Question on shock equation in Dynare code

Dear Professor Pfeifer,

In LWZ(2013)( Land-price dynamics and macroeconomic fluctuations, Econometrica), they assume that total factor productivity Z_t is composed of a permanent component Z_{t}^{p} and transitory componet \nu_{zt} such that {{Z}_{t}}=Z_{t}^{p}{{\nu }_{zt}}. The permanent component Z_{t}^{p} follows Z_{t}^{p}=Z_{t-1}^{p}{{\lambda }_{zt}}, and the steady state of {\lambda }_{zt} represent the growth rate of Z_{t}^{p}.

I do not know how to write the equation Z_{t}^{p}=Z_{t-1}^{p}{{\lambda }_{zt}} into Dynare. It seems that the steady state residual of this equation is not equal to zero. Would you please give any advice to deal with this problem?

Thank you for reading and really appreciate your kindness.

You need to detrend the model. Currently, there is a unit root with drift.