I have the following conceptual questions related to deterministic and stochastic simulations for models with occasionally binding constraints (OBC, e.g. lower bound constraint on interest rates).
Let’s assume I have a non-linear model (meaning non-linearities not only due to the OBC but also in other model equations):
- Ignoring the OBC, stoch_simul(order=1) and simul should give me the same IRFs to a one-time shock in the first period, correct?
- If I now want to have IRFs respecting the OBC, I could use the max-operator in simul or some toolbox (like OccBin or DynareOBC). As these toolboxes usually also work with stoch_simul(order=1), should the IRFs to a one-time shock in the first period not be the same as in the deterministic simul? I doubt it as this would render these toolboxes redundant, but I don’t understand where the difference comes from.
- As another option I could use extended_path. If I understand it correctly, this will deliver the same IRFs to a one-time shock in the first period as simul, correct?
- Maybe somehow unrelated: Could you confirm whether manually linearising the equations and then using model (linear); … stoch_simul; is exactly the same as the non-linear equations with model; … stoch_simul(order=1); or will Dynare include some correction terms?
I know that these things have partially been discussed/answered already. But I don’t get my head around what first-order toolboxes do differently compared to the deterministic simulation in which I can easily use non-linear operators like max or min.
I hope you can help me on this.