%NCC.M
clc
clear all
format compact

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

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

DH =20;% KAPA*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;

dist=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] = ncc_variables(laL_o_rL, laH_o_rH,a, DL, DH);

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

lapLH = exp(WL*aH) * RSTAR; 
lapLL = exp(WL*aL)*RSTAR;

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

lapHL = exp(WH*aL)*RSTAR;
lapHH = exp(WH*aH)*RSTAR; 

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];

aL = aLnew;
aH = aHnew;

dist = max(abs(anew-aold))

iter = iter+1

end

save 1000_50