Seems unit root problem

Hi professor
I have a nonlinear dsge model. From my equations it seems that there is no unit root problem (i.e. there is no first order lagged variable with coefficient one), but i’m not sure about the structural unit root (my model is closed economy). when i ru n the model i have two main problems:
1- by model diagnosis command, the result show that there is colinearity between two ar(1) processes (shocks of productivity investment and loan to value).
2- in impulse response system, when the shocks get to model, the responses of private capital and output don’t return to zero and remained persistent.
Any help is appreciated.

But that means there is a unit root. Without seeing the mod-file, it is impossible to provide further diagnostics.

Hi professor
Best regards.

model_diagnostics indicates a singularity issue, but not a unit root. My hunch is that it has to do with your steady_state-operator in some equations where you are trying to determine something endogenously that cannot be determined in that way. See

Hi
Thanks for your reply
I have two problem:
1- In my previous model, i make two variables constant (capital price (q) and loan to value (lv)), and run the model. But dynare sensitivity give an error that

0% of the prior support gives unique saddle-path solution.
0% of the prior support gives explosive dynamics.

when i search about this error, i find that it’s because of steady state operator and should not consider some variable as exogenous!!!
2- if my model does not have unit root, why some eigenvalues are very close to one (0.9837 and 0.97)?

would you please according to my model, guide me to how i can find a solution?
Best regards

  1. Sorry, but I don’t understand your first point. A value in steady state is always a constant. The question is how you try to compute that constant.
  2. A unit root is an eigenvalue of exactly 1, not one close to 1. Something close to 1 will only give you large persistence, but not permanence.

Hi
Thanks for your prompt reply

in your last post, you give an example about fisher equation and said:
" The problem arises when you try to simultaneously compute the steady state of inflation and the nominal interest endogenously from the model and use

r/steady_state(r)=(pi/steady_state(pi))^1.5

This cannot work, because any steady state combination satisfying the Fisher equation is a steady state and there are infinitely many such combinations. In contrast, in the two other examples, either picking rbar or pibar solves this indeterminacy by picking one particular combination."

my question is whether for finding steady state of variables, there must be only one unknown variable in any equation and others determined exogenously?
if not, it’s not possible to find an amount for pi in other sector of model and then find r from euler equation?
Because you know that it’s not possible to use fisher equation for finding pi and r simultaneously in steady state block; because dynare give an error that “in the ‘steady_state_model’ block, variable ‘pi’ is undefined in the declaration of variable ‘r’”.

Best regards

model_diagnostics complains about equation 29:

exp(psi) /exp(steady_state (psi))=(exp(psi(-1)) / exp(steady_state (psi))) ^ rhop * exp(varpsi);

Are you sure that the steady state of psi can be endogenously determined?

In steady state block i find steady state value of psi from capital private accumulation. Is it right?

That is fine and the reason why the model runs. But you should define the steady state as a parameter you set in your steady state file and use that one instead of the steady state operator. As mentioned above, any value for psi should work.

Hi professor
I omit the steady_state operator and replace them by exogenous parameters (blv and bpsi in parameters block). dynare diagnosis runs and said that there is no obvious problem.
but dynare sensitivity command is not good and send this massage that:
0.0% of the prior support gives unique saddle-path solution.
0.0% of the prior support gives explosive dynamics.

I do’nt know where is the source of problem? when i find value of psi and lv endogenously, dyanre diagnosis sent massege that there is colinearity between two. but when i exogenously fix steady state value of psi and lv, dynare sensivity sent massege that there is no steady state!!!
would you please help me?

Please provide the updated version that gives the above result.

Hi professor
I attached the last version of my model, would you please help me?
Best regards.
macr.prud.mod (19.3 KB)

What am I supposed to do with the file? It runs on my machine without any problem.

Hi
If you check model diagnosis, it gives an error that there is colinearity between psi and lv equations.
I change an steady state operator (i.e. steady_state (psi) and steady_state(lv)) to fixed parameter (i.e. bpsi and blv); but dynare sensitivity gives an error that : .0% of the prior support gives unique saddle-path solution.
0.0% of the prior support gives explosive dynamics.

For 100.0% of the prior support dynare could not find a solution.

For 100.0% The steadystate routine thrown an exception (inconsistent deep parameters).

could you please check the irf’s? because the shocks are persistent and don’t get back to zero.
Would you please check the model again and help me?
Best regards.

mac_prud2.mod (19.3 KB)

That’s because your steady state file is incorrect. If you change aa=0.7 the steady state file does not work.

Hi professor
by using a separate steady state file, i can solve model diagnosis and dynare sensitivity problem simultaneously, but as you said if i change some parameters (like aa, ddk, etc.) by small amount, residuals of two above mentioned equations (i.e. lv and psi) become nonzero and dynare give an error that: Error in steady (line 104).
I have another question, is there any problem that coefficient of policy function equal 1? in my model, response of variable y (i.e. output) to productivity shock (vara) equal one? Is it a sign of unit root?
would you please help me to solve this problem.

Sorry, but I don’t understand your post.

  1. A steady state file returns a steady state (or an error code) for every possible parameter combination. If that is not the case when you vary some parameters, then your computation is wrong.
  2. No, you cannot read of a unit root from one coefficient in the policy rule, because the shocks will also affect other variables entering the policy function with a lag. That is why you need to look at the eigenvalues of the transition matrix. Dynare’s check-command does that.