Get innovations of news shocks with acutal data

General DSGE Modeling
1

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
u_t=\rho_Ru_{t-1}+\epsilon^0_{R,t}+\epsilon^4_{R,t-4}

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,
Young

2

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.

3

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?

4

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

5

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.