Hello!

I’ve created a small NK model with banks and a money growth equation. My code seems to be correct, except I keep getting the following error:

“The steady state has NaNs or Inf”

I figured out that that means that my values for the initval block are incorrect, but I’m unsure as to how to actually compute them. I was previously told that I can just keep all values (Except for the interest rate) as 0, but evidently, that is not working. I have given the model below.

``````var ch cb r i l w z y d q m;
varexo eps_e;
parameters BETA, ETA, KTILDE, XSS, GAMMA, SIGMA, ALPHAM, PHIM, CHI;
BETA = 0.985;
ETA = 0.276;
KTILDE = 0.0858;
XSS = 1.2;
GAMMA = 0.065;
SIGMA = 0.5;
ALPHAM = 0.1250;
PHIM = 0.95;
CHI = 0.74;
STDERR_AE = 0.0029;

model;
1/ch = BETA*(r/(ch(+1)*i(+1))); // euler eq
w/ch = l^(ETA-1);
i = BETA*i(+1)-KTILDE*((1/z)-log(XSS));
y = l;
w*l = (z*y)/(1+q);
(1-GAMMA)/cb = BETA*(d*((1+r)/cb(+1)));
1/cb = BETA*(q*((1+r)/cb(+1)));
y = ch;
m = SIGMA*m(-1);
m^(-PHIM) = BETA*((r(-1)-1)/(y(+1)*i(+1)*ALPHAM)) + eps_e;
eps_e = CHI*eps_e(-1);
end;

initval;
ch = 0;
cb = 0;
r = 0.1;
i = 0;
l = 0;
w = 0;
z = 0;
y = 0;
d = 0;
q = 0;
m = 0;
end;

shocks;
var eps_e; stderr 100*STDERR_AE;
end;

stoch_simul(dr_algo=0,order=1,irf=20);
``````

Would appreciate any help. Thank you!

You set zero for variables initial values in the model.

Your DSGE model is non-linear and is not log-linear. In Log-linear models steady states are 0 but in non-linear models steady state values are not 0.

1 Like

Right, that makes sense. Would it be better to log linearise my equations and keep SS values as zero or keep the equations as is and calculate the SS values instead?

See

Oh okay. I thought steady state values are taken as 0 (for most variables) upon log linearisation. Then in that case I’m better off leaving my equations as is (i.e. non-linear) and calculating the steady state values, right?

Yes, correct.

And just to confirm, I do that by a) dropping time subscripts, and then b) substituting parameter values…right?

Yes, that is the typical way to proceed. You are trying to express all steady state variables as functions of the parameters only.

Okay. Thank you so much! I have been extremely confused about the appropriate way to proceed

Regarding this question I posted a while back; I tried solving the system of equations for the steady state values of my variables, using matlab, but for some reason, fsolve stops prematurely. No matter how much I extend my evaluation or iteration limit.
I have now tried to log-linearise my model and keep steady state values (for the most part) as 0, as I was advised/taught by my lecturer. I am being told ‘the steady state has Nans or inf’ and I’m struggling to understand what to do now.

I have given my code below,

``````var ir c l y w r id iq q d f i n m z o;
varexo eps_e;
parameters ETA ALPHAM SIGMAM ALPHAD SIGMAD ALPHAR SIGMAR THETA BETA GAMMA PHID PHIQ RHOR RHOI RHOY CHI;
ETA = 2.7;
ALPHAM = 1.25;
SIGMAM = 0.95;
ALPHAR = 1.25;
SIGMAR = 0.95;
THETA = 0.57;
BETA = 0.9823;
GAMMA = 0.18;
PHID = 0.5;
PHIQ = -0.5;
RHOR = 0.829;
RHOI = 0.89;
RHOY = -0.017;
CHI = 0.75;
STDERR_AE = 0.0029;

model;
1/exp(c) = BETA*exp(r - i(+1) - c(+1)) ;
w - l = (ETA-1)*c ;
y = l ;
y = c ;
id = f - d ;
i = BETA*i(+1) - (1 - THETA)*(1 - BETA*THETA)*z/THETA ;
o = CHI*o(-1) + eps_e ;
r = RHOR*r(-1) + (1 - RHOR)*((RHOI + 1)*i + RHOY*y) + o;
w + l = z + y - q - iq ;
q + w = f + ((1 - GAMMA)*d + n)/f ;
n = (1 + iq)*n(-1) + (((iq - id)*d) + ((iq - ir)*f))/((1 + iq)*n(-1)) ;
c = ALPHAM*SIGMAM*m + BETA*(c(+1) + i(+1)) ;
c = ALPHAR*SIGMAR*r + BETA*(c(+1) + i(+1)) ;
iq = PHIQ + q + ir + w - n + (q*(1 + PHIQ)*w)/n ;
id = PHID + GAMMA + ir - PHID ;
end;

initval;
ir = 0.01;
c = 0;
l = 0;
y = 0;
w = 0;
r = 0.5;
id = 0.01;
iq = 0.01;
q = 0;
d = 0.4;
f = 0;
i = 1;
n = 0;
m = 0.5;
z = 0;
o = 0;
end;

shocks;
var eps_e; stderr 100*STDERR_AE;
end;

stoch_simul(dr_algo=0,order=1,irf=20) y i ir q c;

``````

thank you!

Your linearization is wrong. For example, why is there `exp(c)`?

That’s the linearised form we used in class. Since my Euler equation was exactly the same, I used the same thing

Either your notes are wrong or you made a mistake in class. A division by an exponential function is clearly not linear.