%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 14.461 Blanchard-Kahn for Open Economy Dynamics                         %
%        FLEXIBLE EXCHANGE RATE                                           %
% ----------------------------------------------------------------------- %
% Suman Basu, September 2005                                              %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

tic

% Starting the program
clear

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Parameter values                                                        %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
alpha = 0.5;
beta = 0.1;
gamma = 20;
phi = 0.8;
pstar = 0;
estar = 0;

% Set matrix and stochastic steady state
a11 = 1 + phi + beta/alpha + 1/(alpha*gamma);
a12 = - phi - 1/(alpha*gamma);
a13 = - beta/alpha;
a21 = 1;
a22 = 0;
a23 = 0;
a31 = phi;
a32 = - phi;
a33 = 1;
M = [a11 a12 a13; a21 a22 a23; a31 a32 a33];
yss = 0;
pss = pstar;
ess = estar;
X = [0; 0; 0];

%Decompose matrix and solve for price level;
[V, J] = jordan(M)
Z = inv(V);
X(2) = 2;
X(3) = ess;
xstable = -(Z(2,2)/Z(2,1))*X(2)-(Z(2,3)/Z(2,1))*X(3);
X(1) = xstable;

% No. of periods
T = 20;

% Set up grid for graphing
price = zeros(1, T);
price(1,1) = X(2);
price(1,2) = X(1);

% Generate impulse response
for i = 1:T-2
    X = M*X;
    price(1, i + 2) = X(1);
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Graph time series                                                       %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% plot(1:T, price); grid
% title('Evolution of price level in FLEXIBLE exchange rate economy, mbar > m')

%Decompose matrix and solve for price level;
[V, J] = jordan(M)
Z = inv(V);
X(2) = 1;
N = Z(1,2)*Z(2,3)/Z(1,3)-Z(2,2);
D = Z(2,1)-Z(1,1)*Z(2,3)/Z(1,3);
x1stable = (N/D)*X(2);
x3stable = -(Z(1,1)/Z(1,3))*x1stable - (Z(1,2)/Z(1,3))*X(2);
X(1) = x1stable;
X(3) = x3stable;

% No. of periods
T = 30;

% Set up grid for graphing
price = zeros(1, T);
price(1,1) = X(2);
price(1,2) = X(1);

% Generate impulse response
for i = 1:T-2
    X = M*X;
    price(1, i + 2) = X(1);
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Graph time series                                                       %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
plot(1:T, price); grid
title('Evolution of price level in FLEXIBLE exchange rate economy, mbar = m')


toc