# Structural shock in measurement equation

Dear Johannes,
Can structural shock appear in measurement equation?
If a structural shock appears in measurement equation, and the number of shocks equals the number of observable variables, assuming the VARMA process is invertible, does a DSGE-VAR exist? I mean if there is a structural shock appearing in measurement equation, does a DSGE-VAR model exist? On page 629 of the attached paper, the sentiment shock appears in measurement equation, in this case, assuming invertibility conditions are satisfied, does a DSGE-VAR exist?
A Bayesian dynamic stochastic general equilibrium model of stock market bubbles and business cycles.pdf (424.4 KB)

Thank you very much and look forward to hearing from you.
Best regards,
Jesse

1. A structural shock by definition does not appear in the measurement equation. Rather, this is measurement error.
2. What do you mean with DSGE-VAR? A DSGE-VAR in the true sense of Del Negro/Schorfheide? Or whether there is a finite order VAR representation of the model solution?

Dear Johannes,
Thank you, but on page 629 of the attached paper, the sentiment shock theta appears in measurement equation, the observable variable sentiment cannot be directly measured by state variables, because there is not state variable called sentiment, however, in the model, the sentiment shock represents the growth ratio of old relative to new stock bubbles, and stock bubbles are state variables, besides, the sentiment observable variable is also related to output growth, therefore, the observable consumer sentiment variables is mapped to a combination of state variables-output growth and bubble growth, however, since bubble growth equals the sentiment shock, I think that is why sentiment shock appears in measurement equation. please refer to page 629 of the PDF attachment above, I mean the invertibility condition of a DSGE-VAR in the true sense of Del Negro/Schorfheide, does a DSGE-VAR exist if the structural shock appears in the measurement equation?

1. I see. Here the initial state space is augmented by the structural shock, i.e. the structural shock is treated as a state.
2. Having a shock as a state tends to make it more unlikely that a finite order VAR representation exists. But regardless of the specifics, you can never be sure. That’s why generally you would need to check, e.g. using the ABCD-test.

Thank you very, could I know what is the ABCD-test? is this a test for the existence of DSGE-VAR representation?

See DSGE_mod/FV_et_al_2007 at master · JohannesPfeifer/DSGE_mod · GitHub and the reference therein.