///MONETARY POLICY AND WELFARE IN A SMALL OPEN ECONOMY - Bianca De Paoli (2004-2006)
///Internship report - Universidad del Rosario (UR) / Banco de la República (BR)
///Departamento de Modelos Macroeconómicos
///Ramón Eduardo Hernández Ortega 
///Tutor: Jesús Bejarano Rojas (BR) - Manuel Ramírez (UR)
 
close all;

//n --> infinito para que el tamaño relativo del país local frente al foráneo sea casi cero y por tanto
//se pueda hablar de una economía pequeña y abierta

var ph rs y c c_star g  epy int infl int_star infl_star  tao bf d f p_tilda;

varexo e_c e_y e_g e_miu;


parameters beta eta lam alpha sigma theta delta rho_epy rho_c rho_g rho_miu v rho phi k gamma lx1 lx2 lx3 l phis phi_y phi_infl phi_q miu_bar; 

	beta 		=	0.99;
	eta 		=	0.47;
	lam 		=	0.25;
	alpha 		=	0.66;
	sigma 		=	10;
	theta 		=	0.8;
	delta 		=	0.0001;
	rho_epy 	=	0.66;
	rho_c 		=	0.66;
	rho_g 		=	0.94;
	rho_miu 	=	0.99;
	v			=	1-lam;
	rho			=	1;
	phi			=	1;	//Costo de ajuste
    k           =   (1-alpha*beta)*(1-alpha)/(alpha*(1+sigma*eta));
    gamma       =   theta*lam*(2-lam)/(1-lam);
    lx1         =   (1/((rho+eta)+(l*eta)))*(-l*(miu_bar^(-1))+(1-lam)-(miu_bar^(-1)));
    lx2         =   (1/((rho+eta)+(l*eta)))*(rho*((miu_bar^(-1))-(1-lam))+(1-lam)*(eta-rho));
    lx3         =   (1/((rho+eta)+(l*eta)))*(-(rho*theta-1)*(1-lam)*(miu_bar^(-1))-(eta*theta+1));
    l           =   (rho*theta-1)*lam*(2-lam);
    phi_y       =   (eta+rho)*(1-phis)+((rho-1)*(-l*(1-phis)-(lam-phis))/(1+l))+lx1*((eta+rho)+eta*(eta+1)-((rho*(rho-1))/(1+l)))-lx2*(((1-lam)^2)*lam*(rho*theta-1)/(1+l));
    phi_q       =   -((lam+l)*(rho-1))/((1-lam)*(rho^2))+lx1*l*(rho-1-l)/((1-lam)*(rho^2))+lx2*((lam*(rho*theta-1)*(rho*theta*(1-lam)+lam+l)))/((rho^2))+lx3*(lam*(theta-1))/(1-lam);
    phi_infl    =   sigma/(miu_bar*k)+(1+eta)*(sigma/k)*lx1;
    phis        =   1-1/miu_bar;
    miu_bar     =   sigma/(sigma-1);
model;

	 1=(v*(exp(ph)^(1-theta))+(1-v)*(exp(rs)^(1-theta)));   //Inflación local

	 exp(c)+exp(rs)*exp(bf)/(exp(int_star)*exp(bf)^(delta))=exp(rs)*exp(bf(-1))/exp(infl_star)+(exp(tao))*exp(y)*exp(ph);    //BOP

     (exp(int)/exp(infl(+1)))=(exp(int_star))*exp(bf)^(delta)*(exp(rs(+1))/(exp(rs)*exp(infl_star(+1))));  //UIP

     exp(y)=(exp(ph)^(-theta))*(((1-lam)*exp(c)+lam*(((1/exp(rs))^(-theta))*exp(c_star)))+(g));            //Demanda

     ((exp(epy)^(-eta))*(exp(y)^eta))=((exp(c)^(-rho))*exp(y));                                            //
     
     exp(d)=(exp(y)*1/exp(tao)*(((exp(epy)^(-eta))*(exp(y)^eta))))+alpha*beta*exp(d(+1));                     //d
	 exp(f)=((exp(c)^(-rho))*exp(y))+alpha*beta*(1/exp(infl(+1)))*exp(f(+1));                               //f
	 exp(p_tilda)=sigma/(sigma-1)*exp(d)/exp(f);                                                            //p_tilda
     
     1=alpha*(((exp(ph(-1))/exp(ph))*exp(infl))^(1-sigma))+(1-alpha)*((exp(p_tilda)))^(1-sigma); //ph

     //exp(int)=((exp(infl))^1.5)*1/beta*exp(rs);   
	 
     
	 c_star=rho_c*c_star(-1)+e_c;
	 g=rho_g*g(-1)+e_g;
     epy=rho_epy*epy(-1)+e_y;
     tao=rho_miu*tao(-1)+e_miu;
     exp(int_star)=(exp(infl_star)^1.5)*1/beta;
	 exp(infl_star)=1;
	 
end;


initval;

	tao				=	log(1);
	epy				=	log(1);
	c_star 			=	log(1);
	g 				=	log(1);
	c 				=	log(1);
	ph 				=	log(1);
	rs 				=	log(1);
	int 			=	log((1/beta));
	infl 			=	log(1);
	int_star 		=	log((1/beta)); 
	infl_star		=	log(1);
	bf				=	log(1);
	y 				=	log((exp(ph)^(-theta))*(((1-lam)*exp(c)+lam*(((1/exp(rs))^(-theta))*exp(c_star)))+(g)));
	p_tilda         =   log(sigma/(sigma-1)*exp(d)/exp(f));

end;


shocks;

	//var e_c;
	//stderr 0.0129;
	var	e_y;
	stderr 0.0071;
	//var e_g;
	//stderr 0.0062;
	//var e_miu;
	//stderr 0.0013;
	
end;

//stoch_simul(order=1);
planner_objective 0.5*phi_y*y^2+0.5*phi_q*rs^2+0.5*phi_infl*infl^2;;
ramsey_policy(planner_discount=0.99);

//write_latex_dynamic_model;
//write_latex_static_model ;