 # Problems with model setting of bank sector

Dear Professor Pfeifer,

I’ve got a little confused with Zhang(2010)'s model setting. Would you please give any advice? Thank you very much.
Zhang（2010）.pdf (404.7 KB)

In this paper, households suply bank equity e_{t+1} and receive R_{t}^{e}\left( 1-{{\phi }_{t}} \right){{e}_{t}} in every period, in which {\phi}_t represents the default rate of banks. Meanwhile, the cost of bank funding is R_{t}^{f}{{L}_{t}}=R_{t}^{e}{{e}_{t}}+R_{t}^{d}{{d}_{t}}. Is it proper to set the model like this? How should I understand the disappeared part R_{t}^{e}{{\phi }_{t}}{{e}_{t}}?

I don’t really know the answer. The timing in equation (32) is strange and is different to what you wrote down as well as inconsistent with the household budget constraint.

Dear Professor Pfeifer,

I’m sorry that I just lag the variables for one period. But the confusing thing to me is that where the R_{t}^{e}{{\phi }_{t}}{{e}_{t}} goes when the banks default? Is there any authoritative papers considering the macroprudential policy in the bank sector?

This is not my literature, so I don’t really know the answer. But I agree that what you point out is strange as there seem to resources unaccounted for. Firms seem to pay for equity costs that never end up at households. Maybe that is a way of modeling deadweigh losses of default. But the paper seems not to be explicit about this.

Dear Professor Pfeifer,

How should I deal with this deadweigh losses of default? Or could I just set R_{t}^{f}{{L}_{t}}=(1-{{\phi}_{t}})R_{t}^{e}{{e}_{t}}+R_{t}^{d}{{d}_{t}} in the bank sector?

I would probably go for the latter. But again, I am not familiar enough with the model to give a definite answer.

Dear Professor Pfeifer,