Dear Johannes,
I am reading a paper about the finite-order VAR representation of the DSGE model, please refer to page 101 of the PDF attachment.
the state space representation of the DSGE model:
state transition equation: Xt=AXt-1+BWt
measurement equation: Yt=CXt-1+DWt
shock equation: Wt=HWt+epsilont
the paper says that if all eigenvalues of the matrix A-BD^{-1}C are less than 1 in modulus, then a VAR with infinite order exists,
if all I-[A-BD^{-1}C)L] is unimodular, then a finite-order VAR exists.
My questions are:
(1) what is the sufficient condition for the existence of the DSGE-VAR model, is the condition ‘all eigenvalues of the matrix A-BD^{-1}C are less than 1 in modulus’? or the condition ‘all I-[A-BD^{-1}C)L] is unimodular’? Do the two conditions contradict with each other?
1-s2.0-S0165176513001845-main.pdf (367.1 KB)
Thank you very much and look forward to hearing from you.
Best regards,
Jesse