%COMPETITIVE_RUN.M
%competitive_run(economy) 
%Compute a second-order accurate level of welfare  and welfare cost measure for a particular interest-rate rule relative to the ramsey-optimal rule in the model devaloped in    ``Optimal,  Simple, and Implementable Monetary and Fiscal Rules,'' by S. Schmitt-Grohe and Martin Uribe (2006). Welfare is measured conditional on the intial state being the ramsey steady state and unconditionally. 
%ECONOMY is a string indicating the parameterization of the monetary policy. Possible values are: 'taylor', 'taylor_simple', 'optimized_no_smoothing', 'inflation_targeting', 'optimized_x_y' where x takes the values 'smoothing' and 'no_smoothing' and y takes the values 'crule', 'brule' 'frule', or 'drule'.
%Prerequisits: RAMSEY_SS.mat (produced by  RAMSEY_SS.M) and COMPETITIVE_F.MAT (produced by COMPETITIVE_F.M) and welfare_ramsey.mat (produced by ramsey_run.m)
%OUtput: A mat file eval([economy '_run.mat'])
%(c) Stephanie Schmitt-Grohe and Martin Uribe, June 2006

function competitive_run(economy) 


load competitive_f %produced by COMPETITIVE_F.M

load ramsey_ss %produced by ramsey_ss.m

%Symbols pertaining to the policy rule
RSTAR = r_cu;
PAISTAR = pai_cu;
OUTPUT = output_cu; 

%Taylor Rule
if strcmp(economy,'taylor')
ALFA_R_CU = 1;
ALFA_R_BA1 = 0;
ALFA_PAI = 1.5;
ALFA_Y = 0.5;
GAMA1 = 0.5;
crule = 1;
brule = 0;
frule = 0;
drule = 0;


%Simple Taylor Rule
elseif strcmp(economy,'taylor_simple')
ALFA_R_CU = 1;
ALFA_R_BA1 = 0;
ALFA_PAI = 1.5;
ALFA_Y = 0;
GAMA1 = 0.5;
crule = 1;
brule = 0;
frule = 0;
drule = 0;

%Inflation Targeting
elseif strcmp(economy,'inflation_targeting')
ALFA_R_CU = 0;
ALFA_R_BA1 = 0;
ALFA_PAI = 1;
ALFA_Y = 0;
GAMA1 = 0.5;
crule = 1;
brule = 0;
frule = 0;
drule = 0;

%Optimized Rules
else 
eval(['load ' economy '.mat']) %produced by competitive_optimized.m
end

approx = 2;

num_eval

[gx,hx,exitflag] = gx_hx(nfy,nfx,nfyp,nfxp);
disp('done with gx_hx')

if exitflag==1

[gxx,hxx] = gxx_hxx_noloop(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')

%Recall that the innovation to the state vector is given by sig * ETAMATRIX * eps_{t+1}, where sig 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;

[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
eval(['conditional_welfare_' economy ' = vt_cu  +  gss(1)  * sig^2 / 2']) 

%welfare cost realtive to Ramsey
load welfare_ramsey; %produced by ramsey_run.m
grss = (conditional_welfare_ramsey - ss_welfare_ramsey) * 2 / sig_ramsey^2;

eval(['conditional_welfare_cost_' economy ' = (grss-gss(1))/((1-SIGMA)*ss_welfare_ramsey+1/(1-BETTA))*sig^2/2*100']);


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

eval(['unconditional_welfare_' economy ' = Ey(1) + ss_welfare_ramsey']);


%Uncionditional welfare cost
eval(['unconditional_welfare_cost_' economy ' = (unconditional_welfare_ramsey-Ey(1) - ss_welfare_ramsey)/((1-SIGMA)*ss_welfare_ramsey+1/(1-BETTA))*100']);


eval(['save ' economy '_run.mat'])

end %if exitflag==1