Hi, I have a non-linear model. I have log linearized all the equations except the exogenous shock, which is an AR(1) shock to variable u^b_t in the non-linear model. I have inserted the two following equations in Dynare:

u_b= (1-rho_b)+\rho_b*u_b(-1)+\sigma_b*e_b;

#\hat{u}_b=log(u_b);

I have the following error for the second equation (#3):

ERROR: If the model is declared linear the second derivatives must be equal to zero.

The following equations had non-zero second derivatives:

* Eq # 3

I wanted to know how I should linearize the shock equation or solve this error in another way.

Is there any way that I can have a nonlinear equation in a linear model?