Constant series as observables in bayesian estimation

Dear All,

Suppose that x(t) is an endogenous variable of my model and X(obs) is my observable. Then I would specify my measurement equation as x(obs)=x(t). However, in the data x(obs) is constant.

My question is, should I trust the data, impose x(t)=constant in my model and not use the observable, or should I feed it in anyway and relate it to x(t)?

Thanks!

This is an economic question. Do you think the data is really constant? If yes, you should force the shocks of the model to explain the constancy of the observable by including it.

Thank you for your reply. I have another question. Are the smoothed shocks computed with the Kalman filter anyhow related to the structural shocks identified through a VAR?

Thanks!

To be more precise, if I have

x(obs)=x(t) and x(t)=rho*x(t-1)+e(t)

is the smoothed value of e(t) related to the identified values I would find by running a VAR with x(obs)=rho*x(obs)(-1)+e(t) ?

Yes and no. The reason you need smoothed shocks is is that some states are unobserved. The DSGE model shocks are by definition structural shocks, while the VAR residuals are first of all reduced form shocks (they only coincide for a single AR process as shown in your example). If you have an sVAR where the structural shocks are identified, they should ideally be the same.

An important difference is that sVAR shocks should correspond to the filtered shocks (as you only use information up to time t), while the smoothed shocks use information up to the last time point.

Thank you Jpfeifer. This is an interesting issue. I think I will go through it in more detail.

Best