Sidrauski model cannot work in Dynare

Howdy

I spent many hours trying to make this Sidrauski money-in-the-utility-function model work in Dynare with limited success. In particular, I kept getting the error message Impossible to find the steady state. Could someone please help me with this technical issue? Many thanks in advance.

Kind regards!!

Andy

sidrauski.m (6.0 KB)
sidrauski.mod (1.2 KB)

Below I present the residual value for each equation and the error message:

Residuals of the static equations:

Equation number 1 : -0.21827
Equation number 2 : 0.61868
Equation number 3 : 0.43584
Equation number 4 : -0.15188
Equation number 5 : -0.066393
Equation number 6 : 0.038664
Equation number 7 : -7.0867e-007
Equation number 8 : -0.13587

error: Impossible to find the steady state. Either the model doesn’t have a steady state, there are an infinity of steady states, or the guess values are to
o far from the solution

  1. Are you sure your model has a steady state, i.e. did you correctly remove the growth trend that is presumably in the model?
  2. Please only do an exp()-substitution once the model runs
  3. The defined R does not show up in the model.
  4. The equation
mu=(1-phi)*mud + phi*mu(-1) + e;

implies that mu has steady state mud. You should define it as such.

Dear Professor Pfeifer

Thanks for your prompt response. I appreciate your help and guidance. In fact, I am grateful to have the opportunity to learn Dynare-Octave as a fresh tool for running stochastic simulation for DSGE models.

I followed you advice to modify my Dynare model code (sidrauski.mod). Also, I would like to attach the Dynare numerical project spec and my hand-written steady-state solutions (see also the JPEG attachments). I tried running one of your sample codes successfully in Dynare-Octave with smooth and fabulous output results and nice impulse-response charts. There might still be some egregious error(s) in my new Sidrauski code snippets. However, I continued to experience the same error message: Impossible to find the steady state…

Below I attach again the complete output and error message. While we can see some improvement in Equations #1, #2, #4, #5, and #6, the other residual errors seem too large for Dynare to find the steady state…

It is my first time to use Dynare-Octave, so I would really appreciate your meticulous help and guidance on this technical issue. Would you be kind enough to help modify my Sidrauski model code snippets to make this stochastic simulation work in practice? Then I would use the exponential-logarithmic operator to transform every random variable in terms of percent deviations from the steady state. Many thanks for your kind advice in advance!!

Kind regards!!

Andy

NB. As a new user, I can only upload one picture at a time. For this reason, I need to upload my hand-written notes with steady-state solutions in subsequent replies.

sidrauski.mod (1.0 KB)

Residuals of the static equations:

Equation number 1 : -0.0013296
Equation number 2 : -5.6458e-005
Equation number 3 : 0.060371
Equation number 4 : 1.3483e-005
Equation number 5 : -0.0013431
Equation number 6 : 9.4694e-007
Equation number 7 : 0.09359
Equation number 8 : -0.86382

error: Impossible to find the steady state. Either the model doesn’t have a steady state, there are an infinity of steady states, or the guess values are
too far from the solution

Here is the first page of my hand-written notes!

Here is the second page of my hand-written notes!

y= c+k(+1)-(1-delta)*k +(1+mu)*m(+1)-m -mu*m;
i= k(+1)-(1-delta)*k;
y= c+i;

are mutually exclusive. If you plug in for i in the second equation, you will not get the first. Note also that k needs to be predetermined.