Decentralized and social planner's equilibria in Bianchi (2011)

Hi there!

I’m trying to replicate Bianchi (2011)'s “Overborrowing and Systemic Externalities
in the Business Cycle”. Concretely, I want to solve for the decentralized and the social planner’s equilibria, assuming that the borrowing constraint is always binding.

The social planner’s problem is solved successfully (i.e., the steady state is found, Blanchard-Kahn condition is satisfied), whereas the decentralized problem does not satisfy the B-K criterion, even though the only difference between both is that in the former, the FONC with respect to tradable consumption is

lambda = a*c^(-sigma)*(ct/c)^(-1/xi) + mu*(kappa*p*(cn/ct)*(1/xi));

In the latter, this becomes

lambda = a*c^(-sigma)*(ct/c)^(-1/xi);

Any ideas on how to approach this challenge? I have attached the .mod files.
bianchi_ce.mod (1.6 KB)
bianchi_sp.mod (1.6 KB)

Are you sure that the FOC is correct?

Hi, Professor Pfeifer,

I uploaded the corrected mod files. I was using the notation of Schmitt-Grohé & Uribe (2021) instead of the original syntaxis of Bianchi (2011). This could have been a source of confusion.

Increasing omega, which gauges preference for tradable consumption, enables the model to satisfy the BK condition. Nonetheless, the IRFs are oscillatory, despite all eigenvalues being real numbers.

I already checked the timing and it looks okay. Any insight on this issue?
remit_ce.mod (1.7 KB)
remit_sp.mod (1.7 KB)