Does the extent of difference between DSGE impulse responses and DSGE-VAR impulse response indicate the level of model misspecification

Dear Johannes,
I have formulated a DSGE model and a DSGE-VAR model, which uses DSGE cross-equation restrictions as prior, however, there are some differences between impulse responses generated by the DSGE model and impulse responses generated by the associated DSGE-VAR model, there are differences between the two sets of impulse responses, although these differences are not significant, I am wondering that does no significant difference in the two sets of impulse responses indicate no serious model misspecification in the underlying DSGE model? or even a little but insignificant differences in two sets of impulse responses may still signal potential model misspecification in DSGE models?
Thank you very much and look forward to hearing from you.
Best regards,

  1. Yes, the differences between the two indicate whether the data reject the cross-equation restrictions implied by the DSGE model.
  2. Keep in mind that all models are necessarily wrong. Thus, small differences are usually no reason to worry.