One period iid shock

Hi, I just have a quick question: would period 1 iid shock (w/o persistent) in perfect foresight simulation is equivalent to stochastic counterpart? Also, would that be considered as a MIT shock? Lastly, if the model has an occasionally binding constraint, would it still be equivalent?

Thank you in advance!

If it’s in the first period, the answer is yes for MIT. Otherwise no, because it would be anticipated.
It will generally not be equivalent to a full stochastic model if certainty equivalence does not hold (in most nonlinear models).

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