%RAMSEY_RUN.M
%Compute a second-order approximation of the Ramsey equilibrium conditions of the model developed in  ``Optimal,  Simple, and Implementable Monetary and Fiscal Rules,'' by S. Schmitt-Grohe and Martin Uribe (2006)
%(c) Stephanie Schmitt-Grohe and Martin Uribe, May 2006

%Prerequisits: run RAMSEY_SS.mat (produced by  RAMSEY_SS.M) and RAMSEY_F.MAT (produced by RAMSEY_F.M)
%Output: RAMSEY_RUN.MAT 

clear all

load ramsey_f %produced by RAMSEY_F.M

load ramsey_ss %This is saved automatically, when running ramsey_ss.m


approx = 2;

num_eval

[gx,hx] = gx_hx(nfy,nfx,nfyp,nfxp);
disp('done with gx_hx')
%Recall that the innovation to the state vector is given by sigma * ETAMATRIX * eps_{t+1}, where sigma is a scalar, ETAMATRIX is a nx*ne matrix and eps_t is a vector of exogenous innovations of size neX1 distributed (0,I);
ne=2; 
ETAMATRIX = zeros(size(fx,2),ne); 

%The gov't purchases and techno shocks take the last 2 elements of the state vector x (see ramsey_f.M). Thus,
ETAMATRIX(end-1,1)=STD_EPSG;
ETAMATRIX(end,2)=STD_EPSZ;



if approx==2

[gxx,hxx] = gxx_hxx(nfx,nfxp,nfy,nfyp,nfypyp,nfypy,nfypxp,nfypx,nfyyp,nfyy,nfyxp,nfyx,nfxpyp,nfxpy,nfxpxp,nfxpx,nfxyp,nfxy,nfxxp,nfxx,hx,gx);

disp('done with gxx_hxx')

[gss,hss] = gss_hss(nfx,nfxp,nfy,nfyp,nfypyp,nfypy,nfypxp,nfypx,nfyyp,nfyy,nfyxp,nfyx,nfxpyp,nfxpy,nfxpxp,nfxpx,nfxyp,nfxy,nfxxp,nfxx,hx,gx,gxx,ETAMATRIX);

disp('done with gss_hss')

sig =1;

conditional_welfare = vt_cu  +  gss(1)  * sig^2 / 2

[Ey,Ex] = unconditional_mean(gx, hx, gxx, hxx, gss, hss, ETAMATRIX, 1);

unconditional_welfare = Ey(1) + vt_cu; 

end %if approx==2

save ramsey_run.mat

%material for computing welfare costs (used in competitive_run.m)
conditional_welfare_ramsey=conditional_welfare;
unconditional_welfare_ramsey=unconditional_welfare;
ss_welfare_ramsey = vt_cu;
sig_ramsey = sig;

save welfare_ramsey.mat BETTA  SIGMA sig_ramsey    conditional_welfare_ramsey unconditional_welfare_ramsey ss_welfare_ramsey