# Practicing dynare sargent chapter 11

Hey guys! I’ve tried to run Sargent’s code (chapter 11) from practicing dynare but it didn’t work out under dynare 4.3.1…

%-----------------------------------------------------------------------------------------------
% 1. Defining variables
%-----------------------------------------------------------------------------------------------
// Declares the endogenous variables consumption (’c’) capital stock (’k’);
var c k;
// declares the exogenous variables consumption tax (’tauc’),
// capital tax(’tauk’), government spending(’g’)
varexo tauc tauk g;
parameters bet gam del alpha A;
%-----------------------------------------------------------------------------------------------
% 2. Calibration and alignment convention
%-----------------------------------------------------------------------------------------------
bet=.95; // discount factor
gam=2; // CRRA parameter
del=.2; // depreciation rate
alpha=.33; // capital’s share
A=1; // productivity
// Alignment convention:
// g tauc tauk are now columns of ex_. Because of a bad design decision the date of ex_(1,
// doesn’t necessarily match the date in endogenous variables. Whether they match depends on
// the number of lag periods in endogenous versus exogenous variables.
// These decisions and the timing conventions mean that
// k(1) records the initial steady state, while k(102) records the terminal steady state values.
// For j > 1, k(j) records the variables for j-1th simulation where the capital stock decision
// taken in j-1th simulation i.e stock at the beginning of period j.
// The variable ex_ also follows a different timing convention i.e
// ex_(j, records the value of exogenous variables in the jth simulation.
// The jump in the government policy is reflected in ex_(11,1) for instance.
%-----------------------------------------------------------------------------------------------
% 3. Model
%-----------------------------------------------------------------------------------------------
model;
// equation 11.3.8.a
k=Ak(-1)^alpha+(1-del)k(-1)-c-g;
// equation 11.3.8e + 11.3.8.g
c^(-gam)= bet
(c(+1)^(-gam))
((1+tauc)/(1+tauc(+1)))((1-del) + (1-tauk(+1))alphaAk^(alpha-1));
end;
%-----------------------------------------------------------------------------------------------
% 4. Computation
%-----------------------------------------------------------------------------------------------
initval;
k=1.5;
c=0.6;
g = .2;
tauc = 0;
tauk = 0;
end;
steady;
// put this in if you want to start from the initial steady state,comment it out to start
// from the indicated values
// The following values determine the new steady state after the shocks.
endval;
k=1.5;
c=0.6;
g =.4;
tauc =0;
tauk =0;
end;
steady;
// We use ’steady’ again and the endval provided are initial guesses for dynare to compute the ss.
// The following lines produce a g sequence with a once and for all jump in g
// we use ’shocks’ to undo that for the first 10 periods (t=0 until t=9)and leave g at
// it’s initial value of 0
// Note : period j refers to the value in the jth simulation
shocks;
var g;
periods 1:10;
values 0.2;
end;
// now solve the model
simul(periods=100);
// Compute the initial steady state for consumption to later do the plots.
c0=c(1);
k0 = k(1);
// g is in ex_(:,1) since it is stored in alphabetical order
g0 = ex0_(3);

%-----------------------------------------------------------------------------------------------
% 5. Graphs and plots for other endogenous variables
%-----------------------------------------------------------------------------------------------

// Let N be the periods to plot
N=40;
// The following equation compute the other endogenous variables use in the plots below
// Since they are function of capital and consumption, so we can compute them from the solved
// model above.
// These equations were taken from page 371 of RMT3
rbig0=1/bet;
rbig=c(2:101).^(-gam)./(betc(3:102).^(-gam));
nq0=alpha
Ak0^(alpha-1);
nq=alpha
Ak(1:100).^(alpha-1);
wq0=A
k0^alpha-k0alphaAk0^(alpha-1);
wq=A
k(1:100).^alpha-k(1:100).alphaA.*k(1:100).^(alpha-1);

// Now we plot the responses of the endogenous variables to the shock.
x=0:N-1;
figure(1)
// subplot for capital ’k’
subplot(2,2,1)
plot(x,[k0ones(N,1)],’–k’, x,k(1:N),’k’,’LineWidth’,1.5)
title(’k’,’Fontsize’,12)
set(gca,’Fontsize’,12)
// subplot for consumption ’c’
subplot(2,2,2)
plot(x,[c0
ones(N,1)],’–k’, x,c(2:N+1),’k’,’LineWidth’,1.5)
title(’c’,’Fontsize’,12)
set(gca,’Fontsize’,12)
// subplot for cost of capital ’R_bar’
subplot(2,2,3)
plot(x,[rbig0ones(N,1)],’–k’, x,rbig(1:N),’k’,’LineWidth’,1.5)
title(’$\overline{R}$’,’interpreter’, ’latex’,’Fontsize’,12)
set(gca,’Fontsize’,12)
// subplot for rental rate ’eta’
subplot(2,2,4)
plot(x,[nq0
ones(N,1)],’–k’, x,nq(1:N),’k’,’LineWidth’,1.5)
title(’\eta’,’Fontsize’,12)
set(gca,’Fontsize’,12)
// subplot for the experiment proposed
subplot(2,3,5)
plot([0:9],ex_(3)(1:10),’k’,’LineWidth’,1.5);
hold on;
plot([10:N-1],ex_(3)(11:N,1),’k’,’LineWidth’,1.5);
hold on;
plot(x,[g0*ones(N,1)],’–k’,’LineWidth’,1.5)
title(’g’,’Fontsize’,12)
axis([0 N -.1 .5])
set(gca,’Fontsize’,12)
print -depsc fig_g.eps

I get the following error: ??? Error: File: jonas.m Line: 138 Column: 23
The input character is not valid in MATLAB statements or expressions.

Error in ==> dynare at 120
evalin(‘base’,fname) ;

I think that something goes wrong with respect to the plots…
I hope that somebody can help me, thanks in advance!

I’ve found a solution by myself!!!

Just in case someone is interested in the code —> see attachement
gshock.mod (1.46 KB)

Thanks for explaining and sharing the code for the updated dynare version