Reference for determining domestic bonds

In an older post on how to determine the dynamics of domestic bonds (, which are otherwise indeterminate, there is the following suggestion by jpfeifer :

In closed economy models you can generate something similar by having a borrowing constraint where the Lagrange multiplier on the constraint increases in debt and therefore creates a “utility premium”.

The intuition is similar to Schmitt-Grohe/Uribe on open economies and the trick works in practice, but does anyone has a reference to an article where this is actually done?

For example Iacoviello (2005) in the American Economic Review has something like this. His equation (7) contains a Lagrange multiplier, effectively determining the borrowing of entrepreneurs.