%% cgg2c.dyn
%  Claida, Gali, Gertler two country NK open economy model, JME 2002
%  Parameter names correpsond to version in Chapter 9 of Monetary Theory
%  and Policy, 4th edition.
%
%  Modified 7/27/2018 to distinguish between efficient output gap (output minus the efficient level)
%  and the flex-price output gap (output minus flex price output) that appears in the NKPC.
%
var 
xh,      //  Flex-price output gap, home
xf,      //  Flex-price output gap, foreign
xeh,     //  Output minus efficient output, home
xef,     //  Output minus efficient output, foreign
yflexh,  //  Flex-price output, home
yflexf,  //  Flex-price output, foreign
yeffh,   //  Efficient output, home
yefff,   //  Efficient output, foreign
yh,      //  Actual output, home
yf,      //  Actual output, foreign
pih,     //  Domestic price inflation
pif,     //  Foreign price inflation
picpih,  //  CPI inflation, home
picpif,  //  CPI, foreign
s,       //  Terms of trade
sgap,    //  s - sflex
ph,      //  Domestic price level
pf,      //  Foreign price level (in foreign currency)
e,       //  Nominal exchange rate
ih,      //  Nominal interest rate, home
if,      //  Nominal interest rate, foreign
rnh,     //  Natural interest rate, home
rnf,     //  Natural interest rate, foreign
ah,      //  Domestic productivity shock
af,      //  Foreign productivity shock
vh,      //  Monetary policy shock, home
vf,      //  Monetary policy shock, foreign 
muwh,    //  Cost Push Shock, home
muwf;    //  Cost Push Shock, foreign

varexo 
e_ah,        // Productivity, home
e_af,        // Productivity, foreign
e_vh,        // Policy, home
e_vf,        // Policy, foreign
e_muwh,      // Cost shock, home
e_muwf;      // Cost shock, foreign

parameters
savefig,    // = 1 to save figure
lambda,     // Weight on output gap in loss function
beta,       // Subjective discount factor
sigma,      // Consumption index coef. in utility function
eta,        // Inverse labor supply elasticitys
xi,         // Price elasticity, individual goods
alphah,     // Used to compare home policies, = 0 for opt disc, == 1 for Taylor rule
alphach,    // Opt commitment if alpha = 0 and alphac = 1
alphaf,     // Used to compare foreing policies, = 0 for opt disc, == 1 for Taylor rule
alphacf,    // Opt commitment if alpha = 0 and alphac = 1
gamma,      // Degree of openness
omega,      // Calvo parameter (Fraction of firms not adjusting prices)
kappa,      // Inflation elasticity w.r.t output gap
//  Home Taylor rule parameters
phi_pih,    // Taylor Rule Coef. on domestic inflation
phi_cpih,   // Taylor coefficient on cpi inflation  
phi_xh,     // Taylor Rule Coef. on output-gap 
phi_eh,     // Taylor Rule Coef. on exchange rate 
//  Foreign taylor rule parameters
phi_pif,    // Taylor Rule Coef. on domestic inflation
phi_cpif,   // Taylor coefficient on cpi inflation  
phi_xf,     // Taylor Rule Coef. on output-gap 
phi_ef,     // Taylor Rule Coef. on exchange rate 

// Domestic shocks
rho_ah       // Tech. Shock persistance
rho_vh,      // Monetary Policy Shock persistance
rho_muwh,    // Cost push shock persistance
sde_ah,      // Standard deviation for tech. shock
sde_vh,      // Standard deviation for mon. policy shock
sde_muwh,    // Stadard deviation for cost push shock

// Foreign shocks
rho_af,      // Tech. Shock persistance
rho_vf,      // Monetary Policy Shock persistance
rho_muwf,    // Cost push shock persistance
sde_af,      // Standard deviation for tech. shock
sde_vf,      // Standard deviation for mon. policy shock
sde_muwf;    // Stadard deviation for cost push shock

// parameter values from Gali-Monacelli (REStud 2005)
savefig = 0; // set to = 1 to save figure
alphah   = 0; 
alphach  = 0;
alphaf   = 0;
alphacf  = 0;
beta    = 0.99; 
sigma   = 1; 
eta     = 3;   
xi      = 6;
gamma   = 0.4;
omega   = 0.75; 
kappa   = (1-omega)*(1-omega*beta)/omega;
lambda  = (sigma+eta)*kappa/xi;
phi_pih= 1.5;
phi_cpih= 0;   
phi_xh  = 0; 
phi_eh   = 0;
phi_pif= 1.5;
phi_cpif= 0;   
phi_xf  = phi_xh; 
phi_ef  = -phi_eh;
rho_ah  = 0.66; 
sde_ah  = 0.71; 
rho_vh  = 0.75;
sde_vh  = 0.25; // Standard deviation for mon. policy shock
rho_muwh = 0.7;
sde_muwh = 0.25;  // Stadard deviation for cost push shock

rho_af   = rho_ah;
rho_vf   = rho_vh;
rho_muwf = rho_muwh;
sde_af   = sde_ah;
sde_vf   = sde_vh;
sde_muwf = sde_muwh;

model(linear);

xh      = yh - yflexh;
xeh     = yh - yeffh;
(eta+sigma - gamma*(sigma-1))*yflexh = -gamma*(sigma-1)*yflexf + (1+eta)*ah - muwh;
(eta+sigma - gamma*(sigma-1))*yeffh = -gamma*(sigma-1)*yefff + (1+eta)*ah;
xh      = xh(+1) - (1/sigma)*(ih - picpih(+1) - rnh) - gamma*(s(+1) - s);
rnh     = sigma*(yflexh(+1) - yflexh);
pih     = beta*pih(+1) + kappa*(eta+sigma-gamma*(sigma-1))*xh;
// Taylor rule
//ih - phi_pih*pih + phi_cpih*picpih + phi_xh*xh + phi_eh*e + vh;
0 = alphah*(ih - phi_pih*pih - phi_cpih*picpih - phi_xh*xh - phi_eh*e - vh) + (1-alphah)*(kappa*(eta+gamma+sigma*(1-gamma))*pih + lambda*(xeh - alphach*xeh(-1)));
// Optimal discretion
//kappa*(eta+gamma+sigma*(1-gamma))*pih + lambda*xeh = 0;
ph      = ph(-1) + pih;
picpih  = pih + gamma*(s - s(-1));

// Foreign economy
xf      = yf - yflexf;
xef     = yf - yefff;
(eta+sigma-(1-gamma)*(sigma-1))*yflexf = -(1-gamma)*(sigma-1)*yflexh + (1+eta)*af - muwf;
(eta+sigma-(1-gamma)*(sigma-1))*yefff = -(1-gamma)*(sigma-1)*yeffh + (1+eta)*af;
xf      = xf(+1) - (1/sigma)*(if - picpif(+1) - rnf) + (1 - gamma)*(s(+1) - s);
rnf     = sigma*(yflexf(+1) - yflexf);
pif     = beta*pif(+1) + kappa*(eta+sigma - (1-gamma)*(sigma-1))*xf;
//if = phi_pif*pif + phi_cpif*picpi + phi_xf*xf + phi_ef*e + vf;
0 = alphaf*(if - phi_pif*pif - phi_cpif*picpif - phi_xf*xf - phi_ef*e - vf) + (1-alphaf)*(kappa*(eta+gamma+sigma*(1-gamma))*pif + lambda*(xef - alphacf*xef(-1)));
pf      = pf(-1) + pif;
picpif  = pif - (1-gamma)*(s - s(-1));

s       = yh - yf;
sgap    = xh - xf;
e       = s  + ph - pf;

ah      = rho_ah*ah(-1) + e_ah;
vh      = rho_vh*vh(-1) + e_vh;
muwh    = rho_muwh*muwh(-1) + e_muwh;
af      = rho_af*af(-1) + e_af;
vf      = rho_vf*vf(-1) + e_vf;
muwf    = rho_muwf*muwf(-1) + e_muwf;


end;

steady;
check;

shocks; 
//var e_ah    = (sde_ah)^2;
//var e_vh    = (sde_vh)^2;
var e_muwh  = (sde_muwh)^2;
var e_af    = (sde_af)^2;
var e_vf    = (sde_vf)^2;
var e_muwf  = (sde_muwf)^2;
end;
/////////////////////////////////////////

/*
planner_objective pih^2 + lambda*xeh^2;
ramsey_policy(planner_discount=0.99, order = 1,irf=15) ;
//discretionary_policy(irf=40,planner_discount=0.99,order=1,instruments=(i),nograph,solve_maxit=10000);
OOPT.MODELS.oo2CNK_ramsey =   oo_;
save OOPT_2CNK_ramsey;
*/
/////////////////////////////////////////
/////////////////////////////////////////
// Computing Theoretical Moments and IRF's
////////////////////////////////////////

// Taylor rules
alphah  = 1; 
alphach = 0;
alphaf  = 1;
alphacf = 0;
stoch_simul(order=1,ar=1,irf=20,nograph,noprint);
OOPT.MODELS.oo2CNK_TR =   oo_;
save OOPT_2CNK_TR;


// Optimal discretion
alphah  = 0; 
alphach = 0;
alphaf  = 0;
alphacf = 0;
stoch_simul(order=1,ar=1,irf=20,nograph,noprint);
OOPT.MODELS.oo2CNK =   oo_;
save OOPT_2CNK;


// Optimal commitment
alphah  = 0;
alphach = 1;
alphaf  = 0;
alphacf = 1; 
stoch_simul(order=1,ar=1,irf=20,nograph,noprint);
OOPT.MODELS.oo2CNK_1 =   oo_;
save OOPT_2CNK_1;


// Fixed exchange rate
alphah = 1;
phi_cpi = 0;
phi_pih = 1.5;
phi_eh   = 10;
alphaf = 0; 
check;
stoch_simul(order=1,ar=1,irf=20,nograph,noprint);
OOPT.MODELS.oo2CNK_2 =   oo_;
save OOPT_2CNK_2;

// CPI inflation rule
alphah = 1;
phi_cpi = 1.5;
phi_pih = 0;
phi_eh   = 0;
alphaf = 0; 
check;
stoch_simul(order=1,ar=1,irf=20,nograph,noprint);
OOPT.MODELS.oo2CNK_3 =   oo_;
save OOPT_2CNK_3;

/*
// Nash, optimal discretion in both
alphah = 0;
alphach = 0;
alphaf = 0; 
alphach = 0;
check;
stoch_simul(order=1,ar=1,irf=20,nograph,noprint);
OOPT.MODELS.oo2CNK_4 =   oo_;
save OOPT_2CNK_4;
*/

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

// Figure 1 of chapter 9
OOPT.NN=12;
OOPT.plot_color={':dr' '-ok' ':*b'}
OOPT.shocks_names={'e_muwh'};
OOPT.tit_shocks={'Domestic Cost Shock'};
OOPT.type_models={ 'oo2CNK' 'oo2CNK_1' 'oo2CNK_2'};
OOPT.legend_models={ 'Optimal discretion' 'Optimal commitment' 'Fixed exchange rate'}
OOPT.list_endo={'xeh' 'pih' 'picpih' 's'  'ph' 'e' };
OOPT.label_variables={'Efficent output gap' 'Domestic price inflation' 'CPI Inflation' 'Terms of trade' 'Domestic price level'  'Nominal exchange rate' };
plot_comp(OOPT);
//print -depsc2 'C:\Users\CEW\Dropbox\4thedition\Chpt9\graphics_ch9\ch9_figure_1';

/*
OOPT.NN=12;
OOPT.plot_color={'-*b' ':xr' 'o-k'}
OOPT.shocks_names={'e_muwh'};
OOPT.tit_shocks={'Domestic Cost Shock'};
OOPT.type_models={'oo2CNK_TR' 'oo2CNK' 'oo2CNK_1'};
OOPT.legend_models={'Taylor rules' 'Optimal discretion' 'Optimal commitment'}
OOPT.list_endo={'xh' 'pih' 'pif' 'ih' 'if' 'picpih' 'ph' 's' 'e' };
OOPT.label_variables={'Dom. Output gap' 'Dom. Inflation' 'For. Inflation' 'Domestic nominal rate' 'Foreign nominal rate' 'Dom. CPI Inflation' 'Domestic price level' 'Terms of Trade'  'Nominal exchange rate' };
plot_comp(OOPT);

OOPT.NN=12;
OOPT.plot_color={':dr' '-ok'}
OOPT.shocks_names={'e_vh'};
OOPT.tit_shocks={'Monetary Policy Shock'};
OOPT.type_models={ 'oo2CNK_TR' 'oo2CNK_3'};
OOPT.legend_models={ 'Dom. inflation rule' 'CPI inflation rule'}
OOPT.list_endo={'xh' 'pih' 'picpih' 's'  'ph' 'e' };
OOPT.label_variables={'Output gap' 'Domestic price inflation' 'CPI Inflation' 'Terms of trade' 'Domestic price level'  'Nominal exchange rate' };
plot_comp(OOPT);
print -depsc2 'cgg2c_policyshock';
*/

/*
OOPT.NN=12;
OOPT.plot_color={'-b' ':r' '-.k' }
OOPT.shocks_names={'e_muwh'};
OOPT.tit_shocks={'Domestic Cost Shock'};
OOPT.type_models={'oo2CNK' 'oo2CNK_1' 'oo2CNK_2'};
OOPT.legend_models={ 'Taylor Rule' 'Optimal discretion' 'Optimal commitment' }
OOPT.list_endo={'xh' 'pih' 'pif' 'ih' 'if' 'picpi' 'ph' 's' 'e' };
OOPT.label_variables={'Domestic Output gap' 'Domestic Inflation' 'Foreign Inflation' 'Domestic Nominal Rate' 'Foreign Nominal Rate' 'CPI Inflation' 'Domestic price level' 'Terms of Trade'  'Nominal exchange rate' };
plot_comp(OOPT);

OOPT.NN=12;
OOPT.plot_color={'-b' ':r' '-.k' 'og'}
OOPT.shocks_names={'e_muwf'};
OOPT.tit_shocks={'Foreign Cost Shock'};
OOPT.type_models={'oo2CNK' 'oo2CNK_1' 'oo2CNK_2' 'oo2CNK_3'};
OOPT.legend_models={ 'Taylor Rule' 'Optimal discretion' 'Optimal commitment' 'Fixed Exchange Rate'}
OOPT.list_endo={'xh' 'pih' 'picpi' 's' 'p' 'e' };
//OOPT.list_endo={'xh' 'pih' 'pif' 'ih' 'if' 'picpi' 'ph' 's' 'e' };
OOPT.label_variables={'Domestic Output gap' 'Domestic Inflation' 'CPI Inflation' 'Terms of Trade' 'Domestic price level' 'Nominal exchange rate' };
//OOPT.label_variables={'Domestic Output gap' 'Domestic Inflation' 'Foreign Inflation' 'Domestic Nominal Rate' 'Foreign Nominal Rate' 'CPI Inflation' 'Domestic price level' 'Terms of Trade'  'Nominal exchange rate' };
plot_comp(OOPT);
//print -depsc2 'cgg2c_muwf_polices';

OOPT.NN=12;
OOPT.plot_color={'-b' ':r' }
OOPT.shocks_names={'e_muwh'};
OOPT.tit_shocks={'Domestic Cost Shock'};
OOPT.type_models={ 'oo2CNK_1'  'oo2CNK_4'};
OOPT.legend_models={ 'H opt disc, F TR' 'Both Optimal discretion' }
OOPT.list_endo={'xh' 'pih' 'pif' 'ih' 'if' 'picpi' 'ph' 's' 'e' };
OOPT.label_variables={'Domestic Output gap' 'Domestic Inflation' 'Foreign Inflation' 'Domestic Nominal Rate' 'Foreign Nominal Rate' 'CPI Inflation' 'Domestic price level' 'Terms of Trade'  'Nominal exchange rate' };
plot_comp(OOPT);


OOPTT.NN=12;
OOPT.plot_color={'-b' ':r'}
OOPT.shocks_names={'e_muwh'};
OOPT.tit_shocks={'Domestic Cost Shock'};
OOPT.type_models={'oo2CNK_1'};
OOPT.legend_models={'Taylor Rule'}
OOPT.list_endo={'xh' 'pih' 'pif' 'ih' 'if' 'picpi' 'ph' 's' 'e' };
OOPT.label_variables={'H Output gap' 'H Inflation' 'F Inflation' 'Domestic i' 'Foreign i' 'CPI Inflation' 'Domestic price level' 'Terms of Trade'  'Nominal exchange rate' };
plot_comp(OOPT);


OOPT.NN=12;
OOPT.plot_color={'-b' ':r'}
OOPT.shocks_names={'e_muwf'};
OOPT.tit_shocks={'Foreign Cost Shock'};
OOPT.type_models={'oo2CNK'};
OOPT.legend_models={'Optimal discretion'}
OOPT.list_endo={'xh' 'xf' 'ih' 'pih' 'picpi' 'ph' 's' 'e' 'q'};
OOPT.label_variables={'H Output gap' 'F Output Gap' 'Domestic i' 'Foreign i' 'Dom. Inflation' 'CPI Inflation' 'Domestic price level' 'Terms of Trade'  'Nominal exchange rate' };
plot_comp(OOPT);

OOPT.NN=12;
OOPT.plot_color={'-b' ':r'}
OOPT.shocks_names={'e_muwh'};
OOPT.tit_shocks={'Domestic Cost Shock'};
OOPT.type_models={'oo2CNK' 'oo2CNK_1'};
OOPT.legend_models={'Dom. Infl. Target' 'CPI Infl Target'}
OOPT.list_endo={'xf' 'xh' 'ih' 'pih' 'picpi' 'ph' 's' 'e' 'q'};
OOPT.label_variables={'Output' 'Output Gap' 'Nominal interest rate' 'Dom. Inflation' 'CPI Inflation' 'Domestic price level' 'Terms of Trade'  'Nominal exchange rate' 'Real exchange rate'};
plot_comp(OOPT);
*/

/*
OOPT.NN=12;
OOPT.plot_color={'-b' ':r' '-.g'}
OOPT.shocks_names={'e_a'};
OOPT.tit_shocks={'Productivity Shock'};
OOPT.type_models={'ooSOE' 'ooSOE_1' 'ooSOE_2'};
OOPT.legend_models={'Dom. Inflation' 'CPI Inflation' 'Nominal Exch. Rate'}
OOPT.list_endo={'y' 'x' 'i' 'pih' 'picpi' 'ph' 's' 'e' 'q'};
OOPT.label_variables={'Output' 'Output Gap' 'Nominal interest rate' 'Dom. Inflation' 'CPI Inflation' 'Domestic price level' 'Terms of Trade'  'Nominal exchange rate' 'Real exchange rate'};
plot_comp(OOPT);
if savefig == 1
print -depsc2 'gmsoe_ch9_baseline';
end


OOPT.NN=12;
OOPT.plot_color={'--k' ':k' '-.k' 'o-k'}
OOPT.shocks_names={'e_a'};
OOPT.tit_shocks={'Productivity Shock'};
OOPT.type_models={'ooSOE' 'ooSOE_1' 'ooSOE_2' 'ooSOE_3'};
OOPT.legend_models={'Dom. Inflation' 'CPI Inflation' 'Nominal Exch. Rate' 'Optimal'}
OOPT.list_endo={'y' 'x' 'i' 'pih' 'picpi' 'ph' 's' 'e' 'q'};
OOPT.label_variables={'y' 'x' 'i' 'domestic inflation' 'cpi inflation' 'dom. price level' 's'  'e' 'q'};
plot_comp(OOPT);
//if savefig == 1
//print -depsc2 'gmsoe_ch9_e_a';
//end


OOPT.NN=12;
OOPT.plot_color={'o-b' 'b--' 'r--' 'd-r'};
OOPT.shocks_names={'e_af'};
OOPT.tit_shocks={'Foreign Income Shock'};
OOPT.type_models={'oo2CNK_TR' 'oo2CNK' 'oo2CNK_2' 'oo2CNK_3'};
OOPT.legend_models={'Taylor rule' 'Opt disc' 'CPI Infl Target' 'Fixed exch rate'}
OOPT.list_endo={'y' 'x' 'i' 'pih' 'picpi' 'ph' 's' 'e' 'q'};
OOPT.label_variables={'Output' 'Output Gap' 'Nominal interest rate' 'Domestic Inflation' 'CPI Inflation' 'Domestic price level' 'Terms of Trade'  'Nominal exchange rate' 'Real exchange rate'};
plot_comp(OOPT);

OOPT.NN=12;
OOPT.plot_color={'d-r'};
OOPT.shocks_names={'e_af'};
OOPT.tit_shocks={'Foreign Income Shock'};
OOPT.type_models={'oo2CNK_3'};
OOPT.legend_models={'Taylor rule' 'Opt disc' 'CPI Infl Target' 'Fixed exch rate'}
OOPT.list_endo={'y' 'x' 'i' 'pih' 'picpi' 'ph' 's' 'e' 'q'};
OOPT.label_variables={'Output' 'Output Gap' 'Nominal interest rate' 'Domestic Inflation' 'CPI Inflation' 'Domestic price level' 'Terms of Trade'  'Nominal exchange rate' 'Real exchange rate'};
plot_comp(OOPT);
*/