Hello friends,
I am working on a New Keynesian model, including banks. I have set up initial values and try to get some results. However, I face three problems:

The steadystate values of some variables are not what I can get with pen and paper, e.g., the steadystate interest rate (R) given by Dynare is much larger than its steadystate value, which I derive analytically: \dfrac{1}{\beta}  1.

Even though resid; returns all residuals equal to zero, some residuals will not be zero if I change parameters. For example, \mu is the default probability of banks in my model. I can get zero residuals only if I set it as a number between 0.00 and 0.008, which is actually not realistic! There is the same issue with some other parameters.

Finally, the rank condition is not satisfied. I get the following error:
There are 10 eigenvalue(s) larger than 1 in modulus
for 10 forwardlooking variable(s)
The rank condition ISN’T verified!
I tried different timing settings regarding loans, deposits, and net worth, but every time I end up with the unverified rank condition.
I am really baffled. I have been working on these problems for days, but I cannot resolve the issues. I have tried simpler models with fewer equations and different values for parameters, but the problems are still there. Model diagnostics does not find a problem in the code either.
I will be thankful if someone can help me resolve these issues.
I attach the mod file for reference.
giobanking.mod (7.3 KB)