Estimate News shock

Estimation ML/Bayesian estimation
1

Hi everyone,
I am trying to estimate a news shock and I would like some clarifications regarding the way to do that.
As far as I understood, it is possible to easily model it by adding a lagged “varexo” like here:

At=rho_a*At(-1)+e_a+news_a(-4);

in this case, the agent anticipates a future shock that will materialize with 100% probability 4 periods from now. Is it correct?
I would like to know how it is possible to estimate a “pure news shock”, i.e. a shock that is anticipated but does not materialize. In order to do that, I would need a new surprise shock, equal in value and opposite in sign to the anticipated one. How can I model that? I thought of something like

At=rho_a*At(-1)+e_a+e_surprise+news_a(-4);
e_surprise=-news(-4)

but it is probably wrong. Is there any way to model it?

Thanks
Leonardo

2

This is not feasible, because it is not consistent with a rational expectations equilibrium. You can have a one-time pure news shocks where a surprise shock counteracts a news shocks. But having that systematically over the sample is not feasible, because agents would figure out that news never realize. With the structure you have in mind, nothing would happen, because people would know that four periods later this will not actually happen.