- You are neglecting the different scale in the mode_check-plot. The likelihood line is the green line at the top of the figure that merges with the boundary of the subplot. It is the massively informative prior that gives the blue line the shape.
Regarding the interpretation of the identification strength graph, please see Pfeifer (2014): “An Introduction to Graphs in Dynare” at sites.google.com/site/pfeiferecon/dynare. The identification strength is generally evaluate for the posterior with Bayesian estimation and for the likelihood with ML. Thus, the prior plays a role.