%CC.M
%This program approximates the equilibrium of the economy with an aggregate debt limit and financial rents accruing to domestic residents. The output is a pair of vectors of parameters, aL and aH, which parameterize the variable R_t*c_t as exp(X*aL) if the current productivity shock is z^1 and as exp(X*aH) if the current productivity shock is z^2, where X is a matrix defined below. 
%
%Calls CC_VARIABLES.M
%

clc
clear all
format compact

%Deep parameters and steady-state values
[RSTAR, SIG, OMEGA, BETTA1, ALFA, MU, z, PAIZ, KAPA, Kss,  QQss, Css, Hss, LAss, Ass, Yss, BETTAss] = cc_ss;


zL = z(1);
zH = z(2);

DH = KAPA*QQss*Kss;%upper bound on debt

DL = -10; %lower bound on debt

m = 1000; %number of grid points

n = 50; %number of regressors

a = chebygrid(DL,DH,m); %debt grid in levels 

X = chebyreg(m,n); %regressors
D = inv(X'*X);

%Regression Parameters Low state
aL = zeros(n,1);
aL(1) =  log(LAss/RSTAR);%log(LAss/RSTAR*.5);

%Regression Parameters High state
aH = aL;

uu = 0.01;
u = 1;

dist=1; dist_old =1;
iter =1;

while dist>1e-12

laL_o_rL = exp(X*aL) ;
laH_o_rH = exp(X*aH);

[rL, rH, laH, laL, hL, hH, yL, yH, cL, cH, apL, apH, bettaL, bettaH] = cc_variables(laL_o_rL, laH_o_rH,a, DL, DH);

WL = chebyreg2(apL,DL,DH,n);
WH = chebyreg2(apH,DL,DH,n);

lapLH_o_rpLH = exp(WL*aH); 
lapLL_o_rpLL = exp(WL*aL);

[rpLL, rpLH, lapLH, lapLL] = cc_variables(lapLL_o_rpLL, lapLH_o_rpLH,apL, DL, DH);

lapL = [lapLL lapLH] * PAIZ(1,:)';

lapHL_o_rpHL = exp(WH*aL);
lapHH_o_rpHH = exp(WH*aH); 

[rpHL, rpHH, lapHH, lapHL] = cc_variables(lapHL_o_rpHL, lapHH_o_rpHH,apH, DL, DH);

lapH = [lapHL lapHH] * PAIZ(2,:)';

rhsL = log (bettaL .* lapL);
rhsH = log (bettaH .* lapH);

aLold = aL;
aHold = aH;
aold = [aLold;aHold];

aLnew = D*X'*rhsL;
aHnew = D*X'*rhsH; 

anew = [aLnew;aHnew];

dist = max(abs(anew-aold))

u = (uu + u*(1-uu)) * (dist<=dist_old) + 0.01*(dist>dist_old);

[dist<dist_old u]

dist_old = dist;

aL = aLnew*u + aLold *(1-u);
aH = aHnew*u + aHold*(1-u);

dist_old = dist;

end

save 2000_100