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script_FT.m
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script_FT.m
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%%==============================================================================
%% Run a Fair-Taylor (1983) algorithm to solve the DSGE model using actual technology series
%% Compute a weekly series for unemployment, and a weekly series for labor market tightness
%%==============================================================================
clear all; close all;
global apos thpos npos mplpos hpos wpos Rpos ynum upos
%% --- Setup ------
setup; data_1964_2009;
whp=10^5; % Weight on HP filter
%% --- As initial guess, solve for stochastic equilibrium ---
[TH,TH0]=MCSOLVE(PI,A);
%% --- Position of variables ---
apos=1; % technology
thpos = 2; % market tightness
npos = 3; % employment
upos = 4; % unemployment
mplpos = 5; % a*n^(alpha-1)
wpos =6; % w*a^gamma
Rpos = 7; % c*a/q(th)
hpos=8; % hire
ynum=8;
%% --- Initial guess of solution in any state: use stochastic steady-state ---values: ynum*ns
Y=zeros(ynum,ns);
Y(apos,:)=A;
Y(thpos,:)=TH;
Y(upos,:)=u(TH);
Y(npos,:)=(1-Y(upos,:))./(1-s);
Y(mplpos,:)=A.*Y(npos,:).^(alpha-1);
Y(wpos,:)=w.*A.^gamma;
Y(Rpos,:)=c.*A./q(TH);
Y(hpos,:)=s.*Y(npos,:);
%% --- Construct 3D array of expectation based on stochastic solutions: ---ynum*ns*k1
k2=400;%sufficiently long horizon to cover type-III iterations
EA=EXPECTEDMC(PI,A,k2);% ns*k2
ETH=EXPECTEDMC(PI,TH,k2);
EY=zeros(ynum,ns,k2+1);%ynum*ns*k2
EY(apos,:,:)=EA;
EY(thpos,:,:)=ETH;
EY(upos,:,:)=u(ETH);
EY(hpos,:,:)=f(ETH).*u(ETH);
EY(wpos,:,:)=w.*EA.^gamma;
EN=(1-u(ETH))./(1-s);
EY(npos,:,:)=EN;
EY(mplpos,:,:)=alpha.*EA.*EN.^(alpha-1);
EY(Rpos,:,:)=c.*EA./q(ETH);
YLR=STEADYGE(w,gamma);%steady state
%% --- Run the Fair-Taylor algorithm ---
n0=(1-ux(1))./(1-s); % Level of employment in data at t=-1
[WYt]=SIMULFT(TH,A,wamc,n0,EY,YLR);
Yt=WYt(:,1:12:end); % Extract quarterly series from weekly series
%% --- Plot decomposition of unemployment obtained with FT ---
At=Yt(apos,:);
Ut=Yt(upos,:);
ut0=hpfilter(log(Ut),whp);
ut1=exp(ut0);
Uthp=nairu.*ut1;
THt=Yt(thpos,:);
URt=max(1-((alpha./w).^(1./(1-alpha)).*At.^((1-gamma)./(1-alpha))),0);
UFt=Ut-URt;
YY=[UFt',URt'];
xt=[1,1+4.*10,1+4.*20,1+4.*30,1+4.*40]; % Plot on 1964--2009 period
xx=[1:nsample];
figure(1)
clf
harea=area(xx,YY);
set(get(harea(1),'Children'),'FaceColor',[.5 .9 .6],...
'EdgeColor','k',...
'LineWidth',3)
set(get(harea(2),'Children'),'FaceColor',[0 0 1],...
'EdgeColor','k',...
'LineWidth',3)
ylabel('Unemployment rate','FontSize',22)
ylim([0,.1])
set(gca,'Layer','top')
set(gca,'YGrid','on')
set(gca,'XGrid','on')
set(gca,'XTick',xt)
set(gca,'XTickLabel','1964|1974|1984|1994|2004')
set(gca,'FontSize',22)
gtext('\leftarrow Rationing unemp.','FontSize',22)
gtext('Frictional unemp.','FontSize',22)
print('-depsc','DECOFT2.eps')
%% --- Compare actual and predicted unemployment ---
figure(3)
clf
plot(Uthp,'--r','LineWidth',4)
hold on
plot(ux,'-b','LineWidth',4)
ylabel('Unemployment rate','FontSize',22)
set(gca,'YGrid','on','XGrid','on','FontSize',22)
ylim([0,0.1])
xlim([1,pas])
set(gca,'XTick',xt)
set(gca,'XTickLabel','1964|1974|1984|1994|2004')
h_legend=legend('Simulated','Actual');
set(h_legend,'FontSize',22,'Location','NorthWest');
print('-depsc','UFTHP.eps')
figure(12)
clf
plot(Uthp,'--r','LineWidth',4)
hold on
plot(Ut,'-b','LineWidth',4)
ylabel('Unemployment rate','FontSize',22)
set(gca,'YGrid','on','XGrid','on','FontSize',22)
ylim([0,0.1])
xlim([1,pas])
set(gca,'XTick',xt)
set(gca,'XTickLabel','1964|1974|1984|1994|2004')
h_legend=legend('Simulated and HP-filtered','Simulated');
set(h_legend,'FontSize',22,'Location','NorthWest');
print('-depsc','UFTHPcomp.eps')
figure(13)
clf
plot(ux,'-b','LineWidth',4)
hold on
plot(Ut,'--r','LineWidth',4)
plot(Uthp,'-.','Color',[0 0.5 0],'LineWidth',4)
ylabel('Unemployment rate','FontSize',22)
set(gca,'YGrid','on','XGrid','on','FontSize',22)
ylim([0,0.1])
xlim([1,pas])
set(gca,'XTick',xt)
set(gca,'XTickLabel','1964|1974|1984|1994|2004')
h_legend=legend('Actual','Simulated','Simulated and HP-filtered');
set(h_legend,'FontSize',22,'Location','NorthWest');
print('-depsc','UFTHPcomptot.eps')
%% --- Compare all different solution methods ---
figure(2)
clf
plot(Ut,'-b','LineWidth',4)
hold on
plot(u(TH(amc)),'--r','LineWidth',4)
plot(u(TH0(amc)),':','Color',[0,0.5,0],'LineWidth',4)
set(gca,'YGrid','on')
set(gca,'XGrid','on')
set(gca,'FontSize',22)
xlim([0,182])
ylim([0,0.14])
ylabel('Unemployment rate','FontSize',22)
set(gca,'XTick',xt)
set(gca,'XTickLabel','1964|1974|1984|1994|2004')
h_legend=legend('Exact solution','Stochastic steady states','Steady states');
set(h_legend,'FontSize',22);
print('-depsc','solutionsU2.eps')
figure(12)
clf
plot(THt,'-b','LineWidth',4)
hold on
plot(TH(amc),'--r','LineWidth',4)
plot(TH0(amc),':','Color',[0,0.5,0],'LineWidth',4)
set(gca,'YGrid','on')
set(gca,'XGrid','on')
set(gca,'FontSize',22)
xlim([0,182])
ylabel('Labor market tightness','FontSize',22)
set(gca,'XTick',xt)
set(gca,'XTickLabel','1964|1974|1984|1994|2004')
h_legend=legend('Exact solution','Stochastic steady states','Steady states');
set(h_legend,'FontSize',22);
print('-depsc','solutionsTH2.eps')
%% --- Compare exact with steady-state ---
figure(10)
clf
plot(Ut,'-b','LineWidth',4)
hold on
plot(u(TH0(amc)),'--r','LineWidth',4)
set(gca,'YGrid','on')
set(gca,'XGrid','on')
set(gca,'FontSize',22)
xlim([0,182])
ylim([0,0.14])
ylabel('Unemployment rate','FontSize',22)
set(gca,'XTick',xt)
set(gca,'XTickLabel','1964|1974|1984|1994|2004')
h_legend=legend('Exact solution','Steady states');
set(h_legend,'FontSize',22);
print('-depsc','solutionsU6.eps')
figure(11)
clf
plot(THt,'-b','LineWidth',4)
hold on
plot(TH0(amc),'--r','LineWidth',4)
set(gca,'YGrid','on')
set(gca,'XGrid','on')
set(gca,'FontSize',22)
xlim([0,182])
ylim([0,2])
ylabel('Labor market tightness','FontSize',22)
set(gca,'XTick',xt)
set(gca,'XTickLabel','1964|1974|1984|1994|2004')
h_legend=legend('Exact solution','Steady states');
set(h_legend,'FontSize',22);
print('-depsc','solutionsTH6.eps')
%% --- Compare exact with stochastic steady-state ---
figure(13)
clf
plot(Ut,'-b','LineWidth',4)
hold on
plot(u(TH(amc)),'--r','LineWidth',4)
set(gca,'YGrid','on')
set(gca,'XGrid','on')
set(gca,'FontSize',22)
xlim([0,182])
ylim([0,0.14])
ylabel('Unemployment rate','FontSize',22)
set(gca,'XTick',xt)
set(gca,'XTickLabel','1964|1974|1984|1994|2004')
h_legend=legend('Exact solution','Stochastic steady states');
set(h_legend,'FontSize',22);
print('-depsc','solutionsU5.eps')
figure(14)
clf
plot(THt,'-b','LineWidth',4)
hold on
plot(TH(amc),'--r','LineWidth',4)
set(gca,'YGrid','on')
set(gca,'XGrid','on')
set(gca,'FontSize',22)
xlim([0,182])
ylim([0,2])
ylabel('Labor market tightness','FontSize',22)
set(gca,'XTick',xt)
set(gca,'XTickLabel','1964|1974|1984|1994|2004')
h_legend=legend('Exact solution','Stochastic steady states');
set(h_legend,'FontSize',22);
print('-depsc','solutionsTH5.eps')