%
%  ber.m  -- solves Burnside, Eichenbaum and Rebelo (JPE, 1993) model
%
%  George Hall
%  Brandeis Univeristy
%  October 2006

close all
clear
global TE nx

nx = 5;     % number of state varibles
nu = 3;     % number of control variables 
nz = nx+nu;
%
%  set initial parameter values 
%                       
TE     = 1369;
alpha  = 0.654;         
delta  = 0.021;         
beta   = 1.03^(-.25);    
muA    = -0.023;         
muG    = 0.0904;         
rhoA   = 0.982;         
rhoG   = 0.987;         
gamma1  = 1.004;         
gamma2  = 1.002;         
h1     = 37*13;
xi     = 60;
v      = 3.61;         
sigmaA = 0.0053;         
sigmaG = 0.014;         
%
%   compute steady state for detrended (but still in levels) economy
%
pstar = [alpha; beta; delta; muA; muG; rhoA; rhoG; h1; v; xi; gamma1 ];
[zstar] = sstate(pstar);
zSS = log(zstar);
%
%     Create State Space Representation and map
%     problem into the Optimal Linear Regulator
%     Framework.
%
%        max  X'qX + U'rU + 2U'wX
%
%        s.t  X(t+1) = A1 X(t) + B U(t) + C w(t+1)
%
%     where X' = [ 1  Z(t) log(G)(t) log(K)(t) log(N1)(t) ]
%
%     and  U' = [ log(N1)(t+1) log(W)(t) log(K)(t+1) ]
%
[r,dr_dz,d2r_dz2 ] = derret(zSS,pstar);
%
%   Use formula from Hansen, McGrattan & Sargent to get matricies 
%
e = [ 1 0 0 0 0 0 0 0]';
M = e*( r - dr_dz'*zSS + .5*zSS'*d2r_dz2'*zSS)*e' + ...
    .5*( e*dr_dz' + dr_dz*e' - e*zSS'*d2r_dz2 - d2r_dz2*zSS*e' + d2r_dz2 );
Qmat = M(1:nx,1:nx);
Rmat = M(nx+1:nz,nx+1:nz);
Wmat = M(1:nx,nx+1:nz);
%
%   form the A,B,C,G,D matricies
%
A1=  [      1         0        0         0      0;
           muA      rhoA       0         0      0;
           muG        0      rhoG        0      0;
            0         0        0         0      0;
            0         0        0         0      0];

B = [       0         0        0;
            0         0        0;
            0         0        0;   
            0         0        1;
            1         0        0];

C = [      0        0; 
         sigmaA     0;
           0     sigmaG; 
           0        0;
           0        0];

%
%    solve for decison rules:  U(t) = -F X(t)
%
[F,P] = olrp(beta,A1,B,Qmat,Rmat,Wmat);
%
%
%
A = A1 - B*F;
%
%    Let's print out some impulse response functions    
%
ny=12;
[G] = getGber2(zSS,pstar,F);
disp('Labor Hoarding: Technology Shock' );

C = [      0;
           1;
           0;
           0;
           0 ];

[Y2sim,X] = bimpulse(A,C,G,zeros(ny,1),1,50);

figure(1)
plot([2:50]',Y2sim(2:50,[6 8]));
title('Labor Hoarding: Tech. Shock on employment and effort');
legend('employ','effort');
print -dpsc2 ber_imp_resp.ps

figure(2)
plot([2:50]',Y2sim(2:50,[1 5 6 8]));
title('Labor Hoarding: Tech. Shock on q,k,n,e');
legend('output','capital','hours','effort');
print -dpsc2 -append ber_imp_resp.ps

figure(3)
plot([2:50]',Y2sim(2:50,[1 2 3]));
title('Labor Hoarding: Tech. Shock on q,c,i');
legend('output','consumption','investment');
print -dpsc2 -append ber_imp_resp.ps

figure(4)
plot([2:50]',Y2sim(2:50,[10 11]));
title('Labor Hoarding: Tech. Shock on Technology & Solow Residual');
legend('technology','Solow residual');
print -dpsc2 -append ber_imp_resp.ps

disp('im pausing: hit return key');
pause

disp('Labor Hoarding: Government Shock' );

C = [      0;
           0;
           1;
           0;
           0];

[Y3sim,X] = bimpulse(A,C,G,zeros(ny,1),1,50);

figure(5)
plot([2:50]',Y3sim(2:50,[6 8]));
title('Labor Hoarding: Gov Shock on employment and effort');
legend('employ','effort');
print -dpsc2 -append ber_imp_resp.ps

figure(6)
plot([2:50]',Y3sim(2:50,[1 5 6 8]));
title('Labor Hoarding: Gov Shock on q,k,n,e');
legend('output','capital','hours','effort');
print -dpsc2 -append ber_imp_resp.ps

figure(7)
plot([2:50]',Y3sim(2:50,[1 2 3]));
title('Labor Hoarding: Gov. Shock on q,c,i');
legend('output','consumption','investment');
print -dpsc2 -append ber_imp_resp.ps

figure(8)
plot([2:50]',Y3sim(2:50,[10 11]));
title('Labor Hoarding: Gov Shock on Technology & Solow Residual');
legend('technology','Solow residual');
print -dpsc2 -append ber_imp_resp.ps