Simple NK model with matching frictions - puzzle

Dear all,

I have a problem with generating plausible impulse responses after the MP shock using the NK model with matching frictions. I have tried to replicate the paper by Krause and Lubik:
“The (Ir)relevance of Real Wage Rigidity in the New Keynesian Model with Search Frictions” and I get negative response of the interest rate, and positive response of output after the MP shock. I have then simplified the model by making the separation rate exogenous, and the problem is still there. It should be a problem of timing but I cannot figure it out.

As I understand it KL assume that matches become productive only in the next period but are subject to the separation risk immediatley. I have replicated the model that assumes that matches become productive in the same period, as well as the model that assumes that matches become productive in the next period but are not subject to separation risk and these seem fine.

I have attached the mod.file for the simplified model based on KL assumptions regardig the timing (money growth rule is replaced by the Taylor rule). If anybody has any idea about this I would be very gratefull for any help.

I have tried to make sure that there is no mistake in the derivations of equations and the code, but it is still possible that this is just a matter of some mistake that I did in which case I apologise.
KL_exogenous.mod (2.77 KB)

Hi, do you mind posting the version with endogenous separation?