How to make the SS equal to 0?

[jpfeifer]

Dynare has a stock at the end of period timing convention, while you used a stock at the beginning of period convention for capital. The predetermined_variables command tells Dynare about this difference in timing.

Regarding replication results, the standard answer is

Having difficulty replicating Gertler, Sala Trigari (2008)'s IRFs

Something like this is very hard to debug. I would recommend checking all equations again, including the timing. Make use of Dynare’s LaTeX-capabilities for this. Do the same for the parameters. If the difference still persists, either the equations in the Appendix are wrong or the original authors did a mistake. Usually, I recommend working the nonlinear model, because it makes it easier to check the equations and the correctness/consistency of the steady states.