Problem with Blanchard Kahn conditions

Stochastic simulations
1

Dear all,

I have a model with a saver, a borrower, and housing (similar to the housing literature evolving around Iacoviello and others).

Housing supply is fixed, and I have also fixed the housing demand of savers, so that all the action is in the borrowers.
I have a collateral constraint that is the average between the standard kiyotaki moore and debt last year, where the average parameter is gamma.

The problem is that the model works for very high gamma’s, over 0.97. But Blanchard-Kahn conditions are not satisfied for all other gamma’s. For some gamma’s (specially high values), I get an indeterminacy. For most of gamma’s (all gammas below some point) I get no stable equilibrium.

I have carefully checked the timing and everything else, but I can’t see the problem, and I would greatly appreciate if you wouldn’t mind to have a look. I’m pretty sure there must be a problem with the code, as there are many similar models in the literature with gamma=0 directly (which is the standard collateral constraint).

In a previous version, I had the standard collateral constraint (gamma=0), and fixed housing, but without fixing the housing supply of the savers. In that version everything was working perfectly. My problems began when I fixed the housing of the savers.

Here is the mod file, and a separate matlab file that sets the parameters, calculates the steady state and calls the mod file.

Thank you, indeed.

nkpc_v1.mod (4.7 KB) param_nkpc.m (3.5 KB)

2

By the way, just in case it might be of interest. I put together here the previous version of the model: where the total housing supply is still fixed, but not fixed for the savers, and with the same collateral constraint as in my post (for easy comparison).

(In case you’re wondering: the reason why I fix the housing of the savers (following a few papers in the literature) is to avoid savers and borrowers to trade large amounts of housing between them after the shock).

All problems show up when going from this version of the model to the version of the main post (it just deletes one equation and variable, and changes other equation).

Thanks, indeed.

nkpc_v1.mod (5.9 KB) param_nkpc.m (3.6 KB)

3

With 0.97 your IRFs are oscillating. With 0.99 they look OK. Have tried varying other parameters of the model to get an indication of what is going on economically in the model. When I move from 0.975 to 0.9725 I can see the IRFs qualitatively changing in that Y overshoots in the second period. Maybe there is a reason the model does not work for different values, i.e. there is no bug.

4

Thank you Johannes, I appreciate very much that you had a look and your feedback. Before creating this account, I learnt a whole lot out of your comments across many threads. Thank you.
jose