappa)/((1+eta*epsilon)*epsilon);
lambda = kappa/epsilon;

model(linear);

x = x(+1) - (1/sigma)*(r-rn);                     // Dynamic IS curve
pi = beta*pi(+1) + kappa*x + u;                   // New Keynessian Phillips curve
rn = sigma*((1+eta)/(eta+sigma))*(z(+1)-z);       // Natural interest rate
r = i - pi(+1);                                   // Real interest rate   
z = rho_z*z(-1) + e_z;
u = rho_u*u(-1) + e_u;
 
end;

shocks; 
//var e_z = (sde_z)^2;
var e_u = (sde_u)^2;

end;

/////////////////////////////////////////
// Computing theoretical moments and IRF's under optimal policy
////////////////////////////////////////
planner_objective (pi^2 + lambda*(x^2) );
discretionary_policy(irf=40,planner_discount=0.99,order=1,instruments=(i),nograph);

OOPT.MODELS.ooNKM_optd =   oo_;
OOPT_NKM_optd = OOPT.MODELS.ooNKM_optd;
save OOPT_NKM_optd;

OOPT.NN=12;
OOPT.plot_color={'o-b'};
OOPT.shocks_names={'e_u'};
OOPT.tit_shocks={'Cost Shock'};
OOPT.type_models={'ooNKM_optd'};
OOPT.legend_models={'Opt. Discretion'};
OOPT.list_endo={'pi' 'x' 'i' 'r' 'rn' 'u'};
OOPT.label_variables={'Inflation Rate' 'Output Gap' 'Nominal Interest Rate' 'Real Interest Rate' 'Natural Interest Rate' 'Cost Shock'};
plot_comp(OOPT);
print -depsc2 'Figure 2'


/*
planner_objective pi^2 + lambda*(x^2);
discretionary_policy(planner_discount=0.99,order=1,instruments=(i),nograph); //,solve_maxit=10000);
//vv = diag(oo_.var);

Objective = (1/(1-beta))*(vv(10) + lambda*vv(6));

rho_u = 0.8;
discretionary_policy(planner_discount=0.99,nograph,noprint);
//stoch_simul(order=1,ar=1,irf=20,nograph,noprint);
OOPT.MODELS.ooNKM_optd_1 =   oo_;
OOPT_NKM_optd_1 = OOPT.MODELS.ooNKM_optd_1;
save OOPT_NKM_optd_1;



/////////////////////////////////////////
// Plotting Impulse-Response functions
// This part uses the plot_comp function in order to do multiple IRFS graphs.
////////////////////////////////////////

OOPT.NN=12;
OOPT.plot_color={'o-b'};
OOPT.shocks_names={'e_z'};
OOPT.tit_shocks={'Technology Shock'};
OOPT.type_models={'ooNKM_optd'};
OOPT.legend_models={'Discretion'};
OOPT.list_endo={'pi' 'x' 'i' 'r' 'rn' 'z'};
OOPT.label_variables={'Inflation Rate' 'Output Gap' 'Nominal Interest Rate' 'Real Interest Rate' 'Natural Interest Rate' 'Technology Shock'};
plot_comp(OOPT);
print -depsc2 'Figure 1'

OOPT.NN=12;
OOPT.plot_color={'o-b' 'd-r'};
OOPT.shocks_names={'e_u'};
OOPT.tit_shocks={'Cost Push Shock'};
OOPT.type_models={'ooNKM_4' 'ooNKM_optd_1'};
OOPT.legend_models={'\rho_u=0' '\rho_u=0.8'};
OOPT.list_endo={'pi' 'x' 'i' 'r' 'rn' 'u'};
OOPT.label_variables={'Inflation Rate' 'Output Gap' 'Nominal Interest Rate' 'Real Interest Rate' 'Natural Interest Rate' 'Cost Shock'};
plot_comp(OOPT);
print -depsc2 'Figure 1'


OOPT.NN=12;
OOPT.plot_color={'o-b'};
OOPT.shocks_names={'e_u'};
OOPT.tit_shocks={'Persistent Cost Push Shock'};
OOPT.type_models={'ooNKM_optd_1'};
OOPT.legend_models={'Discretion'};
OOPT.list_endo={'pi' 'x' 'i' 'r' 'rn' 'u'};
OOPT.label_variables={'Inflation Rate' 'Output Gap' 'Nominal Interest Rate' 'Real Interest Rate' 'Natural Interest Rate' 'Cost Shock'};
plot_comp(OOPT);
print -depsc2 'Figure 1'
*/