Paying Interest on Reserves as a way of crowding out the Shadow Banking System?

More later...seems like it would be an simple model to write with potentially interesting contact with reality. 

In general, shouldn't interest on reserves crowd out maturity transformation?  But how big is this effect?  Big enough to matter?  It should also (strongly) interact with the zero bound on interest and hence with inflation. 

You'd think this model would already exist and would be well known.  But, hey, it's monetary economics.