Help: Replication of Jaimovich and Rebelo


#1

Dear All:

Attached is my code trying to replicating the paper “Can News Drive Up Business Cycles” by Jaimovich and Rebelo. I log-linearze the system by hand. Since they don’t specify the functional form of investment and utilization adjustment cost, I use simple quadratic setting. The parameters are named following traditions. I checked the steady states and the co-efficients in the linearized system, and they seem to be right, except some rounding errors (at the magnitude of 1e-15).

However, the generated IRFs are quite different from what JR get in the paper. I looked into details. The most problematic part of my code is the NEGATIVE eigenvlue in the system, which looks weird. The transition matrix shows huge response to technology shocks.

If you can find any bugs in my code, I really appreciate you help…
jrreplicate_v2.mod (12.6 KB)


#2

Here is another version of the code, but it doesn’t work either. The funny part is that there are only 15 endogneous variables, but dynare thinks there are 17. I don’t know how to fix it.
jr_v3.mod (4.3 KB)


#3

An error on line 96-99. Put :

shocks;
var e_ng;stderr 0.01;
var e_nz;stderr 0.01;
end;


#4

If you are interested in replication you may also want to take a look at this:


#6

Hi, did you get the code to work? My steady state seemed wrong but I think I checked everything and I don’t know what to do now. Here is my code, any help will be greatly appreciated.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Can news about the future drive the business cycle?
% 
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Calibration and Preliminary Computation

sigma0=1; 
theta0=1.4; % labor elasticity
beta0=0.985; % subjective discount factor
alpha0=0.64; % labor share in production
gamma0=0.001;
delta0 =0.025;
psi0=2.3; % only needs to be greater than 0
phi0 = 1.3; % Adjustment cost param
para2=0.025/(1/0.15-0.5);
para1= (1/0.15-1)*0.025/(1/0.15-0.5); %Util Param.

rho_a=0.95; 
rho_z=0.95; 
%% Definition of the Rational Expectations Model

% state variables: k0 a0 z0 x0 epsa0 epsz0
% z0 state or choice??
% choice variables: y0 c0 i0 n0 w0 r0 u0 delta_u0 lambda0 eta0 mu0 
syms k0 a0 X0 epsa0 epsz0
syms k1 a1 X1 epsa1 epsz1
syms z0 c0 i0 n0 gdp0 u0 lambda0 eta0 mu0 if0
syms z1 c1 i1 n1 gdp1 u1 lambda1 eta1 mu1 if1

%arguments of the F function

x0 = [k0 a0 X0 epsa0 epsz0]; 
x1 = [k1 a1 X1 epsa1 epsz1]; 
y0 = [z0 c0 i0 n0 gdp0 u0 lambda0 eta0 mu0 if0]; 
y1 = [z1 c1 i1 n1 gdp1 u1 lambda1 eta1 mu1 if1];
nx=length(x0); ny=length(y0);n0=nx+ny;


% equilibrium equations
f1=(c0-(psi0*(n0^theta0)*X1))^(-sigma0)+(mu0*gamma0*(X0/c0)^(1-gamma0))-lambda0; %7
f2=(c0-(psi0*(n0^theta0)*X1))^(-sigma0)*psi0*(n0^theta0) + mu0 - beta0*mu1*(1-gamma0)*((c1/X1)^gamma0); %8
f3=(c0-(psi0*(n0^theta0)*X1))^(-sigma0)*theta0*psi0*(n0^(theta0-1))*X1 - lambda0*alpha0*a0*(u0*k0/n0)^(1-alpha0); %9
f4=a0*(u0*k0)^(1-alpha0)*n0^alpha0-c0 - i0/z0; %5

% quadratic form
% f(u0)=para1*u0+para2/2*u0^2
% phi(i/i(-1))= phi0/2*(if0/i0-1)^2
f5=lambda0*(1-alpha0)*a0*(n0/u0)^alpha0*k0^(1-alpha0)-eta0*k0*(para1+para2*u0); %10
f6=eta0-beta0*lambda1*(1-alpha0)*a1*(n1/k1)^alpha0*u1^(1-alpha0) - eta1*(1-(para1*u0+para2/2*u0^2)); %11
f7=lambda0/z0 - eta0*(1-(phi0/2*(if0/i0-1)^2)-phi0*(if0/i0-1)*(if0/i0))-beta0*eta1*phi0*(if1/if0-1)*(if1/if0)^2; %12
f8=X1-(c0^gamma0)*X0^(1-gamma0); %2
f9= k1- i0*(1-phi0/2*(if0/i0-1)^2)-(1-(para1*u0+para2/2*u0^2))*k0 ; %6
f10=gdp0-i0/z0; %4
f11=if0-i1;
% exogenous processes

f12=log(a1)-rho_a*log(a0)-log(epsa0);
f13=log(z1)-rho_z*log(z0)-log(epsz0);
f14=log(epsa1)-0.0*log(epsa0);
f15=log(epsz1)-0.0*log(epsz0);

% f function
f=[f1;f2;f3;f4;f6;f6;f7;f8;f9;f10;f11;f12;f13;f14;f15];
z= [x0 x1 y0 y1];
fl = subs(f, z, exp(z)); 


%% Steady State
as=1;zs=1;us=1;epsa=1;epsz=1;
nkratio=((1/beta0-1+delta0)/(1-alpha0))^(1/alpha0); %11& %12
ckratio=(nkratio^alpha0-delta0); %4
cnratio=ckratio/(nkratio); % 
% Para10=(alpha0*nkratio^(alpha0-1)); 
% Para20=(theta0*cnratio-Para10*gamma0/((beta0*(1-gamma0)-1)))*psi0;
% N_ss=(Para10/Para20)^(1/theta0);
paran1 = theta0*psi0*cnratio/(alpha0*nkratio^(alpha0-1));
paran2 = psi0*gamma0/(beta0*(1-gamma0)-1);
N_ss=(1/(paran1-paran2))^(1/theta0);

%%#N_ss=(Para3/psi)^(1/theta);
%psi=alpha*nkratio^(alpha-1)/((theta*cnratio+((gamma/(beta*(1-gamma)-1))*alpha*nkratio^(alpha-1)))*N_ss^theta);
C_ss=N_ss*cnratio; %
K_ss=N_ss/nkratio; %
I_ss=K_ss*delta0;  %
Y_ss=K_ss^(1-alpha0)*N_ss^alpha0; %
X_ss=C_ss; %
Para1=(C_ss-psi0*N_ss^theta0*X_ss)^(-sigma0); %
% Para2=(C_ss-psi0*N_ss^theta0*X_ss);
Mu_ss=Para1*psi0*N_ss^theta0/(beta0*(1-gamma0)-1); %
Lam_ss=Para1+gamma0*Mu_ss; %
% etas = Lam_ss*(1-alpha0)*Y_ss/(K_ss*(para1+para2*us));
etas =Lam_ss;
%log transformation of the steady state values
n0=log(N_ss);n1=n0;
c0=log(C_ss);c1=c0;
k0=log(K_ss);k1=k0;
i0=log(I_ss);i1=i0;
if0=log(I_ss);if1=if0;
gdp0=log(Y_ss);gdp1=gdp0;
X0=log(X_ss);X1=X0;
mu0 =log(Mu_ss);mu1=mu0;
lambda0 =log(Lam_ss);lambda1=lambda0; 
eta0 =log(etas);eta1=eta0; 
u0=log(us);u1=u0;
a0=log(as);a1=a0;
z0=log(zs);z1=z0;
epsa0=log(epsa);epsa1=epsa0;
epsz0=log(epsz);epsz1=epsz0;


%test the steady state
fs=double(eval(fl(:)))

if max(abs(fs))>=1e-10; error('Incorrect Approximation Point at 0'); end


%% Approximation procedure

%Compute analytical derivatives of f
[fx,fxp,fy,fyp,fypyp,fypy,fypxp,fypx,fyyp,fyy,fyxp,fyx,fxpyp,fxpy,fxpxp,fxpx,fxyp,fxy,fxxp,fxx]=anal_deriv(fl,x0,y0,x1,y1);

%Order of approximation desired 
approx = 1;

%Obtain numerical derivatives of f evaluated at the steady state
num_eval

%First-order approximation
[gx,hx,exitflag] = gx_hx(nfy,nfx,nfyp,nfxp);



%% IRF 
T=100;X0=1:T;

% Technology shock
x0=[0;0;0;0;1;0];
[IR]=ir(gx,hx,x0,T);

fig01=figure('Color','w','Position',[100 100 600 400]);
ind={'1' '2' '5' '7'};
name={'c' 'n' 'gdp' 'a'};
ni=length(name);
for i0=1:ni
    j=eval(ind{i0});    
    subplot(2,2,i0), plot(X0,IR(:,j),'LineWidth',2,'MarkerSize',5);
    title(name{i0},'FontSize',10);
    set(gca,'xtick',0:10:T,'FontSize',10)
    axis([X0(1) X0(end) ylim]);     
  %  ticks_format('%2.0f', '%2.2f');
end

% Government spending shock
x0=[0;0;0;0;0;1];
[IR]=ir(gx,hx,x0,T);

fig02=figure('Color','w','Position',[100 100 600 400]);
X0=1:T;
ind={'1' '2' '5' '8'};
name={'c' 'n' 'gdp' 'g'};
ni=length(name);
for i0=1:ni
    j=eval(ind{i0});
    subplot(2,2,i0), plot(X0,IR(:,j),'LineWidth',2,'MarkerSize',5);
    title(name{i0},'FontSize',10);
    set(gca,'xtick',0:10:T,'FontSize',10)
    axis([X0(1) X0(end) ylim]);     
 %   ticks_format('%2.0f', '%2.2f');
end



%% Second Moments
% zx=[eye(nx);gx]; %all variables
% eta=[0 1]';
% varshock=csigea^2*eta*eta';
% [sigz,sigx]=mom(zx,hx,varshock);



%% 
%end rbc.m

#7

Sorry, but this is a Dynare forum. I doubt that people will be bothering with your SGU codes.