With the availability of rich data sets, new research has tried to establish how rigid prices really are and thus whether monetary models with rigid prices make sense at all. Currently, the two most interesting exercices are Martin Eichenbaum, Nir Jaimovich and Sergio Rebelo and Mark Bils and Pete Klenow, the latter being previously discussed on this blog. What this research highlights is that while some prices are rigid, others are not, and there is considerable diversity. Theory, like Mikhail Golosov and Robert E. Lucas, Jr. we discussed before, cannot account for this diversity.
Hirokazu Ishise and Nao Sudo devise a theory that brings dispersion in rigidities. They show that differences in good characteristics, along the dimensions of durability, luxuriousness and proportion of cash payments yields such dispersion. This is a model of limited participation: agents cannot rebalance their portfolio in the face of monetary shocks until it is their turn. One may argue that this should be endogenous and thus it could wash away any remaining rigidity, but it is a start.
What is particularly interesting is that the model yields responses to monetary shocks by different good characteristics like in the data: more durable, more luxurious and less cash intensive goods respond more to monetary impulses.