# Banks with leverage constraints

Dear Dynare-Users,

I have the following problem:
I have a model with a microfounded bank. This bank can increase its effort e_{t} to rise the probability p(e_{t}) to find a good creditor. Thus the law of motion of aggregate bank net worth N_{t} is the following:

where d_{t} are deposits of the bank, R_{g}{t+1} is the interest paid by good creditors ( R{b}{t+1} is the interest paid by bad creditors) and R^{d}{g,t+1} is the interest paid by banks with good investors (R^{d}_{b,t+1} is the interest paid by banks with bad investors).

Now, the problem is how to type in this equation in dynare. I talked to the authors of the paper (Christiano, Ikeda (2014)) and Mr. Ikeada told me to write this equation in current terms as the equation has no expectation operator. So the dynare code will be:

Doing this the mod-file works fine.

Then I do the following thing: I incorporate a levarge constraint as follows:

N_{t}*Lev = N_{t}+d_{t}, and Lev some parameter.

Then running the model again with this leverage constraint and the above presented code does NOT work anymore. Dynare tells me that the BK conditions are not fulfilled (“Blanchard Kahn conditions are not satisfied: no stable equilibrium”). If I instead change the timing of the law of motion of aggregate bank net worth as follows:

the code runs.

WHAT IS THE PROBLEM?

(My guess is the following: if I add a leverage constraint, I have a condition for the current bank net worth N_{t}, as the bank can decide over d_{t}. Thus adding a law of motion in current terms I have an additional equation for N_{t} and the system is overidentified. However, if I add a law of motion for N_{t+1} this is no problem anymore. Am I rigth?)

IF ANYONE HAS EXPERICENCE WITH THIS ISSUES PLEASE ANSWER ME. I AM ALSO WILLING TO SHARE MY DYNARE CODE OF THE CHRISTIANO AND IKEDA (2014) MODEL!

Best regards,
Daniel

Hello, I am also interested in the topic of banks’ leverage constraint.
The latest paper I have found is “Financial fragility, sovereign default risk and the limits to commercial bank bail-outs”, do you have any new idea about this or your own dynare codes?