Relaxing one or more of these assumptions can restore a more meaningful role to money even in this model framework. For instance, Christiano, Motto and Rostagno (2007) extend the basic New Keynesian model by including various measures of money and credit. They thereby achieve a rather detailed and more realistic description of financial markets and the transmission process.
In addition, acknowledging model uncertainty and the quest for a robust policy framework, it can be shown that taking monetary factors into account may lead to more desirable outcomes compared with a purely New Keynesian framework (Kilponen/Leitemo (2007)). And it is exactly the need for a more robust framework in the face of uncertainty that is the main motivation for the Eurosystem’s two-pillar approach.