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alternative_identification.m
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alternative_identification.m
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%////////////////////////////////////////////////////////////////%
%//////- Structural-VAR (Assessment Idetificatiojn) - ///////%
%////////////////////////////////////////////////////////////////%
clc;
clear;
%---
z1=xlsread('Data_oil_1.xlsx');
time=(1973+1/12:1/12:2019)';
RAC = [z1(:,1)]; % US Refiner Acquisition Cost of Crude Oil
WTI = [z1(:,2)]; % West Texas Intermediate Oil Price
Oil_p = [z1(:,3)]; % Global Oil production
Oil_i = [z1(:,4)]; % OECD oil invetories
Kil_i = [z1(:,5)]; % A proxy of Global economic activity
Ham_i = [z1(:,6)]; % 2 years growth in global industry production
%Montly Percentage change in global crude oil production
[T,~]=size(Oil_p);
for i =1: size(Oil_p,2)
for ii=2 : size(Oil_p,1)
goil_p(ii-1,i)=((Oil_p(ii,i)-Oil_p(ii-1,i)))*100;
end
end
%Montly Percentage change in OECD oil inventories
[T,~]=size(Oil_i);
for i =1: size(Oil_i,2)
for ii=2 : size(Oil_i,1)
goil_i(ii-1,i)=((Oil_i(ii,i)-Oil_i(ii-1,i)))*100;
end
end
% Anual Percentage change in global crude oil production
gaoil_p=100*((Oil_p(13:T,1)./Oil_p(1:T-12,1))-1);
%% VAR Estimation
%The model is estimating using seasonal dummies and 24 autoregressive lags
% Information assemble. The sample goes from 1973m2 to 2006m12
%z2= [goil_p Kil_i(2:T,:) RAC(2:T,:) goil_i ];
z3= [goil_p Kil_i(2:T,:) RAC(2:T,:) ];
mmm=size(z3,2);
pp=24;
Horiz=18;
no_ofIRF=535;
NO_MAX_TRIALS=100000;
which_Shock_plot=3;
which_Shock_plot_1=2;
which_Shock_plot_2=1;
[AR_3d,Chol_Var] = VAR_OLS(z3,pp,1,[]);
Ai_mat = dyn_multipliers(mmm,pp,AR_3d,Horiz);
%-----------------------------------------------%
%//// Impulse Responses by sign restriction ////%
%-----------------------------------------------%
[Q] = sing_restriction(Ai_mat,Chol_Var,NO_MAX_TRIALS);
%Oil Production
for ii=1:1:no_ofIRF
[Q] = sing_restriction(Ai_mat,Chol_Var,NO_MAX_TRIALS);
Store_Q(:,ii)=Q(:);
Shock_2=zeros(3,1); Shock_2(which_Shock_plot_2,1)=1;
IRF3d_2(:,:,ii)=Sirf(mmm,Horiz,Ai_mat,Chol_Var*Q,Shock_2)';
for shsh = 1:3
Shock=zeros(3,1); Shock(shsh,1)=1;
IRF4d_2(:,:,shsh,ii)=Sirf(mmm,Horiz,Ai_mat,Chol_Var*Q,Shock)';
end
clear Q
end
%Econoic Activity
for ii=1:1:no_ofIRF
[Q] = sing_restriction(Ai_mat,Chol_Var,NO_MAX_TRIALS);
Store_Q(:,ii)=Q(:);
Shock_1=zeros(3,1); Shock_1(which_Shock_plot_1,1)=1;
IRF3d_1(:,:,ii)=Sirf(mmm,Horiz,Ai_mat,Chol_Var*Q,Shock_1)';
for shsh = 1:3
Shock=zeros(3,1); Shock(shsh,1)=1;
IRF4d_1(:,:,shsh,ii)=Sirf(mmm,Horiz,Ai_mat,Chol_Var*Q,Shock)';
end
clear Q
end
%Real Price of Oil
for ii=1:1:no_ofIRF
[Q] = sing_restriction(Ai_mat,Chol_Var,NO_MAX_TRIALS);
Store_Q(:,ii)=Q(:);
Shock=zeros(3,1); Shock(which_Shock_plot,1)=1;
IRF3d(:,:,ii)=Sirf(mmm,Horiz,Ai_mat,Chol_Var*Q,Shock)';
for shsh = 1:3
Shock=zeros(3,1); Shock(shsh,1)=1;
IRF4d(:,:,shsh,ii)=Sirf(mmm,Horiz,Ai_mat,Chol_Var*Q,Shock)';
end
clear Q
end
%%
%---------------------------------------------%
%----------------- Ploting--------------------%
%---------------------------------------------%
TITLES=['Oil Supply Shock(-) ';...
'Oil Supply Shock(-) ';...
'Oil Supply Shock (+) ';...
'Aggregate Demand Shock(+) ';...
'Aggregate Demand Shock(+) ';...
'Aggregate Demand Shock(+) ';...
'Oil-Specific Demand Shock(+)';...
'Oil-Specific Demand Shock(-)';...
'Oil-Specific Demand Shock(+)';];
labels=['Oil Production ';...
'Real Activity ';...
'Real Price of Oil';...
'Oil Production ';...
'Real Activity ';...
'Real Price of Oil';...
'Oil Production ';...
'Real Activity ';...
'Real Price of Oil';];
for variab=1:1:mmm
figure(1)
subplot(1,3,variab);
PLOT_IRF=[];
for ii=1:1:no_ofIRF
PLOT_IRF=[PLOT_IRF IRF3d_2(:,variab,ii)];
end
plot([0:1:Horiz]',[PLOT_IRF],'linewidth',.1,'color','b');
xlim([0 Horiz])
title(TITLES(3*(which_Shock_plot_2-1)+variab,:),'FontSize',11);
ylabel(labels(3*(which_Shock_plot_2-1)+variab,:),'FontSize',11);
sgtitle('Graph: Impulse Responses (Identification by sign-restrictions)' )
end
for variab=1:1:mmm
figure(2)
subplot(1,3,variab);
PLOT_IRF=[];
for ii=1:1:no_ofIRF
PLOT_IRF=[PLOT_IRF IRF3d_1(:,variab,ii)];
end
plot([0:1:Horiz]',[PLOT_IRF],'linewidth',.1,'color','b');
xlim([0 Horiz])
title(TITLES(3*(which_Shock_plot_1-1)+variab,:),'FontSize',11);
ylabel(labels(3*(which_Shock_plot_1-1)+variab,:),'FontSize',11);
sgtitle('Graph: Impulse Responses (Identification by sign-restrictions)' )
end
for variab=1:1:mmm
figure(3)
subplot(1,3,variab);
PLOT_IRF=[];
for ii=1:1:no_ofIRF
PLOT_IRF=[PLOT_IRF IRF3d(:,variab,ii)];
end
plot([0:1:Horiz]',[PLOT_IRF],'linewidth',.1,'color','b');
xlim([0 Horiz])
title(TITLES(3*(which_Shock_plot-1)+variab,:),'FontSize',11);
ylabel(labels(3*(which_Shock_plot-1)+variab,:),'FontSize',11);
sgtitle('Graph: Impulse Responses (Identification by sign-restrictions)' )
end
%%
%-------------------------------------------%
%--------- Median Impulse Responses---------%
%-------------------------------------------%
low_quant = .16;
up_quant = .84;
for d1 = 1:size(IRF4d,1)
for d2 = 1:size(IRF4d,2)
for shsh = 1:size(IRF4d,3)
IRF3d_MED(d1,d2,shsh)=median(squeeze(IRF4d(d1,d2,shsh,:)));
IRF3d_UP(d1,d2,shsh)=quantile(squeeze(IRF4d(d1,d2,shsh,:)),up_quant);
IRF3d_DOWN(d1,d2,shsh)=quantile(squeeze(IRF4d(d1,d2,shsh,:)),low_quant);
end
end
end
zirf_med_1=IRF3d_MED(:,1,1);% Oil Supply to Oil production
zirf_med_2=IRF3d_MED(:,2,1);%Aggregate demand to Oil produciton
zirf_med_3=IRF3d_MED(:,3,1);%Specific-demand to Oil production
zirf_med_4=IRF3d_MED(:,1,2);%Oil supply to real activity
zirf_med_5=IRF3d_MED(:,2,2);%Aggregate demand to real activity
zirf_med_6=IRF3d_MED(:,3,2);%Specific-demand to Oil production
zirf_med_7=IRF3d_MED(:,1,3);%Oil supply to real price of oil
zirf_med_8=IRF3d_MED(:,2,3);% Aggregate demand to real price
zirf_med_9=IRF3d_MED(:,3,3);%Oil-specific demand to real price of oil
%--------------------------------------
TITLES=['Oil Supply Shock(-) ';...
'Oil Supply Shock(-) ';...
'Oil Supply Shock(+) ';...
'Aggregate Demand Shock(+) ';...
'Aggregate Demand Shock(+) ';...
'Aggregate Demand Shock(+) ';...
'Oil-Specific Demand Shock(+)';...
'Oil-Specific Demand Shock(-)';...
'Oil-Specific Demand Shock(+)';];
labels=['Oil Production ';...
'Real Activity ';...
'Real Price of Oil';...
'Oil Production ';...
'Real Activity ';...
'Real Price of Oil';...
'Oil Production ';...
'Real Activity ';...
'Real Price of Oil';];
% Ploting
for ii=1:1:3;
for variab=1:1:mmm
figure(4)
subplot(3,3,3*(ii-1)+variab);
plot([0:1:Horiz]',[IRF3d_MED(:,variab,ii)'],'linewidth',2);
hold
plot([0:1:Horiz]',[IRF3d_DOWN(:,variab,ii) IRF3d_UP(:,variab,ii)],'linewidth',1,'LineStyle','--','color','k');
title(TITLES(3*(ii-1)+variab,:),'FontSize',11);
ylabel(labels(3*(ii-1)+variab,:),'FontSize',11);
xlim([0 Horiz])
sgtitle('Graph: Impulse Responses (Identification by sign-restrictions)' )
end
end
%% Choleski vs Sign Restriction Identification
%First, SVAR estimation by Choleski decomposition
[T, N] = size(z3);
Horiz_1=24;
[A_2,SIGMA_2, Uhat_2, V_2]=lsvarcsa(z3,Horiz_1);
mm_2=size(z3,2);
B0inv_2=chol(SIGMA_2(1:N,1:N))';
J_1=[eye(N,N) zeros(N,N*(Horiz_1-1))];
IRF_storage_2=reshape(J_1*A_2^0*J_1'*B0inv_2,N^2,1);
for i=1:T-Horiz_1-1
IRF_storage_2=([IRF_storage_2 reshape(J_1*A_2^i*J_1'*B0inv_2,N^2,1)]);
end;
IRF_storage_2_w=IRF_storage_2
IRF_storage_2=IRF_storage_2(:,1:19)'
%--Ploting the impulses responses with and with-out inventories
hh = 18;
figure(5);
subplot(3,3,1);
plot([0:hh]',[zirf_med_1],'linewidth',2)
hold on;
plot([0:hh]',[zeros(hh+1,1) IRF_storage_2(:,1) ],'linewidth',1,'LineStyle','-','color','k');
xlim([0 hh])
legend([], 'Sign-Restriction' , 'Recursive Restriction', 'Location', 'best')
ylabel('Oil production','fontsize',11)
title('Oil supply shock','fontsize',11)
set(gcf, 'color', 'w')
legend('boxoff');
hold off;
subplot(3,3,4);
plot([0:hh]',[zirf_med_2],'linewidth',2)
hold on;
plot([0:hh]',[zeros(hh+1,1) IRF_storage_2(:,2) ],'linewidth',1,'LineStyle','-','color','k');
xlim([0 hh])
legend([], 'Sign-Restriction' , 'Rescursive Restriction', 'Location', 'best')
ylabel('Oil production','fontsize',11)
title('Aggregate demand shock','fontsize',11)
set(gcf, 'color', 'w')
legend('boxoff');
hold off;
subplot(3,3,7);
plot([0:hh]',[zirf_med_3],'linewidth',2)
hold on;
plot([0:hh]',[zeros(hh+1,1) IRF_storage_2(:,3) ],'linewidth',1,'LineStyle','-','color','k');
xlim([0 hh])
legend([], 'Sing Restriction' , 'Recursive Restriction', 'Location', 'best')
ylabel('Oil production','fontsize',11)
title('Oil-specific demand shock','fontsize',11)
set(gcf, 'color', 'w')
legend('boxoff');
hold off;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
subplot(3,3,2);
plot([0:hh]',[zirf_med_4],'linewidth',2)
hold on;
plot([0:hh]',[zeros(hh+1,1) IRF_storage_2(:,4) ],'linewidth',1,'LineStyle','-','color','k');
xlim([0 hh])
legend([], 'Sing-Restriction' , 'Recursive Restriction', 'Location', 'best')
ylabel('Real Activity','fontsize',11)
title('Oil supply shock','fontsize',11)
set(gcf, 'color', 'w')
legend('boxoff');
hold off;
subplot(3,3,5);
plot([0:hh]',[zirf_med_5],'linewidth',2)
hold on;
plot([0:hh]',[zeros(hh+1,1) IRF_storage_2(:,5) ],'linewidth',1,'LineStyle','-','color','k');
xlim([0 hh])
legend([], 'Sing-Restrcition' , 'Recursive Restriction', 'Location', 'best')
ylabel('Real Activity','fontsize',11)
title('Aggregate demand shock','fontsize',11)
set(gcf, 'color', 'w')
legend('boxoff');
hold off;
subplot(3,3,8);
plot([0:hh]',[zirf_med_6],'linewidth',2)
hold on;
plot([0:hh]',[zeros(hh+1,1) IRF_storage_2(:,6) ],'linewidth',1,'LineStyle','-','color','k');
xlim([0 hh])
legend([], 'Sing-Restriction' , 'Recursive Restriction', 'Location', 'best')
ylabel('Real Activity','fontsize',11)
title('Oil-specific demand shock','fontsize',11)
set(gcf, 'color', 'w')
legend('boxoff');
hold off;
%%%%%%%%%%%%%%%%%%%%%%%
subplot(3,3,3);
plot([0:hh]',[zirf_med_7],'linewidth',2)
hold on;
plot([0:hh]',[zeros(hh+1,1) IRF_storage_2(:,7) ],'linewidth',1,'LineStyle','-','color','k');
xlim([0 hh])
legend([], 'Sing-Restriction' , 'Recursive Restriction', 'Location', 'best')
ylabel('Real oil price','fontsize',11)
title('Oil supply shock','fontsize',11)
set(gcf, 'color', 'w')
legend('boxoff');
hold off;
subplot(3,3,6);
plot([0:hh]',[zirf_med_8],'linewidth',2)
hold on;
plot([0:hh]',[zeros(hh+1,1) IRF_storage_2(:,8) ],'linewidth',1,'LineStyle','-','color','k');
xlim([0 hh])
legend([], 'Sing-Restrcition' , 'Recursive Restriction', 'Location', 'best')
ylabel('Real oil price','fontsize',11)
title('Aggregate demand shock','fontsize',11)
set(gcf, 'color', 'w')
legend('boxoff');
hold off;
subplot(3,3,9);
plot([0:hh]',[zirf_med_9],'linewidth',2)
hold on;
plot([0:hh]',[zeros(hh+1,1) IRF_storage_2(:,9) ],'linewidth',1,'LineStyle','-','color','k');
xlim([0 hh])
legend([], 'Sing-Restriction' , 'Recursive Restriction', 'Location', 'best')
ylabel('Real oil price','fontsize',11)
title('Oil-specific demand shock','fontsize',11)
set(gcf, 'color', 'w')
legend('boxoff');
hold off;
sgtitle('Graph: Structural Impulse Responses' )
%////////////////////////////////////////////////////////////////////////////////////////
%////////////////////////////////////////////////////////////////////////////////////////
figure(6);
subplot(3,3,1);
plot([0:hh]',[zirf_med_1],'linewidth',2)
hold on;
plot([0:hh]',[zeros(hh+1,1) -cumsum(squeeze(IRF_storage_2(:,1))) ],'linewidth',1,'LineStyle','-','color','k');
xlim([0 hh])
legend([], 'Sign-Restriction' , 'Recursive Restriction', 'Location', 'best')
ylabel('Oil production','fontsize',11)
title('Oil supply shock','fontsize',11)
set(gcf, 'color', 'w')
legend('boxoff');
hold off;
subplot(3,3,4);
plot([0:hh]',[zirf_med_2],'linewidth',2)
hold on;
plot([0:hh]',[zeros(hh+1,1) IRF_storage_2(:,2) ],'linewidth',1,'LineStyle','-','color','k');
xlim([0 hh])
legend([], 'Sign-Restriction' , 'Rescursive Restriction', 'Location', 'best')
ylabel('Oil production','fontsize',11)
title('Aggregate demand shock','fontsize',11)
set(gcf, 'color', 'w')
legend('boxoff');
hold off;
subplot(3,3,7);
plot([0:hh]',[zirf_med_3],'linewidth',2)
hold on;
plot([0:hh]',[zeros(hh+1,1) IRF_storage_2(:,3) ],'linewidth',1,'LineStyle','-','color','k');
xlim([0 hh])
legend([], 'Sing Restriction' , 'Recursive Restriction', 'Location', 'best')
ylabel('Oil production','fontsize',11)
title('Oil-specific demand shock','fontsize',11)
set(gcf, 'color', 'w')
legend('boxoff');
hold off;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
subplot(3,3,2);
plot([0:hh]',[zirf_med_4],'linewidth',2)
hold on;
plot([0:hh]',[zeros(hh+1,1) cumsum(IRF_storage_2(:,4)) ],'linewidth',1,'LineStyle','-','color','k');
xlim([0 hh])
legend([], 'Sing-Restriction' , 'Recursive Restriction', 'Location', 'best')
ylabel('Real Activity','fontsize',11)
title('Oil supply shock','fontsize',11)
set(gcf, 'color', 'w')
legend('boxoff');
hold off;
subplot(3,3,5);
plot([0:hh]',[zirf_med_5],'linewidth',2)
hold on;
plot([0:hh]',[zeros(hh+1,1) IRF_storage_2(:,5) ],'linewidth',1,'LineStyle','-','color','k');
xlim([0 hh])
legend([], 'Sing-Restrcition' , 'Recursive Restriction', 'Location', 'best')
ylabel('Real Activity','fontsize',11)
title('Aggregate demand shock','fontsize',11)
set(gcf, 'color', 'w')
legend('boxoff');
hold off;
subplot(3,3,8);
plot([0:hh]',[zirf_med_6],'linewidth',2)
hold on;
plot([0:hh]',[zeros(hh+1,1) IRF_storage_2(:,6) ],'linewidth',1,'LineStyle','-','color','k');
xlim([0 hh])
legend([], 'Sing-Restriction' , 'Recursive Restriction', 'Location', 'best')
ylabel('Real Activity','fontsize',11)
title('Oil-specific demand shock','fontsize',11)
set(gcf, 'color', 'w')
legend('boxoff');
hold off;
%%%%%%%%%%%%%%%%%%%%%%%
subplot(3,3,3);
plot([0:hh]',[zirf_med_7],'linewidth',2)
hold on;
plot([0:hh]',[zeros(hh+1,1) cumsum(IRF_storage_2(:,7)) ],'linewidth',1,'LineStyle','-','color','k');
xlim([0 hh])
legend([], 'Sing-Restriction' , 'Recursive Restriction', 'Location', 'best')
ylabel('Real oil price','fontsize',11)
title('Oil supply shock','fontsize',11)
set(gcf, 'color', 'w')
legend('boxoff');
hold off;
subplot(3,3,6);
plot([0:hh]',[zirf_med_8],'linewidth',2)
hold on;
plot([0:hh]',[zeros(hh+1,1) IRF_storage_2(:,8) ],'linewidth',1,'LineStyle','-','color','k');
xlim([0 hh])
legend([], 'Sing-Restrcition' , 'Recursive Restriction', 'Location', 'best')
ylabel('Real oil price','fontsize',11)
title('Aggregate demand shock','fontsize',11)
set(gcf, 'color', 'w')
legend('boxoff');
hold off;
subplot(3,3,9);
plot([0:hh]',[zirf_med_9],'linewidth',2)
hold on;
plot([0:hh]',[zeros(hh+1,1) IRF_storage_2(:,9) ],'linewidth',1,'LineStyle','-','color','k');
xlim([0 hh])
legend([], 'Sing-Restriction' , 'Recursive Restriction', 'Location', 'best')
ylabel('Real oil price','fontsize',11)
title('Oil-specific demand shock','fontsize',11)
set(gcf, 'color', 'w')
legend('boxoff');
hold off;
sgtitle('Graph: Structural Impulse Responses' )
%////////////////////////////////////////////////////////////////////////////////
%///////////////////////////////////////////////////////////////////////////////