clc; format short g; clear all; close all;

 
% import data from Excel
X = importdata('econ7720_VAR_data.xls')


% define variables for the VAR 
Y = X.data.Sheet1(:,1);                     % Y = log of real GDP
P = X.data.Sheet1(:,2);                     % P = log of implicit GDP deflator
PCOM = X.data.Sheet1(:,3);                  % PCOM = smoothed change in index of sensitive commodity prices
FF = X.data.Sheet1(:,4);                    % FF = federal funds rate    
NBR = X.data.Sheet1(:,5);                   % TR = log of total reserves
TR = X.data.Sheet1(:,6);                    % NBR = log of nonborrowed reserves + extended credit
M1 = X.data.Sheet1(:,7);                    % M1 = log of M1 money stock
M2 = X.data.Sheet1(:,8);                    % M2 = log of M2 money stock
MB = X.data.Sheet1(:,9);                    % MB = log of M0 money stock (monetary base)



% First Identification Scheme: 
% X1(t) = [Y(t) P(t) PCOM(t)]'  S(t) = FF(t)  X2(t) = [NBR(t) TR(t) M(t)]'    
%--------------------------------------------------------------------------
% estimate the reduced-form VAR(p)
p = 4;                                      % p = desired lag length 
output1 = var([Y P PCOM FF NBR TR M1],p,1)  

% use Sims triangular (resursive) identification procedure
T = 20;                                     % desired horizon for impulse response functions
s = 1;                                      % desired horizon for variance decompositions    
output2 = sims_ident(output1,T,s) 

% graph the identified impulse response function to a monetary shock
time = [0:1:T];
n = output1.neqs;

irf_Y = output2.pIRF(n*3+1,:);
irf_P = output2.pIRF(n*3+2,:);
irf_PCOM = output2.pIRF(n*3+3,:);
irf_FF = output2.pIRF(n*3+4,:);
irf_NBR = output2.pIRF(n*3+5,:);
irf_TR = output2.pIRF(n*3+6,:);
irf_M = output2.pIRF(n*3+7,:);

figure,
subplot(4,2,1)
plot(time,irf_Y), title('Y'), axis([-2 T -.8 .2]), grid on
subplot(4,2,2)
plot(time,irf_P), title('P'), axis([-2 T -.9 .2]), grid on
subplot(4,2,3)
plot(time,irf_PCOM), title('PCOM'), axis([-2 T -.25 .15]), grid on
subplot(4,2,4)
plot(time,irf_FF), title('FF'), axis([-2 T -.6 1]), grid on
subplot(4,2,5)
plot(time,irf_NBR), title('NBR'), axis([-2 T -1 .8]), grid on
subplot(4,2,6)
plot(time,irf_TR), title('TR'), axis([-2 T -.8 .6]), grid on
subplot(4,2,7)
plot(time,irf_M), title('M'), axis([-2 T -.6 .3]), grid on
%--------------------------------------------------------------------------



% % Second Identification Scheme: 
% % X1(t) = [Y(t) P(t) PCOM(t)]'  S(t) = NBR(t)  X2(t) = [FF(t) TR(t) M(t)]'    
% %--------------------------------------------------------------------------
% % estimate the reduced-form VAR(p)
% p = 4;                                      % p = desired lag length 
% output1 = var([Y P PCOM NBR FF TR M1],p,1)  
% 
% % use Sims triangular (resursive) identification procedure
% T = 20;                                     % desired horizon for impulse response functions
% s = 1;                                      % desired horizon for variance decompositions    
% output2 = sims_ident(output1,T,s)
% 
% % graph the identified impulse response function to a monetary shock
% time = [0:1:T];
% n = output1.neqs;
% 
% irf_Y = output2.nIRF(n*3+1,:);
% irf_P = output2.nIRF(n*3+2,:);
% irf_PCOM = output2.nIRF(n*3+3,:);
% irf_NBR = output2.nIRF(n*3+4,:);
% irf_FF = output2.nIRF(n*3+5,:);
% irf_TR = output2.nIRF(n*3+6,:);
% irf_M = output2.nIRF(n*3+7,:);
% 
% figure,
% subplot(4,2,1)
% plot(time,irf_Y), title('Y'), axis([-2 T -.6 .2]), grid on
% subplot(4,2,2)
% plot(time,irf_P), title('P'), axis([-2 T -.6 .2]), grid on
% subplot(4,2,3)
% plot(time,irf_PCOM), title('PCOM'), axis([-2 T -.20 .10]), grid on
% subplot(4,2,4)
% plot(time,irf_NBR), title('NBR'), axis([-2 T -2 .90]), grid on
% subplot(4,2,5)
% plot(time,irf_FF), title('FF'), axis([-2 T -.3 .6]), grid on
% subplot(4,2,6)
% plot(time,irf_TR), title('TR'), axis([-2 T -1.25 .5]), grid on
% subplot(4,2,7)
% plot(time,irf_M), title('M'), axis([-2 T -.75 .25]), grid on
% %--------------------------------------------------------------------------



% % Third Identification Scheme: 
% % X1(t) = [Y(t) P(t) PCOM(t) TR(t)]'  S(t) = NBR(t)  X2(t) = [FF(t) M(t)]'    
% %--------------------------------------------------------------------------
% % estimate the reduced-form VAR(p)
% p = 4;                                      % p = desired lag length 
% output1 = var([Y P PCOM TR NBR FF M1],p,1)  
% 
% % use Sims triangular (resursive) identification procedure
% T = 20;                                     % desired horizon for impulse response functions
% s = 1;                                      % desired horizon for variance decompositions    
% output2 = sims_ident(output1,T,s)
% 
% % graph the identified impulse response function to a monetary shock
% time = [0:1:T];
% n = output1.neqs;
% 
% irf_Y = output2.nIRF(n*4+1,:);
% irf_P = output2.nIRF(n*4+2,:);
% irf_PCOM = output2.nIRF(n*4+3,:);
% irf_TR = output2.nIRF(n*4+4,:);
% irf_NBR = output2.nIRF(n*4+5,:);
% irf_FF = output2.nIRF(n*4+6,:);
% irf_M = output2.nIRF(n*4+7,:);
% 
% figure,
% subplot(4,2,1)
% plot(time,irf_Y), title('Y'), axis([-2 T -.8 .2]), grid on
% subplot(4,2,2)
% plot(time,irf_P), title('P'), axis([-2 T -.7 .2]), grid on
% subplot(4,2,3)
% plot(time,irf_PCOM), title('PCOM'), axis([-2 T -.2 .2]), grid on
% subplot(4,2,4)
% plot(time,irf_TR), title('TR'), axis([-2 T -.6 .8]), grid on
% subplot(4,2,5)
% plot(time,irf_NBR), title('NBR'), axis([-2 T -1.5 1]), grid on
% subplot(4,2,6)
% plot(time,irf_FF), title('FF'), axis([-2 T -.4 .8]), grid on
% subplot(4,2,7)
% plot(time,irf_M), title('M'), axis([-2 T -.5 .5]), grid on
% %--------------------------------------------------------------------------



% % First Robustness Check: exclude Y(t) from policymaker's information set
% % X1(t) = [P(t) PCOM(t)]'  S(t) = FF(t)  X2(t) = [Y(t) NBR(t) TR(t) M(t)]'    
% %--------------------------------------------------------------------------
% % estimate the reduced-form VAR(p)
% p = 4;                                      % p = desired lag length 
% output1 = var([P PCOM FF Y NBR TR M1],p,1)  
% 
% % use Sims triangular (resursive) identification procedure
% T = 20;                                     % desired horizon for impulse response functions
% s = 1;                                      % desired horizon for variance decompositions    
% output2 = sims_ident(output1,T,s)
% 
% % graph the identified impulse response function to a monetary shock
% time = [0:1:T];
% n = output1.neqs;
% 
% irf_Y = output2.pIRF(n*2+4,:);
% 
% figure,
% plot(time,irf_Y), title('Y'), axis([-2 T -.8 .3]), grid on
% % %--------------------------------------------------------------------------



% % Second Robustness Check: exclude PCOM(t) from the VAR altogether
% % X1(t) = [Y(t) P(t)]'  S(t) = FF(t)  X2(t) = [NBR(t) TR(t) M(t)]'    
% %--------------------------------------------------------------------------
% % estimate the reduced-form VAR(p)
% p = 4;                                      % p = desired lag length 
% output1 = var([Y P FF NBR TR M1],p,1)  
% 
% % use Sims triangular (resursive) identification procedure
% T = 20;                                     % desired horizon for impulse response functions
% s = 1;                                      % desired horizon for variance decompositions    
% output2 = sims_ident(output1,T,s)
% 
% % graph the identified impulse response function to a monetary shock
% time = [0:1:T];
% n = output1.neqs;
% 
% irf_P = output2.pIRF(n*2+2,:);
% 
% figure,
% plot(time,irf_P), title('P'), axis([-2 T -.5 .5]), grid on
% %--------------------------------------------------------------------------



% % Third Robustness Check: equate policy with shocks to MB, M1, or M2
% % X1(t) = [Y(t) P(t) PCOM(t)]'  S(t) = M(t)  X2(t) = [FF(t) NBR(t)]'    
% %--------------------------------------------------------------------------
% % estimate the reduced-form VAR(p)
% p = 4;                                      % p = desired lag length 
% output1 = var([Y P PCOM M2 FF NBR],p,1)  
% 
% % use Sims triangular (resursive) identification procedure
% T = 20;                                     % desired horizon for impulse response functions
% s = 1;                                      % desired horizon for variance decompositions    
% output2 = sims_ident(output1,T,s)
% 
% % graph the identified impulse response function to a monetary shock
% time = [0:1:T];
% n = output1.neqs;
% 
% irf_Y = output2.nIRF(n*3+1,:);
% irf_P = output2.nIRF(n*3+2,:);
% irf_PCOM = output2.nIRF(n*3+3,:);
% irf_M = output2.nIRF(n*3+4,:);
% irf_FF = output2.nIRF(n*3+5,:);
% irf_NBR = output2.nIRF(n*3+6,:);
% 
% 
% figure,
% subplot(3,2,1)
% plot(time,irf_Y), title('Y'), grid on
% subplot(3,2,2)
% plot(time,irf_P), title('P'), grid on
% subplot(3,2,3)
% plot(time,irf_PCOM), title('PCOM'), grid on
% subplot(3,2,4)
% plot(time,irf_M), title('M'), grid on
% subplot(3,2,5)
% plot(time,irf_FF), title('FF'), grid on
% subplot(3,2,6)
% plot(time,irf_NBR), title('NBR'), grid on
% %--------------------------------------------------------------------------