These aspects are poorly developed in our standard econometric macro-models, as well as in the benchmark new-Keynesian model which is so prominent in the academic literature. For the time being, it is difficult to reproduce these statistical relationships and their time-varying nature in state-of-the-art structural models.
That is the main reason why the Eurosystem's monetary policy strategy now deals with these aspects in a separate pillar. But it would obviously be extremely useful to have models that can integrate these relationships in a structural way. This is clearly the way forward for research on these issues.