Cannot find steady state: Dynare paper replication

[robreim]

Hi.

I have been trying the last few weeks to replicate the paper 'Macroprudential Measures, Housing Markets, and
Monetary Policy' by Margarita Rubio and Jose A. Carrasco-Gallego, which is available through the dynare website. See also attached.
It seems that I entered the equations of the Steady State correctly (see pp. 22 & 23). However, I have not been able to find the Steady State, so I have few questions I hope you can help me with. I am not an advanced economics student, so bear with me.

1. Lambda is the 'multiplier on the borrowing constraint'. For me it's not clear if its a variable, or a parameter and if so, what value I should assign to it.
2. I have already read through the Dynare forum considering finding plausible initial values, since I have no clue how to solve a system of nonlinear equations. However, until now I have been unsuccessful in simply taking a good guess taking into account plausible values (such as y is larger than c ), so I hope you can give me some tips.
3. Was I correct in making expectation equations into auxiliary variables?

Find the script and the paper attached. I'd be very glad to receive any feedback. Thank you very much in advance.

[jpfeifer]

You might not like it, but for a problem like this, analytically computing the steady state is often the only viable solution.

1.) The multiplier is a variable, not a parameter. Its steady state value follows from the steady state equations (e.g. 32)
2.) For nonstandard models, there is unfortunately no good guidance. As said above, use pencil and paper.
3.) Please be more explicit what you mean. I am not familiar with the paper.

[blant]

How did you solve this? I have the same problem...