Question about parameter that changes with steady-state

I’m trying to find a steady-state of a dsge model with two sectors.
I tried to capture the limited labor mobility in the model, so I have CES function for aggregate labor such as

L = [\xi_d^{-1/\lambda} L_d^{(1+\lambda)/\lambda} + (1-\xi_d)^{-1/\lambda} L_o^{(1+\lambda)/\lambda}]^{\lambda/(1+\lambda)}

where \xi_d is steady-state ratio of labor of sector d, L_d/L.

What I’m trying to do is, first of all, derive steady-state without a shock.
And then, derive new steady-state with permanent tax shock.
And finally, I want to derive the transition between the two steady-states with perfect foresight algorithm in dynare.

In my dynare code, I set the parameter value of \xi_d = 1/2 so that old steady-state of L_d and L_o as 1/2, respectively.
But with the permanent tax shock, the new steady-state of sectoral labor will change, and so will the value of \xi_d.
I did find the old steady-state, but failed to find the new steady-state with the shock.
In this case, how could I derive the new steady-state? I’m not sure how I can I set different parameter value for different steady-state.

Thank you for your help!!

nonlinear_model4.mod (8.5 KB)

I am not sure I understand. Why would a parameter change after a shock? That would make the parameter a variable.

It is because \xi_d is ratio of steady-state value of labor in sector d relative to the aggregate labor. When permanent tax shock occurs, labor of each sector changes permanently so that the value of \xi_d changes.
Oh, do I have to put \xi_d as a variable in such case?

I guess you have to rethink your approach. A permanent shock should lead to a new steady state for the variables, given the value of the parameters. Put differently, for a given \xi_d you should observe L_d,L_o to permanently change.