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decomposition_shocks.m
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decomposition_shocks.m
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%%==============================================================================
%% Back-out shocks to match data exactly, and compute decomposition accordingly
%% For simplicity: abstract from dynamics (turnover dynamics do not matter, recruiting dynamics are not very important)
%%==============================================================================
%% --- Setup ---
bayesdata; % Calibration and weekly data: anl, unl, nnl, thnl, wnl
xt=[1,1+4.*10,1+4.*20,1+4.*30,1+4.*40]; % Plot on 1964--2009 period
xx=[1:182];
fth=@(n,omega)(1./omega.*s.*n./(1-(1-s).*n)).^(1./(1-eta));
ur2=@(ax,wx)max(1-(wx./(alpha.*ax)).^(-1./(1-alpha)),0);
%% --- Backout technology to match employment ---
nx=nnl;
ux=unl;
thx=fth(nx,omega);
ay=((alpha.*nx.^(alpha-1)-r.*c./q(thx))./w).^(1./(gamma-1));
ury=ur(ay);ufy=ux-ury;
%% --- Plot ---
UFt=ufy(1:12:end);
URt=ury(1:12:end);
YY=[UFt',URt'];
figure(10)
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',['deco1.eps'])
figure(11)
clf
plot(ay(1:12:end),'--r','LineWidth',4)
hold on
plot(anl(1:12:end),'-b','LineWidth',4)
ylabel('Technology','FontSize',22)
set(gca,'YGrid','on','XGrid','on','FontSize',22)
xlim([1,182])
set(gca,'XTick',xt)
set(gca,'XTickLabel','1964|1974|1984|1994|2004')
h_legend=legend('Estimated','Actual');
set(h_legend,'FontSize',22);
print('-depsc',['shocka.eps'])
%% --- Backout wage shocks, given that technology is observed ---
ax=anl;
wy=alpha.*ax.*nx.^(alpha-1)-r.*c.*ax./q(thx);
ury=ur2(ax,wy);ufy=ux-ury;
%% --- Plot ---
UFt=ufy(1:12:end);
URt=ury(1:12:end);
YY=[UFt',URt'];
figure(12)
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',['deco2.eps'])
figure(13)
clf
plot(wy(1:12:end),'--r','LineWidth',4)
hold on
plot(wnl(1:12:end),'-b','LineWidth',4)
ylabel('Wage','FontSize',22)
set(gca,'YGrid','on','XGrid','on','FontSize',22)
xlim([1,182])
set(gca,'XTick',xt)
set(gca,'XTickLabel','1964|1974|1984|1994|2004')
h_legend=legend('Estimated','Actual');
set(h_legend,'FontSize',22);
print('-depsc',['shockw.eps'])
figure(15)
clf
plot(wy(end-34.*12+1:12:end),'--r','LineWidth',4)
hold on
plot(wnl(end-34.*12+1:12:end),'-b','LineWidth',4)
plot(ecirwx,'.-m','LineWidth',4)
ylabel('Wage','FontSize',22)
set(gca,'YGrid','on','XGrid','on','FontSize',22)
xlim([1,34])
set(gca,'XTick',xt)
set(gca,'XTickLabel','1964|1974|1984|1994|2004')
h_legend=legend('Estimated','CPS','ECI');
set(h_legend,'FontSize',22);
print('-depsc',['shockeciw.eps'])
%% --- Backout matching shocks, given that technology and wages are observed ---
nx=nnl;
ux=unl;
thx=fth(nx,omega);
ax=anl;
wx=eciwnl;
ax=ax(end-33.*12:end);
nx=nx(end-33.*12:end);
thx=thx(end-33.*12:end);
ux=ux(end-33.*12:end);
omegay=((alpha.*ax.*nx.^(alpha-1)-wx)./(r.*c.*ax.*thx.^eta)).^(-1);
ury=ur2(ax,wx);ufy=ux-ury;
%% --- Plot ---
UFt=ufy(1:12:end);
URt=ury(1:12:end);
YY=[UFt',URt'];
figure(14)
clf
harea=area([1:34],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',['deco3.eps'])
figure(15)
clf
plot(omegay(1:12:end),'--r','LineWidth',4)
ylabel('Matching efficiency','FontSize',22)
set(gca,'YGrid','on','XGrid','on','FontSize',22)
xlim([1,182])
set(gca,'XTick',xt)
set(gca,'XTickLabel','1964|1974|1984|1994|2004')
h_legend = legend('Estimated','Actual');
set(h_legend,'FontSize',22);
print('-depsc',['shockomega.eps'])
%% --- Backout matching shocks, given that technology is observed ---
ax=anl;
wx=w.*ax.^gamma;
omegay=((alpha.*ax.*nx.^(alpha-1)-wx)./(r.*c.*ax.*thx.^eta)).^(-1);
ury=ur2(ax,wx);ufy=ux-ury;
%% --- Plot ---
UFt=ufy(1:12:end);
URt=ury(1:12:end);
YY=[UFt',URt'];
figure(12)
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',['deco4.eps'])
omegad=(s.*nnl./unl).*thnl.^(eta-1);
figure(13)
clf
plot(omegad(1:12:end),'-b','LineWidth',4)
ylabel('Matching efficiency','FontSize',22)
set(gca,'YGrid','on','XGrid','on','FontSize',22)
xlim([1,182])
set(gca,'XTick',xt)
set(gca,'XTickLabel','1964|1974|1984|1994|2004')
print('-depsc',['shockomega3.eps'])
%% --- Backout wage shocks, given that technology and matching are observed ---
omegad=(s.*nnl./unl).*thnl.^(eta-1);
omegax=omegad;
thx=fth(nx,omegax);
wy=(alpha.*ax.*nx.^(alpha-1))-(r.*c.*ax./omegax.*thx.^eta);
ury=ur2(ax,wy);ufy=ux-ury;
%% --- Plot ---
UFt=ufy(1:12:end);
URt=ury(1:12:end);
YY=[UFt',URt'];
figure(14)
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',['deco5.eps'])
figure(13)
clf
plot(wy(1:12:end),'--r','LineWidth',4)
hold on
plot(wnl(1:12:end),'-b','LineWidth',4)
ylabel('Wage','FontSize',22)
set(gca,'YGrid','on','XGrid','on','FontSize',22)
xlim([1,182])
set(gca,'XTick',xt)
set(gca,'XTickLabel','1964|1974|1984|1994|2004')
h_legend=legend('Estimated','Actual');
set(h_legend,'FontSize',22);
print('-depsc',['shockw2.eps'])