Get innovations of news shocks with acutal data

Hi all,

I am trying to bootstrap innovations from anticipated and unticipated news shocks. By doing so, I firstly get residuals (=LHS-RHS), {u_t}, by dynamic.m functions generated by Dynare. E.g. R_t =\rho R_{t-1}+(1-\rho)*[\rho_{\pi }*\pi_t +\rho_y*(y_t-y^f_t)]+u_t
where u_t is monetary policy shock. I can get what the residuals are with actual data.

As there are news shocks, the structure of u_t is

If there is no news shock, I could estimate \rho_R and get innovations, unanticipated shocks, \epsilon^0_{R,t} by using a VAR.

However, if there are news shocks, how could I get the two innovations separately?

Many thanks,

That cannot be done based on a single equation. You need to estimate a system to achieve that. Typically, you would estimate the the full model.

Hi Prof. Pfeifer,

This equation is just one of the equations in the model. I have the full model and real data. I can estimate the model and get the residuals, u_t and etc. But since the residuals have two innovations unanticipated shock, \epsilon^0_{R,t}, and anticipated shock, \epsilon^4_{R,t-4}, is there any technique to estimate the two kinds of innovations separately?

You can run the Kalman smoother on your model. It will provide the estimated shocks. We did that for example in

Thanks Prof. Pfeifer, I have read the paper in advance but I didn’t find the replication files as you usually upload. I will try the Kalman smoother.