%TVCC.M
%Compute equilibrium dynamics in an economy with an aggregate collateral constraint studied in ``Individual versus Aggregate Coolateral Constraints and the Overborrowing Syndrome,'' by Martin Uribe. The aggregate collateral constraint is  of the form a_{t+1} <= kappa q_t k^*, where A_{t+1} denotes aggregate external debt due in t+1, q_t is the price of land, k^* is the fixed aggregae supply of land, and kappa is a parameter. Rents from financial rationing are assumed to accrue to domestic households. Equilibrium is computed using the Chebyshev parameterized expectations method. 
%(c) Martin Uribe, April 27, 2006. 

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] = tvcc_ss;

%Values of productivity shock
zL = z(1);
zH = z(2);

%Debt limits
DH = 7.14;
DL = -6; 

m = 1000; %number of grid points for debt

n = 30; %number of parameters in Chebyshev parameterization

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

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

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

a1L = zeros(n,1);
a1L(1) =  log(1);

%Regression Parameters High state
aH = aL;
a1H = a1L;

dist=1;  %distance
lambda = 0.01; %smoothing parameter

while dist>1e-12


%Parameterizing the object U_c(c_t,h_t)/R_t
laL_o_rL = exp(X*aL) ;
laH_o_rH = exp(X*aH);

%Parameterizing the price of land q_t
qL = exp(X*a1L) ;
qH = exp(X*a1H);

%Obtain other endogenous variables
[rL, rH, laL, laH, hL, hH, yL, yH, cL, cH, apL, apH, bettaL, bettaH] = tvcc_variables(laL_o_rL, laH_o_rH, qL, qH, a, DL, DH);


%Parameterizing U_c(c_t+1,h_t+1)/R_t+1

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

laLL_o_rLL = exp(WL*aL);
laLH_o_rLH = exp(WL*aH); 
laHL_o_rHL = exp(WH*aL);
laHH_o_rHH = exp(WH*aH); 


%Parameterizing q_t+1
qLL = exp(WL*a1L);
qLH = exp(WL*a1H); 
qHL = exp(WH*a1L);
qHH = exp(WH*a1H); 

%Obtaining future vaules of other endogenous variables
[rLL, rLH, laLL, laLH, hLL, hLH, yLL, yLH, cLL, cLH, apLL, apLH, bettaLL, bettaLH] = tvcc_variables(laLL_o_rLL, laLH_o_rLH, qLL, qLH, apL, DL, DH);

[rHL, rHH, laHL, laHH, hHL, hHH, yHL, yHH, cHL, cHH, apHL, apHH, bettaHL, bettaHH] = tvcc_variables(laHL_o_rHL, laHH_o_rHH, qHL, qHH, apH, DL, DH);


%Expected value of U_c(c_t+1,h_t+1)
ElapL = [laLL laLH] * PAIZ(1,:)';
ElapH = [laHL laHH] * PAIZ(2,:)';


%Compute the RHS of the bond Euler equation
rhsL = log (bettaL .* ElapL);
rhsH = log (bettaH .* ElapH);

%Compute the RHS of the price-of-land Euler equation
xLL = laLL .* (qLL + exp(zL) * ALFA * (hLL/Kss).^(1-ALFA) );

xLH = laLH .* (qLH + exp(zH) * ALFA * (hLH/Kss).^(1-ALFA) );

xHL = laHL .* (qHL + exp(zL) * ALFA * (hHL/Kss).^(1-ALFA) );

xHH = laHH .* (qHH + exp(zH) * ALFA * (hHH/Kss).^(1-ALFA) );

ExpL = [xLL xLH] * PAIZ(1,:)';
ExpH = [xHL xHH] * PAIZ(2,:)';

rhs1L = log(bettaL .* ExpL ./ laL);
rhs1H = log (bettaH .* ExpH ./ laH);

%Store old value of parameter vector
aLold = aL;
aHold = aH;
aold = [aLold; aHold];

a1Lold = a1L;
a1Hold = a1H;
a1old = [a1Lold; a1Hold];

Aold = [aold; a1old];

%Compute new parameter vectors by OLS
aLnew = D*X'*rhsL;
aHnew = D*X'*rhsH; 
anew = [aLnew;aHnew];

a1Lnew = D*X'*rhs1L;
a1Hnew = D*X'*rhs1H; 
a1new = [a1Lnew;a1Hnew];

Anew = [anew; a1new];

%Compute distance between old and new parameter
dist_old = dist;
dist = max(abs(Anew-Aold));

%Reset smoothing parameter
if dist<dist_old
lambda = 1 + 0.99 * (lambda-1);
else
lambda = 0.01;
end

%Update parameter vectors
aL = aLnew*lambda+aLold*(1-lambda);
aH = aHnew*lambda+aHold*(1-lambda);
a1L = a1Lnew*lambda+a1Lold*(1-lambda);
a1H = a1Hnew*lambda+a1Hold*(1-lambda);

dist 
lambda


end