Inflation Expectation Shock

General DSGE Modeling
1

Hi everyone
I want to include inflation expectation shock in my model. Ascari et al (2022) have included this shock in their model
Ascari et al 2022.rar (2.8 MB)

in p 13:

image
image1010×527 51.2 KB

Now my question is about how to code this issue in dynare.
Should I add two new endogenous variables (and equations )to the model?
pi_e(+1)
and
eps_pi(+1):

pi(+1)=pi_e(+1)exp(eps_pi(+1));
eps_pi(+1)=(rho_pi)(eps_pi)+sigma_pi*u_eps(+1);

var
pi_e
eps_pi

varexo
u_eps

parameters
rho_pi
sigma_pi

Thank you for guiding me in this matter.

2

You may need to ask the authors because the timing looks off. The object on the left has information set at time t. It’s odd that the shock on the right is dated time t+1.
I would have expected that you need to define

pi_aux=pi(+1);
E_t_pi_tp1=pi_aux*e^epsilon_pi;