 Jacobian of the static model is singular and contains elements that are not real or are infinite

tviniwaigo.mod (1.0 KB)

It seems like that we have written everything correctly, but code still does not work.
It tells us that the Jacobian of the static model is singular and the Jacobian matrix evaluated at the steady state contains elements that are not real or are infinite.
Could you please anyone look at our code and tell us what is wrong with this code?

Execute

alpha = 0.4;
beta = 0.95;
sigma = 1;
delta = 0.1;
chi = 2;
rho = 0.95;
Ass=1;
Css=((((1+beta*delta-beta)/(alpha*beta)^(alpha/(alpha-1)))*(1-alpha))/chi)^(1/delta);
Kss=Css/(((1+beta*delta-beta)/(alpha*beta))-delta);
Lss=Css/((1+beta*delta-beta)/(alpha*beta))^(alpha/(alpha-1))-delta*((1+beta*delta-beta)/(alpha*beta))^(1/(alpha-1));
Yss=(Css/(((1+beta*delta-beta)/(alpha*beta))-delta))^alpha*(Css/((1+beta*delta-beta)/(alpha*beta))^(alpha/(alpha-1))-delta*((1+beta*delta-beta)/(alpha*beta))^(1/(alpha-1)))^(1-alpha);

in Matlab to see that these values do not make sense. They are essentially 0. Also, delete the initval-block. In a linearized model, the steady states are 0.

Even if we delete initval-block it gives us same problem. We also tried to change the values of parameters, but it still writes that Jacobian matrix evaluated at the steady state contains elements that are not real or are infinite.

I am pretty sure that there is a mistake somewhere in

Css=((((1+beta*delta-beta)/(alpha*beta)^(alpha/(alpha-1)))*(1-alpha))/chi)^(1/delta);
Kss=Css/(((1+beta*delta-beta)/(alpha*beta))-delta);
Lss=Css/((1+beta*delta-beta)/(alpha*beta))^(alpha/(alpha-1))-delta*((1+beta*delta-beta)/(alpha*beta))^(1/(alpha-1));
Yss=(Css/(((1+beta*delta-beta)/(alpha*beta))-delta))^alpha*(Css/((1+beta*delta-beta)/(alpha*beta))^(alpha/(alpha-1))-delta*((1+beta*delta-beta)/(alpha*beta))^(1/(alpha-1)))^(1-alpha);

These values do not make sense.

We were asked to express these values by the Kss/Lss and in order to make it simpler we just plugged the value of Kss/Lss .

But why is Css equal to 0?

Yeap, i found mistake in the second equation (Css), instead of 1/sigma I wrote 1/delta. However, not it has a problem with a whole model. It says that it is impossible to find the steady state (the sum of square residuals of the static equations is 0.0003). Either the model doesn’t have a steady state or there are an infinity of steady states Check whether your model is truly linear or whether there is a mistake in linearization. I am trying to find mistake in linearizing but I could not find any of it. Moreover, we found linearized versions of our equations in YouTube and it is the same.

updated.mod (1.1 KB)
This is updated file.

I am not sure what you are doing. Yss is complex, so there must be a mistake in that equation.

sigma*Css = A+alpha*(K(-1)-L);

is not a proper linearization. It may be

sigma*Css*C = A+alpha*(K(-1)-L);

Check out
updated.mod (953 Bytes)

Thanks a lot, yeap there is a typo in sigmaCssC = A+alpha*(K(-1)-L); and I simply wrote Yss=Css-delta*Kss. Now it works perfectly.
Thanks a lot, again.