Will linearize and log linearized irfs the same

There are different ways to log-linearize at first order, but they should all results in the same outcome. @Olivia If you are unsure how to do this, then you should not be linearizing by hand. It’s too error-prone. Let the compute do it. See also Why do we log linearize a model by hand?

Regarding steady state 0: in this case, you do not log-linearize, you linearize. Thus, the IRFs should be identical to the nonlinear version at first order.